-- - - DNA 5741T FIRE AIRBLAST AND UNDERGROUND EFFECTS FROM NUCLEAR EXPLOSIONS-SOME ' CURRENT PROGRESS 1Harold L Brode Dale A Larson Richard D Small Stephen J · Speicher 1 Frank J Thomas Pacific - Sierra _Research C r poration 1456 Cloverleaf Boulevard • Santa Monica California 90404 · 1 January 1981 ·· Topical Report for Period 1 •December 1979-1 January 1981 CONTRACT No DNA 001-80-C-0065 l• · Distribution limited to U S Government agencies only Proprietary Information 25 November 1981 Other requests for this document must be referred to the Director Defense Nuclear Agency Washington D C 20305 f•• THIS WORK SPONSORED BY THE DEFENSE NUCLEAR AGENCY UNDER RDT E RMSSCODE B310080464 P99OAXDB00154 H2590D L t ' ' t·· I r· 1•··· ' r• Prepared for I I ' -' Director DEFENSE 'NUCLEAR AGENCY Washington D C 20305 • Destroy this report when it is no longer needed Do not return to sender f PLEASE NOTIFY THE DEFENSE NUCLEAR AGENCY ATTN STTI WASHINGTON D C 20305 IF YOUR ADDRESS IS INCORRECT IF YOU WISH TO BE DELETED FROM THE DISTRIBUTION LIST OR IF THE ADDRESSEE IS NO LONGER EMPLOYED BY YOUR ORGANIZATION ''I _ - i - 0 N-1 _ _ UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAGE Wl en Data Entered ·--- r READ INSTRUCTIONS BEFORE COMPLETING FORM REPORT DOCUMENTATION PAGE GOVT ACCESSION NO • 3 REPORT NUMBER 1 DNA 5741T 4 Tl TLE and Subtitle 5 RECIPIENT'S CATALOG NUMBER TYPE OF REPORT 6 PERIOD COVERED Topi ca 1 Report for Period l Dec 79-1 Jan 81 FIRE AIRBLAST AND UNDERGROUND EFFECTS FROM NUCLEAR EXPLOSIONS-SOME CURRENT PROGRESS 6 PERFORMING ORG REPORT NUMBER PSR Report 1109 7 a AUTHOR sJ Harold L Brode Dale A Larson Richard D Small Stephen J Speicher Frank J Thomas DNA 001-80-C-0065 9 PERFORMING ORGANIZATION NAME ANO ADDRESS 10 PROGRAM ELEMENT PROJECT TASK AREA Pacific-Sierra Research Corporation 1456 Cloverfield Boulevard Santa Monica Ca 1i forni a 90404 I 1 a WORK UNIT NUMBERS Subtask P99QAXDBOOl-54 12 CONTROLLlNG OFFICE NAME AND ADDRESS Director Defense Nuclear Agency Washington D C 20305 14 CONTRACT OR GRANT NUMBER rJ REPORT DATE l January 1981 13 NUMBER OF PAGES 244 MONITORING AGENCY NAME 4 ADDRESS i different from Controlling Olfice IS SECURITY CLASS of thjs report UNCLASSIFIED 1s _ 16 DECLASSIFICATION DOWNGRADING SCHEDULE DISTRIBUTION STATEMENT of thfa Report Distribution limited to U S government agencies only Proprietary Information 25 November 1981 Other requests for this document must be referred to Di rector Defense Nuclear Agency Washington D C 20305 17 DISTRIBUTION STATEMENT of the abstract entered in Block 20 if different from Report 18 SUPPLEMENTARY NOTES This work sponsored by the Defense Nuclear Agency under RDT E RMSS Code B310080464 P99QAXDB00154 H2590D 19 - ' ' KEY WORDS Continue on rev se aide ii nec uu ary and identify by block number Peak Overpressure Dynamic Pressure Height of Burst Nuclear Effects Large-scale Fires 20 Firestorms Cavity Decoupling Time of arrival Fi re Damage Fireball Underground Testing Shock Tube Civil Defense Nuclear Detection Seismic Detection ABSTRACT Continue reveru aide if necesaary and Identify by block number This report covers research on nuclear-effects-related topics such as airblast large area fires and underground testing Analytic approximations are provided for the peak overpressure including the double peak phenomenon and for dynamic pressure as a function of height of burst and time Fires accompanying nuclear warfare are covered from three perspectives The first is a general review of urban superfires This is fol 1owed by an analytic modeling study of such fires as they pertain to fire-generated winds air '· DD FORM 1 JAN 73 1473 EDITION OF 1 NOV 65 IS OBSOLETE UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAGE When Data Ent•red UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAGE Whcn Dbt o Entered 19 KEY WORDS Continued Containment Mach Reflection Blast Impulse Blast Duration 20 Thermal Radiation Simulation of Nuclear Effects Blast Waves in Tubes ABSTRACT Continued temperatures and atmospheric effects the model derives simplified differential expressions for the gas dynamics of large-scale fires Finally a · methodology for predicting fire damage is outlined and a flow diagram for a fire-damage prediction program is presented Current information on cavity decoupling of underground nuclear tests from distant seismic signals is reviewed and the potential contribution from additional underground testing is evaluated Also discussed is the application of nuclear explosives to drive a large shock tube allowing high overpressure and fireball exposures The fireball phenomena to be simulated are detailed questions regarding instrumentation and structural response in this hostile environment are explored Other alternatives for simulating high-pressure flows are examined and some details of a nuclear-shock-tube concept are discussed including a method for reducing radioactive contamination in the test section UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAGE When Dara Entered PREFACE This final report summarizes 1980 results for a number of studies conducted under contract DNAOOl-80-C-0065 for the Defense Nuclear Agency DNA Most of the subjects addressed under this contract have found appropriate extensions in continuing research Neverthe- less each chapter in the present report stands independently as a useful contribution to research on nuclear effects Many of our results have already been disseminat d beyond the immediate DNA nuclear effects community The fire research is of interest to the Federal Emergency Management Agency and others concerned with civil defense by several federal agencies The airblast fits are already being used The cavity decoupling issue is of con- cern to the Defense Advanced Research Projects Agency and the nucl ardriven shock tube has long been of interest to the U S Air Force Robert M Henson Eugene T Herrin and William E Ogle who coauthored Chap 8 are associated with Energy Systems Inc Anchorage Alaska 1 TABLE OF CONTENTS Chapter PREFACE 1 1 INTRODUCTION AND SUMMARY 3 2 LARGE-SCALE URBAN FIRES 6 3 METHODOLOGY FOR PREDICTING URBAN FIRE DAMAGE FROM NUCLEAR BURSTS 34 4 LARGE AREA FIRE--AN ANALYTIC MODEL 56 5 ANALYTIC APPROXIMATION FOR PEAK OVERPRESSURE VERSUS BURST HEIGHT AND GROUND RANGE OVER AN IDEAL SURFACE 121 ANALYTIC APPROXIMATION FOR DYNAMIC PRESSURE VERSUS TIME 141 REVISED PROCEDURE FOR ANALYTIC APPROXIMATION OF DYNAMIC PRESSURE VERSUS TIME - 176 CAVITY DECOUPLING OF UNDERGROUND NUCLEAR EXPLOSIONS 207 TESTING RESPONSE TO FIREBALL ENVIRONMENTS NEEDS AND TECHNIQUES 215 6 7 8 9 2 CHAP'I' ER 1 INTRODUCTION AND SUMMARY 3 This report comprises eight topical reports dealing with different aspects of fire airblast and underground effects of nuclear explosions Three concentrate on fire research The first gives an overview of large-scale urban fires and reviews the outstanding questions and unresolved issues relevant to such fires which are very likely in th event of nuclear attack The second considers the con- struction of a program for predicting the probable damage from massive fires as well as the probability of fire spread and outlines a computer program that includes some generalized flow diagrams The third presents a simplified analytic model of the major features of gas dynamics during large-scale fires focusing on a mathematical formulation for the flow field that permits predictions of winds temperatures and burn rates The latter two reports should be considered progress reports rather than final statements The program for fire prediction has not progressed beyond the flow diagram and logic organization stage Likewise the analytic model does not yet include specific examples with quantitative results Further useful information is antici- pated from the current follow-on effort in both fire-damage-prediction modeling and analytic modeling Another three reports concentrate on airblast The first pre- sents an analytic approximation to the peak overpressure height-ofburst curves for ideal surfaces as defined by the revisions currently being incorporated into DNA handbooks The second and third provide analytic approximations to the dynamic pressure from nuclear explosions The latter two reports while depending on the peak overpressure to fix the peak dynamic pressure also provide an approximation to the time-history of the dynamic pressure and therefore the dynamic pressure impulse Although much has been accomplished in the development of analytic approximations to the overpressure time-history and overpressure impulse fits for range and heights of burst the final version of that fit is being completed under the current follow-on contract The final two reports are contributions to the undergroundtest-concept working group The first discusses cavity decoupling 4 of underground nuclear·explosions and the relevance of research on this subject to underground testing The second examines the rationale for and problems in developing a nuclear-driven shock tube It does not include the details of preliminary designs or certain quantitative results of early calculations Consequently a revised report is in progress under the current contract Considerable additional effort was expended in areas that did not result in topical reports--notably in support of the cratering and airblast working groups on subjects of other nuclear hazards on naval nuclear effects in connection with a cavity underground xperiment to investigate crater coupling in various areas of strategic or tactical applications and in some support of preparations for SAGE meetings 5 CHAPTER 2 LARGE-SCALE URB AN FIRES Harold L Brode 6 It is fortunate that large-scale fires are rare events since they are very destructive and a serious threat to life Our concern with massive fires is restricted in this instance to large urban area fires fires that involve many structures burning simultaneously There are some features of such large area fires-that are not important in the more frequent localized city fire which may present new and unanticipated hazards to life and property during a large-scale fire It is in the hope that a better understanding of the nature of such large-scale fires can lead to measures for minimizing casualties and damage that the current research is being pursued Tragic experience has taught us that a variety of major disturbances can lead to large-scale fires • Earthquakes-as in San Francisco 1906 • Civil disorder--as in the Watts riots 1965 • Explosions or crashes of ships aircraft trains or trucks-as in the Texas City ship explosion 1947 • Accidental ignitions associated with no serious disruption-as in the great Chicago fire 1871 said to have been started by an overturned lantern in a shed Interestingly eight blocks of Chicago had burned the day before due to another accidental ignition • Warfare-as in the sacking of Rome Napoleon's occupation of Moscow or World War II Massive fires can and do occur under such a wide range of disruptive circumstances that their characteristics and consequences are of grave concern to those responsible for public safety and protection A massive fire has several unique and interrelated characteristics all of which necessarily derive from the enormous size of the burning area--it could cover hundreds of square miles 7 Perhaps most significant the air drawn in by such a fire could lead to winds exceeding hurricane speed--more than two hundred miles per hour The winds in turn fan the flames driving temperatures in the superfire above those normally associated with isolated building fires or even the most serious forest fires Temperatures are further increased by radiation entrapment in the large area covered by the flames Such magnitude and intensity greatly accelerate the progress of the fire It may peak in an hour or less but then having heated most fuels to combusion levels may keep burning for days Finally the vast amounts of gas smoke hot air and ashes generated by the fire may cause high casualties The very size of the burning region precludes escape for most of those caught within the area In World War II for example many casualties were attributed to carbon monoxide poisoning and heat exhaustion in the larger firestorms Those factors are less signifi- cant in smaller fires where escape or rescue are easier Because of the unfamiliar aspects of the superfire and its unusual intensity and magnitude we must reevaluate the adequacy of emergency plans to deal with such fires NATURE AND CONSEQUENCES OF SUPERFIRES The dynamics of a large area fire involve physical and chemical phenomena--and hence dangers--that simply do not exist in more conventional fires or exist only to a minor degree For example the loss of life in World War II firestorms proved to be much higher than that in isolated building fires started by scattered bombing raids Not only were many people injured by collapsing structures but many while trying to escape were caught in the holocaust in the streets and burning areas outside their failing structures Due to the higher burning rates high winds and higher temperatures property damage is much more severe and complete in large-scale fires In addition such signs of disorganization as ineffective firefighting poor evacuation control looting civil disorder loss of other services and disruption of utilities are likely to be severe and widespread Finally dele- terious psychological factors arise when large groups of people 8 experience the simultaneous loss of living quarters possessions and loved ones • In short we should be concerned about superfires because Sources or causes of such fires are both probable enough and serious enough to affect public safety • Experience with such fires is almost nonexistent and promises to be sufficiently different from that with conventional fires to merit special attention • The conseq ences of such fires are very costly in both life and property loss making measures to mitigate them well worthwhile The speci l hazards of a large-scale fire derive from its unique characteristics in such a fire Figure 1 suggests the involvement of the atmosphere Picture a burning area many miles in diameter the flames reaching hundreds of feet into the air the flames carrying burn products carbon monoxide and water vapor A plume rises above smoke ash brands carbon dioxide Unlike the plume from a smaller more conventional fire this one is perhaps as wide as it is tall and it may well up above the atmosphere in a fountain of burn products This great upsurge of mass and energy generates a huge toroidal circulation the rising plume feeding a flood of gases outward at some high altitude which in turn cool and cause a subsiding fallout and a downflow of air toward the outskirts of the fire at ground level Perhaps the most unusual and important consequence is the extremely high winds rushing into the burning region further increasing burning rates l orology Such winds may exceed any experienced in natural mete- Indeed the flames near the periphery may be laid nearly flat by the inrushing winds Exceedingly fierce burning rates may result in the total combustion of all fuels within the fire area and the melting or destruction of many noncombustible structural materials The wind alone may cause extensive damage to structures outside the burning area A detailed analysis of large-scale fires would include many of the pertinent variables listed in Table 1 9 Although the size of the -- --- - a · - ' a • - a a s CL U 0 E ttl ' 0 s a E Q J -- 0 s 'C C ttl a E -Cl -- a i Cl • - LL J 10 r Table 1 Physical characteristics of burning zone Size of burning area Size of potential burnable area Flame height Combustion rates Total heat released Gas generation Temperatures Expansion and buoyancy of plume Topography Fuel types Fuel density Fuel combustibility Firebreaks and fuel distribution Construction continuity Combustibility of building contents Building sizes actively burning area is most crucial the extent and nature of the smoke column is also important its rate of rise the altitude to which it rises i e the degree of buoyancy of plume components the smoke ash and brands carried aloft -the amount of spreading or growth of the plume the degree of mixing with the atmosphere and the various physical components and reaction rates of combustion products within the plume and their influence upon the local meteorology for example large fires often generate rain As noted in connection with atmospheric recirculation we are particularly interested in the development of hurricane-force surface winds feeding the fire the influence of such winds on fire spread the generation of fire whirls and the distribution of firebrands and -ash PAST LARGE-SC ALE FIRES Table 2 lists some well known large-scale urban fires disasters of the past two of which illustrate very different dynamics and consequences The great London fire of 1666 destroyed a large area of the old city yet very few lives were lost Like the Chicago fire of 1871 this one spread slowly enough from a single ignition point that people were able to escape the flames The 1906 earthquake in San Francisco on the other hand generated some 30 separate ignitions that burned a great deal of the city with considerable loss of life 11 The earthquake Table 2 City Year London 1666 New York City 1835 Charleston South Carolina 1838 Pittsburgh 1845 Philadelphia 1865 Portland Maine 1866 Chicago 1871 Boston San Francisco 1872 1906 Halifax Tokyo 1917 1923 1925 1932 1925 1931 1934 1938 1942 Nigata Yamanaka Hakodate Takaoka Boston Muramatsu Texas City Chungking Brussels Chelsea l 946 1947 1949 1967 1973 Some past large-scale urban fires Deaths Burned Area km 2 Comments 8 1 8 Burned 5 days 13 000 homes lost 50 8 6 Burned 1 day 98 500 homeless 17 500 homes lost 452 12 Earthquake-generated explosions and fires 30 ignitions burned 3 days 100 000 homeless 2000 2000 Generated firestorm 1000 Explosion and fire burned 3 days 3000 injured 300 missing 510 1000 250 Fertilizer ship explosion Burned 6 hours 400 homes lost--many firemen involved interrupted normal firefighting capabilities and broke water mains so the fires spread and burned essentially uncontrolled During World War II many bombing raids were designed to start fires because in industrial or urban areas fire could cause more damage than could comparable loads of high-explosive bombs Firebomb- ing occurred in some 71 German cities or urban centers Table 3 gives a partial list of centers in which significant loss of life occurred 12 2 3 4 ' ' As the table indicates some of those cities suffered a kind of fire- storm action with very fierce burning In most such cases the loss of life was much higher than in cities where individual fires did not coalesce Table 3 City Dresden Hamburg Berlin Darmstadt Casualties in German cities firebombed during World War II Population in thousands Deathsa in thousands Burned Area ha 300b gob 4420 135-250 42% 35-100 45% 52 1% 1950 1180 17b 8-15 49% 390 Kassel Heilborn Cologne WuppertalBarmen Augsburg Duisburg Bremen Schweinfurt Pirmasens Brunswick 55b 78 757 6-9 13% 6-8 10% 3 8-5 6 1% 760 9b 12b 410 434 1b 50 216 2 6-5 2 3 1 1 5-2 6 1 2 1 0 0 6 0 56 260 160 Braunswig 241 34% 16% 1% 0 3% 100% 1% 0 3% 0 52 0 2% Comments Firestorm Firestorm Many small fires many raids no firestorm Firestorm deaths due 90% to asphyxiation Firestorm Firestorm Deaths due 65% to fire Firestorm 23 000 rescued Firestorm NOTE A total of 71 German cities were attacked with firebombs This table lists 15 in which significant loss of life occurred In total German cities suffered 500 000 to 800 000 deaths Some 49 of the 71 cities lost at least 39 percent of all residential units e numbers in parentheses indicate the percentage of the population at risk in the vicinity of the fire who died or if that statistic is unknown the percentage of the total population of the city bPopulation at risk ·' Figure· 2 an aerial view of burned-out buildings in the center of Hamburg discloses the extent of the destruction from the firestorm in that city The photograph shows that the flames burned on both sides of a ve·ry wide street Only the shells of some of the buildings were 13 Reproduced from Fire and the Aw War C0pyri11htC 19A6 National Fira Pro111ction Ann Figure 2 Aerial view of burned-out ·residential area of Hamburg left standing a tribute to their massive masonry construction Ordi- nary fires could burn out a single such building leaving the abutting structures unscathed tures consumed Only in firestorm circumstances were all struc- Large segments of the population succumbed about 45 percent of those at risk--see Table 3 Figure 3 shows the desic- cated -corpses of -victims of heat prostration and carbon monoxide poisoning--the most common causes of death in basement shelters Fig- ure 4 shows the corpse of a man who had been caught in the flames heat and high winds in the streets of Hamburg during the firestorm Figure 5--a view of the burned-out center old part of Dresden--shows similar consequences Here the three- to five-story buildings were mostly centuries old The high density of structures loaded with com- bustibles contributed to the intensity of the fire masonry walls collapsed Note that many old Loss of life in this fire may have been the largest in history--135 000 to 250 000'dead In all the European bombing the most intense damage and the greatest civilian loss of life--as well as the greatest impact on the 14 Figure 3 Desiccated corpses Hamburg Raproduc ed from Fl and the Air War CopyrightC 19 16 National Fi Protaction Arm Figure 4 Body of man caught in street Hamburg 15 Reproducad from Figure 5 Th• DfltnlctJon of Of'Nden London 1963 Aerial view of burned-out buildings at center of Old Dresden 16 German war effort--resulted from these firestorms The Allied planning staffs found that creating such fires was neither simple nor easy A multitude of crews manning hundreds upon hundreds of bombers dropped high explosives as well as firebombs in order to break up tile roofs and deter firefighters while lighting fires within the buildings In most cities the German defense was well organized including effective air defenses with both fighter aircraft and antiaircraft batteries They could generally harass the Allied bombers enough that their bomb drops were inaccurate or missed the targets completely thus reducing the density of ignitions Such defense measures were augmented with extensive firebreaks to inhibit the spread of fire In addition European building policy had long dictated firewalls between adjacent structures to prevent the spread of fire from building to building The Germans also built elaborate shelter systems--both basement shelters and where water tables were too high to permit underground construction large above-ground bunkers Finally they had fairly sophisticated fire- fighting equipment ample water supplies and well-trained firefighting crews They had thousands of trained firefighters to combat some of the worst fires often quite successfully limiting the damage and providing extensive rescue and medical aid Throughout most of the war the Germans were busy with repair and rehabilitation In Germany the firebombing and the consequent firefighting developed over a period of several years 1941 through 1945 In Japan on the other hand the bombing attacks began in 1945 and peaked in a matter of a few months Japanese defenses were more primitive at that late stage in the war and their air defenses were relatively ineffective Moreover Japanese cities had primitive or antiquated fire- fighting equipment and quite inadequate training for firemen To make matters worse Japanese construction practices did not emphasize builtin fire containment Structures tended to be close together with few intervening firewalls or firebreaks although by 1945 many Japanese cities--including Hiroshima--were busy creating firebreaks Despite the value of firebreaks in containing fires with well-defined origins however they are less effective in impeding fires started by area sources such as earthquakes firebombing raids or nuclear explosions 17 Firebreaks in Tokyo failed to stop the spread of fire there and the fires set by the raid in one-third of the city spread to engulf another third of Tokyo-Yokohama In addition by 1945 the U S Air Force had acquired the much bigger B-29 bombers that could carry heavier bomb loads than the aircraft used in Europe They were also able to fly relatively low- altitude bombing runs allowing crews to concentrate firebombs in the most susceptible areas Some 65 Japanese cities were firebombed in those months of 1945 including Tokyo the first hit and worst damaged Osaka Kobe Kyoto Nagoya and Kunugaya the last attacked Figure 6 is an aerial view of a portion of the city of Nagoya showing in the foreground some of the effects of fire Along the canal the firebreak under construction can be seen in the background the dense construction of Japanese cities is evident In the last weeks of the war the atomic bombs dropped on Hiroshima and Nagasaki started fires in nearly every structure within a mile of the burst Most of the buildings within that distance from ground zero in the city of Hiroshima were totally destroyed by the resulting firestorm Fires in Nagasaki were also of firestorm intensity but not as large in area coverage because of variations in the density of structures and the g eater importance of topographical features The Tokyo fire re- sulting from the first of the 1945 firebomb raids on Japan caused more casualties than resulted from either the Hiroshima or Nagasaki attacks and a much larger area was destroyed in Tokyo 41 km 2 compared with 11 km 2 at Hiroshima But these latter were small cities attacked with what may now be considered low-yield nuclear weapons Larger cities have more to burn and larger yield weapons expose more to ignition FIRES FROM NUCLEAR WARFARE Today the greatest military threat comes from nuclear weapons--in general weapons of a thousand times larger yield than those used in Hiroshima 14 kT and Nagasaki 23 kT Although radiation and the initial blast would cause great damage fires represent the most serious threat to J ife and property in a nuclear attack 18 Fires are Ctl 0 0 Ctl z 40 i 0 µ u QJ Vl µ i 0 I -0 QJ i i 0 40 3 QJ LL 19 created both by the initial thermal radiation--that is the bright light and intense heat of the radiating fireball and by the physical disruptions caused by the nuclear blast wave--that is the scattering of existing fires as well as the overturning bursting and spilling of fuel containers or combustibles With so many ignitions expected throughout large areas the individual fires will almost certainly grow then amalgamate into one great conflagration That fire may in turn be driven before the wind or become a firestorm that burns in super-bonfire fashion at high intensity--generating hurricane-force surface winds and an enormous rising column of smoke and hot gases Primary Fires In primary fires ignited by a nuclear burst--i e those started by the intense thermal radiation--many factors determine whether exposed fuels will ignite or not Table 4 enumerates the principal fac- tors characterizing the source the transmission and the exposed materials that control ignition In addition other factors can be important such as air temperature blast-flame interactions dust obscurations or reflections from surrounding materials Table 4 Source Factors Weapon yield Burst height Fireball contaminants Fireball shape Factors influencing primary fires Transmission Factors Material Factors Distance from burst Visibility transmissivity Clouds fog mist Smoke haze smog dust Humidity water vapor rain Altitude air density Fireball shadowing Color Reflectivity Conductivity Density Thickness Moisture content Flammability Surface roughness Exposure angle Atmospheric bursts--in the air above the target--demonstrate a complex time history of thermal radiation with a double peak and a pulse that lasts for megaton weapons for several seconds If bursts occur at very high altitudes where the air is so rarefied that the 20 fireball dissipates rapidly then the thermal pulse may be more intense but last for mere milliseconds The pulse of light from a burst out- side the earth's atmosphere may last-even shorter times being measured in microseconds Yet each is capable of igniting fires Sketches of such bursts are shown in Fig 7 together with corresponding graphs of the thermal flux as a function of time Secondary Fires Secondary fires are those ignited as a result of mechanical disruption by the blast wave by ground motion or by debris impact from a nuclear detonation Much of the damage from conventional high- explosive bombing in World War II was due to disruption fires How- ever there is little record of such fires playing a significant role in the firebomb raids In the atomic bombings of Hiroshima and Nagasaki the relative importance of secondary fires has never been satisfactorily resolved Certainly there were many opportunities for charcoal cooking fires hibachis to be overturned and brought into contact with flammables Nevertheless very few specific fire starts either primary or secondary have been documented for either city Experience with disruptive events such as explosions earthquakes hurricanes and bombing raids suggests a long list of potential fire sources in elements common to modern urban areas Spilled volatiles Broken pipelines Vehicle impacts railroads trucks autos Burnable detonatable dust raised Friction spark fires started Overturned space water heaters with gas ignited by pilot lights Open flames Arc or spark ignitions Short circuits Hypergolic or exothermic chemical spills Broken furnaces or boilers Scattered cooking fires Ruptured fuel tanks Because of its intensity a nuclear blast would greatly exacerbate these same sources Multiple nuclear bursts would even further in- crease the probability of secondary fires If the first burst was followed by additional bursts then fuels exposed by the first might be ignited by the subsequent thermal pulses 21 In addition the fires ' ' • ' N N SEA LEVEL HIGH ALTITUDE SPACE _Time s Figure 7 Sketches of high-altitude bursts and effects of altitude on thermal pulse initiated by the first bomb might be spread by blast winds from subsequent bursts POSSIBLE MITIGATING MEASURES In light of the enormous carnage and confusion accompanying a nuclear attack and the unprecedented potential for casualties and damage from the subsequent fires it is often said that few meaningful preventive or mitigating safety measures can be taken and that our greatest hope is to avoid entirely the use of nuclear weapops The more I learn about nuclear weapon effects the more convinced I am that their use should be avoided But since we are not free to dictate to the world what weapons may be used it may be important to question the notion that nothing much can be done to minimize loss of life and damage Reasonable and modest civil defense preparations have been very effective in reducing the harmful effects of both natural and man-made disasters For example the occasional mass rescues of persons caught in firestorms in Germany in World War II required considerable prior planning and preparation The fires were fought for days by thousands of trained firefighters Some rescues were accomplished by creating a water spray tunnel leading to shelters within the burning region Some massive shelters were constructed and inade safe by deep burial or by heat-resistant construction but they seldom had adequate sources of fresh air for firestorm survival Successful rescues during large-scale fires are possible only with training disc pline organization experience timely acquisition of accurate information and maintenance of good communications Such a capability was developed gradually as the war progressed and the need became more acute as bombing raids increased in frequency and intensity When it comes to preparations the hard questions are usually not what can be done but what should be done in the context of limited budgets rising objections to inconvenience and regulation and no obvious or iIIm1ediate need for such expenditure and effort Before advocating an extensive and sophisticated shelter program acquisition of techniques appropriate for massive fires or promoting 23 a particular plan for community recovery or repair in the aftermath of a superfire we must understand what actions are possible before during or after a nuclear attack Before an attack many measures are both possible and prudent--construction of fire- and blast-resistant shelters planning for mass evacuations -training of personnel for fighting large-scale fires providing extraordinary water storage protecting firefighting equipment and personnel from blast and fire creating storage and availability for essential emergency materials providing protection for particularly sensitive communication and command elements--all properly the responsibilities of professional_' firefighters urban planners arid administrators and emergency management authori ies Plans and budgets must be worked out for dealing realistically with the extraordinary problems and expenses and convincing arguments put forward to convince legislators and funding agencies of the need for support While a massive fire is rag ng conventional firefighting organizations become overwhelmed and coordinated actions are extremely difficult such was often the case in World War II even with welltrained and organized rescue and fire-suppression crews Although some rescue and evacuation may be possible as well as limited peripheral fire suppression the inner portions of a firestorm defy any prolonged or concerted effort And the ever-present threat of more nuclear bursts is likely to preclude meaningful action Postattack activities are primarily related to relief and relocation of displaced and homeless persons and to reconstruction or rehabilitation of facilities Here again thoughtful planning and stockpiling of crucial items can greatly speed recovery Table 5 lists the most obvious measures for preventing or mitigating the consequences of superfires Although most of the measures listed may be self-evident the details of how to accomplish each are far from clear and may depend a good deal on local conditions as well as on our appreciation of the forces that govern a superfire Reloca- tion may be the ideal solution but both residential and industrial locations are determined by a great many factors and the hazards of a large-scale fire may be thought too unlikely to influence a decision 24 Table 5 Civil defense actions related to superfires Preparatory Actions Firefighting Actions Relocat·e industries or residential complexes Construct fireresistant structures Plan for evacuation Aid local water storage Provide thermal protection Train and educate professionals Build fire- and gasproof shelters Suppress flames Rescue and evacuate Limit damage Maintain access Establish connnunications Provide emergency fresh air oxygen Postfire Actions Provide relief Reconstruct essential facilities Relocate industries and residences Rehabilitate damaged structures Revise regulations For example consider the many residences in Southern California that are built on the sites of burned out homes in the highly flammable mo untains Location in areas of low-density fuel and population would reduce the fire hazard but might not meet the overriding economic needs of an industry or the life-style criteria of a household In addition to nonflammable exteriors walls roofs window frames and removal of combustibles from around or in key structures wind resistance and structural dynamics under high external heat loads may be important Underground or below-grade construction is particularly suited to resisting massive fires and nuclear effects blast debris impacts thermal and nuclear radiation Partially buried buildings are often advocated as energy conserving as well Mass evacuations seldom go smoothly without considerable planning and some rehearsal Evacuation within an urban area already engulfed by fire requires heroic effort high-performance equipment good communication and cooperation between well-trained and experienced crews and considerable planning Such a rescue was accomplished in a 1944 incendiary attack on Brunswick Germany where the fire burned for six days Large firefighting crews 4500 men created a water spray screen or tunnel leading to shelters within the burning area then evacuated 23 000 people through the heart of the raging firestorm 25 However many died inside shelters before the rescuers could reach th em Most shelters provided little protection from the total devastation of a firestorm In one basement shelter for example only 9 out of 104 persons were revived the others had been killed by carbon monoxide and heat Moreover simple evacuation to open spaces such as parks river banks and railroad yards often proved inadequate in the firestorms of World War II Since then urban areas have expanded and the likeli- hood of simultaneous ignitions over larger areas has increased so evacuation problems are likewise seriously exacerbated However with training organization and practice very impressive evacuations become practical Witness the evacuation each evening by more than one million people from Manhattan Island Local water storage and mobile emergency pumping capacity are much-needed assets during major fires or disasters since sudden demand combined with damaged distribution systems make for unreliable conventional sources in times of emergency Where possible below-grade storage and auxiliary power pumps with both blast and thermal protection would be more reliable Such protection could be important in the event of earthquake hurricane or flood as well as nuclear attack Water requirements vary for control of local fires but demand may grow considerably during a massive fire when water may be used to provide_ long-term cooling and spray screens to protect against heat and flames from surrounding areas Thermal protection in the form of reflective outer coverings for structures and equipment or window protection with nonflammable and reflective closures e g aluminum foil may be helpful in reducing ignitions from nuclear bursts as well as in combating the radiation from surrounding fires In great firestorms however high winds may strip coverings break windows and transport heat convectively making radiation shielding of minimal value without further protective measures Covering machines and critical pieces of equipment with masses of earth '• · after encasing them in grease or plastic could provide good thermal protection as well as blast and debris-impact resistance 26 Of particular importance--because of the accompanying physical damage from blast and other effects--is the maintenance of access and communication In many cases in burning German cities effective co- ordination of firefighters ceased with loss of communications The fires raced out of control and rescue operations were much inhibited Ready access and communications are essential to effective damage limitation and mitigation and require thorough planning and proven equipment as well as protected radios and telephone systems Training and experience under emergency conditions or in simulated exercises are equally vital Few emergency crews function efficiently without some prior exposure to similar conditions or to simulated emergency action The problem is to know what to simulate since the mass fire is unfamiliar and how to simulate it since the environment is likely to be of extreme winds temperatures and durations Even experienced firefighters may not comprehend how very limited will be the opportunities to operate withdraw move about co1Illllunicate or seek shelter within a mass fire they may need special indoctrination and training to successfully confront the unusually life-threatening environment of a superfire Recovery can be much accelerated through advance planning and stocking of key equipment and supplies Since local sources of such items are likely to be unavailable it is of relatively greater importance to provide and protect the most crucial materials Before making and implementing such plans however we must construct a model of the postfire circumstances using it to analyze the constraints imposed on postfire operations the postfire objectives be will be available What will be the damage What are the priorities What should What manpower What skills will be most needed THE MESSAGE TO REMEMBER To be effective advance planning and preparations should take into account the unique dynamics and consequences of a superfire which derive from very large areas burning simultaneously Unlike most urban fires which involve a single or a few buildings superfires resulting from nuclear attack will develop from many tens of thousands of ignitions 27 over a vast area and will converge into a single enormous fire Very little effective firefighting is possible at the peak of such a massive fire and even extraordinary lifesaving or survival techniques would be of limited usefulness The violent environment created by such fierce firestorms is difficult to appreciate since we have never experienced fires of such large dimensions Some indications from history and from our approximate calculations suggest that large-scale fires would be accompanied by hurricane-force winds that would fill the air in the fire area with hot gas and flames Even outside the burning area the winds themselves could cause considerable damage and prohibit effective evacuation rescue or firefighting Entire buildings could be blown down and streets blocked at considerable distances from the burning area In such a holocaust the utility and adequacy of prior preparations and plans will depend on the extent to which planners have comprehended the need for efforts well beyond the normal measures for fire protection and suppression There is a great potential for saving lives and limiting damage from such large-scale fires but special planning and coordinated actions are necessary Special construction or even relocation would be necessary to ensure survival of any industry and its employees Partially buried or below-grade designs and isolated sites may become more acceptable when the true nature of massive fires is better understood and nuclear attack perhaps more innnediately probable Unfortunately such relocation and construction require years and strategic warning or changes in threat perception can occur in much shorter times What to expect Plan for very high winds very high temperatures and often poisonous gases in or near a superfire · Plan on little ef- fective firefighting rescue or evacuation during such a fire Plan on superfires accompanying a nuclear attack and being a likely consequence of several other large-scale disasters such as earthquakes hurricanes explosions or large spills of combustibles--any of which could overwhelm conventional means of fire suppression and spread fire over large urban areas 28 IMPORTANT RESEARCH·STILL NEEDED It is clear that we know very little about either the dynamics or the consequences of superfires--especially those resulting from nuclear attack Indeed we have scarcely formulated the questions that must be answered For example what is the probability that a superfire would result from a nuclear attack on an urban area That is would a superfire result from every attack most some few is the rationale for the decision Is it calculable What Is it highly dependent on weather on the structure of the attacked city on the nature of the nuclear attack What are the impcrtant variables damage would be exclusively due to fire rather than blast fire damage different from blast damage More severe What How is More permanent What is the relationship of fire damage to postattack recovery relative to that for blast damage Are blasted structures more easily rehabilitated Other questions relate to casualties or hazards to life Most deaths in Hiroshima resulted from fire--but directly or indirectly That is were the victims initially trapped by blast and only subsequently killed by fire During the major raids in Germany and Japan many died becau e fire filled the streets and cut off escape routes whereas relatively few died in the localized fires ignited by scattered and less intense raids Will fire spread be important What are typical fire spread ranges That is what percentage of the total fire area i s beyond the initial ignition area Obvionsly if the fire is started by an isolated source-- as in Chicago in 1871--the spread area comprises the total area engulfed by flames A large fire raid or nuclear attack however causes multiple primary and secondary ignitions over a large area which then merge and spread over an even greater area Therefore we must calculate the threat of fire spreading into undamaged or only partially damaged regions as well as the dependence of fire size on variables such as nuclear yield height of burst and atmospheric transmission What sort of winds can be expected to accompany such fires fast How long might they blow 29 How How high might they reach into the atmosphere What would be the scaling for these winds versus yield fire size density of fuel intensity of burning atmospheric conditions have What effect would Is topography important environments would be produced by a superfire What local That is what concen- trations of carbon dioxide carbon monoxide smoke hot air and so on At what velocity would fire-generated winds themselves de- stroy buildings independent of the fire itself What size of fire generates such winds and what type of construction resists wind damage What is the decay pattern for winds outside the fire That is how rapidly do wind velocities fall as a function of range beyond the fire How can the effects of fire be included in targeting That is how can the targeteers or damage assessment methodologies take into account the additional damage due to fire How can civil defenders prepare for the consequences of phenomena unique to large-scale fires What will constitute adequate shelter and rescue Must shelters pro- vide a fresh air supply other than that drawn in from outside on the streets oxygen Must they have stored compressed or liquid air or bottled Will it be possible to create rescue avenues in such fires or will the burn products--such as carbon monoxide--poison the firefighters and rescue perBonnel thus crippling civil defense operations Will the winds themselves hamper or prevent rescue efforts Presuming surface winds are a major problem how effectively would nonflammable areas such as rivers very wide streets or firebreaks blo k large-scale fires and thus reduce the attendant surface winds Might analytic models of superfires provide useful quantita- tive descriptions of the holocaust environment That is will we be able to easily predict the fire environment as a function of the more obvious variables--yield height of burst nature of the city type and density of construction available fuel Using current analytic models how much can we predict about the scaling of winds or circulation burning rate and influence of fire circulation on burning rate or other behavior of superfires 30 Research could help delineate the damage expected from a superfire and could aid both those planning or assessing nuclear weapon attacks and those planning defense against such attacks As long ·as the consequences are so poorly understood little effort is justified in including fire damage in targeting considerations--meaning not only that much damage is not counted but also that much larger attacks than necessary may be planned On the defense side efforts at sheltering or evacuation might be drastically affected by the consequences of large-scale fires Some areas where research on large-scale fires would be of help are as follows Spread by fire-induced winds role of high winds in flame dynamics Spread by radiation radiation environments in large area fires Spread by brands possible enhanced firespread by brands in high winds Life threats in shelters added hazards in a superfir Death and destruction due to fire winds hurricane forces outside the fire Effectiveness of firebreaks value in the context of 1arge- scale fires Effectiveness of thermal shielding can fire ignitions be re- duced and superfires avoided Possibilities for rescue what kinds of organizations and equipment would be effective in a superfire Possibilities for effective fire suppression planning and preparations in the face of large area fires Appropriate overall planning a nd organization to deal with superfires Multiple bu r sts the increased hazards of fire starts from more than one burst BZast-fire interaotions blast waves can blow out or spread fires and thus add or subtract from the hazard Seoonda ty fires the role disruption fires play in large area fires Agencies such as the Defense Nuclear Agency or the Federal Emergency Management Agency currently sponsor research on nuclear 31 effects and in particular work toward a better understanding of the damage and life-hazards possible from nuclear-induced fires Some of their fire research efforts are aimed at the above problem areas but a coordinated program has been slow to materialize Greater program emphasis and corresponding budgetary attention to the subject would help bring the importance of understanding large area fires into focus 32 REFERENCES 1 Small R D and H L Brode Physics of Large Urban Fires Pacific-Sierra Research Corporation Report 1010 March 1980 2 Bond H ed Fire and the Air War National Fire Protection Association Boston 1946 3 Taylor D H Methodology for Estimating Casualties from High Intensity Attacks SAI February 1978 4 Irving D The Destruction of Dr esden Wm Kimber and Co London 1963 33 CHAPTER 3 METHODOLOGY FOR PREDICTING URBAN FIRE DAMAGE FROM NUCLEAR BURSTS Richard D Small Harold L Brode 34 The work reported in this chapter is an initial effort to develop a capability for predicting damage from nuclear-weapon-induced fires The result will be an algorithm that assists the user in evaluating nuclear-induced fire effects in any urban-industrial area There already exist fire-damage or fire-spread prediction codes such as the Stanford Research Institute program as modified by Science Applications Inc Our objective is to provide a more flexible program that can acconnnodate a detailed analysis of fire damage in specific cities as well as very general predictions of the extent of fires in unspecified urban areas More important the program's results should be compatible with targeting procedures and its predictions should be as reliable as those for blast damage If the latter can be ac- complished then a distinct improvement is possible in targeting and in the effective application of nuclear weapons Further such a reliable prediction technique may allow more realistic evaluation of collateral damage hazards and defensive actions This section details the organization of a master computer code Our goal is a code that computes fire damage but we include blast effects because of the interdependence of blast and thermal processes The current vulnerability number VN system for treating blast effects can be incorporated--possibly with minor modifications--into the suggested format In addition to providing an outline for a final user code the flowcharts Figs 1 through 8 provide a framework into which future research results should fit The relationships between the various fire-related physical processes are clarified and areas in which our current understanding or predictive capabilities are deficient can be evaluated Thus monitoring the development and progress of relevant fire research will be assisted and useful guidance for remaining work may result Drake M K M P Fricks D Groce C J Rindfleisch Jr J B Swenson and W A Woolson An Interim Report on Collateral Dcunage DNA Report 47342 Science Applications Inc October 1978 35 INP IT1 u - -wd o _filN ° TAIIGET D£VEL0f'Mf NT Olffll'UT inftilfdlcamd 1g•0 N Nl l MS•0 --c- 0 - C tr -ilt-- -IT-1w e•t _ __·'o MAISFIM YB CW CT _1rn fcw offira •-- • t Figure 1 36 MAIN program sffw u lnpyt• cootd I TARGETJ °' fTJN1C wE utpUt9in Jlt 11 TAAGET ait bildl ----- ATM03PHEIIE 1 -o •a CITY YU l afiratypial_ o VN --- TAIIGET W£ATHEII FJRBAl L r r••nti ir es_ - MATIIER TA tGET W£J ntER O - - i f F -r at TOA tor bsa NO -- __ _- _ _ - IIUSTFLAME TARGET DEBRIS YES la•ln T Figure 2 WEAPON EFFECT subprogram 37 Interpolation routine to determine weapon damage and distribution of ignitions Input from subroutine TARGET and results in subroutine PB-CITY Interpolate blast damage Interpolate to find debris field TARGET Interpolate for distribution of combustibles RELIABILITY PB-CITY Interpolate to find ignition distribution Reevaluate civil defense capability Output calculated results OUTPUT Return Figure 3 DAMAGE EVALUATION subprogram 38 MULTIBURST E Entry evaluates target damage Input postburst city conditions and assess damage PB-CITY Output damage evaluation OUTPUT Return MULTIBURSTTD Entry redefines target for next burst s Redefine atmosphere ATMOSPHERE PB-CITY Read data from PB-CITY and redefine subroutine TARGET TARGET Return Figure 4 MULTIBURST subprogram 39 Cak ulata dlftreiopmem of fires from 1mt1al 1gr11uon d11tril mon Input is ITmulFO btoutme TARGET lo Output is in subroutine PB-CITY TARGET Calculam ignitions extu91ished by civil dafeftle - - Oeum ine flatholl9r of interior ignitions RELIABILITY WEATHER RELIABILITY l 11111 1lts PB-CITY • output OUTPUT Figure 5 FIRE DEVELOPMENT subprogram 40 Determines whether mass fire or conflagration Input is postburst city and ambient conditions Determine the distribution of available combustibles and firebreaks PB-ClTY Determine the initial ignition distribution Define ambient conditions wind rain WEATHER Establish local atmospheric conditions ATMOSPHERE Determine applied civil defense in force CIVIL DEFENSE Judge whether mass fire or conflagration occurs RELIABILITY Output of result OUTPUT Return Figure 6 TYPE DETERMINATION subprogram 41 Calculates fire destruction from mass fire Input is postburst city and ambient conditions All output is in PB-CITY Read in initial data PB-CITY Calculate heat release WEATHER COMBUSTION ZONE Calculate mass fire iterative WEATHER PLUME ATMOSPHERE RECIRCULATION Calculate internal spread burnout CIVIL DEFENSE Update city data PB-CITY Output of results OUTPUT Return Figure 7 MASS FIRE subprogram 42 Calculates fire destruction from conflagration Input is postburst city and ambient conditions All output is in PB-CITY Define fire front and immediate fuel bed in detail I I PB-CITY CIVIL DEFENSE I I WEATHER Define ambient conditions ATMOSPHERE Calculate radiation convection fire spread and update PB-CITY I I PB-CITY ' Determine local burnout and output results OUTPUT Return Figure 8 CONFLAGRATION subprogram 43 ' One of our objectives in designing this code is to alloy immediate development of a program utilizing existing theories and correlations Initially large uncertainties may be inherent in the re- sulting code it is hoped they will be clearly indicated As research results become available and are incorporated in the program some uncertainties will be reduced and the confidence level increased This procedure should aid in directing program improvements while providing a state-of-the-art method for predicting fire damage The design of the fire damage algorithm includes a main program MAIN and 27 subprograms MAIN directs the calculation of all rele- vant physical processes from the instant of the nuclear burst until final burnout Additionally MAIN manages the data flow to the sub- programs as well as input and output to internal and external files and devices It is designed to operate using multiple time scales A short-time clock is used to compute blast and thermal effects and a long-time clock to calculate fire effects The program logic admits multiburst nonsimultaneous situations and different large-scale fire situations firestorms or more general conflagrations MAIN manages both data and program flow it does not involve new technology and can be set up at the outset The program is intended to provide predic- tions even when very little input data can be provided--the accuracy or reliability of results presumably improving with more detailed inputs Initial target-specific data are input in the first segment of MAIN thr ugh such subroutines as CITY CIVIL DEFENSE and WEATHER Display and evaluation of the subject data are provided Complete specification of the target and weapon data may but need not include • Urban map detailing physical characteristics of the target by location Level of detail may range from simple area definition to very specific identification of structure types and building density and distribution including firebreaks • Active and passive civil defense measures applicable to immediate preburst and long-term hours target vulnerability 44 • Weather conditions that may affect target vulnerability and fire development • Local atmospheric conditions thermodynamic state of the atmosphere particulate content and visibility • Weapon s data including yields locations and burst times • Target computation coordinates If any of these descriptors are missing the subroutines provide average or typical values so that the prediction can proceed The MAIN program computes the blast and thermal effects on the chosen targets INPUT 3 for each time step defined such that the thermal input before and after damage due to the blast can be calculated separately and estimates made for the various burst INPUT 2 interactions at each target The time increments depend both on the target coordinates and on the weapon s yields and locations At each node the interaction of the weapon effect with a specific building may be considered While the calculation can be per- formed several ways a thermal effects target-rating system similar to the VN blast-rating system might provide a practical and efficient computational method The calculation basically requires a definition of the target in sufficient detail to assign both a thermal and a blast rating An optimum data base would include a complete descrip- tion of each building in the target area however identification of a limited number of buildings or types of buildings can be used as a basis for interpolation or extrapolation over an entire urban area The preattack target definition is input through the subroutine CITY and the data necessary for computation transferred to TARGET Active and passive civil defense measures may considerably influence both near- and long-term effects If effective civil defense measures are anticipated accounting must be made for them in calculating the density of initial ignitions as well as in calculating fire development and control of spread Meteorological data are input to subroutines WEATHER and ATMOSPHERE Weather data include past and present moisture levels extent of cloud 45 cover and wind velocities Some exterior ignitions may be affected by rain or other moisture possibly increasing the long-time clock and allowing for effective civil defense measures and fire development will depend on ambient wind velocities Atmospheric conditions affect fireball dynamics and transmission of thermal radiation as well as influence the plume characteristics of the subsequent large area fire Furthermore the atmosphere around any urban area will be drastically modified by a nuclear weapon burst Modification of the atmospheric conditions may include dust smoke and particulates as relevant to calculations of transmission from subsequent bursts and to fire spread by radiation MAIN accepts the initial data and sets up data files and subroutines for each class of data see Fig 1 Separate data sub- routines are used for flexibility and efficiency during the course of the computation and as an aid to parameter and sensitivity studies ·-· While a calculation procedure that allows consideration of specific targets at prescribed INPUT 3 coordinates is used an interpolation routine subroutine DAMAGE EVALUATION is also included to provide a continuous analysis of the damage and a distribution of ignitions If specific target structures are not called out the interpolation routine will still provide a damage distribution After the input of initial data an output segment is specified s·o as to allow evaluation and display of the given data base Manual interactive user input can be entered at this point to either supplement the data base or override previous input With the initial conditions specified computation begins in the program segment NUCLEAR BURST Weapon effect and damage calculations are performed in called subroutines The NUCLEAR BURST segment of MAIN defines the short-time clqck used in calculating immediate burst effects As the characteristic time for all 99 percent thermal radiation to reach the target is longer than the time required for the shock wave to sweep an entire city a maximum time T WE is max Collateral-damage-type geometries may require modification of this criterion 46 defined as the calculation time interval Should another burst occur INPUT 2 within that interval the calculation interval is redefined tnew burst - t OJ The time steps t are chosen so that the shock wave s will be allowed to interact with the targets as Tmax WE at the predefined coordinates Subprogram WEAPON EFFECT is called to perform detailed computations of the blast and thermal effects at each node At the end of the calculation interval subroutine DAMAGE EVALUATION is called to interpolate the results between coordinates and thereby provide a continuous map of the damaged urban area The program segment MULTIBURST deals with multiburst situations Initially the damaged target is evaluated subroutine MULTIBURST E to allow the user to assess the value of an additional burst If an- other burst is programmed MULTIBURST TD is used and the target redefined to account for the previous burst Control is then returned to the previous segment NUCLEAR BURST and the weapon effect calculations performed for the new burst If there are no additional bursts control transfers to the following segment DEVELOPMENT of ignitions At this stage the calculation time interval must be redefined While weapon effects are manifested in seconds the growth of interior and exterior ignitions into complete building fires may require an interval T max FD · of several minutes to an hour Therefore an intermediate time clock is defined and the fire development calculated in subroutine FIRE DEVELOPMENT If an additional burst is programmed within this calculation interval Tmax FD is redefined and control returns to MULTIBURST for evaluating and redefining the target then to NUCLEAR BURST for calculating the new burst effects At the conclusion of the intermediate time clock a subprogram is provided FIRE TYPE to determine whether a mass fire or conflagration is developing It is conceivable that a mass fire will occur in the primary target area while a lesser conflagration will develop in the surrounding or adjacent areas FIRE TYPE examines the dis- tribution of combustibles and ignitions considers weather and civil defense factors and determines the type of fire Control is then passed to the final segment of MAIN in which the characteristics of the fire are calculated 47 At this point the time scale is redefined to reflect the interval required for the fire to act be it a mass fire or conflagration The calculation of fire damage burnout requires an interval T of tens of hours max B As before the computation is incremental and an appropriate duration and time step long-term time clock are defined Should an additional burst be planned in this interval Tmax Bis redefined at that time control is passed first to MULTIBURST and then to NUCLEAR BURST At each time step in CALCULATE FIRE either the MASS FIRE or CONFLAGRATION subprogram is called and the result tested for burnout The calculation proceeds until either the prescribed time interval is reached or complete burnout is achieved MAIN directs the computation in time and does not involve new technology The relevant physical processes and interactions are computed entirely in the called subprograms While some aspects of the calculation can now be performed with sufficient accuracy others can only be approximated and several of the subroutines cannot be constructed without further research The following paragraphs briefly discuss the subprogram logic we end by evaluating the research development needed for constructing all requisite subroutines Detailed calculation of the major physical processes is performed in the subprograms WEAPON EFFECT MASS FIRE and CONFLAGRATION each of which calls subroutines that compartmentalize the physical events This compartmentalization allows constructing and operating the basic program at an early date with subprograms and subroutines developing and changing as information becomes available or as research dictates The breakdown allows a clear definition of the unknowns The input from MAIN into the subprogram WEAPON EFFECT consists of the number of yields burst locations and heights and other spe · - cifications for the active at time t 0 weapons a set of computation coordinates appropriate tim intervals and the target description For the first entry into WEAPON EFFECT the target data are defined from the preburst data base CITY · - - In subsequent entries the target is described by an updated TARGET In either event at each coordinate a specific representative building is defined and a blast and thermal rating applied to it 48 A thermal rating system will need to be developed to account for building contents and surroundings position with respect to adjacent structures susceptibility to interior and exterior primary ignitions or secondary ignitions and susceptibility to ignition from adjacent burning buildings At each time increment the computation is stepped in space radially and circumferentially The integrated thermal radiation re- ceived at each target from each burst is computed through subroutines FIREBALL TRANSMISSION and TARGET THERMAL which in turn use data from ATMOSPHERE WEATHER and TARGET The target at r 8 is then n checked to see whether ignition has occurred n If the shock wave's time of arrival is within a prescribed error limit t TOA± E blasteffect computations are performed at r 8 n n Subroutines are in- eluded for calculating BLAST DAMAGE BLAST FLAME interactions DEBRIS distribution SECONDARY fire starts and modification of the CIVIL DEFENSE posture in TARGET All calculations are used to update the target status The computation is serially incremented in angle radius rid time Should another burst be activated before T is reached max the current computation is stored so it can be continued on the next entry After control is returned to NUCLEAR BURST subprogram DAMAGE EVALUATION is called Its purpose is to interpolate the computations at specific coordinates and present a continuous damage spectrum The results are stored in PB-CITY then called in later subprograms specific to the long-term fire calculation The interpolation proce- dure includes provisions for estimating the reliability of the result of the weapon-caused damage and its output Control is returned to MAIN which then calls MULTIBURST The first entry- is to MULTIBURST E which evaluates the efficacy of additional bursts on the target area The evaluation is based on data passed from the interpolation routine in PB-CITY If an addi- tional burst is programmed reentry into the MULTIBURST subprogram is effected at MULTIBURST TD In this segment the target is redefined for initiating an additional burst calculation ATMOSPHERE is similarly redefined to include the effects of smoke and dust raised by the previous burst s 49 The characteristic time for irrµ nediate weapon effects to occur is several seconds Development of building fires from ignited points can require 5 to 60 min The FIRE DEVELOPMENT subprogram calculates the number of structure fires developing from the initial ignitions Input to this subroutine is the state of the city as determined in PB-CITY Modifications to the initial distribution of ignitions by civil defense actions are allowed for in CIVIL DEFENSE Finally the FIRE DEVELOPMENT subprogram calculates whether a building fire develops from an ignition interpolates the resulting fire distribution makes an entry in subprogram DAMAGE EVALUATION updates PB-CITY and provides output information Subprogram TYPE DETERMINATION reads in all postburst information and on the basis of the distribution of developed and developing initial ignitions weather and atmosphere judges whether a mass fire or conflagration will develop The subroutine RELIABILITY assigns a confidence level to the judgment depending on the detail provided on input and on the uncertainties and variabilities inherent in each step in the computation of fire growth and development Evaluating long-term urban fire damage is performed in either MASS FIRE or CONFLAGRATION The required input is passed to these subprograms through subroutines PB-CITY WEATHER ATMOSPHERE and CIVIL DEFENSE Output is contained in an updated PB-CITY Subprogram MASS FIRE computes fire damage using an iterative procedure involving the combustion zone flaming urban area column subroutine PLUME and meso-scale recirculation The subprogram computation is quasi- steady with time incremented in MAIN Burnout is tested in the sub- program for its effects on the amount of heat released in the combustion zone • I After damage levels are measured in the CALCULATE FIRE segment of MAIN the computation is either continued or stopped If the predefined burnout criteria are attained external device output is called and the calculation repeated for additional bursts Computation of a conflagration fire spread on a front uses a ·· _ · 1•• ' marching procedure in which the computation advances with the fire's propagation Because the computation is performed in a zone around the fire front some description of local structure is necessary 50 PB-CITY Burnout is tested in CONFLAGRATION to determine the loca- tion and speed of the fire front As with MASS FIRE the extent of damage is tested in MAIN and the calculation accordingly continued or interrupted In designing the program flow subroutines describing relevant physical processes were included irrespective of whether sufficient knowledge currently exists to describe the physics This is espec- ially true for the segments used in computing the fire physics and to some extent in computing burst-related effects Inclusion of all relevant physical processes provides a framework for augmenting or improving the code without major recoding of the program as research results become available The urban fire damage algorithm can repre- sent the changing state of the art with minimal updating effort The 27 subprograms can be divided into four groups input data data management burst-related physics and fire-related physics -- The first group CITY CIVIl DEFENSE WEATHER ATMOSPHERE does not involve development of new technology however it must be flexible enough to allow either unspecified inputs or a completely specified data base describing the target in detail Similarly the data man- agement group MANUAL INPUT OUTPUT TARGET and PB-CITY does not require any new development in technology but should be able to accommodate both detailed input and very general cases Many burst-related phenomena are well understood and existing codes or methods that describe them can be modified for inclusion in this urban fire damage algorithm Subprogram WEAPON EFFECT directs the near-time burst calculations and requires virtually no new technology The suggested calculation procedure is based on the VN system for computing blast damage and calls for a similar rating system to measure thermal vulnerabilities and damage Development of a thermal rating system that leads to a practical efficient calculation procedure seems possible Research will be required although the tech- nology base appears at hand An important complication to developing a thermal rating system however will be the need to include the effects of blast on thermal vulnerability broken windows exposed 51 contents removed roofing etc can drastically lower a structure's ignition-resistance Weapon effects as needed in FIREBALL DAMAGE EVALUATION TARGET THERMAL and BLAST DAMAGE can be modeled using currently available methods and codes Certain criteria as in DAMAGE EVALUATION may need reexamination as regards fire destruction or damage due to heat and smoke Additional weapon effects are computed in subroutines TRANSMISSION BLAST FLAME DEBRIS SECONDARY and RELIABILITY In all these sub- routines further research would be useful in describing the phenomenon or its interactions with structural characteristics A more complete understanding of the transmission of thermal radiation would help as would better estimates of secondary ignitions Additionally criteria for determining the confidence level of the fire damage predictions will need development at the outset Initially the subroutines cal- culating blast-flame interactions debris distribution and secondary fires can be based on only crude theories or estimates search could significantly improve the initial estimates Future reIt should be noted that including these routines from the outset permits parametric studies that can provide insight into the relative importance of each effect The final burst-related subprogram is MULTIBURST which evaluates the damage of previous bursts and redefines the target in the event of an additional burst Subroutine ATMOSPHERE is modified by MULTI- BURST TD to account for dust and smoke as these will greatly affect the transmission of thermal radiation to the target from subsequent bursts Methods for estimating the amount of dust and smoke need to be developed as well as procedures for computing the reduction in transmission of the ensuing thermal radiation ' • ·• • ' ' A further group of eight subprograms is related exclusively to thermal effects As part of the WEAPON EFFECT subprogram subroutine IGNITION is called to determine whether combustion is initiated by the fireball radiation Although a substantial data base both labor- atory and weapon-test data exists upon which to determine if primary ignitions do occur the data are subject to critical reexamination Further ignition limits need to be determined for many modern 52 materials not previously exposed to thermal radiation A currently well-developed aspect of predicting fire growth is in calculating FIRE DEVELOPMENT flashover Codes to rigorously compute flashover can be appended to the urban fire damage algorithm although development of correlations to predict flashover based on the thermal rating system would be more practical in most targeting or civil defense exercises The type of fire large area or conflagration that will develop after a weapon bursts depends on the state of the damaged city the density and distribution of ignitions primary and secondary and ambient weather Subroutine TYPE DETERMINATION defines the type of fire from the state of the postblast city Judgments can currently be made as to the type of fire although as our understanding of large area fires and conflagrations improves the criteria can be made more rigorous The characteristics of a long-term city fire are calculated by the subprograms MASS FIRE which includes subroutines PLUME COMBUSTION ZONE and RECIRCULATION and CONFLAGRATION The calculation must now rely on stochastic methods that cannot however account for many basic physical interactions Current and projected research will significantly improve our predictive capability and should be incorporated in the algorithm as early as possible 53 NOMENCLATURE n index N NB MB counters--used in MAIN NW R r number of weapons active at time t outer radius of target area e axisymmetric t coordinates time t 0 initial time at start of weapon effect calculation t1 maximum time allotted for calculating short-time weapon effects maximum process time 2 min for 99 percent of thermal radiation to hit target maximum process time 30 min for development of initial ignitions to building fires maximum process time 10 to 24 hr for calculation of urban fires TOA shock-wave time of arrival E error limit for determining if shock at r 0 n n at time t OP shock wave overpressure P test overpressure at which desired damage level achieved 54 LIST OF SUBPROGRAMS ATMOSPHERE BLAST DAMAGE BLAST FLAME CITY CIVIL DEFENSE COMBUSTION ZONE CONFLAGRATION DAMAGE EVALUATION DEBRIS FIREBALL FIRE DEVELOPMENT IGNITION MANUAL INPUT MASS FIRE MULTIBURST OUTPUT PB-CITY PLUME RECIRCULATION RELIABILITY SECONDARY TARGET TARGET THERMAL TRANSMISSION TYPE DETERMINATION WEAPON EFFECT WEATHER 55 CHAPTER 4 LARGE AREA FIRE--AN ANALYTIC MODEL Dale A Larson Richard D Small ·· · 56 SECTION 1 OVERVIEW Large-scale fires have devastated urban areas in both wartime and peacetime During World War II firebombing raids sometimes led to firestorms that destroyed entire urban areas While concentrated bombing raids were necessary to initiate and ensure firestorm development in target cities the two atomic weapon bursts over Hiroshima and Nagasaki caused immense fire destruction The fires that resulted from these low-yield nuclear bomb bursts and those from the firebombing using many thousands of 2 kg thermite bombs caused extensive damage and destruction The damage due to fire was much greater and more complete than that due to blast from the nuclear bombs or from equal tonnages of high-explosive bombs History tells of city after city destroyed or severely damaged by fires--many times set as acts of war--but the simultaneous burning of large urban areas is a modern phenomenon that began in World War II and is projected as a consequence of any future nuclear attack on cities Moreover modern nuclear weapons have the potential for causing even larger area fires than those of World War II The World War II firestorms involved relatively extensive areas 2 2 2 Hiroshima 12 km Dresden 21 to 28 km Hamburg 21 km and survivor reports describe fires much more violent than is common with burning front line fires or individual building fires Hurricane- force fire winds were reported and high street-level temperatures indicated All combustibles in the firestorm areas burned with tremendous loss of life--even in shelters It is hence clear that large area fires simultaneous burning over a whole area give rise to phenomena not present in small fires For the present we define a small fire as one in which flame height is comparable to or greater than the typical horizontal dimension of the fuel bed and all dimensions are much smaller than the scale height of the atmosphere Large area fires are those in which 57 Megaton-yield nuclear weapons are expected to light fires primary and secondary over even greater areas than in the past For example a 1 megaton burst height-of-burst 700 m can irradiate an area 7 km from ground ZP ro with 30 cal cm2 of thermal radiation-more than sufficient to ignite lightweight household goods and many typical exterior materials In a few tens of minutes urban areas of more than 180 km 2 could be on fire leading to firestorms at least ten times as great as those of World War II It is reasonable to expect that phenomena observed in the earlier large-scale fires will be dwarfed in comparison with the effects of these nuclear-induced superfires that could engulf whole urban areas Despite the fact that numerous significant large-scale fires have occurred the documentation of these events e g Irving 1963 Miller 1968a 1968b Miller and Kerr 1965 is fragmentary anecdotal and imprecise and contains few quantitative observations Accordingly current understanding of the physics of firestorms and hence predictive capability is fairly limited Past analyses have relied either on stochastic formulations Miller Jenkins and Keller 1970 for treating urban fires resulting from a given weapon burst or on extrapolation from small-fire theory Lommasson 1965 1967 Lommasson et al 1968 Neither approach has described the special features anticipated for large-scale firestorms Experimental work has not to date provided much insight into the nature and characteristics of firestorms One difficulty is that even Jarge experiments such as Oper- ation Flambeau Countryman 1964 are only small-scale compared with what we can expect from actual large urban fires A consistent physical model based on scalings of the full conservation equations has recently been developed Small and Brode 980 - - The aspect ratio mean flame height divided by typical burn- ing area width of the burning urban area is of major importance it has been found that the characteristic velocities induced fire winds are proportional to the heat release and inversely proportional to the aspect ratio Small and Brode proposed a complete flow the typical urban burning dimension is the same order as the scale height of the atmosphere and the ratio of flame height to fire width is low 58 pattern that identifies the major physics of large area fires A principal feature of their model is that a simultaneously burning large urban area significantly perturbs the local atmosphere and hence drives an external vortex recirculation flow that pumps ambient air to the combustion zone The following describes a first effort at theoretically modeling the hydrodynamics and thermodynamics of superfires Since the work is still in progress the results presented are interim The thrust of the work is to analytically ascertain the special features of large area fires and to construct a model that will predict the velocity temperature pressure and density distributions throughout a burning area and its surroundings While conclusions are still tentative it is apparent that higher velocities than previously experienced will occur in superfires due simply to the large scale of the event Fur- ther high velocities extend past the outer edge of the fire into relatively undamaged areas The resulting wind and drag forces may exceed natural winds and structural resistances for appreciable distances beyond the fire and cause additional damage not previously acknowledged as probable MODEL OVERVIEW The basic features of a large area fire are illustrated in Fig 1 The principal elements are a strongly buoyant high-velocity flow through and about the combustion region the burning urban area a natural convection column above the combustion zone and meso-scale atmospheric recirculation Characteristic dimensions of the combustion zone are mean flame height Land horizontal extent of the burning region D The ratio L D defines a small parameter E L D that represents the aspect ratio of the burning urban area For the present analysis Land D are taken to be of the order 102 m and 104 m respectively Above the burning region the convection column is expected to rise through much of the atmosphere and accordingly have a height-to-width ratio D H 0 1 -that is the column should have similar horizontal and vertical extent above the burning city 59 Plume heights comparable in y Natural convection plume Figure 1 Schematic of large area fire magnitude to the atmosphere scale height H were observed in Dresden Irving 1963 and Hiroshima Thomas and Witts 1978 We anticipate that the plumes or columns above large area fires can be characterized by D H 0 1 Small fires building fires bonfires in the open have long narrow plumes characterized by D H 1 The differ- ence though important has not been considered in previous work The entire flow is driven by the interactions occurring in the combustion zone The basic results of interest wind velocities · temperature density pressure levels and combustion rates all need to be found in this region Thus while the combustion zone is con- t •· - siderably smaller than either the free convection column or the recirculation region it assumes primary importance in our analytic modeling and must be considered in detail as a separate component For the present we focus on the basic flow pattern in the combustion zone rather than on details of the combustion process The effect of the combustion process is therefore simply modeled by a volum source of heat addition in the combustion zone 60 The convection column is driven by the buoyancy generated by the combustion processes The massive heat addition in the combustion zone significantly perturbs the atmosphere and causes a mesa-scale recirculation--a phenomenon similar to that observed on still nights for an urban heat island Delage and Taylor 1970 The analytic model for large area fires is thus a multicomponent one In each region different physical phenomena govern the hydro- dynamics and thermodynamics of the flow Appropriately scaled equa- tions of mass momentum and energy conservation plus an equation of state are introduced for each component An overall description of the airflow can be provided by suitably matching the solutions to those various equation sets The basic results of interest concern the solu- tions in and around the combustion zone However to obtain these solutions it is necessary to determine the solutions in the other regions as well because the appropriate boundary conditions are interdependent Solutions for the combustion zone and convection column determine the characteristics of the recirculating flow which in turn provides the inflow velocity distribution in the combustion zone As depicted in Fig 2 more than three simple regions must actually be considered Analysis shows that the convection plume is not o f the standard long thin type but rather more like the potential core of a plume with temperature and vertical velocity profiles of basically top-hat shape The plume r gion of Fig 1 must therefore be subdivided into regions II and III as in Fig 2 Equations describing the physics over most of the plume region are not appropriate at the side of the top hat where there are very large shears and thermal gradients A new region V must also be introduced in the upper part of the atmosphere Equations other than those appropriate for regions II III and IV are required for describing the relatively large horizontal velocities that develop there as convection column air is ultimately spread laterally Finally since the high-velocity winds character- istic of large area fires occur in regious around as well as in the burning zone we redefine the first major component of the overall 61 y V Top outflow layer III Side mixing layer Il Convec ion column IV Recirculation region I Source layer X Combustion zone Figure 2 Components of large area fire airflow as the high-speed flow throu·gh a layer some hundreds of meters thick which contains but is somewhat larger than the actual combustion zone Piecemeal analysis is facilitated by this enlargement of the burning zone ANALYSIS S1Jl1MARY A unified quantitative description of the physics of large area fires has been developed for most of the component regions defined · • • in Fig 2--including complete coordinated analyses of the mean airflow in the source layer convection column and mixing layers on the sides of the convection column i e regions I II and III nature of the pressure density and temperature fields in the 62 The recirculation region IV has also been ascertained The essential features of the overall recirculating airflow are then completely described once the velocity fields in this region are calculated This determination requires a study of the airflow in region V the top outflow region and also of the sink-like flow at the bottom of the recirculation region These studies are being pursued in an ex- tension of the work reported here The coordinated analyses of the airflow in regions I II III and IV are described in Sec 3 and Appendixes A and B The approach Small and Brode 1980 is to use the combustion-zone aspect ratio E L D as a small parameter construct suitable asymptotic expan- sions for the model solutions in each region then match the expansions in a unified manner Analysis shows that the characteristic horizontal velocity scale in and around the combustion zone is approximately 240 km hr 150 mph for D 10 4 m and appears to increase linearly with QD The average airflow in the combustion zone itself _ hatched part of region I in Fig 2 must be found by numerical computation but the equation set to be solved is considerably simpler than that posed by the full set of state and conservation laws Furthermore this equation set can be solved analytically in region I above the combustion zone An explicit analytic solution that suitably matches the overall solutions for region I can also be found for the airflow equations that are appropriate to region II That solution represents aver- tical flow with temperature density and pressure having top-hat profiles independent of the horizontal coordinate at all heights Similarly a partial analysis of the flow equations appropriate for region IV shows that temperature density and pressure are functions of height alone in this region as well Differences in temperature density and pressure as well as velocity between regions II and IV are smoothed out in region III which straddles the side of the top hat Since the flow equations appropriate for this intermediate region contain diffusional smoothing terms these equations are less amenable to explicit analysis than those used in other regions and must also be solved by numerical 63 computation It is anticipated that numerical computation will also be necessary in determining the region IV velocity fields As de- scribed further below the region IV airflow is expected to be generally vortex-like but to exhibit a strong sink-flow behavior near the entrance of the combustion zone The properties of the recircu- lation flow should depend functionally on the magnitude of heat release in the combustion zone and to a lesser degree on dissipative forces 64 SECTION 2 MODEL PHYSICS The dominant physical effect in the combustion zone is the heat addition resulting from the fir s In and around this zone the flow is treated as that of an ideal compressible gas being heated by ongoing combustion processes then rising under buoyant forces to expand further as it rises in the atmosphere For the present the combustion mechanisms are not considered in detail the overall combustion effect is simply taken to be a volumetric heat addition in the combustion zone Details of the combustion process particu- late concentrations gas generation etc are avoided but may subsequently be considered as model refinements Shear forces are considered small compared with the large buoyant forces present in the combustion zone Diffusion of heat in the burning region is a weak effect compared with heat addition due to combustion and can be accounted for by modifying the heat addition rate The principal departure from previous fire research Morton Taylor and Turner 1956 Murgai and Emmons 1960 Murgai 1962 Smith Morton and Leslie 1975 is that the combustion zone is treated as a separate distinct region and heat is supplied volumetrically rather than at the boundary Further due to the large changes in temperature but small changes in pressure Mccaffrey 1979 the Boussinesq approximation is not employed in the combustion region The flow is also taken to be that of an ideal compressible gas in the column and recirculation regions however there are no volume sources of heat and dissipative transport mechanisms for both heat and momentum are no longer negligible Hot light air from the com- bustion zone rises in the column mixing and spreading_slightly then expanding significantly in the upper atmosphere H D 10 4 m The air is then recirculated to the combustion zone in a vortex-like See Appendix C for list of symbols 65 pattern ·since the column is so wide aspect ratio D H 1 compared with D H 1 for standard plumes entrainment and mixing of nonheated and heated air occurs principally very near the sides of the column the temperature and velocity profiles in the column are therefore of top-hat shape Some mixing takes place in the free convection column region II but the largest shears and thermal gradients occur in region III a side-mixing layer The main vortical recirculation takes place in region IV fed to some extent by flow from region V where horizontal velocities become large as the convection column air spills out on top of the atmosphere-just as warm fluid from an artesian spring spreads on a pond Since the vortex recirculation occurs over a height of order H and the combustion zone has a height L H the final recirculation stage is sink-like Constriction of a relatively thick layer of recirculating air away from the combustion zone into the thin layer entering the zone necessarily leads to a considerable increase in velocities within this zone SCALINGS The conservation equations for mass momentum and energy and an equation of state appropriate to the steady-state description o f a two-dimensional large area fire are as follows axa pu ay pv 0 2 1 P pRT • 66 Here the various and k are diffusion coefficients representing 1J 1 all dissipative processes molecular and turbulent for momentum and heat It is assumed that the Reynolds stresses may be approximated as proportionaJ to appropriate second-derivative terms Q • q x y is the volumetric heat addition rate due to combustion with Q the mean rate and q x y a specified spatial distribution all other variables have their usual meanings Small and Brode 1980 Pressure density and temperature are expected to be of the same order of magnitude in all regions of interest as they are in the far-field atmosphere ground-level atmospheric values hence serve as nominal scales for these variables Since the driving force for a firestorm's entire airflow lies in the combustion zone the model uses the characteristic dimension and flow speeds of that zone as nominal scales denoted by for spatial coordinates and velocities x D y u L U 2 2 v £IT U yet to be chosen Here subscript a refers to ground-level atmospheric values E t 10-z « 1 for L _ 10 2 m D 10 4 m 2 3 and U is chosen such that the terms for convective transport and heat addition rate in the fourth expression in Eq 2 1 balance that is so the equation represents a flow driven by combustion heating As we show below U 240 km hr is the indicated scale for L 10 2 m and D 10 4 m The scaling between u and vis chosen to preserve the continuity equation Eq 2 1 subject to the x and y scalings The nominal scalings in Eq 2 2 are appropriate for the study of firestorm airflow in region I see Fig 2 rescalings For example for H D and E Other regions require as in Eq 2 3 the appro- priate scaling for yin regions II Ill and IV is y H in contrast to Eq 2 2 All rescalings are discussed as needed in Sec 3 67 MATHEMATICAL MODEL The nondimensional version of Eq 2 1 obtained by scaling Eq 2 1 as in Eq a 2 2 is a x pu -ay pv o p ou u dX av p u clx p u clxclT p 0 • ' - 2 2 cl u 1 cl u 1 clP 01 dX E Mll dX2 E Ml2 cly2 v cly - 1 1 c p E 2 cly - Eo 1 p 01 V 'Y - au v cly av cly 'Y 1 u PX V 2 d V E1'121 ax2 1 E M22 yp 3q x y EK cly2 a2T 1 clx2 o o a2 V K2 pT E o2T cly2 2 4 where 02 M J J - gD t FaUL ' i ' Ki p p i ' 1010 lan • hr 1080 km • hr-l P UL for 1 -1 2 for D i j 10 4 m 2 a 'Y 2 5 1 4 and q - 0 for y 1 68 and or Jxl 1 2 6 Setting 8 1 so that the heat released by combustion is the dominant term we determine the nominal velocity scale U from the last expression in Eq 2 5 as 2 7 For L 10 2 m D 10 4 m and QL 58 x 10- 3 cal m2 - sec DCPA 1973 we therefore have U 240 km hr From Eq 2 5 we also then have o1 o2 2 8 O E and Eq 2 4 can be rewritten in final form as a P pu a pv 0 2 9 PT where B _£ 0 1 01 2 10 The various M and K are phenomenological coefficients that lJ l describe the extent of the turbulent forces At present it is only possible to estimate the magnitudes of these coefficients in each 69 region relying on physical understanding of the balance of forces and crude calculations to approximate the and k 1J 1 While phe- nomenological theories such as mixing-length theory can provide useful approximations for the turbulent forces in most of the regions II III IV V of this component model they are not applicable to the turbulence generated by the fire in region I In view of the scalings applied to region I and in consideration of the limit E • 0 we assume that the pressure and buoyancy forces are large compared with the diffusive forces i e for E • 0 M k 1J 1 • 0 The effect of turbulence in region I provides only a correction to the basic flow 70 SECTION 3 MODEL ANALYSIS Here we present a unified description of the overall airflow generated by a large area fire using asymptotic analysis in the limit where the combustion zone aspect ratio E L D tends towards zero The analysis involves constructing asymptotic expansions for the solution to the mathematical model equations Eq 2 9 in each component region defined in Fig 2 and suitably matching the various expansions The matching proceeds as diagrammed in Fig 3 Ex- pansions in the two parts of region I the combustion zone and the area above it are carried out separately then matched An expan- sion in region II is then developed and matched to the expansion in the upper part of region I Finally a partial expansion in region IV is developed and matched with the region II expansion by means of yet another expansion in the intermediate region III The last step in the bas ic overall flow description is the completion of the region IV expansion and its matching with the inflow in region I Iterative steps may involve further intermediate analysis in one or both of regions IA and IB in Fig For the moment 3 ts left arbitrary it is defined later in this section The solution expansions for region I are based directly on the model equations Eq 2 9 In other regions expansions are derived from rescaled versions of those equations In all regions however the expansions ave the same general form namely u 2 3 uO E -ul £ U2 E u 3 V 2 3 vo_ £-vl E· v 2 £ v 3 p PO EJ l E 2 3 p Po £ pl E Pz E p 3 2 Pz E 3p - i 3 T TO E T1 E ZT E T 2 3 71 3 1 Y EY V V --1-t- - - I I - -1- - IV I I I I l Im I I I I I I I II II I - -'-t - I I ----t-t- -----1' I I I IA- - -- -t --- - E- -- -- 7 t- r-- - - -- -r I -1 IV YI --1- --t---- IB I I 11 I I I I I I DI I I IB 1 0 i---- Q E Figure 3 Matching diagram for asymptotic so1ution of mathematical model equations 72 O d X Below we focus on determining the leading-order terms in the expansions The leading-order equations which describe the basic flow structure for a large area fire are introduced and solutions discussed Derivations and further discussion are given in Appendixes A and B SOURCE LAYER Substituting Eq 3 1 into Eq 2 9 and assuming all M 1 K 1 gives the leading-order equation set in region I 1 3 2 The momentum equations here are actually first-order correction ones ap 0 ox 0 and aP 0 ay 0 imply that P0 constant and changes in pressure are at most O E which is consistent with experimental evidence on small unenclosed fires The leading-order equations Mccaffrey 1979 The equation set in Eq 3 2 is to be solved subject to the natural boundary conditions a along y 0 VO 0 b along x 0 uo 0 dVO oP 1 ap 0 ax ax ox 73 c TO -- -- 0 dX 3 3 i e there can be no flow into the ground and the flow is synnnetric about the x 0 line Since the diffusion terms are small with re- spect to the pressure and buoyancy terms second derivatives do not appear in the leading-order equations and the no-slip condition at y 0 cannot be specified as a boundary condition need for an additional rescaling e g y region near y Ey This implies the in which a thin 0 is defined and turbulent forces balance pressure and inertia forces to leading order Since the addition of a thin region near y 0 does not affect the basic flow structure in region I we proceed with the model development as defined we will treat the thin subregion in future research The solution of Eq 3 2 divides into two parts bustion zone itself i e where O y In the com- 1 q x y is in general nonzero it seems the solution must be determined by numerical computation Outside the combustion zone though q x y is zero and the solution may be found by analytical methods Before discussing the analytic solution we note that whereas q x y is by definition zero outside the combustion zone radiation is an important factor in the energy balance in that area and must ultimately be included in the model Studies of plume behavior Murgai 1962 show that including radiation effects causes the thermodynamic variables to rapidly approach the local outside atmospheric values This finding is consistent with Mccaffrey 1979 whose measurements showed temperature rapidly approaching atmospheric values in the region near the fire Radiation effects have been modeled Murgai 1962 by assuming either a flux term of the form 3 4 or a diffusion term of the form 3 5 74 where c is a constant and Ta the local ambient temperature To elucidate the general form of the solution we ignore the effect of radiation for the sake of analytic simplicity and determine the basi flow structure Future work will include the effect of radia- tion with q x y replaced by q x y -q ra d' with q ra d as given in Eq 3 4 or 3 5 As shown in Appendix A a stream or pseudostream function w x y can be defined for Eq 3 2 by 3 6 in the region outside the combustion zone The general solution of Eq 3 2 is then given by - i uo ay VQ TO TO l J P1 P1 x 1 - ax Po Al Po - Po r J TO y Pody 3 7 1 with$ required to satisfy 3 8 and the forms of the functions P1 x 1 p0 w and E W being arbitrary In general the behavior along they 1 line of the solution to Eq 3 2 inside the combustion zone determines the forms of the three functions for example p0 must be continuous across the line the complete solution outside the combustion zone is then found by a simple numerical integration of the ordinary differential equation in Eq 3 8 As further shown in Appendix A however 75 suitably matching the outside solution to a solution inside region II the convection column actually restricts the former to the following form uo - 0 Po - poo Pl P10 - VO ' TO V 00 x - Po pm 3 9 Ap 00 y - 1 where p00 and P10 are constants to be determined and v00 x is a function of x alone also to be determined is a function of x alone as well The solution of Eq 3 2 inside the combustion zone must satisfy the boundary conditions in Eq 3 3 If the solution is to match · with that for Eq 3 9 the inside solution must satisfy the further boundary conditions that P1 p 0 and T0 are each constant and that u 0 0 along they 1 line Analytic solutions to this boundary value problem have been sought in various ways for example by similarity solution methods by means of coordinate changes but no approach has succeeded and it appears that the problem must be solved numerically A significant reduction in the problem's complexity is effected however by introducing the strec lII function x y defined by 3 10 compare Eq 3 6 • I As Appendix A shows the five equations in Eq 3 2 the boundary conditions in Eq 3 3 and the additional y 1 boundary conditions just mentioned can be simplified to 76 Po - oy 3y 3y ax ax Po 0P0 AB - ax subject to the following conditions a along y 0 iJJ b along x 0 lJJ c along y 1 0 0 dY a2 2 ay 0 Po poo The boundary value problem is actually an eigenvalue problem P 0 and p00 may be chosen as required to find an appropriate solution Such freedom is presumably necessary to adjust the solution to match with solutions in regions II and IV Fig 3 and hence complete the unified description of the overall flow for a large area fire Once an appropriate numerical solution of Eq 3 11 is constructed including choices of P0 and p00 the complete solution of Eq 3 2 inside the combustion zone is given by v O - P1o • and 3 12 77 with P10 now arbitrary and subject to eventual determination by matching requirements The continuation of the solution above the combustion zone is then given by Eq 3 9 with 3 13 Since u0 0 in Eq 3 9 the flow in the upper part of the source layer is nearly vertical deviations from the vertical coming only from correction terms in the expansion for the solution to the model equations As we show below such is also the case for the flow in the convection colUlllil above the source layer CONVECTION COLUMN Since the characteristic height Hof the convection column is on 4 2 the order of D 10 m and not L 10 m Fig 1 the vertical spatial coordinate must be rescaled as y Ey 3 14 To preserve continu±ty in rescaling Eq 2 9 we nominally assume u O E in the column and introduce the further rescaling u u - E where u is of order 1 Subject to Eqs 3 14 and 3 15 the nominal rescaling of Eq 2 9 is then a clx pu a 3 15 cly pv 0 p pT 3 16 where q x y is dropped because it is identically zero everywhere above the combustion zone We will show that this version of Eq 2 9 is appropriate for the study of both the convection column and the recirculation zone regions II and IV Fig 2 but that it must be further rescaled for the side mixing layer region III where large shears and thermal gradients give large horizontal derivatives The leading-order equations to be obtained from Eq 3 16 in the limit E • 0 clearly depend on the magnitude of the various M • and K • l J l Considering first the convection colunm we note that it is basically a vertical flow with the dominant shear represented by 3v ox apply mixing-length theory to estimate • 1J We· Modeling turbulent dif- fusion in this manner is implicitly an approximation in that it infers knowledge of the structure of the turbulence However in the absence of a definitive understanding of the local turbulence and in the interest of obtaining a leading-order approximation we use conventional mixing-length theory and estimate the turbulent diffusion coefficients for the convection column as follows 3 17 where 1 is the mixing length and v and x are the scaled order one variables in Eq 3 16 Assuming t aD where a 1 then M • K J J l Recalling that D a 10 -1 a 2 av ax 3 18 10 4 m and assuming a mixing length£ 10 3 m yields and hence M Ki O E J J 79 3 19 in the convection column That expression is consistent with the mixing coefficients _used by Smith Morton and Leslie 1975 and by Delage and Taylor 1970 In the side mixing layers xis rescaled and we expect the M and K to be at least one order of magnitude 1J l larger From Eq 3 1 Eq 3 15 and the assumption that u the convection column the appropriate expansion for u in 0 £ in region II is 3 20 Substituting into Eq 3 16 the expansions for -v P p and Tin Eq 3 1 Eq 3 19 and Eq 3 20 the leading-order equation set in region II is pO ul no ax aTo - r-1 aPoax aPo ay v O dy - y ul vO 3 21 In what follows we show that a unified description of a large area fire can be constructed with the convection column flow governed by Eq 3 21 if we set 3 22 80 Moreover further analysis suggests that a unified description is not possible if Eq 3 22 does not hold We therefore postulate Eq 3 22 and use it in Eq 3 21 to derive the final leading-order equation set for region II -· 3 23 Appendix A shows that the unique solution of Eq 3 23 that matches as y• O with the region I solution in Eq 3 9 as y • oo is 3 24 where Pm is the constant value of PO in region I With P0 pO and TO as in Eq 3 24 the thermodynamic state in the convection column 81 is that of a specific adiabatic atmosphere Furthermore in view of the velocity scalings in Eq 2 2 the rescaling in Eq 3 15 the expansion in Eq 3 20 and the forms of u1 and v 0 in Eq 3 24 the flow in the column is basically vertical the dimensional vertical velocity is much larger than the dimensional horizontal velocity RECIRCULATION REGION As pointed out earlier Eq 3 16 is the appropriately scaled version of Eq 2 9 for studying the fJ ow in the recirculation region IV and as with the convection column the leading-order equations to be obtained from Eq 3 16 in the nitudes of the M and K • 1J 0 limit depend on the mag- E • From mixing-length theory we expect 1 values for the M and K in the recirculation region to be similar 1J 1 to those in the convection column We note however that the re- circulation flow is basically bvo-dimensional with comparable shear in both x and y directions For the present analysis we therefore rely·on published estimates for the turbulent coefficients Owing to the uncertainty of the levels of turbulence a considerable spread of values has been used in past stµdies Delage and Taylor 1970 use M and K O E p 50 m2 sec Smith 1J i 3 2 1J a 1 2 Morton and Leslie 1975 use O E Mi_j Ki O E which 2 corresponds to 5 m sec G p 500 m2 sec It is interesting 1J· a that despite the spread of values the numerical results are all similar Relative to the above studies fairly large values of the diffusion coefficients M 0 1 G p 2000 m2 sec were used 1J 1J by Estoque and Bhumralkar 1969 a Consistent with the ordering per- formed in the convection column we adopt M K lJ circulation region l O E for the re- We recognize that this choice warrants critical reexamination in the future however the basic flow structure should remain qualitatively the same Substituting Eq 3 20 and the expansions for v P p and T defined in Eq 3 1 into Eq 3 16 we show the leading-order equa tion set in region IV to be the basic one initially developed for region II--i e Eq 3 21 In the convection column region II a nearly vertical flow is reasonable and the corresponding solution 82 of Eq 3 21 Eq 3 24 has u1 0 This clearly cannot be the case in region IV where the vertical recirculation requires that dimensional horizontal and vertical velocities and hence u1 and v 0 be the same order of magnitude The region IV solution therefore cannot be found by the reduction used in the analysis of Eq 3 21 for region II in fact the solution cannot be completely found at all without recourse to further lower order perturbation analysis That is as shown in Appendix A the last four equations in Eq 3 21 are useful only in determining the thermodynamic state leaving just the first equation 3 25 to relate the remaining two unknowns u1 and v 0 Another relation- ship between u1 and v 0 which is provided by lower order analysis involves still further relationships with new lower order variables All the relationships are easily derived from analysis of lower order equation sets As shown in Appendix A i 0 p0 and T0 must all be functions of y alone and satisfy d Po dy dTO Po dy Apo 0 X y-1 dPO dy · 3 26 Th solution of Eq 3 26 that appropriately gives pressure density and temperature at atmospheric values along the ground y O is 83 TO • 1 - A Po Po Y 1 y 1-A y l y 1 - A Y 1 y C -1 tf- -l 3 27 This solution also represents an adiabatic atmosphere though not the same atmosphere as in region II compare Eq 3 24 --pC0 the density just above the combustion zone must be less than 1 for example The leading-order flow field u1 v 0 in region IV remains to be found SIDE MIXING LAYER Differences in temperature density pressure and velocity between the convection column and the atmospheric recirculation region are smoothed out in a thin mixing layer region III along the side of the column Since the smoothing involves horizontal diffusion of heat and momentum the leading-order equations for the flow in this layer must retain horizontal diffusion terms from the rescaled version of the basic model equations Eq 2 9 For that flow the coordinate rescaling 3 28 proves appropriate continuity is preserved subject to ii O E -- which is required in order for the mixing-layer flow to match the convection column flow where u1 0 A characteristic mixing-layer thickness of O E is implied by Eq 3 28 a 1 in Fig 3 Appendix A shows that subject to Eq 3 28 and the requirement that horizontal diffusion be a dominant effect in the side mixing layer the leading-order equation set for the flow in that layer is given by 84 -B aP O ay _ a v0 2 Apo M21 ax2 o Here all variables with single subscripts are as in Eq 3 1 and M11 M21 and are the rescalings of M11 M21 and K1 Formally the mixing-layer flow is nearly vertical both u 1 and u0 are taken The flow actually represents a transition to be identically zero between the vertical flow in the convection column and the vortexlike flow in the atmospheric rP circulation region however from the final boundary condition introduced in Eq 3 30b u 2 must grow toward infinity as x • ro The leading-order set in Eq 3 29 is to be solved subject to the boundary conditions 85 and l y Po - 1 - A y y l 3 30 where p00 and v 00 x are as in Eq 3 9 P00 is as in Eq 3 24 and vIV and uIV are the v 0 and u1 velocity fields yet to be found in region IV These conditions are prescribed to ensure that the model equation solutions developed thus far for regions II III and IV are smoothly matched and thus provide the basis for a unified description of the hydrodynamics and thermodynamics of a large area fire The solution of Eq 3 29 which is subject to Eq 3 30 must seemingly be numerically computed DISCUSSION The model equations may admit a second overall solution which could describe some large area fires The solution represents a flow with the same basic components as depicted in Fig 1 but the convection plume is somewhat thinner A schematic illustration of the com- ponents of this flow is given in Fig 4 to be compared with Fig 3 - The second analytic possibility results from inspecting the be- ·• havior of the region I flow in the limit y 00 • - Previously stream- lines rose vertically from the combustion zone which implied the development of a thick column Alternatively all streamlines from the combustion zone could asymptotically approach the x line as y- 00 • 0 center- This converging flow is to be matched as y 00 with a plU le solution in region II Fig 4 however and is spread somewhat 86 V Top outflow layer y ✓ I IV Recircu at on region Il Thin plume J X Figure 4 Schematic flow for alternative model solution by diffusion of heat and momentum Therefore convergence to a point is mathematical only the physical import being that the flow forms a thin plume In this type of flow behavior the side mixing layer-- necessary in the earlier treatment--is not required as the thinner column can adjust to its surrounding atmospheric state through diffusion because the plume aspect ratio is no longer unity While the thick column solution seems appropriate for most physical cases the thin plume structure may occur as the result of certain burning rates in an urban cross section This issue requires further study Construction of this second type of solution is outlined ·below with a more complete derivation presented in Appendix B Constructing a solution also involves the use and matching of asymptotic expansions the matching proceeds as diagrammed in Fig 5 compare Figs 2 3 and 4 Expansions for the solution in the source layer and the thin 87 y E y V I r- - - - I ---- I I IV V · I I I I I • I II II ------- -t- -t- I• I I J- IV ------ • I 0 E X Figure 5 Matching diagram for second asymptotic solution plume region regions I and II respectively are joined by means of an intermediate expansion in corner zone Ia thickness of the thin plume--and hence The characteristic B refer on the magnitudes of the diffusion coefficients basic model equations Eq 2 9 to Fig 5 --depends M and K in the 1 1 For concreteness we consider the sample case where and M E3 2 3 31 12 88 A A where all M and K are 0 1 1J A As we discuss shortly choosing 1 S 1 2 that is defining a characteristic plume thickness 0 E 1 2D which is on the order of several kilometers is appropriate for this particular case Other selections for the M and K1 lead to other J J S choices for Subject to Eq 3 31 the following expansions prove appropriate for the unified description of the solution to Eq 2 9 over regions I Ia and II Fig 5 3 2 3 2 2 u u0 E u112 Eul E u 3 Z e u 2 • • • p po 1 2 E 1 2 T TO E pl 2 e Pl e Tl 2 e T1 E 3 2 3 2 2 p3 2 e P2 ••• 2 3 32 TJ Z e T2 ••• The leading-order term in the expansion for v must be O l E 1 2 for mass to be conserved while the air in region I--which has order one scaled width--is funneled into regions Ia and II--which have O e 112 width for S 1 2 In region I however v O E and v_112 0 and the leadingorder equations derived after substituting Eqs 3 31 and 3 32 into Eq 2 9 are exactly those of Eq 3 2 • · · ' ' 89 3 33 These equations must be solved subject to the first boundary condition in Eq 3 3 namely along y Vo 0 0 3 34 but the solution need not satisfy the boundary conditions along x 0 in Eq 3 3 which now serve as restrictions on the solution in region Ia Great flexibility is therefore afforded in the selec- tion of a solution to Eq 3 33 Presumably this flexibility is necessary for an eventual final matching of solutions in regions I and IV and by continuation elsewhere as well In any case solu- tions to Eq 3 33 are to be constructed as previously specified by numerical computation for O y 1 where qt O and from the solution of Eq 3 8 numerically if necessary and using Eq 3 7 for y 1 where q 0 The solution for y 1 is now not of the special type in Eq 3 9 solution streamlines i e lines of constant defined in Eqs 3 6 and 3 10 are to or and as sweep in toward the x 0 synnnetry line and not go straight upwards In region Ia the region I flow that converges towards the x 0 symmetry axis is turned upwards by pressure and strong shear forces A rescaling of the x coordinate that gives a leading-order model equation set appropriate for the description of this turning flow is 3 35 90 As shown in Appendix B the resul ant leading-order equation set is a2u 0 -- M - ax 11 ai2 3P1 3 36 which takes into account the diffusion of both horizontal momentum With x rescaled as in Eq 3 35 the characteristic thickness of region Ia is 0 £ 112 S 1 2 Fig 5 and heat Equation 3 36 is to be solved subject to the following boundary conditions a along y 0 v-1 2 0 b along X uo c as x ex 0 v-1 2 av_l 2 0 ax c pl 3Pa aTO ox ax ax -·- - - - _- 0 0 u 0 u 1 x p l PI x y y Po 1 y TO T1 y p x x 91 3 37 where uI PI' PI and TI are the region I solutions of Eq 3 33 In Eq 3 36 P0 is also to have the same constant value it has in region I It and Eq 3 37c are prescribed so that the region I and region Ia solutions match smoothly The solution of Eq 3 36 sub- ject to the boundary conditions in Eq 3 37 must presumably be found by numerical computation of this solution as y- 00 As we discuss shortly the behavior is then to be used in the model description of the airflow in the thin plume region II In region II the flow that is turned in region Ia rises almost vertically in something of a standard plume vertical momentum finally The x rescaling in Eq 3 35 is also appropriate for region II so the scaled plume thickness is O s 112 J as is they being diffused rescaling in Eq 3 14 as well since H D L E As shown in Appendix B the equation set that must be solved to provide the leading-order velocity fields in region II is then -B ap 2 - ax 2 A M 11 a ul -- ax2 0 0 3 38 where p0 pl Z' P1 pJ Z' T0 Tl Z' T1 TJ Z' and P1 as well as P 0 P112 and P312 are all functions of y alone that are to be determined from a matching of the solution expansions in regions II and IV These functions are found to satisfy the following equation sets 92 dTO dy Po Y - 1 dP 0 dy ' y 3 39 dPl 2 dy pO dTl 2 dy Apl 2 O ' pl 2 dTO dy - y y- 1 dP1 2 dy ' 3 40 dP 1 dy _ Apl O ' dT 1 Po dy dT1 2 pl 2 dy y _ y dT0 _ pl dy l dP 1 dy ' 3 41 dP 3 2 dy Ap3 2 O ' The general solutions of these sets are easily found Eqs 3 40 3 41 and 3 42 are linear systems and Eq 3 39 is exactly Eq 3 26 its solutions all having dT0 dy as a constant and thus 93 representing an adiabatic atmosphere Any one choice of solutions can be made to match the prescribed conditions of the far-field atmosphere as x £x • 00 A simple nominal choice is to take P0 p 0 and T 0 as in Eq 3 27 and then set Pl Z Pl Z Tl Z P1 Pl T1 p3 2 P3 z T3 2 O The basic equation set in Eq 3 38 is to be solved subject to the following boundary conditions a as y v_112 P2 P2 and T2 profiles in x tend towards corresponding· y • 00 profiles from 0 • the region Ia solution the u 1 profile x similarly matches with the 1 £ u 0 u 1 solution from region Ia b along c as x x• oo 0 u 1 P 2 p 2 and T2 profiles in y tend towards corresponding x • 0 profiles from the region IV solution v_ 112 • 0 3 43 Conditions a and c are required for the solution expansions in regions Ia II and IV to match smoothly and condition b is the natural analog of b in Eq 3 37 and in Eq 3 3 The solu- tion of Eq 3 38 subject to Eq 3 43 must presumably also be found by numerical computation However as shown in Appendix B Eq 3 38 may preliminarily be reduced to the following single equation for v_ 112 alone 2 a v-1 2 ax 2 tJ t P2oo Y - PoT2 00 Y - P1 2T3 2 - plTl - P3 2T1 2 3 44 94 Here P 200 y and T200 y are to be the far-field x x 00 atmospheric pressure and temperature profiles at second order in the Eq 3 1 expansion Further discussion of the model equations appropriate for the description of the flow in region IV is presented in Appendix B 95 REFERENCES Countryman C M Mass Fires and Fire Behavior U S Department of Agriculture U S Forest Service Research Paper PSW-19 1964 DCPA Attack Environment Manual Chap 3 '' What the Planner Needs to Know about Fire Ignition and Spread U S Defense Civil Preparedness Agency and U S Department of Defense June 1973 Delage Y and P A Taylor Nume ical Studies of Heat Island Circulations Boundary-Layer Meteorology Vol 1 1970 pp 201-226 Estoque M A and C M Bhumralkar Flow over a Localized Heat Source Monthly Weather RevieuJ Vol 97 No 12 1969 pp 850-859 Irving D Destruction of Dresden Wm Kimber and Co London 1963 Lee S and H W Emmons A Study of Natural Convection above a Line Fire J Fluid Mech Vol 11 1961 pp 353-368 Lommasson T E Firestorm Analysis The Dikewood Corporation Report DC-TN-2046-1 1967 - - Preliminary Investigation of Firestorm Sta f't-Criteria The Dikewood Corporation Report DC-TN-1050-1 1965 ---- et al A ''Firestorm Existence and Buildup Hypothesis The Dikewood Corporation Report DC-FR-1058 0 September 1968 DASA Report 2174 Mccaffrey B J Pu I'ely Buoyant Diffusion Flames Some Experimental Results National Bureau of Standards Washington D C Report NBSIR79-1910 October 1979 Miller C F Appendixes 1 through 19 to the Hcuriburg Po lice President's Report on the La Pge Saale Air Attacks on Hcuriburg Germany in WWII prepared for OCD by Stanford Research Institute December 1968a -- ---- ' · - Sumncrl' f of Damage Inflicted by Air Raids on the Cit y of Hcuribu rg in the Period July 25 to August 3 1943 Stanford Research Institute Report NRDL-TRC-68-30 July 1968b • - · ----- and J W Kerr Field Notes on World War II Germa n Fire Experience Stanford Research Institute SRI Project MU-5070 October 1965 Miller R K M E Jenki ns and J A Keller Analysis of Four Models of Nuclear-Caused Ignitions and Ea rly Fires in Urban Areas The Dikewood Corporation Report DC-FR-1210 August 1970 96 Morton B R Forced Plumes J Fluid Mech Vol 5 1959 pp 151-163 C Taylor and J S Turner Turbulent Gravitational Convection from Maintained and Instantaneous Sources Proc Roy Soc A Vol 24 1956 pp 1-23 Murgai M P Radiative Transfer Effects in Natural Convections above Fires Fluid Mech Vol 12 1962 pp 441-448 ----- and H W Emmons Natural Convection above Fires J Fluid Mech Vol 8 1960 pp 622-624 Small R D and H L Brode Physics of La I'ge Urban Fires PacificSierra Research Corporation Report 1010 March 1980 Smith R K E R Morton and L M Leslie The Role of Dynamic Pressure in Generating Fire Wind J Fluid Mech Vol 68 1975 pp 1-19 Thomas G and M M Witts Enola Gery Pocket Books New York June 1978 97 '· - · 98 APPENDIX A ANALYTIC DEVELOPMENT 1 This appendix completes the derivation of the model described in Sec 3 The discussion is based on the matching diagram in Fig 3 of the text analyses of the flow in regions I II IV and III are completed in turn SOURCE LAYER The general solution in Eqs 3 7 and 3 8 for Eq 3 2 with q x y 0 is derived as follows For q x y 0 the energy equa- tion in Eq 3 2 can be rewritten as A l this and the equation of state can then bP usPd to rewrite the first equation as the incompressible continuity equation A 2 The stream function defined by Eq 3 6 can then be introduced with Eq A 1 integrated to yield A 3 and P1 eliminated from the second and third expressions in Eq 3 2 to provide the following single equation for x y alone A 4 99 This equation can be rewritten as a $ U t l¥ ABy l- • pJ 7 2 ABy l0 1 0 ' A 5 which has the general solution of Eq 3 8 with E w an arbitrary function of wJ The solutions in Eq 3 7 then follow from Eqs 3 6 and A 3 and an elementary integration of the third equation in Eq 3 2 The reduction of Eq A 4 to Eq A 5 begins by rewriting Eq A 4 as O_ - Po l J ay £ ax n n _rr - _rr - a w J 2 ay2 ay2 As can easily be checked 100 axay axay ay2 ax _ ay ay-2 f Olj l_ P0 1 J oy ox Olj l_ oy X GIT 2 A - Y ox l_ ay El AB Y 2 l f tl El ABy l- ol J a ox Po 1 J lf lrOO Jl PoliJ j 2 ox 2 A y oy A 7 which can be used in Eq A 6 to complete the reduction We now show that the solution in Eqs 3 7 and 3 8 must actually be of the specific form of Eq 3 9 to represent a flow of the type sketched in Fig 2 Streamlines lines of constant 1j l or lj 1-- compare Eq 3 10 passing through the combustion zone must be bent sharply upwards they tend toward lines of constant and order one x as y • 00 so the heated air is not simply swept into a thin plume of the type sketched in Fig 4 That is 31jJ 3y u 0 and all its derivatives must tend toward zero as y • 00 so that from Eq A 4 3p 0 3x and hence p 0 • a constant--say p00--in that limit Eq 3 7 for ally 1 Therefore from A 8 Similarly if the second equation in Eq 3 2 is satisfied as y • 00 with u 0 • 0 P1 x 1 must be identically constant--say P10--and this second equation can be simplified to A 9 Subject to the conditions that u 0 • 0 as y • 00 the solution of this equation is u 0 uo t J 0 and the solution in Eq 3 7 is as in Eq 3 9 the choice of v 00 x being arbitrary 101 • 0 The boundary value problem posed for xi 1 and O y 1 by Eqs 3 2 3 3 and 3 9 is reduced to Eq 3 11 in the following way Subject to the first expression in Eq 3 2 the stream function defined by Eq 3 10 can be introduced and the first equation in Eq 3 11 derived by eliminating P1 from the second and third equations in Eq 3 2 The second equation in Eq 3 11 is then obtained by combining the fourth and fifth equations in Eq 3 2 The first two boundary conditions in Eq 3 11 are derived from the first two condition a and u0 0 in condition b in Eq 3 3 tion 3 10 v 0 0 Equa- along y 0 and u 0 0 along x 0 imply that $ is a constant which we arbitrarily take to be zero along y 0 ap 0 ax 0 0 and x No further conditions need be prescribed along x 0 and so forth are automatically satisfied along this line as long as 0 and the first expression in Eq 2 5 is satisfied The other boundary conditions in Eq 3 11 represent the required solution match with Eq 3 9 along y 1 Po P00 and a ay u 0 0 a e clearly necessary and a2 ay 2 0 must also hold if the first equation in Eq 3 11 is to be satisfied along that line CONVECTION COLUMN The general solution of Eq 3 23 is derived as follows the second equation PO must be a function of y alone From From the third and fifth equations the same must be true for p0 and T0 and these three functions must satisfy Eq 3 26 --that is dP0 --- Ap 0 dy dT0 Po dy 0 y _l dP 0 Y dy the second equation coming from the fourth in Eq 3 23 Substitut- ing the first equation into the second shows that dT 0 dy -A y - 1 y 102 from that the system is easily integrated to yield the general solution A 11 T00 and p00 being arbitrary 3 23 is integrated as Finally the first equation in Eq f x Po y A 12 f x being an arbitrary function of x alone If T0 p0 and v 0 in Eqs A 11 and A 12 are to match the region I values in Eq 3 9 as y • 0 T00 p00 and f x must clearly be chosen as follows p 00 f x pCOV00 x A 13 where P00 is the constant value of P0 in region I Substituting Eq A 13 into Eqs A 11 and A 12 gives Eq 3 24 As discussed in Sec 3 the leading-order region II equations in Eq 3 23 are derived under the assumptions governing the M J J and K in Eq 3 19 J We now consider the changes in Eq 3 23 and hence in Eq 3 24 that follow if the assumption for the K in J Eq 3 19 does not hold For the basically vertical convection column flow we assume K1 K2 and hence do not consider changes 103 in K2 If 0 1 a rederivation of the leading-order region II equations following that used to obtain Eq 3 23 results in exactly the same formulas as in Eq 3 23 except that the fourth equation is modified to dTO Po a y y r_1 apa 0 1S 8 2To ax 2 y A 14 But as discussed above the second third and fifth equations in Eq 3 23 imply that P0 p0--and hence T0--are functions of y alone The 1S_ 8 2T0 ax 2 term in Eq A 14 is thus identically zero and the leading-order equations subject to K1 being 0 1 are completely the same as those in Eq 3 23 Similarly if Kl 1 a rederivation of the leading-order region II equations results in Eq 3 23 except that the fourth equation is modified to 0 • A 15 P 0 p0 and T0 are again required to be functions of y alone so that this equation is identically satisfied these functions must also satisfy dP 0 -- dy A Ap 0 0 A 16 further equation is required for determining these functions com- pare Eq A 10 which must come from a study of lower order terms in the Eq 3 1 expansions However such a study is unimportant the point is that P0 p 0 and T0 are functions of y alone that is tops in top-hat profiles no matter what K1 is and the leadingorder region II solution for K1 Eis qualitatively the same as in Eq 3 24 for Kl O E 104 RECIRCULATION REGION In Eq 3 21 as well as Eq 3 23 the second third and fifth equations imply that P0 p 0 and T0 are all functions of y alone the third fourth and fifth equations then reducing to Eq 3 26 The second through fifth equations thus serve to determine P 0 p 0 and T0 as a solution set for Eq 3 26 but provide no information about the velocity fields u 1 and v 0 which must be found by future analysis of lower order equation sets The general solution of Eq 3 26 is as in Eq A 11 T00 and p00 being arbitrary Since temperature density and pressure are scaled with ground-level atmospheric values compare Eq 2 2 these values are represented nondimensionally by T0 Po P0 1 If Eq A 11 is to reduce to this for y 0 i e at ground level it must be that A 17 in which case Eq A 11 becomes Eq 3 27 SIDE MIXING LAYER The leading-order region III equations in Eq 3 29 are derived as follows Subject to the coordinate rescaling in Eq 3 28 the basic model equations in Eq 3 16 become a pu Ea pv P ii a_ii dX p 0 2ii EM a - a Mn a a 2i i By E3 ax E dX2 12 ay2 u x Ev y - E2 a AP M21 32v EM a2v ay E ai2 22 ay2 0 P Ev 0 A 18 PT 105 Substituting the expansions in Eq 3 1 for v P P and T and the expansion in Eq 3 20 for u into Eq A 18 gives leading-order equations as in Eq 3 29 as long as u1 0 and M11 M21 and K1 are chosen such that the a2u ax 2 a2v ax 2 and a 2T ax2 terms appear As discussed in Sec 3 these choices represented by order one values for M11 M12 and K1 in Eq 3 29 reflect the physical fact that horizontal diffusion smoothing is a principal effect in the side mixing layer Second derivatives of y are seen from Eq A 18 to be of lower order than those in x accordingly they do not appear in Eq 3 29 This omission is consistent with previous shear layer analyses Morton 1959 Lee and Emmons 1961 The choice for u1 is made sp that solution expansions for regions II and III can be suitably matched 106 APPENDIX B ANALYTIC DEVELOPMENT 2 This appendix completes the derivation of the model description in Sec 3 of the firestorm airflow sketched in Fig 4 The discussion is based on the matching diagram in Fig 5 and follows the order of analysis in Sec 3 The analysis in Sec 3 of the region I flow is self-contained The leading-order equations in Eq 3 36 for the region Ia solution are derived as follows Subject to the coordinate rescaling in Eq 3 35 and the sample diffusion coefficient choices in Eq 3 31 the basic model equations in Eq 2 9 become a ax pu a pv 0 £1 2 ay p u a e 1 2 v du _ ay P u axclv p dX £ B £ d ax M_ l 2v av - -B- ay e 5 2 --ii a 2 u dX2 £1 2 M_ --12 c1ay22u aPay £ Ap EM21 a2v £3 2 M a 2v A2 22 2 ox oy u axclT £1 2vaT y - 1 u c P £1 2 v c p ay ax ay Y e 1 2 q e 1 2 x Y K1 lT ax2 £112 K a2 2 T ay2 B l P PT Straightforward substitution of the expansions in Eq 3 32 into Eq B l results in the leading-order region Ia equations as in Eq 3 36 with 8P 1 2 ax 8P_ 112 ay 0 so Pl Z as well as PO must be constant Subject to the further coordinate rescaling in Eq 3 14 and the associated velocity rescaling in Eq 3 15 Eq B l becomes 107 axa P pu E 1 2 a cly pv 0 u axa £112 aya _ a M11 a-zu s3 2 M a 2u £3 ax ax2 12 ay2 v £ P u axa El 2 vaya _ -B- a Ap M a 2 v E5 2 M a 2v £5 2 ay 21 ax2 22 ay2 P aT- u 3x aT Y--'--- 1 uaP- E 112 v - ay Y E P ax ap E 112 v - ay aax22T £3 2 K2 ayz a2T pT with q B 2 0 u should 3 14 for y 0 1 Under the velocity rescaling in Eq 3 15 be 0 1 to preserve continuity under the rescaling in Eq From Eq 3 32 the appropriate expansion for u u E is therefore u u1 E1 2 uJ Z Substituting this expression for Eu 2 u and ••• B 3 the expansions for v P p and Tin Eq 3 32 into Eq B 2 we develop the following hierarchy of perturbation equations 0 13 e ••• •a 0 Ef 2 apo -- ax oPl 2 ox clP 0 ay 108 0 B 4 0 APa 0 B 5 0 2 clPl 2 cly O Apl 2 O • B 6 E 2 B 7 clP2 -B - clx M 11 clP3 2 cly Ap3 2 cl u 1 -2- ax2 0 O 2 cl T __ o o ai2 B 8 0 11 2 e B 9 0 1 B 10 109 plus unneeded equations involving M 11 and M21 B 11 plus unneeded equations 0 E B 12 ··· plus unneeded equations B 13 plus unneeded equations 110 B 14 plus unneeded equations The first three equations in Eq 3 38 are derived from the first equation in Eq B 10 the first equation in Eq B 8 and the second equation in Eq B 9 respectively The fifth equation in Eq 3 38 follows from Eq B 14 and the fourth equation comes from the first equation in Eq B 12 once the righthand side is shown to be zero Proof involves the derivation of Eqs 3 39 through 3 42 as follows From the first equations of Eqs B 4 B 5 B 6 and B 7 P0 Pl Z' P1 and P312 must be functions of y alone From the second equations in Eqs B 5 B 6 B 7 and B 8 the same must be true for p 0 p112 p1 and p 312 and the first equations in Eqs 3 39 through 3 42 must hold From the final equations in Eqs B 10 B 11 B 12 and B 13 tions of y must hold r0 T112 T1 and T312 must also be funcalone and the final equations in Eqs 3 39 through 3 42 The final equations in Eqs B 8 and B 9 are therefore automatically satisfied and the second equation in Eq B 10 and first equation in Eq B 11 reduce to Po aTo - ay r -y- i aPclyo o B 15 and B 16 respectively The second equation in Eq 3 39 follows from Eq B 15 using Eq B 15 in Eq B 16 give 111 aTO y - 1 ----aPl 2 - aTl 2 p ---'- p o ay 1 2 ay - ay - Y 0 from which the second equation in Eq 3 40 follows B 17 ' We show shortly that the second equations in Eqs 3 41 and 3 42 must be satisfied as well if solution expansions in regions II and IV are to be smoothly matched This completes the derivation of the equation sets in Eqs 3 39 through 3 42 The fourth equation in Eq 3 38 is then derived by using those equations With x derivatives set equal to zero in the righthand side of the first equation in Eq B 12 that side is made identically zero by using the second equations in Eqs 3 40 3 41 and 3 42 The second expressions in Eqs 3 41 and 3 42 are derived by considering the region IV solution expansion In the atmospheric recirculation region the x coordinate must be rescaled back from x to x compare Eq 3 35 by x e 1 2 x B 18 Subject to this rescaling the basic model equations in Eq B 2 become a ax p u • ' i• • - aya pu pv 0 av Vay av ax 2T EK a 2T p u axdT a r - 1 u axap a -5 _ a £1 2 ax2 ay2 v p ay y v pT ay 2 B 19 112 In the vortex-like recirculating flow of region IV horizontal and vertical velocities must have the same magnitude order discussed in Sec 3 for recirculation as sketched in Fig 2 Keeping u in the region as in Eq B 3 we must require B 20 0 in the Eq 3 32 expansion for v Subject to this rescaling sub- stituting the expansion in Eq B 3 for u and the expansions for v P p and Tin Eq 3 32 into Eq B 19 results in a hierarchy of perturbation equations very similar to thos in Eqs B 4 through B 14 In particular from the second third and fifth equations in Eq B 19 it is found that aP 312 aP 2 ox oPl 2 8y oP3 2 8y Ap3 2 Apl 2 O ' 0 B 21 O 0 B 22 and B 23 so that P 2 p 2 and T2 as well as P 0 p0 T0 P112 P112 Tl Z' P1 P1 T1 P312 PJ Z' and T312 are all functions of y alone the first 113 and third equations in Eqs 3 39 through 3 42 being satisfied by the last twelve of these as in region II Additionally it is found from the fourth equation in Eq B 19 that the last twelve functions must satisfy the second equations in Eqs 3 39 through 3 42 in the same way the second equations in Eqs 3 39 and 3 40 were explicitly derived in the region II analysis P312 P312 and T312 are all functions of y Thus since P1 p1 T1 alone in both region II and region IV a smooth matching of the region II and region IV solution expansions requires that these functions satisfy the same equations in both regions In particular these functions must satisfy the second equations in Eqs 3 41 and 3 42 in region II Finally Eq 3 38 is reduced to Eq 3 44 The first equa- tion in Eq 3 38 can be rewritten as B 24 and· the second integrated in x to yield B 25 Here P200 y is the region IV P 2 y profile that is the x 00 farfield atmosphere so that the region II and region IV solution expansions match smoothly From the fourth equation in Eq 3 38 T2 must be a linear function of with coefficients depending on y The x only such function that matches smoothly as x 00 with the region IV T2 y profile--say T200 y --is the profile itself Thus B 26 and from the fifth equation in Eq 3 38 114 P2 T b -G y and B 27 Substituting the forms for p2 and P2 in Eqs B 27 and B 25 into the third equation of Eq 3 38 and using Eq B 24 we have a a h CY -dt Pov-1 z 2 2112 · Bf M Pzm Y - P Lt P0 1 v_ 2 - G Y B 28 from which Eq 3 44 follows 115 116 APPENDIX C SYMBOLS A B dimensionless constants c constant of proportionality c p specific heat capacity at constant pressure D half-width of combustion zone E f arbitrary constants of integration g gravitational acceleration H scale height of atmosphere kl k2 rs dimensionless K2 effective thermal conductivities including turbulence effects Kl res aling of heat-diffusion coefficients 1S rs K2 rescalings of and K2 R mixing length L mean height of combustion zone Mll' Ml2' M21' M22 Mll' M21 A A A Mll' Ml2' M21' M22 p dimensionless momentum diffusion coefficients rescalings of M11 and M21 rescalings of Mll' M12 M21 M22 p pressure a ground-level atmospheric pressure in far field Po Pl' P2 P3 leading-order pressure in correction pressures in E • E - 0 0 limit limit plO constant value of P1 at top of combustion zone p 00 constant value of 117 po at top of combustion zone Pl 2' p3 2 correction pressure in e p 0 limit PI solution of Eq 3 33 for region I 200 far-field P 2 q dimensionless volumetric heat addition rate distribution in combustion zone Q - volume heat source qrad volumetric heat flux due to radiation R universal gas constant T temperature T ground-level atmospheric temperature in far fielil a TO leading-order temperature in e Tl' T2 T3 correction temperatures in e Too 0 limit 0 limit constant value of T0 at top of combustion zone Tl 2' T3 2 correction temperatures in e 0 limit TCX far-field ambient temperature in radiation law TI T0 solution of Eq 3 33 for region I T200 far-field T2 u horizontal velocity u rescaled horizontal velocity u 0 leading-order horizontal velocity in e ul Uz u3 correction horizontal velocities in e • • 0 limit 0 limit UIV u 1 solution for region IV ul 2' u3 2 correction horizontal velocities in e 0 limit uI u0 u v solution of Eq 3 33 for region I horizontal velocity scale vertical velocity v 0 leading-order vertical velocity in e 0 limit and correction term 118 v1 v 2 v 3 correction vertical velocities in 0 limit E • v 00 vertical velocity versus x profile at top of combustion zone v0 solution for region IV v-1 2 leading-order vertical velocity in E vl 2' v3 2 correction vertical velocities in E • • 0 limit 0 limit x horizontal position coordinate _ x rescaled horizontal coordinate x rescaled horizontal coordinate y vertical position coordinate _ y y rescaled vertical coordinate rescaled vertical coordinate a dimensionless constant A a exponent such that side mixing layer thickness is E 8 dimensionless constant B exponent such that thin plume thickness is EB y ratio of specific heats o1 o2 E dimensionless constants combustion zone aspect ratio effective kinematic viscosities including turbulence effects p density pa ground-level atmospheric density in far field Po leading-order density in pl' P2 P3 correction densities in poo E- E • 0 limit 0 limit constant value of Po at top of combustion zone 119 a Poo Pco defined by Eqs A 11 and A 13 Pl 2' p3 2 correction densities in PI VJ p0 solution of Eq E • 0 limit 3 33 for region I incompressible stream function compressible stream function 1 J 120 CHAPTER 5 ANALYTIC APPROXIMATION FOR PEAK OVERPRESSURE VERSUS BURST HEIGHT AND GROUND RANGE OVER AN IDEAL SURFACE Stephen J Speicher Harold L Brode 121 One analytic approximation to the revised EM-1 HOB peak overpressure curves is reported in Chap 7 The procedure uses an inter- polation scheme between similarities in the HOB curves the curves are illustrated in Figs 1 through 3 below Another procedure was reported at an Airblast Working Group meeting at DNA on 12 December 1979 It did not provide as good a fit to the new EM-1 curves but was somewhat simpler and more direct Subsequent refinement of the earlier form has resulted in a better fit It is suggested that this modified procedure be used in calcu- lations of peak overpressure since it is simpler and more accurate We intend to use it in our analytic approximations to pressure-time histories now being derived To proceed given x the scaled ground range and y the scaled height of burst an overpressure is calculated as follows lx2 y 2 r z y x t kft kTl 3 The peak overpressure in psi and kft kTl 3 is then given as Lll r z 10 47 ra z b z d z • e z h z r y rc z 1 0 f z rg z psi where z 1 22 3 908z 2 - ----5 1 810 2z The range of pressures for which the procedure is intended is from 1 to 10 000 P si 7 kPa to 70 MPa all distances are in scaled kilofeet kft kT173 or kilometers km kTl 3 tTo avoid the singularity in z as x 0 it is suggested that a small number limit be placed on x and the magnitude of z be limited so as not to overflow when z is raised to the 18th power These values are machine-dependent 122 soo----------------------- 400 - 'I I I- ''I I - f I 0 0 ' - J Cl iii I c ' ' I I l 30Q 200 500 Ground range ft kT1l3 Figure l Near-ideal peak overpressure HOB vs ground range curves 123 I 10 ---- ---- -- ----i-- --- --- ------g ai------ - -€ I - a 30 0 0 en -- 5 • c 0 - r 41 Cl J - • 2 t Ground Range 100 ft kT1 3 · Figure 2 Peak overpressure HOB curves for ideal surface 20-70 psi 124 7 - r I t -E N ln ' 0 'l5 -' c C'I ·cu J ''' 2 Ground range kft kr1 3 Figure 3 Peak overpressure HOB curves for near-ideal ideal surfaces b z 2 321 c z d z 18 6 · 195 z 1 1 113z18 1 17 0 6692 0 02415z 17 1 4164z 8 • 1 149z18 1 1 641z18 4 153 1 1 1 2 771z 2 · 5 ' 76 1 75 -4 l6 6 25 z 8 257z 1 3 219z 1 1 _382 z18 e z 1 _ 0 004642z 1 f z 0 03831z 0 6096 18 0 003886z18 ' 17 15z 2 879z9 25 1 2 359z 14 • 5 g z 1 83 1 2 71 66z 3 2 5 361z 6 1 0 3139z and 5 h z r y - 64 67z 0 2905 1 441 5z 5 l 389z 1 49 03z 5 8 808z1 · 5 1 154 sz 3 · 5 0 0014 ar ------------ ----''----------1 5 2 1 - 0 158 ar 0 0486 ar · 0 00128 ar J l 2y • The peak overpressure in kPa and Ian is Y r in z y x and 126 km 1 3 kT Li P r z B 10 47 ctr a z b z d z • e z h z r ar c z 1 f z ar g z y where h z r y 5 0 2905 _ ___ ________ - 64 67z 1 441 5z 5 1 5 l 389z 8 808z • ------ ------3 5 5 1 49 03z 1 154 5z · 2 0 0014 ar ---------------'----'-----------1 5 2 l - 0 158 ar 0 0486 ar • a 0 3048 100 B 14 504 -1 0 00128 ar l 2y ' kft km ' kPa psi Figures 4 through 8 show pressure contour plots generated using the above formulas for ranges of 1500 to 10 000 psi Fig 4 200 to 1500 psi Fig 5 30 to 200 psi Fig 6 6 to 30 psi Fig 7 and 1 to 6 psi Fig 8 The Appendix provides_ a series of test cases that may be used to verify application of the analytic approximation formulas Comparisons with the EM-1 revised curves are provided for 5000 1000 200 50 10 and 1 psi in Figs 9 through 14 Since the dis- parity is much less than the accuracy of the original curves and very much less than the scatter in supporting data we suggest that the fitgenerated curves could be substituted without loss of validity There would then be no difference between displayed curve3 and analytic approximations to confuse the novice user 127 1500 70 10000 PSI CON OURS 2 i OE-01 1500 1 -26E-Ol 8-40E-02 •• ' 4-20E-02 II LI al 0 c Cl w J c u o o 4-20E-02 8-40E-02 SCALED GR CKFT CKT 1 3 l l · · '• Figure 4 · 128 1 68E-Oi 2 i 0E-0i 200 TO 1500 PSI CONTOURS 4-00E-01 - J 20E-01 2- 0E-01 1 6 E-01 • 8 00E- J2 0 _ ' LL m 0 I C w J c rr o o 8-00E-02 l 60£-01 SCALED GR CKFTICKT•• ' 1 3JJJ Figure 5 129 2-40£-01 3 20£-01 4-00£-01 30 TO 200 PSI CONTOURS 8-00E-01 _ 30 6 40E-0i 4-80E-0i 3 0E-01 ' • 1-GOE-01 u a i 0 J C w o J u rr o i • G0E-01 6-40E-01 SCALED GR IKFT CKT•• 1 3JJJ Figure 6 130 8 JOE-01 6 iO 30 PSI CONTOURS 2 JOE-OO soE-oo -20E-oo • • 4-00E-01 ' IZl 0 c 0 w _ tr o Q 4-00E-01 8-00E-01 SCALED GR tKFT tKT•• ' l 3 Figure 7 131 1 -20E•OO 1 -60E• ' l0 O 6 PSI CONTOURS 6 JOE JO 3 00E•OO •• ' i SOE•OO a i 0 t C LI I J c rr o o SCALED GR CKFT I CKT 0 JJ l Figure 8 132 nMCAc-snr---J 5000 PS· T C u ri l · U • • i 20i ID FiT i 50E-Oi X a 0 r Cl LL -J • I I I ••• I I· I • I ' I I I l •• ' ' ' ' I ' ' • ' rm ' ' I ' I T 1 T'r' T' ' ' ' ' r' c CF X 3 o SCALED R J OOE-G 2 f JOE-8c tKFT ' KT•• i 'J Figure 9 133 3 JOE-G i 20E-O i JE-G ·1000 PSI r Of -1l P A i P -l S r N i I_ • SOL • IO -- F 1T -- p E ' 2 4GE-Gi J - i- X X 1 i • C E-Oi X X i 1 1 1 44E-Di -l j 9 COE-Oc --l 3 1 j J 4 • POE-O • J -4 j a -l 0 - i I 0 w V• 1 I I J u r r c ' SCALED t j ti • 1 1 I I I I I II 4 P OE-G R ' F c r-- 9-COE-02 ' i 3 l Figure 10 134 1 i I · • i -44E-Ji ' ''''''''• •••••·••• lT i 2E-C - - 200 PSI COMP ARI SON n· -n -T S 0Ll r1 · ·v - P ' f ' ' I 4-00E-Di J OE-Di 2-40E-Oi i X X J X X § i 60E-o· X J X i§ 8 JOE-Ge X X X j J X -l 1 a o 4 J c er X l 0 r Cl uJ X l I • O SCALED SR 1• •• 11 111 1 I I I 1 I 1 fl OOE-0 i -COE-o K T CKT• i 3 ' Figure 11 135 I • 1 I I I • 1 2-4CF -Oi I I 1 I • I • •• • I • • I • J QE-O 4-0JE-o SOLIO FIT 5 0 P S 1 COf 1 P A R I SON - F E i ✓ 6-40E-O J S i2E-Oi J R4E-Oi j i X X X j X X - lj X j J X i 1 X -l _ 1-28E-o· J l -l - j j j a i Cl i 0 LL l J c r - o 7'TTT TTIT'r I o I l I I I 11 l I I I l I 111 It 11 I 11 II I l 'I' It I I Ill ' 1 l 1 I I I I Ii i ·111 J 28E-Oi 2-c'6E-Oi er SCALED SR CKF CKT•• ' i 3 JI Figure 12 136 3-R4E-Oi l I Ii II I l I S i2E-Oi 6 40F - li _ '10 PSI COMP AR1SON SOL I C -- F I 1 i 40E-OO -i l X - i -- i i -i2E-JO X l i 1 R-40£-0i j --j 3 5-CDE-Oi 1 X J X § i X X -j X X -i X l 80£-0i -3 X -- X X J 1 _ j cc j 0 j r Cl UJ - J c tr o · ·I· I l I ''· '·''I ·I''· ' ·I I • • i I TTTTT f ' ' 'I c s oE-01 · s CJE-Ji Figure 13 137 8-40£- J · 1 i2E c · 1 40F -J PSI COMP P•Sr N J 'l 1· U ·1 7 OE•OC -- § C-OOE- JO X X X X X X M_ c X 0 c Cl w n 1 - c er j • c 0 ' ' •I' -'•••' I' orr •I' O O' ' •I' •' ' ''''''· '•• I' d' '••I•''•• ' •I•'' rn I • • I ' - OE JO CALED GR F t -• ' J JOE O ' l 3 JJ Figure 14 138 I 4- 0E-co • C OOE CO I • JF CO APPENDIX TEST CASES X SCALED GFOUND RANCE crFT KTi# l 3 Y SCALED HOB FT KTtt l 3 P PRESSURE CPSI -ROUNDED TO 4 DECIMAL PLtCES y X r n 08 'J os i _ l iil-i 1 C t _J H 17 2 os OS 19 21 5384 1253 7035 854 3' 14 lOO 9701 oa ' I o n 29 08 11 IJO • t 11 11 7 31°71 0G38 1374¥3730 979 7990 r-2 23 J j 11 r - - n • - ' ' J 3605 303c 14 17 ' l i • j_ n - '7 LI vo 08 l p 706 6 03 26 29 518 6033 11 14 1525 2549 l - 17 14 1059 9104 2 23 11 • l • ·'t 14 t 14 • • 14 • 14 17 • T J 17 17 17 17 17 17 t 2 2 2 ✓ r n l 1 jjt J-W 'j • o a 0 1 oa 1486 246 -I lj 7 r r I -r c 29 08 i 7 I l r n7 t · J 1 '4--t-Cl r 11 i 7 J • 7 • 14 17 769 876 0 2 J 'l o 29 08 11 - -4-54- 688lj 355 1937 284 9511 456 4937 463 8922 14 17 461 9-013 2 23 2 r2 •LO I · iJ JCOO 390 5615 • _ 7 139 23 J J 300 2334 i 14 3 1 73 'io 17 292 40 9 23 284 8394 294 0 18 26 263 805 1 2 213 279 224 584-7 i 23 23 os I o - I 11 211 6172 I 210 3212 PLC 14 17 2 • o 23 26 26 207 3' 67 199 4590 l 7r5318 204 4450 26 n 29 08 187 629 168 3002 29 29 29 11 14 155 11 i5 • o LC I • o 7 159 4008 • -r 150 t 19 145 11·-f 6 1 15 6736 4 8o06 78 722 t 37 9 59 O 29 4 35 - c • JJ I o n 1o35 O 35 1 15 0125 • JJ C'C' 4 37 5970 r r 6 O n 28 1263 17 6802 J 1 4 13 0221 21r9922 75 6 75 8 1 23 2702 15 1 94 10 745 14 6 27 16 693 • J J C'C' J J C'C - • J J 71 75 • •1J nr - 4 95 •C 95 IC - • 7 J 2 5 2 5 2 5 4 5 4 5 4 5 4 5 6 5 i J I C O J 6 5 6 5 1 I s 13 4738 1 1 1 9 5°12 4 0595 1 4 3 5345 1 7 2 9317 2 5338 2 1 1 1 7258 1 8466 1 7932 1 6286 L0435 1 1345 1 4 1 7 2 1 1 1 4 1 7 _1 1633 1 1515 2 140 CHAPTER 6 ANALYTIC APPROXIMATION FOR DYNAMIC PRESSURE VERSUS TIME Harold L Brode Stephen J Speicher - -· - 141 The procedure reported here was contrived to satisfy a limited request for dynamic pressure as a function of burst height for 5 15 and 25 psi at scaled burst heights of 0 200 and 700 ft for 40 kT The procedure which may be extended to broader applications at a later date is designed to use the approximations given in Brode 1970 but can readily be adapted to the new fit to peak overpressure which corresponds to the recently recommended correction curves for EM-1 The steps in the approximation are as follows Given 1 Height of burst HOB y kft 2 Ground range x kft 3 Yield W kT Solve fort a w r free-air burst Step 1 We can derive the free-air-burst time-of-arrival from Eq 5 of Brode 1970 t a where m r 0 5429m 3 2 2 3 - 21 185rm 361 Br m 2383r 2 2 m 2 048rm 2 6872r msec Step 2 So Zve for IS2 s t a W f ree-air burst Next we can solve for free-air-burst peak overpressure at this range HOB and yield using Eq 13 of Brode 1970 with t t a For overpressures above 1000 psi Brade's Eq 13 has been modified to give faster decay from the peak but the correction is irrelevAnt for the dynamic pressure application here which The new fit was reported at the 31 March 1980 meeting at RDA Marina del Rey California of the DNA Airblast Working Group and in PSR's progress re ort for December 1979 through February 1980 on Contract DNAOOl-80-C-0065 142 1 For peak overpressure with t t ' a uses only peak overpressure Brade's Eq 13 becomes s t W a l 4 843m m2 0 6715mta 0 0048lt O Ol 35m ta m2 l 8836mta 0 0216lt psi 2 A simpler form appropriate for peak overpressures is t W s a where t t m 1 05 X 10 6 1 130tl 14 3 psi This expre sion is reasonable from 2 psi to 1 million a psi and is accurate to within 10 percent in the range 2 to 10 000 psi Figure 1 compares the approximation with several calculated results Both Eqs 2 and 3 represent the peak overpressure for a freeair burst as a function of arrival time and yield A surface burst is approximated by the same form with 2W in place of W 2 113 min place of m Step 3 Solve fort x y W HOB a For bursts near but not on the ground surface arrival time is approximated by Eq 16 of Brode 1970 t a x y W t a r W t a r' W ·x y t a r 2W 1 Solve for y for x y for x y t x y W HOB s a Peak overpressure as approximated by Eq 20 of Brode 1970 Step 4 is 143 4 • 0 0 0 ·• •eo Q • • • • • Q • • ' • AFWL-TR-73-55 Rev Needham et al 1975 o RM2248 3800KT F A Scaled IKT Brode 1959 • RM2246 1 7KT F A Scaled IKT Brode 1966 • DASA 2506 FIT P 24 eqn 20 Brode 1970 1 05 X 106 V 1 130 t m 1•14 •• t time of arrival msec m w 1 3 KT1 3 1'--'--'-_ _ _ __ __ 0 001 __ _____ ___ _ _ _ _ _ __ __ _ _ __ _ --_ ____ __ _ _ _ _1 J -L-_ 0 01 0 1 1 _ __ __ -L-W-'- --'-_ _J W J --- J_ l -L Ll llJ4 10 100 1000 Cnmn'iri ' of r 1- ov · ess···-- VPI • ti 10 • Time of arrival msec Figuri 1 • 1-f_ ii · -· - · · _ - 1 ' 1 J P P z H P z s X a 4 E P l 0 4 z J P t W s a 1 - a J P t 2W s a 5 where bP t W and p t 2W are defined by Eq 2 or 3 above s a s a and y z - x t ' a p 1 · 8W 5 · 3rlwfr 0 0215 Eq 1 of Brode 1970 r H P z 1 A 3 2 BP C p3 A 0 743 1 136 - z z 6 1 544 z FP I p2 2 0 0257z 6 0 004435 z 12 ' 4 B z 20 42 35 5z 2500z 2 3 57 z 29 3 z14 ' C l z 2 23z - 0 225 · 0 148 z 2 28 4z 7 0 905 z 7 3 j E P l _____ 0 _0_0_26_5_5_P_ _ _ __ 1 0 0001728P 1 921 x 10- 9P2 0 004218 0 04824P 6 856 x 10- 6P2 1 0 008P 3 844 10-GPZ 145 F 2 07z 2 0 00125 0 0146z 2 z 8 I 40 000 - 17 650z 221 25z 8 1 z 20 ' 2 0 235 z 6 and a Any other definition of the peak-overpressure HOB range relationship can of course be used at this step One example is the new fit for the revised EM-1 curves which take advantage of the similarities in the family of HOB curves from 1 0 to 10 000 psi The behavi0r along the x-axis zero HOB is that of a su face burst for which overpressure can be expressed as a simple function of ground range i 2 4 3 _i_ 3 PD - X psi· 6 X Along the vertical axis zero ground range the behavior is approxi mated by 11 PK - 6 J3 y 7 psi y where x and y are in kft Along a curve through the maximum horizontal range for each isobar y RA in Fig 2 pressure is expressed by SRA l 146 2 3 RA 4 8 - 0 22 RA 8 y Reaion III y RM x RF y ReJion I X Figure 2 Typical isobars and fit regions RA where the curve y RA 1 X 10- 4X2 0 7x1 2 - 0 12X 0 °· 02 1 297x4 · 0 - 0 23 9 Along a curve through the relative minimum above the knees y RM in Fig 2 pressure is approximated as PJ - 14 35 0 056 4 RI l 45 RI 3 71 0 171 RI 4 716 ' 10 1 8 1 3 RF - 4 ly 0 76 - 2 3y0 31 -10 3y - - -·- - - 2 29y · 0 56 1 23ly 2 · 1 1 y2 · 2 Interpolating between the pressures along the four curves y x 0 y 11 0 RA x and x RF y defines peak overpressure for any height of burst y and range x The interpolation is not linear and differs in each region region I between y IS2 In 0 and y RA s 1 - FC PD FC •PE where FC - FB 0 433 l 0llFB 1 0 444 FB 5 and FB In region II between y RA x L RA and x 148 RF y 12 ISP s - FO •PL 1 - FP • FC •PE 13 where FO 0 77 FN 2 · 74 0 23 FN 0 0 FN y y - RA RM RM - RA ' PL- 1 - FH PK FH • PJ FH - 0 093 FG l 03 7 7 FG 2 51 1 7 49 FG Z lS X FG RF and -0 39 0 46 RM 0 _0036 _ 0 092x · 0 69x · 0 006 l 3lx3 ll l - 0 2x0 47 xl 11 In region III SP s PL 14 This fit provides a continuous analytic approximation to the new and improved peak-overpressure curves recommended for EM-1 Step 5 SoZ ve for Q SP HOB s s Peak dynamic pressure in an adiabatic shock is directly related to peak overpressure by the expression 149 - l P s 15 ' where P 0 is the ambient air preshock pressure and y is the effective specific heat ratio for air For overpressures less than 300 psi y may be approximated as 1 4 P 0 14 7 For all overpressures at sea level psi or 10 5 Pa 1 16 y 1 67 Brode 1968 For the revised peak overpressure fit Eqs 6 through 14 peak values do not in 11 ases correspond to shock front values in part of the Mach reflection region the second peak exceeds the shock value so that the Hugoniot shock expression for dynamic pressure is not rigorously valid in that region However since both peak overpressure and dynamic pressure increase in the double Mach region we assume the same relation applies In the regular reflection region effective dynamic pressure does not equal total dynamic pressure since at the surface the flow is constrained to horizonral velocities only An approximate cor- rection for that effect is to express horizontal dynamic pressure as for x y 16a In the Mach reflection region the flow has prssumably been turned paral el to the surface and the horizontal component is the total dynamic pressure for x y 16b Although the transition between regular a d Mach reflection does not occur exactly at x y the approximation brings the horizontal dynamic pressure to zero at the point on the surface directly beneath the burst x 0 and allows full dynamic forces as the shock passes into the Mach region 150 Step 6 Solve for Q t The following approximation for dynamic pressure as a function of HOB range time and yield is based on the observation that dynamic pressure behind the shock front at a y time is a rapidly decreasing function of distance behind the front A reasonable approx- imation is 17 2 2 1 2 · where r 0 x 0 y with x 0 the original ground range of inter h x t h e subsequent soc h k position est an d r x 2 ' y 2 112 wit s ground range Thus if t 0 represents the shock arrival time at the position of interest x 0 y and t represents the shock arrival time at further positions x y Q t QH x and x r and tare related by r x 2 y rr0 9 18 y 2 112 t t a r W Eq l The ninth-power decay is only an approximation to the dynamic pressure behavior behind the shock front at low overpressures 5 to 30 psi The best fit power in this range varies between 8 8 and 10 2 Brode 1966 Figs 37 and 38 the fit is illustrated in Fig 3 Using the above procedure we approximated both overpressure versus time and dynamic pressure versus time for three scaled burst heights three peak overpressures and one yield of 40 kT as requested by George Ullrich of DNA 31 March 1980 The peak overpressures are 5 15 and 25 psi 34 103 and 172 P the scaled burst heights are a 0 200 and 700 ft 0 61 and 312 m Also approximated are the overpressures and dynamic pressures at the same ground range at which 15 psi occurs for a surface burst but at a burst height of 200 ft 151 2 0 t 1 - _ _ _ _· ·_ _ _ _ _ _· _' _ _ j·' _ · _ ' - · · • i f- 11 • · t 1 9 ' ' I m · · · · · L _ ·· ' T · - --· -·t · ···· ··- • • J 7 J· r t l • a - 1 5 ···•' ' • ·· 0 100 '• · '- I• 200 l O • • 1 240 R ml Figure 3 Comparison of dynamic pressures at indicated times from numerical calculation Brode 1966 and current fit 1 7 kT free-air burst 152 In Tables 1 through 10 each time-of-arrival Eq 4 is listed with its corresponding dynamic impulse horizontal component time after time-of-arrival TIME - TOA dynamic pressure horizontal component as defined in Eq 16 and shock ground range G R The impulse is the partial integral I t f_ t Q t dt • 19 to Listed above each table are the relevant yield kT burst height kft initial ground range kft free-air peak overpressure psi at the given initial range time msec peak overpressure OP peak dynamic pressure and horizontal component of the peak dynamic pressure Eq 16 Note that the integration is not carried to the time of velocity reversal which is appreciably longer than the overpressure positive phase Tables 11 through 20 provide similar listings of overpressure overpressure impulse and shock ground range as functions of time or time after initial shock arrival Again yield burst height and initial ground range are given above each table along with free-air overpressure at the given distance time of arrival peak overpressure expected at the given range for a surface burst and peak overpressure for the given HOB The overpressure records are terminated at the end of the positive phase The approximation outlined above makes use of the rapid decay of dynamic pressure behind the shock front from a free-air burst but even that decay may not be rapid enough in the early Mach reflection region Preliminary study of the results of the 200-ft-HOB HULL calculation McNamara Jordano and Lewis 1977 suggests that the dynamic impulse in the Mach region where the second peak is the larger is not as strongly influenced by HOB as are peak overpressure and corresponding peak dynamic pressure This is not likely to be the case unless the early dynamic pressure fades more rapidly behind 153 the shock than does the free-air dynamic pressure Thus dynamic pressure impulse HOB curves should have less pronounced knees This conjecture is a preliminary one based solely on unverified observations from a numerical calculation a physical explanation does not yet exist However if true the fit suggested here would need further modification in the Mach reflection region · 154 Table 1 YIELD HEIGHT OF BURST GROUND RANGE 40 KT 0 KFT 5 591 KFT PEAK OVERPRESSURE 2 9665 PSI TIME OF ARRIVAL 3038 3332 MSEC PEi f OP T TA PEAK DYNAMIC PRES 5791 PSI PEAK HORIZ COMPT 5791 PSI TIME MSEC 30-43 8141 3049 2962 DYN IMPULSE HORIZ TIME-TOA DYN HGRIZ CONPT PSI-MSEC MSEC 3 1509 6 2566 5 4808 10 963 9 3177 16 4464 12 3350 21 9312 3060 26-45 3071 2379 3082 2165 3093 20 2 3104 1890 3115 1829 40 2387 3126 • 1818 45 3570 65 8557 76 8496 87 8485 3148 1946 3170 2272 55 1668 09 8613 r r1c 71 QJ t •' l - J ' - j· 18 2404 'i- ···-- ' r - J PSI 5303 43-8832 5150 29 5542 f- jJ l c-n t-_ Ci' J C __ ' ' '7 •· ' r n - 64 -4376 73 2015 321·L3508 81 488b 176 0176 3236 -4414 3258 5508 3280 6788 89 3269 -t 1 r • r- n-t rc '-tQ 3302 8253 3324 9899 3347 1726 -3649 i 220 2175 103 7608 242 3456 110 4043 264 -4 ·20 # - 'J 116 6947 122 6526 J c _ 2760 - - n r r - 1 -r - 'JD• c 'T 133 6410 3436 0788 348 1J 6345 3525 -2565 i - 0 • i io w_ 3ii1-4 6933 3659 5052 3704 3777 3749 3092 379-4 2986 3878 8052 3963 5025 • l 1-43 5133 152 3918 160 3844 167 5866 174 0827 179 9474 185 2471 190 0404 194 3797 201 4420 207 3294 £ • · t 486 923' 2 531 61 j -t n J 0 j 621 1720 r- i_ i ·- 666 0444 b -r--1 I_ I - _ It ' · I• 710 9760 • J 'J t 'J• 755 965-4 840 4719 925 1692 7 6i -I • i • c---11 J o J _ _ HORIZONTAL DYNAMIC IMPULSE CPSI-SECl 207 155 Table 2 YIELD HEIGHT OF BURST GROUND RANGE PEAK OVERPRESSURE TIME OF ARRIVAL PEAK OP T TA PEAK DYNAMIC PRES PEAK HORIZ COMPT • TIME MSEC 1101 3123 1105 7773 1110 2473 1114 7222 1123 6866 1132 6705 1141 6735 1150 6957 1159 7368 1168 7967 1186 9724 1205 2216 1223 5432 1241 9361 1260 3992 1278 9314 1297 5317 1316 1991 1334 9326 1353 7312 1391 5196 1429 5568 1467 8354 1506 3484 1545 0888 1584 0501 1623 2258 1662 6096 1702 1957 DYN IMPULSE HORIZ TIME-TOA 40 KT 0 KFT 2 977 KFT 9 0659 PSI 1096 8521 MSEC 14 9996 PSI 4 7707 PSI 4 7707 PSI DYN HORIZ COMPTT PSI PSI-MSEC MSEC 20 9714 41 3662 61 2016 80 4940 117 5101 152 5412 185 7022 217 1009 246 8384 275 0096 326 9836 373 6951 415 7171 4 4601 8 9251 4 5020 453 5562 487 66M 518 4255 546 2041 571 3080 594 0143 614 5696 65 0343 679 2420 703 3731 723 3714 739 9941 753 8511 765 4350 775 1452 783 3062 -Y f • CtJ- L SHOCK G F KFT 2 9838 2 9906 13 3951 17 8700 26 8345 35 8183 44 8213 3 7896 3- 5801 53 8435 3 3831 3P059C 3 1979 3 0235 - t JO 2 9975 -4 2496 J • jtJ 7- r 1 -t l l C L - TV i J 62 8846 71 9446 90 1202 108 3694 126 6910 145 0839 163 5470 182 0792 200 6795 219 3470 238 0804 256 8790 294 6674 332 7046 370 9832 2 7050 2 4226 - r - • l ' 3 0180 3 0317 3T04-53 ' -1 Jf - J 3 0864 3 1137 3 14-1 'r 2 1719 1 9491 3' 1958 1 7509 j iJL of COJ l '1- o' 175743 3 2505 L-4170 3 2779 1 2765 3 3053 1 1511 3 3326 3 3600 1 389 8'' ' ' - cw L 7 3 4147 3-469 i 5241 n t'J 3 5789 448 2366 3905 3 6336 487 1979 • t L ' t l '1 -3 6883 - _ • 6954 C' n Ji l '-t 409 4962 ' F l - I - 1 cO J JO 2699 565 7574 • JJ 605 3435 l- JC C' l I j t J'J 'i'lC -Y 3 7977 r n 3 8525 HORIZONTAL DYNAMIC IMPULSE PSI-SEC 7833 156 Table 3 40 KT OF BURST 0 KFT GROUND RANGE 2 316 KFT PEAK OVERPRESSURE 14 7987 PSI TIME OF ARRIVAL 692 4409 r SEC PEAK OP T TA 24 994-4 PSI PEAK DYNAMIC PRES 12 2116 r JJ PEAK HOfUZ CDMPT 12 2116 PSI YIELD HEIGHT rar -T • TIME MSEC 696 3199 700 2060 704 0994 707 9998 715 8222 723 6728 731 5514 -739 4579 747 3920 755 3535 771 3578 787 4692 803 6860 820 0066 836 4293 852 9526 869 5748 886 2946 903 1102 920 0203 954 1181 988 5764 1023 3842 1058 5307 1094 0057 1129 7990 1165 9010 DYt IMPULSE HORIZ CPSI-NSEC 46 4806 91 3224 134 5876 176 3361 255 4960 329 2483 397 9901 462 • 0876 521 8783 577 6735 678 3402 766 2049 843 0108 91-0 2485 969 1949 1020 9454 1066 4414 1106 4931 1141 7990 1172 9622 1224 7701 1265 4383 1297 5155 1322 9338 1343 1654 1359 3380 1372 3198 TIME-TOA t-fSEC HYN HORIZ CGMf'T PSI 3 8789 7 7651 11 6584 15 5589 23 3812 H 2318 39 1104 47 0169 54 9510 62 9125 78 9168 C- ' C J i ' c SHOCt G R KFT ' lll -- n ·' J c •'3 70 10 9059 - -1 - - C -yr r 9 7498 9 0530 L - Jf Uf S 4098 2 ❖ 3843 r 'j L_ - Jf'V '7 ' 'A-Y 7 3158 7 2668 6 7593 2 4254 5 8556 5 0812 95 0282 111 2450 127 656 14-3 9883 160 5116 177 1339 193 8536 210 6692 227 5794 261 6771 296 1354 330 9432 366 0898 401 5647 · 437 3580 473 -4601 4 4163 3 8446 3 3522 2 5622 2 9273 2 5601 2 6169 -·-·-1 9666 'JJ 'J 2 -6443 2 6716 2 -6990 1 3382 f_ - J f 1 • 422 2 8084 f'l • t n 0 1 JO ·' • c • j L i 5073 4028 3213 HORIZONTAL DYNAMIC IMPULSE CPSI-SEC • 157 2 9726 3 0273 3 0820 't ' -r - L J Table 4 YIELD HEIGHT OF BURST GROUND RANGE PEAK OVERPRESSURE TIME OF ARRIVAL PEAK OP T TA PEAK DYNAMIC PRES PEAK HORIZ COMPT TIME MSEC 3580 7616 3586 2916 3591 8228 3597 3549 3608 4225 3619 4943 3630 5703 3641 6505 3652 7349 3663 8235 3686 0130 3708 2189 3730 441 3752 6790 3774 9329 3797 2025 3819 4875 3841 7879 3864 1034 3886 4339 3931 1393 3975 9028 40 KT 684 KFT 6 171 KFT 2 4931 PSI 3575 2327 MSEC 5 0002 PSI 5792 PSI 5792 PSI DYN IMPULSECHORIZ TIME-TOA DYN HORIZ CGMPT PSI-MSEC MSEC PSI SHOCK G F KFT 5 5289 11 0589 16 5900 5719 6 1778 C I 6 1840 3 1826 6 3256 9 4295 12 4950 18 5123 2-4- 3817 30 1071 35 6923 41 1411 46 4572 56 7040 66 4607 75 7525 84 6036 93 0366 101 0730 108 7328 116 0354 122 9986 129 6397 142 0154 153 2856 4020 7232 163 557 4065 5992 4110 5298 4155 5138 4200 5501 4245 6376 4290 7754 4335 9622 4420 8167 4505 8342 4591 0088 172 9250 181 4755 189 2854 196 4240 202 9535 208 9300 214 4041 223 4611 231 1701 237 7461 • • JC4 r r- o1 1 n1- J' J • Jt J 0 22 1222 t r 6 1983 6 2120 J • 10 33 1898 44 2616 • 55 3376 • j 1 •J-'j- Cw- 17 66 4178 4977 4854 4734 4504- 6 2530 J r • 'J i i 4286 • 4-079 C JU J C 7 n JiJ 00 f t ' J --1 ' ' 77 5022 88 5908 110 7803 132 9862 C L Ji J i - ' - O LCO f 6 2804 l - '- 6 3351 155 2082 177 4463 199 7002 3883 6 3898 3697 6 4172 221 9697 3521 6 4-445 244 2548 3354 3196 6 4719 I O 266 -5551 ·' - I C' J QQ I ••• 283 8707 311 2012 3046 C · ·' o • - J cc 2903 0 J • AJ _1 355 9066 400 6701 2639 2401 C t' C- J ' 445 4905 490 3665 1992 ' n7 -0 ' 1817 1658 1514 535 2971 580 2811 625 3174 670 4049 715 5426 760 7295 845 5840 930 6015 -t- n1 • O t f i J I L LCC 1159 0983 0836 0713 1015 7760 HORIZONTAL DYNAMIC IMPULSE PSI-SEC 158 l C'C • r l 6 6 87 I l 6 7181 6 7729 0 - 1 J J 6 8 323 6 9370 6 9917 ' l r c •' - -CJ 7 1012 -1 1' M '7 J C 7 306-4i 7 4090 Table 5 40 KT 684 KFT GROUND RANGE 3 001 KFT PEAK OVERPRESSURE 8 5133 PSI TIME OF ARRIVAL 1209 3571 MSEC PEAK OP CT TAl 14 9964 PSI PEAK DYNAMIC PRES 4 7688 PSI PEAK HORIZ COMPT 4 7688 PSI YIELD HEIGHT OF BURST TIME MSEC 1213 7684 1218 1844 1222 6053 1227 0308 1235 8962 1244 7803 1253 6832 1262 6045 1271 5443 1280 5024 1298 4728 1316 5147 1334 6271 1352 8091 1371 0595 1389 3775 1 07 7620 1426 2122 1444 7271 1463 3057 1500 6508 1538 2404 1576 0676 1614 1260 1652 4090 1690 9105 1729 6245 1768 5452 1807 6669 1846 9842 DYN IMPULSE HORIZ TIME-TOA DYN HCRIZ COMPT PSI-MSEC MSEC 20 7547 40 9796 60 6892 79 8978 116 8632 151 9849 4 4112 185 3622 217 08 0 247 2533 275 9383 329 1619 377 3552 421 0304 460 6437 496 6021 529 2691 558 9693 585 9931 610 6006 633 0247 672 0924 704 6775 731 9325 754 7917 774 0154 790 2236 803 9237 815 5323 825 3922 833 7861 PSI SHOCK G R KFT __ t -Y' ° J '- ' JI 0 8 8273 4 5186 13 2481 17 6737 26 5390 4 3989 4 2826 4 0599 3 8497 35 4232 l' r C ' t J 3 0283 3 0420 44 3260 53 2474 62 1872 71 1452 3 4639 3 2869 3 -0830 3 0967 3 1197 3 1104 89 1 156 n1- -- r L • O t L J -r 107 1575 125 2700 143 4519 2 5376 3 1651 2 2918 3 1925 2 0716 3 2198 161 7023 1 8742 3 2472 180 0203 198 4049 1 6971 1 5380 3 3019 3 3293 291 2936 1 3950 1 2664 1 1505 9519 328 8832 7900 366 7105 • 0 J 0 'l -f J OJ ' 216 8550 235 3699 253 9486 'C ' P I 404 7688 • 5-489 443 0518 596 481 5533 520 2673 559 1880 598 3097 637 6270 3858 ri J C a f J _ r _ t J J JOC 3 3840 3 4387 3 4934 3 5481 J -- - _ iJ O J 0 - r J I J k l JL 3 7670 2740 3 8217 2318 1966 3 8765 t HORIZONTAL DYNAMIC IMPULSE PSI-SEC 159 of- r • J 3 9312 Table 6 YIELD HEIGHT OF BURST 40 KT 684 KFT GROUND RANGE 2 977 KFT PEAK OVERPRESSURE 8 6363 PSI TIME OF ARRIVAL 1193 9169 MSEC PEAK OP T TA 15 2102 P T OJ PEAK DYNAMIC PRES 4 8969 PSI PEAK HORIZ COMPT 4 8969 PSI TIME MSEC 1198 3112 1202 7104 1207 1144 1211 5232 1220 3552 1229 2063 1238 0763 1246 9651 1255 8724 1264 7983 1282 7051 1300 6844 1318 7350 1336 8560 1355 0464 1373 3052 1391 6314 1410 0241 1428 4823 1447 0050 1484 2406 1521 7233 1559 4477 1597 4055 1635 5907 1673 9971 1712 6187 1751 4494 1790 4836 DYN IMPULSE HORIZ TIME-TOA DYN HOIUZ COMPT PSI MSEC PSI-MSEC 4 3943 8 7934 13 1975 17 6063 26 4383 35 2894 H 1593 53 0481 21 2278 41 9095 62 0603 81 6948 119 4687 155 3444 189 4250 221 8075 252 5834 281 8389 336 0901 3as 1n1 429 6295 469 9186 506 4643 539 6415 569 7848 597 1931 622 134 644 8468 684 3791 70 8814 88 7882 106 7674 124 8181 142 9391 161 1295 179 3883 197 7145 216 1071 234 5653 253 0881 290 3237 717 3101 327 8069 744 8206 365 5307 403 4885 441 6737 480 0802 518 7017 J a 07 557 5324 • J _J 596 5667 2329 767 8667 787 2250 803 5284 817 2939 828 9454 838 8314 -r rC' G R KFT r 7C C 4 6379 2 9906 C -1 J r -- n i 77 f'J 3937 ·L 1634 3 0043 3 0180 • - o Ml 3 317 3 7412 3 5477 3 0590 '7 3 3650 3 1925 3 0453 - - - IJ _t _ _ 3 0864 2 8756 3 1137 2 5926 2 3396 2 1132 Liq _ t • J 1 9104 3y2232 3 2505 3f 2779 J 7'1n • LOO 1 5654 1 4188 1 2870 1 1684 3 1685 - J • -inc - l 7 JO 3 3053 J C 3 36 • 9654 3 4147 8001 3 4694 6651 3 5241 5545 3 5789 4637 - 3888 3 6883 I- - I O JJO - -i M 3 7430 1 7C C 3 7977 3 8525 HORIZONTAL DYNAMIC IMPULSE PSI-SEC 8388 160 nn- --n 'l • 0 J• J ' JJ - •J 61 9555 SHOCK Table 7 YIELD HEIGHT OF BURST GROUND RANGE PEAK OVERPRESSURE TIME OF ARRIVAL 40 KT 684 KFT 2 282 KFT 13 9840 PSI 776 1969 MSEC PE AK OP T TA 24 9958 PSI PEAK DYNAMIC PRES 12 2128 PSI PEAK HORIZ COMPT 12 2128 PSI TIME MSEC 779 9936 783 7974 787 6081 791 4259 799 0822 806 7661 814 4773 822 2158 829 9813 837 7736 853 4379 869 2071 885 0796 90L054 17 1289 933 3027 949 5740 965 9414 982 4034 998 9589 1032 3442 1066 0869 1100 1765 1134 6032 1169 3572 1204 4291 1239 8098 1275 4906 DYN IMPULSE HORIZ PSI-MSEC 45 5547 89 6087 132 2150 173 4253 251 8412 325 2419 393 9730 458 3542 518 6821 575 2314 677 9387 768 3679 848 0927 918 4722 980 6813 1035 7375 1084 5235 1127 8055 1166 2502 1200 4380 1257 8994- 1303 6473 1340 2264 1369 5957 1393 2712 1412 4308 1-427 9940 144 6819 TIME-TOA MSEC DYN HORIZ COMF'T SMOCK G R PSI ffT 3 7967 7 6004 11 4112 15 2289 11 7880 11 3792 10 9856 10 6067 9 8907 22 8852 30 5691 38 2804 46 0189 53 7844 61 5767 77 2409 93 0101 108 8826 124 8571 140 9319 L J JL J 2 3093 '7- 8 0390 7 5081 _ • J i L T 0 2i3640 J' - r-r9' 7 0150 6 1307 5 3659 4-f 7033 2 3914 2w4187 2 4461 4 1284 3 6289 2 5008 2 5282 2 5555 J _ 2 6103 2 1956 1 9427 2 6376 1 5266 2 7197 2 7744 9562 7619 6097 JO f 4899 2 8839 2 9386 2 9933 3953 3201 3 0480 3 1027 HOF IZONTAL DYNAMIC IMPULSE PSI-SEC 1 440 6 161 1- r 2r3503 1 2054 358 4062 -- r r 8 6107 ' 393 1602 428 2321 463 6129 499 2936 - c- t -1 - L7JO l l C tO O 323 9796 l Ji r'l 9 2268 3 1941 2 8153 157 1057 173 3770 189 744-4 206 2065 222 7619 256 1473 289 8899 L LCCC Table 8 40 KT YIELD HEIGHT OF BURST GROUND RANGE PEAK OVERPRESSURE TIME OF ARRIVAL 2 394 KFT 8 065 KFT 1 5272 PSI 5489 1631 MSEC PEAK OP T TA 4 9991 PSI PEAK DYNAMIC PRES 5790 PSI PEAK HORIZ COMPT 5790 PSI TIME MSEC 5494 6581 5500 154 5505 6507 5511 1482 5522 1459 5533 1469 5544 1512 5555 1590 5566 1700 5577 1844 5599 2230 5621 2748 5643 3395 5665 4171 5687 5075 5709 6106 5731 7262 5753 8543 5775 9948 5798 1475 5842 4893 5886 8789 5931 3156 5975 7986 6020 3272 6064 9006 6109 5180 6154 1789 6198 8825 6243 6281 6327 6372 6411 7876 6 96 0751 6580 4959 DYN IMPULSE HORIZ TIME-TOA PSI-MSEC 3 1662 6 3021 9 4078 12 4838 18 5476 24 4960 30 3312 36 0557 41 6716 47 1812 57 8895 68 1979 78 1224 87 6785 96 8807 105 7432 114 2794 122 5022 130 4240 138 0565 152 4961 165 9091 178 3735 189 9612 200 7382 210 7652 220 0980 228 7881 236 8829 24-1- 4260 257 2130 nn MSEC C' -- C' I _ I r- n1 n Anc-r • J JOF 8 0923 5460 C l ' CU f 5150 5050 4953 4765 •c -nc- o-'t JO J 4412 4246 4• 86 3933 3787 3646 3511 3381 3136 2911 p2702 2510 li- i ' oJ J _j 2169 2017 1876 1747 n · 8 1197 8 1333 8J1 70 8 1607 8 1744 a 2017 8 2291 tr l C- CY C 1-iC J 8 2838 8 3112 8 3385 8 3659 8 3933 8 4206 8 448 8 5027 8 5574 8 6121 8 6669 8 7216 8 7763 8 8310 8 8857 8 9405 • I l l I J o o 8 9952 1424 1249 9 0978 • 1096 9 2004 9 3030 J964 9 4056 • 1 HORIZONTAL DYNAMIC IMPULSE PSI-SEC 162 8J 07 3 n C•V O C • Q JJ C'P C • C'C' f- 5354 353 3261 397 7158 442 1525 486 6355 531 1640 575 7374 620 3549 665 0157 709 7193 754 4650 838 4741 SHOCK 1- Jr KFT •JO • Jf J L 308 9843 922 6244 JOf I 264 6912 286 8316 1006 912 1091 3328 IJ- - J J 2-42 5631 268 -4374 l n T r C' 5 4949 10 9908 16 4875 21 9851 32 9827 43 9837 54 9881 65 9958 77 0069 88 0212 110 0599 132 1116 154 1763 176 2540 198 3444 220 4474 278 3025 286 9839 COMPT HOR Z Table 9 YIELD 40 KT HEIGHT OF BURST GROUND RANGE 2 394 KFT 4 346 KFr PEAK OVERPRESSURE 3 6289 PSI TIME OF ARRIVAL 2703 1845 MSEC PEAK OP T TA 14 9972 PSI PEAK DYNAMIC PF ES 4 7693 PSI PEAK HOF IZ COMF'T i • - - 07 J PSI TIME MSEC 2707 7280 2712 2748 2716 8249 2721 3783 2730 49-49 2739 6246 2748 7672 2757 9227 2767 0910 2776 2721 2794 6720 2813 1221 2831 6216 2350 1700 2868 7668 2887 4114 2906 1032 2924 8418 2943 6266 2962 4570 3000 2529 3038 2254 3076 3706 3114 6848 3153 1641 3191 8051 3230 6041 3269 5578 3308 6628 3347 9159 3421 9036 3496 381 3571 3287 DYN IMPULSE HORII TIME-TOA DYN HORIZ COMPT PSI-MSEC MSEC PSI 21 4968 42 6679 63 5184 84 0532 124 19-46 163 1320 200 9030 237 5437 273 0894 307 5739 373 4826 -435 5293 493 9492 548 9631 600 7779 6-49 5875 695 5740 738 9079 779 7493 818 2481 888 7404 951 4453 1007 2643 1056 9908 1101 3235 1140 8781 1176 1973 1207 7596 1235 9870 1261 2522 1301 7022 1334 7030 1361 7027 4 5435 9 0903 4J6936 -4 6191 4 5459 13 6404 18 1938 27 3104 36 4401 45 5827 5-4 7382 63 9065 73 0875 91 4875 109 9375 123 4371 146 9855 165 5823 184 2269 202 9187 221 6573 240 4421 4 4739 4 3334 4 1975 4 0661 3 9390 3 8160 3 6970 3 4706 3 2587 3 0603 2 8746 2 7006 r-- 7 • J ·' 2 3851 J ' -'I- l j SHOCK GI r- r KFT -n · n J 1' 4 3596 ' 1 -· 't JCO J - - - 4- • 4- - 3870 4 4007 4 4143 4 280 4 4417 4 -4554 4 4827 4 5101 4 5375 4 56-48 4 5922 4 6195 4 6469 4' 6743 259 2725 1 9827 297 0684 335 0409 373 1861 -411 5003 449 9796 488 6205 527 -4196 566 3732 605 -4783 1 7547 4 7016 4 7290 4 7837 1 5543 4 3384 2 1082 1 3779 1 2226 1 0858 9652 8587 7646 5 1667 6815 5 2215 718 7191 6079 4919 5 2762 5 3788 793 1964 868 1442 3993 5 481-4 3252 5 5840 64-4 7313 i 8931 4 9479 I J • J1J - o 5 0573 5 1120 HORIZONTAL DYNAMIC IMPULSE PSI-SEC 1 3617 163 Table 10 YIELD 40 KT HEIGHT OF BURST 2 394 KFT GROUND RANGE 1 521 KFT PEAK OVERPRESSURE 9 9411 PSI TIME OF ARRIVAL PEAK OP T TA PEAK DYNAMIC PRES PEAK HORIZ COMPT TIME MSEC DYN IMPULSECHORIZ TIME-TOA CPSI -MSEC MSEC 1195 2194 1197 8216 1200 4334 1203 0547 1208 3257 1213 6344 1218 9808 1224 3646 1229 7856 1235 2436 1246 2700 1257 4424 1268 7592 1280 2190 1291 8202 1303 5615 1315 4413 1327 4582 1339 6107 1351 8973 1376 8672 1402 3561 1428 3527 1454 8455 39 8590 59 5516 79 0883 117 6999 155 7069 193 1224 229 9594 266 2311 301 9505 371 7791 439 5457 505 3370 569 2270 631 2738 691 5186 749 9856 806 6842 861 6120 914 7597 1015 6715 1109 3785 1195 9857 1275 7723 1481 8232 1349 1593 1509 2748 1537 1892 1565 5556 1594 1312 1618 3710 1665 2592 1713 9298 1764 2804 1416 6471 20 0090 1478 7535 1535 9685 1588 3113 1628 3431 1694 6261 1751 3907 1800 5445 2 5926 5 19-48 7 8066 10 -4279 15 6989 21 0076 26 3540 31 7378 37 1588 42 6168 53 6432 6-4 8156 76 1324 87 5922 99 1934 110 9347 122 81-45 13-4 8314 146 9839 159 2705 184 2404 209 7293 235 7259 262 2187 28' 1964 316 6480 344 5624 372 9288 401 5044 425 74-42 472 6324 521 3030 571 6536 1192 6267 MSEC 25 0019 PSI 12 2183 PSI 7 7627 PSI DYN HORIZ CDMPT PSI SHOCK G F 7 6726 1 5278 7 5838 7 4963 f I • L • _ l J 7 4101 175483 7 2416 1 562 7 0781 Jl JI 6 9196 6 7660 6 6170 6 4727 6 1971 C' -I C' 1 1 5893 1 6030 L6167 1 6304 1 6577 n 7 '1'-r J 7 J I 5 6928 5 4603 5 2385 5 0254 4 8192 4 6185 i 7 r 'tt l i£ J 1 7398 1r7J S72 1 7945 1 8219 L8493 4 4222 4 2299 3 8566 3 5010 1 9587 2-0134 3 1681 2 8622 2 5856 2 3382 2 2f1179 1 9217 2 '2870 2 3417 1 7454 1 5635 I' tC ' • ·7 JJ L 1 2818 ' 'I c-i ---n £ JJ J 0 1 Q 2 3965 1 0651 2 6564 no 1' 2 7590 0 I b HORIZONTAL DYNAMIC IMPULSE PSI-SEC 1 8005 164 Table 11 40 KT 0 KFT 5 591 KFT 2 9665 PSI 3038 3332 MSEC 4 9996 PSI YIELD HEIGHT OF BURST GROUND RANGE PEAK OVERPRESSURE TIME OF ARRIVAL PEAK OP T TA TIME MSEC 3043 8141 3049 2962 3054J797 3060 2645 3071 2379 3082 2165 3093 2002 3104 1890 3115 1829 3126 1818 3148 1946 3170 2272 3192 2794 3214- 3508 3236 4414 3258 5508 3302 8253 3324 9899 3347 1726 3391 591' 3436 0788 3480 6345 IMPULSE PSI-MSEC 27 2060 54 0305 80 4789 106 5564 157 6182 207 2575 'j C-C' C'i l J J J i J 302 4236 348 0245 392 3514 477 3100 557 5670 633 3646 704 9291 772 4724 836 1929 896 2763 952 8963 1006 2162 1056 3887 1147 8234 1229 2811 1298 6821 JCJ _C IC 1359 8394 3569 9432 14-12 -4725 1457 2190 1494 64-54 1525 2556 1549 4989 1567 7766 1587 1296 1588 7901 ' C 'C 3614 6933 3i59 5 52 704 3777 3 74-9 3092 3794 2986 3878 8052 3963 5 25 TIME-TOA MSEC OIJEF PF ESSUF E PSI SHOCK G F 4 9283 4 8580 4 7387 4 7205 4 5868 4 4569 4 3307 4 2079 4 0885 3 9724 3 7496 5 5978 5 6046 •• J O J l J 5 4808 10 9630 16 4464 21 9312 32 9046 43 8832 54 8669 65 8557 76 8496 87 8485 109 8613 131 8939 153 9461 176 0176 198 1081 220 2175 242 3456 264 -4920 286 6567 308 8393 -r r- nl KFT C l C 5 6183 5 6320 5 6457 5 6593 5 6730 5 6867 5 7004 J Lf i 5 7551 C ri 7 j • J ' 0 J 7 ' 'MC • j JO J 5 7825 3 1487 5 8098 2 9686 C n' l''7 r ' J O J _ 2 7976 _5 8645 2 6349 2 4801 5 8919 2 3328 5 9193 2 1924 5 9466 5 9740 353 2577 1 9306 o 397 7455 4--42 3012 486 9232 531 6100 576 3600 621 1720 666 0444 710 9760 755 9654 840 4719 925 1692 1 6917 1 4730 6 0834 1 • 2722 1 0871 9160 6 1381 6 1929 6 2476 6 3023 643570 6096 6 -4117 6 4665 -4718 165 ' n- v • 'TC ½ ' L 3-427 1214 - 0771 IMPULSE PSI-SEC 1 5953 6 5 212 6 6238 6 7264 Table J 2 YIELD 40 KT 0 KFT HEIGHT OF BURST Gf OUND RANGE 2 977 KFT 9 0659 PSI 1096 8521 MSEC 14 9996 PSI PEAK OVERPRESSURE TIME OF ARRIVAL PEAi OP T TA TIME IMPULSE MSEC PSI-MSEC i14i 6735 1150 6957 1159 7368 1168 7967 1186 9724 1205 2216 1223 5432 12-41 9361 1260 3992 1278 9314 i M t '- • 'T _ 7 · • J _ Ql ERPRESSURE MSEC PSI 372 3794 4 4601 8 9251 13 3951 17 870 26 834-5 484 6793 35 8183 591 6237 H 8213 53 8435 62 8846 71 9446 90 1202 108 3694 126 6910 145 0839 163 5470 182 0792 200 6795 66 0213 1105 7773 1110 2473 1114 7222 1123 6866 TIME-TOA 130 3967 193 1752 254 4036 693 5105 790 6175 883 2037 1055 7083 1212 8299 1356 0877 1486 8082 1606 1517 1715 1346 1814 6494 1 1316 1991 1905 -4-807 219 3470 · -a- ' ' I 1988 3197 2063 7766 2194 528 2301 4-980 2ia7 5525 2454 9811 238 0804 256 8790 294 6674 332 7046 370 9832 409 -4962 448 2366 i - L J j t LO 1353 7312 • 1391 5196 1429 5568 i-467¥8354 1 506 3484 15-45 0888 1584 0501 1622 2258 1662 6096 1702 1957 14- 6085 14 2295 13 8621 13 5059 12 8253 12 1847 11 581411 0127 2505 6307 2541 0062 2562 3-466 487 1979 526 3736 2570 6833 2566 8846 565 7574 605 3435 10 4762 9 9696 9 0382 8 2038 7 4539 2 9838 2 9906 2 9975 3 ' 043 3 0 180 3 0453 3 0590 3 0727 3 0864 3 1137 3 1411 3 1685 3 1958 6 1652 5 6092 3 2232 4 6391 4 2137 3 8220 3 1244 2 5208 3 2505 3 2779 3 3053 7 '7 l ' o 3 3600 3 4147 3 4694 1 9919 1 5230 1 1027 3 5789 7222 3 6883 - 3 7430 3 7977 3 8525 J 4- 0549 - 2414 166 KFT 6 7774 5 1025 IMPULSE PSI-SEC 2 5764 SHOCK G F Table 13 YIELD HEIGHT OF BURST 40 KT 0 KFT 2 316 KFT GROUND RANGE PEAK OVERPRESSURE 14 7987 PSI TIME OF ARRIVAL 692 4409 MSEC PEAK OP T TA 24 9944 PSI TIME MSEC IMPULSE PSI-MSEC 696 3199 700 2060 187 588 8 95 3047 276 9722 TIME-TOA MSEC 3 8789 7 7651 11 6584 15 5589 23 3812 707 9998 Z63 5689 ·Ir ' 528 8067 684 1402 31 2318 830 3059 967 9737 1097 7535 1220 2009 39 1104 47 0169 5-L9510 62 9125 - - J J J o c 7 _ 4579 7 47 3920 - - ' '• - C' 7n J i- J JI 0 1444 96 94 1645 9532 1826 1078 95 0282 111 2450 8 20 0066 1987 9078 127 5656 852 -9526 869 5748 886 2946 213344317 22 54 4304 2382 3842 2488 5484 2583 -9916 143 9883 160 5116 177 1339 r ti' -r r r - t l TCG J 10 23 3342 1094 - H 57 - -I r r ' Jrrr -- i 7 t 7 7' J 2814 3377 2927 9376 3014 2278 3076 1260 3115 9154 3135 4190 SHOf K f KFT 24 1539 23 3483 2 3228 22 5758 2 3165 21 8348 20 4414 21-3433 2 3570 17 9708 16 874-415 8593 1-4- 9181 13 2315 11 7681 10 -4920 2-1843 2 3980 2 4117 2 •f254 2t 37 7 78 9168 787 -4692 803 -6860 oc o c1 ovrnPRESSlJF E PSI 9 3712 8 3809 7 5005 6 7130 193 8536 2 4527 2 -4801 2 075 2 5348 ' l 'i C C- l _IQ _ c-nni - • Ji 7 _J 2 6169 I 6 0043 5 3628 4 7787 2 6990 3 7518 277537 330 9432 2 8737 2 H 91 2 80842 8631 366 0898 1 4326 401 5647 OLO 2 r 9179 2 9726 3 273 210 6692 227 5794 261 6771 296 1354 n'i '1 437 3580 'ii-a - 473 4601 IMPULSE PSI-SEC - f 0 3 1443 _ 167 'i l J ✓ L•O l' l'-1 3 0820 Table 14 YIELD 40 KT HEIGHT OF BURST GROUND RANGE PEAK OVERPRESSURE TIME OF ARRIVAL PEAK OP T TA TIME MSEC j 3 80 7616 3586 2910 3591 8228 3603 4-225 3641T6505 3-052 -7349 ' ' ··- -r- - - JG· J J -C L J IMPULSE PSI-MSEC 27 4703 54 5974 81 355 107 8336 159 7 45 210 3775 259 7378 307 8648 354 7871 400 5324 4B8 5926 S-· 1 -7879 386·4- -1 34 886 4-339 - - - 1 -I '° ' -J'7 7 JJ 1 - 7'- J ovrn F'F ESSU E PSI 5 5289 11 0589 16 5900 KFT 6 1778 6 1846 22 1222 H 2616 55 3376 66 4178 4 7512 4 6311 4 514-0 -4 3996 4 2880 77i-5022 -' i l 07 33 1898 88 5908 110 7803 '7 -t-rnn 4 0725 -- lii ' 'i 6 2393 n • 1n 6 · 280 A -r ' J ooo 0 • J' f 3 6707 3 4833 6 3351 6 3625 3 3043 3 1331 2 9693 'O l 4 _I' _ 651 724' 155 2082 727 1756 798 7840 866 7139 931 1203 177 4463 199 7002 221 9697 244 2548 992 1494 266 5551 1 ' r I _ • 00 C 6 4719 6 4993 1049 939-4 110 4- 6212 1205 1194 1294 5871 288 8707 311 2012 21 5184 6 5266 4-020 7232 1373 8408 4155 5138 1504 5627 1557 2810 14-43 6133 4200 5501 1602 3013 245 6376 429 775 4 1640 1044 1671 124-6 442 i 8167 4505 834-2 4591 C088 1695 754-4 1725 8628 1736 7848 1730 2298 ¥ TIME-TOA MSEC 1 JL 700 L 3708 2189 752 6790 684 KFT 6 171 KFT 2 4931 PSI 3575 2327 MSEC 5 0002 PSI 1-fJ'j C - L OLi d 355 9066 2 3804 2 1208 400 6701 445 4905 490 3665 1 6595 1 4538 1 8812 1 535 2971 I r- l • OL O 580 2811 625 3174 1 0843 670 4049 715 5426 760 7295 845 5840 930 6015 1015 7760 - IMPULSE PSI-SEC 1 7449 168 6 3898 I I t - I° 6l 44-45 6 5 4 6 6 87 6 6634 6 718 1 6 7729 6 8276 6 8821 6 9370 • 9177 7616 6150 4770 2387 0233 7 1012 7 2038 7 3064 1728 7 4090 6 9917 7 0465 Table 15 YIELI1 40 KT HEIGHT OF BURST 684 KFT GROUND RANGE 3 001 KFT PEAK OVERPRESSURE 8 5133 PSI TIME OF ARRIVAL 1209 3571 NSEC PEAK OP CT TA 14 9964 PSI TIME IMPULSE PSI-MSEC TIME-TOA MSEC PSI 213 7684 218¥1844 65 3603 129 2370 14 2923 l r t ' ' 191 i 66 5 4 4112 8 8273 13 2481 1227 0308 252 6959 370¥6686 - 'jJ j i L O lJ 483 4463 i 01 '1Q c _ J f L - - i2f •2 6045 1 71 54 B 1298 4728 1 16 -5147 1334 6 271 694 4530 793 1725 887 -6556 1227 i031 137 6 2217 1513 2114 1639 1064 14-07 7620 14 • - - ·i 7271 1500 6508 1652 4090 16 0 9105 17 9 6245 1762 5452 1807 6669 1846 9842 1754- 8236 1861 1772 1958 SS '09 2048 6093 2130 9068 2275 1284 2395 17 68 2493 8557 2635 7671 2682 3719 271' 5090 2739 4177 2733 8256 Q JERPRESSURE SHOCt GlF FT 14 6394 3 0146 3 0215 1 0' 283 3 o _·zo 13 9547 13 6264 12 9965 26 5390 35 4232 H 3260 12 4001 3 557 1 1 8351 11 2995 10 7914 3 0693 3 0830 3 0967 71 1452 10 3093 3 1104 89 1156 1 7 1575 9 4160 - 1 - r 1 r- n O•O' JO l 3 1651 3 1925 3 2198 3 2472 53 2474 62 1872 125 2700 r c- J i Q J J 143 4519 7 2089 6 6011 6 0452 161 7023 180 0203 198 • 4049 216 8550 235 3699 253 9486 291 2936 328 8832 366 7105 404 7688 443 0518 481 5533 520 2673 559 1880 598 3097 637 6270 J J I 7 l 7 - c ' J L t··-' 5 5354 5 0663 4 6336 4 2333 r-t J LlOL 2 8918 2 3422 1 8533 1 41 2 1 0160 651 9 3165 5 3913£-03 - 2850 IMPULSE PSI-SEC 2 7450 169 I Jf- J•JOO 3 3840 3 4187 3 4934 3 5481 3 6 129 - c-- - Q -O J 0 3 7123 3¥7670 3¼8217 3 8765 3 9312 Table 16 YIELD 40 KT HEIGHT OF BURST 684 KFT GROUND RANGE 2 977 KFT PEAK OVERPRESSURE 8 6363 PSI MSEC TIME OF ARRIVAL 1193 9169 PEAK OP T TA 15 2102 F'SI TIME IMPULSE MSEC PSI-MSEC 66 0315 4 wn 1-4- 845-4 2 9838 02 7104 1207 1i44 130 5539 8 7934 2 9906 193 -6076 liC-C'i -t n J • l 0 13 1975 17 6063 14 -4-909 1-4 1462 13 8110 3 43 374 3329 26 -4383 13 1681 488 1557 35 2894 J L • J J7 3 0180 3 0317 l 246 651 596 9710 H 1593 701 0327 8 JO 1-5788 53 0481 1 318 7350 895 8328 107-4 2416 1237 8406 1387 9773 1525 8420 f -r ti ii l 0 J 0 'tOOl 1373 3052 1768 8483 3 1137 106 7674 124 8181 3 1411 142 9391 161 1295 179 3883 8 6988 7 95-4-2 7 2776 6 6609 3 1685 3 1958 t'1 • 0972 3f2505 5 5804 197 71 5 216 1071 234 5653 2-598 6179 1712 -6187 1790 4836 3 590 3 0727 9 5203 1875 7506 1635¥5 07 rcn- - 11 9836 11 4378 f 1973 9300 206 - a 0•406 2146 6651 1521 7238 1 'i KFT 10 9203 10 4293 1391 6314 1559 477 1597 4-055 PSI 61 9555 70 8814 8 0r - r - OOL 1410 0241 2291 3690 2411 7072 2510 5131 2590 0782 2652 2692 01 JEF PF ESSIJRE TIME-TOA MSEC l 3 0864 3f-2232 3 3053 4 6671 -4 2619 253 0881 290 3237 327 8069 -r -- c- J JO J 365 5307 2 9053 2 3500 403 4885 H1 6737 480 0802 1 8561 L4125 1 0104 3 3600 34-4147 3 4694 3T5789 3 2336 I C n U-'t O 2730 3914 z -- 274-8 b468 r -r'iJ J J •J J 4t 304-0 275-4 2734 596 5667 - 0101 IMPULSE PSI-SEC 2 7546 170 3 7977 3 8525 Table 17 YIELD HEIGHT OF BURST GROUND RANGE 40 KT 684 KFT TIME OF ARRIVAL PEAt OP I T TA 2 282 KFT PEAK OVERPRESSURE 13 9840 PSI TIME MSEC MPULSE SI-MSEC TIME-TOA OIJH PF ESSUF E MSEC PSI 93 44 1 3 358 1761 3 7967 7 6004 11 4112 15 2289 522 5197 L Lt DOJL 184 2296 787 6081 799T0322 272 •430 I - l • r•i O JO r - • '7 Q_ 7y Q l J - '- ' C- J J 30 5691 38 2804 46 0189 53 7844 61 5767 77 2409 n 0101 108 8826 124 8571 140 9319 157 1057 173 3770 964 2479 1096 2088 i221 3317 853T4379 86942071 885T0796 9 i1 0540 917 1289 -49 ' I40 S C ' 5 9414 82 40- 54 99ST 589 1066 0869 1100 17 65 1134 6032 1169 3572 i2 j 4- 4-291 1239 8098 1275 4906 nnc- 82-4- 9874 O f 7 LO L o '1 '1 i1 •I' '1 7'7 r - 776 1969 MSEC PSI 24 9958 1661 2922 1849 8681 2020 5580 2175 2385 2315 5182 2442 7798 2558 21-41 2662 8496 2757 5767 2920 1394 3051 1662 315-4 5323 3233 2453 3289 6744 3325 7083 3342 8797 3342 450-4 SHOCK G F KFT 24 2360 2 2888 23 5043 22 7993 22 1200 20 8338 19 6376 18 5239 17 4858 2 2956 16 5172 2 3025 2 3093 2 3230 2 3367 2 3503 2 3777 15 6125 13 9743 12 5351 2 a-4461 11 2649 10 1385 9 1347 8 2360 2 4735 ' 2 50 8 2i5282 189 7-444 6 6960 2 6103 206 2065 222 7619 256 1473 6 0317 5 4253 4 3570 3 4428 2 6376 2 5829 289 8899 323 9796 358 4062 393 1602 28 2321 463 6129 499 2936 2 6650 2 7197 2 7744 2 6476 IMPULSE PSI-SEC 3 3512 171 1 9458 2 8839 1 3180 7502 2315 - • 2462 2 9386 3 0480 3 1027 Table 18 40 f T YIELD HEIGHT OF BURST GROUND RANGE PEAK OVERPRESSURE TIME OF ARRIVAL 2 394 KFT 8 065 KFT 1 5272 PSI 5489 1631 MSEC 4 9991 PSI PEAK OP CT TA TIME C MSEC 5500 154 IMPUL SE PSI-MSEC TIME-TOA 27 3307 5 4949 10 9908 16 4875 21 9851 54 3885 5505 6507 81 1758 5511 1482 5522 1459 5533 1469 554·L 1512 107 6948 - C J ' i 5087 5075 5709 6106 J - '7 • - r _J 5842 4893 5886 8789 5931 3156 5975 7S ·B6 6020y3272 6064 -9006 J1·J9 5180 6154- 1789 6198 -8825 6243 6281_ 6327 6372 6411 7876 6496 0751 6580 4959 8 0923 8 1060 8 1197 8 1333 8 1470 4 7017 43 9837 4 6 160 - 11c- 54 9881 65 9958 4 5118 35876107 77 0069 405 7909 497 2749 585 0328 669 1843 749 8448 827 1250 901 1316 88 0212 110 0599 132 1116 154 1763 176 2540 198 3444 220 4474 24 2 5631 l I -f c 1 • 7f J 971 9666 • i 8 0855 4- 7991 211 1314 1039 7288 1104 5128 1166 4096 J 70 J -'f- 8 718 8 0786 nn 'l 7 575 8543 5775 9948 - r -1 4 9484 4 8982 4 8485 L 70Lf '71i 1 J J 1 f C OL SHOCK G F KFT - 'i J J J i J 'T '-J 5599 -2230 562 l 2748 OlJEF PRESSUF E PSI 159 9363 ii 577-1844 MSEC 1281 8680 1386 7881 1481 7826 1567 4193 1644 2245 1712 6867 1773 2590 1826 3626 1872 3885 1911 7005 1968 4154 2004 7245 2022 9811 4 4193 4 3284 4 2389 4 0646 3 8960 3 7330 3 5752 3 4226 3 2750 3 1320 264 6912 2 9936 2 8595 286 8316 308 9843 397 7158 42 1525 IJ1 8r5574- 1 8235 1 6290 575 7374 1 -4454 620 3549 665 0157 709 7193 754 4650 838 4741 922 6244 1006 912 1 2721 1 1082 10'11 3328 - IMPULSE PSI-SEC 2 0304 172 8113659 8 39T3 8 4206 8 4480 531 1 640 '00 0 JJ J 8 3112 8 3385 2 481 8 2 2489 '7'i I 2 0298 ''7 'C' 8 2565 8 2838 L L70 'i- 353 3261 8 1607 8 1744 8r-2017 8 '2291 81-5027 8 6121 8 6669 8 7216 848857 8 9405 9530 8060 5503 3180 9 0978 9 2004 1 6 f- 0879 9 4i' 56 8 995 2 TabJ e 19 40 T YIELD HEIGHT OF BURST GROUND RANGE PEAK OVERPRESSURE TIME OF ARRIVAL PEAK OF' T TA TIME MSEC IMP JLSE PSI-MSEC 2 394 KFT 4 346 KFT 3 6289 PSI 2703 1845 MSEC 14 9972 PSI TIME-TOA OVERPRESSURE MSEC PSI SHOCK GIF KFT 2707 7280 712 2748 2716 8249 2721 • 3783 2730 4949 273 i 6246 134 4123 200 2732 265 2529 3 ·2 0113 4 5435 9 0903 13 6404 18 1938 14 7859 14 5776 14 3722 14 1696 27 3104 36 4401 2 - 8 7672 637 2461 45 5827 13 7729 13 3871 13 0118 4 3870 516 5800 2757 9227 754 6939 869 0054 12 6468 12 2917 11 9463 11 2830 10 6546 4 4280 4 n -417 2776 2721 2794 6720 813 1221 283'1 6216 2850 1700 2868 7668 2S87 4114 2906 1032 2 Jtl 6266 962y4570 300 1 2529 3038 -2254 3076 3706 3114 6848 67 - 584 54 7382 980 2602 11- 3 8869 63 9065 73 0B75 91 4875 1396 1846 109 9375 1587 7095 1768 9862 1940 5089 2102 7436 2256 1294 2401 0808 2537 J t '883 2903 9500 3113 91 23 323•' 6 4 l 383' 3 8139 5' 27 • 1 1 96 3308 6628 3347 9159 3421 9036 34% 381 3571 3287 3923 2732 399746132 4057 8i96 4135 9904 4173 2483 4174 076-4 4'-4554 4 48'27 4 5101 5375 4 56 i 8 8 9589 8 4505 7 9677 7 509 7- t 7 9 6 6581 5 8874 5 1878 373 1861 411 500'3 4 i Q 0796 4 4007 4 41-43 9 4945 184 2269 202 9187 221 6573 240 4421 259 2725 297 0684 335 0409 3604 7457 3728 0708 4 3665 4 3733 t0 0592 146 9855 165 5823 315 3 1641 3191 8051 4 3528 4 3596 48B 6205 4 5513 •J 89 31 3 r 0 7 08 9 d 79 718 7191 21 9535 2 5 l 5 Q48 1 7146 1 3626 7688 79-3 1964 868 1442 2481 - 2123 605 47 644 7313 IMPULSE PSI-SEC 4 1899 173 A 7 _90 4 7837 4 8384 5 0• 26 5 0'573 5'1120 5 1667 5 2215 5 2762 5 3788 5 4814 5 5840 Table 20 YIELD 40 KT HEIGHT OF BURST GROUND RANGE PEAK OVERPRESSURE TIME OF ARRIVAL PEAK OP CT TA Trni MSEC 195 2194 197 8216 1200 4334 1203 0547 1208T 257 1213 0344 1218 - 808 IMPULSE PSI-MSEC 6·L3363 190 8429 253 0304 375 3142 494 8689 611 7608 726 0549 -· t 'j n -rnr t i T CJO 837 8148 12 6 2700 1158 839 1339 0107 2 5926 24 6290 1 5278 1 5346 1 5415 1 5483 1 5620 5 1948 7 8066 10 4279 15 6989 21 0076 26 3540 31 7378 37 1588 42 6168 53 6432 64 8156 76 1324 2246 8015 2548 2486 134 8314 146 9839 3T 0 6119 3575 4446 3878i-9595 1537T1 392 40 0y0500 cf t -C -l l i 00 J J JO 4102 0535 4185 0983 42-41 4240 4316 5392 4350 8920 4342 6967 17 S-4 2804 SHOCK G R 110 9347 122 8145 3737 8054 1594¥1312 1618 3710 1665 2592 1713 9298 OtJEF PRESSURE PSI 87 5922 99 1934 29-48 3238 1454 8455 TIME-TOA MSEC 1360 6704 1554 0793 1739 0867 1916 0243 1303 5615 2 394 KFT 1 521 KFT 9 9411 PSI 1192 6267 MSEC 25 0019 PSI 23 9020 23 5477 22 8568 22 1892 1 5757 21 5438 20 9201 1 5893 1 6030 1 6167 20 3172 19 7342 1 6304 18 624' 1 6577 1 6851 1 7125 1 7398 17 5857 16 6101 15 6914 14 3236 14 0008 13 2178 12 4703 11 7546 11 0682 159 2705 184 2404 209T7293 9 7756 8 5840 7 4891 6 4867 5 5704 4 7315 3 9598 262 2187 289 1964 316 6480 344 5624 372 9288 401 5044 425 7442 472 6324 521 3030 571 6536 IMPULSE PSI-SEC 4 3726 174 KFT 1 7672 1 7945 1 8219 1 8493 1 8766 1 9040 1 9587 2 0134 2 0681 2 1229 2 1776 2 2323 2 2870 3 2450 2 5836 2 3417 2 3965 2 0685 1 1487 2698 - 5951 2T4512 2 5538 2 7590 REFERENCES Brode Harold L Height of Burst Effects at High OVerpressures The Rand Corporation RM-6301-DASA 1970 DASA Report 2506 Review of Nuclear Weapons Effects Annu Rev NuaZ Bai 1968 ----- Theoretical Description of the Blast and Fireball for a Sea Level Kiloton Explosion The Rand Corporation RM-2246-PR 1966 ----- Theoretical Description of the Blast and Fireball for a Sea Level Megaton Explosion The Rand Corporation RM-2248 1959 McNamara W R J Jordana GE Tempo and P S Lewis McDonnell Douglas Astronautics Airblast from a One Kiloton Nuclear Burst at 60 mover an·Id eal Surface Contract Report 353 November 1977 Needham Charles E Martin L Havens and Carolyn S Knauth Nuclear Blast Standard 1 K I' Air Force Weapons Laboratory Report AFWLTR-73-55 rev April 1975 175 CHAPTER 7 - REVISED PROCEDURE FOR ANALYTIC APPROXIMATION OF DYNAMIC PRESSURE VERSUS TIME Stephen J Speicher Harold L Brode 176 The procedure for calculating height-of-burst· dynamic pressure given in Chap 6 was contrived to satisfy a limited request in a narrow pressure range The procedure is here extended to the full range of pressure interests using a new analytic fit for the duration of the dynamic pressure positive phase The original form used was Chap 6 Eq 17 9 Q r Q r5 2 2 1 2 where r 0 x0 y with x 0 the original ground range of interest and r x 2 y 2 112 with x the subsequent shock position s ground range Thus if t 0 represents the shock arrival time at the position of interest x0 y and t represents the shock arrival time at further positions x y Chap 6 Eq 18 then and x r and tare related by r x 2 y 2 112 t t r W Chap a 6 Eq 4 The extended procedure now takes the form 1 where n is a variable power such that n r m 0 7917 11 04 14 37 6 291 3m 1 177 28 41 2 and the positive outward wind duration is approximated as U r 0 2455 _ 0 0115 D r m' 0 ·l m' 1 61 43 1 o 7567 c t ray 2 177 - 2 6 147 c r _0 05546 3 where r r 0 t and t 0 are defined above and m w1 3 m' 2W l J The units for these quantities are x y r r 0 kft W m m' kT and kT113 D sec · u The virtue of the new procedure is that the total dynamic impulse can now be calculated to the cutoff of the dynamic positive phase and the variable power n can now track the decay rate changes in different pressure regions More important the correct total dynamic impulse is simulated Figure 1 plots n against r scaled to 1 kT Fig 2 plots D u against r 0 also scaled to 1 kT and compared with the AFWL 1 kT standard Needham Havens and Knauth 1975 The positive phase duration D is a very close approximation within 2 percent to data u presented in Brode 1959 The plot of this approximation with the AFWL data reveals_considerable discrepancy This may be due to dif- ferences in interpretation of the start of the negative phase whic would change both the duration sec and effective range at which the velocity first reverses Tables 1 through 10 show the new procedure applied to the dynamic pressure cases presented in Chap 6 Tables 11 through 20 again show 178 · •· 23 21 19 17 n 15 13 11 9 0 4 6 10 12 1 RADIUS KFT Kr1 3 Figure 1 2 Plot of variable power n versus scaled radius for· l kT 1 0 9 8 -- u Q 2 0 7 6 ---- AFWL 1 KT STANDARD FIT TO BRODE 1959 FOR l KT 5 I- i Cl LU 4 V1 c x i a LU I-' 00 0 3 I- 0 a Cl 2 ' 2 3 IV1 c x J ca 10 100 10000 RADIUS M Figure 2 Comparison of positive phase duration versus range for l kT the new procedure but use the analytic fit for the revised EM-1 curves given in Chap 5 The table below is a SUIImlary comparison of total dynamic impulse 40 kT burst given by the new procedure using the overpressure approximations in Brode 1970 and ey the new procedure using the ap- proximations to the new EM-1 curves see the Appendix Total Dynamic Impulse psi-sec HOB Peak Overpressure psi Limited Form Chap 6 0 0 0 0 684 0 684 0 684 2 394 2 394 2 394 5 15 25 5 15 25 5 15 25 0 2073 0 7833 1 3723 0 2377 0 8337 1 4406 0 2869 1 3617 1 8005 Improved Form Brode 1970 0 1080 0 5969 1 1894 0 1132 0 6192 1 2297 0 1185 0 7863 1 3284 Improved Form with Revised Ms Appendix 0 1043 0 5698 1 1287 0 1068 0 6059 1 2244 0 114 0 7328 1 2169 It is clear that the new procedure tends to reduce the total impulse substantially so at the lower overpressure This occurs because the variable power in Eq 1 tracks a faster decay rate than the constant power used in Eq 17 of Chap 6 The new EM-1 approximations further reduce the total impulse The Appendix contains a numerically more detailed presentation of the new analytic fit The numbers presented in Chap 6 were intended for exposition only and so carried too few significant figures For calculation the numerical definition in the Appendix should be used 181 Table 1 DYNAMIC PRESSURE AND IMPULSE VERSUS TIME BASED ON PEAK OVERPRESSURES FROM BRODE 1970 40 KT HEIGHT OF BURST 0 KFT GROUND RANGE 5 591 KFT PEAK OVERPRESSURE 2 9665 PSI FREE AIR TIME OF ARRIVAL 3038 3332 MSEC PEAK DP T TA 4 9996 PSI PEAK DYNAM C PRES 5791 PSI PEAK HORIZ COMPT 5791 PSI DYNAMIC POS PHASE 1069 4782 MSEC YIELD TIME MSEC 3043 8141 3049 2962 3054 7797 3060 2645 3071 2379 3082 2165 3'093 2002 3104 1890 3115 1829 3126 1818 3148 1946 3170 2272 3192 2794 3214 3508 3236 4414 3258 5508 3280 6788 3302 8253 3324 9899 3347 1726 DYN IMPULSECHORIZ f'SI-MSEC 3 1316 6 1803 3794 2986 3873 8052 3%3 5025 9 1480 12 0368 17 5843 22 8381 27 8124 32 5205 36 9756 41 1899 48 9403 55 36 36 62 0406 67 5452 72 4446 76 7998 80 6666 84 0951 87 1310 89 8157 94 2689 97 7212 100 3806 102 4154 103 9605 105 1239 105 9915 106 6315 107 0973 107 4311 107 8047 107 9772 4- 48 3828 108 400 4133 4388 108 04-69 3391 5910 3436 0788 3480 6345 3525 2565 3569 9432 3614 6933 3659 5052 3704 3777 37 49 092 TIME-TOA MSEC 5 4808 10 9630 16 4464 21 9312 32 9046 43 8832 54 8669 65 8557 76 8496 87 8485 109 8613 131 8939 153 9461 176 0176 198 1081 220 2175 242 3456 264 4920 286 6567 308 8393 353 2577 397 7455 442 3012 486 9232 531 6100 576 3600 621 1720 6b6 0444 710 9760 755 9654 840 4719 925 1692 1010 0495 1095 1055 DYN HOF IZ PSI 5636 5486 5339 5195 4918 4655 4405 4166 3940 3725 3326 2967 2643 2352 2090 1855 16-45 1456 1287 1137 0882 0681 0522 0397 0300 0224 0166 · 0121 8 7895E-03 6 2304E-03 3 557E-03 1 2854E-03 3 5141E-04 -1 0005E-04 C0MPT SHOCK G R KFT 5 5978 5 6046 5 6115 5 6183 5 6320 5 6457 5 6593 5 6730 5 6867 5 7004 5 7277 5 7551 5 7825 5 8098 5 8372 5 8645 5 8919 5 9193 5 9466 5 9740 6 0287 6 0834 6 1381 6 1929 6 2476 6 3023 6 3570 6 4117 6 4665 6 5212 6 6238 6 7264 6 8290 6 9316 HORIZONTAL DYNAMIC IMPULSE CPSI-SEC 1080 182 Table 2 DYNAMIC PRESSURE AND IMPULSE VERSUS TIME BASED ON PEAK OVERPRESSURES FROM BRODE 1970 YIEUI HEIGHT OF BUF ST 40 KT 0 KFT 2 977 KFT PEAK OVERPRESSURE 9 0659 PSI FREE AIR TIME OF ARRIVAL 1096 8521 MSEC PEAK OP CT TA 14 9996 PSI PEAK DYNAMIC PRES 4 7707 PSI PEAK HOR1Z COMPT 4 7707 PSI GROUND RANGE DYNAMIC POS PHASE 807 3099 MSEC TIME MSEC 1101 3123 1105 7773 1110 2473 1114 7222 1123 6866 1132 6705 DYN IMPULSE HOF IZ TIME-TOA DYN HORIZ COMPT SHOCK G F PSI-MSEC MSEC PSI KFT 20 9132 41 1367 4 460 1 8 9251 4 6084 4 4514 4 2995 4 1525 3 8729 2 9838 2 9906 2 9975 3 0043 3 0180 3 0317 3 0453 3 0590 3 0727 3 0864 3 1137 3 1411 3 1685 3 1958 3 2232 3 2505 3 2779 3 3053 3 3326 3 3600 60 6922 79 6005 1141 6735 115 6957 115 5517 149 15-08 180 5442 209 8693 1159 7368 237 2553 1168 7967 1186 9724 262 8239 308 9326 34-9 0587 383 9383 1205 2216 1223 5432 1241 9361 1260 3992 1278 9314 1297 5317 1316 1991 1334 9326 1353 7312 1391 5196 1429 5563 1467 8354 1506 3484 1545 0888 158-1 0501 1623 2258 1662 6096 1702 1957 1741 9782 1817 0804 1892 8184 1969 1592 414 2211 440 4799 4-63 2196 482 8848 499 8666 514 5090 527 1142 547 1869 561 9046 572 6071 580 3169 585 8102 589 6737 592 3495 59-4 1642 595 3654 596 1326 596 8170 13 3951 17 8700 26 8345 35 8183 44 8213 53 8435 62 8846 71 9446 90 1202 108 3694 126 6910 145 0839 163 5470 182 0792 200 6795 219 3470 238 0804 256 8790 294 6674 332 7046 370 9832 409 4962 3 6113 3 3666 3 1378 2 9238 2 7238 2 3620 2 0462 1 7706 1 5304 1 3212 1 1391 9808 8433 7240 6207 4537 3292 2368 1687 48 2366 1187 487 1979 526 3736 565 7574 605 3435 0824 0562 0375 0243 0151 645 1260 596 9842 720 2282 795 9662 5 6 9285 872 3070 4 9854E-03 3 9686E-04 -1 3811E-03 3 4147 3 4694 3 5241 3 5789 3 6336 3 6883 3 7430 3 7977 3 8525 3 9072 4 0098 4 1124 4 2150 HORIZONTAL DYNAMIC IMPULSE PSI-SEC 5969 183 Table 3 DYNAMIC PRESSURE AND IMPULSE VERSUS TIME BASED ON PEAK OVERPRESSURES FROM BRODE 1970 YIELD HEIGHT OF BURST 40 KT O KFT GROUND RANGE 2 316 KFT PEAK OVERPRESSURE TIME OF ARRIVAL PEAK OP CT TA PEAK DYNAMIC PRES PEAK HORIZ COMPT DYNAMIC POS PHASE TIME MSEC 696 3199 700 2060 704 0994 TIME-TOA DYN HORIZ COMPT SHOCK G R MSEC PSI KFT 46 4003 91 0073 133 8911 3 8789 7 7651 11 6584 15 5589 23 3812 11 7177 2 3228 2 3296 2 3365 2 3433 2 3570 2 3707 2 3843 2 3980 2 4117 2 4254 2 4527 2 4801 2 5075 2 53-48 2 5622 2 5895 2 6169 2 6443 2 6716 2 6990 2 7537 2 8084 2 8631 2 9179 2 9726 3 0273 3 0820 3 1367 3 1915 3 2462 3 3488 3 4514 3 5540 3 6566 707 9998 175 1193 252 8493 324 7003 391 1202 452 5217 509 2856 561 7626 655 0540 734 7805 802 9030 861 0955 910 7882 953 2043 989 3905 1020 2434 1046 5308 1068 9112 110-4 0156 1129 3160 1147 4649 1160 4122 1169 5892 117 6 0450 1180 546-4 1183 6522 1185 7680 1187 1869 1188 6317 1189 221-4 1189 -4-111 1189 4295 755 3535 771 3578 787 4692 803 6860 820 0066 836 4293 852 9526 869 5748 886 2946 903 1102 920 0203 954 1181 988 5764 1023 3842 1058 5307 1094 0057 1129 7990 1165 9010 1202 3024 1238 9941 1275 9673 1346 0217 1416 9832 1488 so 2 1561 432 846 9924 HSEC PSI-MSEC 715 8222 723 6728 731 5514 739 4579 747 3920 · --· DYN MPULSE HOF IZ 14 7987 PSI FREE AIR 692 4409 MSEC 24 9944 PSI 12 2116 PSI 12 2116 PSI 11 24-41 10 7900 10 3545 9 5364 8 7838 8 0912 31 2318 39 1104 47 0169 54 9510 62 9125 78 9168 95 0282 111 2450 127 5656 143 9883 160 5116 177 1339 193 8536 210 6692 227 5794 261 6771 296 1354 330 9432 366 0898 401 5647 437 3580 473 4601 509 8614 546 5531 583 5263 653 5807 724 5423 796 3613 868 9910 HORIZONTAL 71-4538 6 8670 6 3267 5 3707 4 5593 3 8702 3 2847 2 7871 2 3641 2 0044 1 6985 1 4385 1 2174 8698 6190 4385 3089 2162 1501 1032 0102 0471 0310 0133 4 9055E-03 1 1728E-03 -2 9307E-04 DYNAMIC IMPULSE 184 PSI-SEC 1 1894 Table 4 DYNAMIC PRESSURE AND IMPULSE VERSUS TIME BASED ON PEAK OVERPRESSURES FROM BRODE 1970 YIELD 40 KT HEIGHT OF BURST 684 KFT GROUND RANGE 6 171 KFT PEAK OlJEF PF ESSURE 2 4931 PS FREE AIR TIME OF ARRilJAL 3575 2327 MSEC PEAK OP T TA 5 0002 PSI PEAK DYNAMIC PRES 5792 PSI PEAK HORIZ COMPT 5792 PSI DYNAMIC POS PHASE 1101 7077 MSEC TIME MSEC DYN IMPULSE HORIZ TIME-TOA DYN HORIZ F'SI-MSEC MSEC PSI 3 1617 6 2432 9 2462 12 1725 17 8018 3580 7616 3586 2916 3591 8228 3597 3549 3608 4225 3619 4943 3630 5703 36-41 6505 3652 7349 3663 8235 3686 0130 3708 2189 3730 441 3752 6790 3774 9329 3797 2025 3819 4875 49 8954 57 0591 63 4807 69 2303 74 3723 78 9654 83 0632 38-41 7879 86 7145 386-4 1034 3886 4339 3931 1393 3975 9028 4020 7232 4-065 5992 89 9639 92 8519 97 6792 4110 5298 4155 5138 4200 5501 4245 6376 4290 7754 4335 9622 4420 8167 4505 8342 4591 0088 4076 3346 4761 8063 23 1451 28 2155 33 0257 37 5877 41 9131 101 4610 104 4060 106 68-47 108 4353 109 7698 110 7781 111 5323 112 0898 112 4961 112 9644 113 1930 113 2862 113 3074 113 2936 5 5289 11 0589 16 5900 5644 5500 5359 22 1222 5221 33 1898 44 2616 55 3376 66 -4178 77 5022 88 5908 110 7803 132 9862 4954 4700 •4'458 4227 4006 3797 3407 3053 2733 2444 155 2082 177 4463 199 7002 221 9697 244 2548 266 5551 288 8707 311 2012 355 9066 400 6701 445 4905 490 3665 535 2971 580 2811 625 3174 670 4049 715 5426 760 7295 845 5840 930 6015 1015 7760 1101 1019 1186 5736 2183 1947 1735 1544 1372 1218 0955 0745 0578 0445 0340 0258 0193 0143 0105 7 6238E-03 3 9091E-03 1 7725E-03 6 0085E-04 2 8437E-06 -2 6601E-04 COMPT SHOCK G F KFT 6 1778 6 1846 6 1915 6 1983 6 2120 6 2257 6 2393 6 2530 6 2667 6 2804 6 3077 6 3351 6 3625 6 3B98 6 4172 6 44-45 6 4719 6 4993 6 5266 6 5540 6 6087 6 6634 6 7181 6 7729 6 8276 6 8823 6 9370 6 9917 7 0465 7 1012 7 2038 7 3064 7 4090 7 5116 7 6142 HORIZONTAL DYNAMIC IMPULSE CPSI-SEC 1132 185 Table 5 DYNAMIC PRESSURE AND IMPULSE VERSUS TIME BASED ON PEAK OVERPRESSURES FROM BRODE 1970 YIELD HEIGHT OF BURST 40 KT PEAK OVERPRESSURE TIME OF ARRIVAL PEAK OF' T TA PEAK DYNAMIC PRES PEAi HORIZ COMF'T DYNAMIC POS PHASE GROUND RANGE TIME MSEC 1213 7684 1218 1844 1222 6053 1227 0308 1235 8962 1244 7803 1253 6832 1262 6045 1271 5443 1280 5024 1298 4728 1316 5147 1334 6271 1352 3091 1371 0595 1389 3775 1407 7620 1426 2122 1444 7271 1463 3057 1500 6508 1538 2404 1576 0676 1614 1260 1652 4090 1690 9105 17 29 6245 1768 5452 18 7 6669 184-6 9842 1921 2130 1996 0778 2071 5 7•3 684 KFT 3 001 KFT 8 5133 PSI FREE AIR 1209 3571 MSEC 14 • 9964 PSI 4 7688 PSI 4 7688 PSI 815 4375 MSEC DYN IMPULSE HORIZ TIME-TOA DYN HORIZ COMPT SHOCK G F PSI-MSEC MSEC PSI KFT 20 6949 4 4112 8 8273 13 2481 17 6737 26 5390 35 4232 44 3260 53 2474 62 1872 71 1452 4 6150 4 4660 4 3214 4 1814 3 0078 3 0146 3 0215 3 9140 3 0420 3 0557 3 0693 3 0830 3 0967 3 1104 3 1377 3 1651 3 1925 3 2198 3 2472 3 2745 3 3019 3 3293 3 3566 3 3840 3 4387 3 4934 3 5481 3 6029 3 6576 40 7437 60 1652 78 9779 114 8441 148 484-4 180 0288 209 6002 237 31-47 263 2819 310 3586 351 6168 387 7334 419 3106 446 8841 470 9298 491 8704 510 0807 525 8931 539 6018 561 6652 578 0767 590 1874 599 0443 605 4548 610 0388 613 2694 615 5058 617 0190 618 0121 618 9489 619 2269 619 2034 3 6629 3 4271 3 2057 2 9978 2 8027 2 4479 2 1356 t 8612 1 6201 1 4085 1 2229 1 0604 89 1156 107 157'5 125 2700 143 4519 161 7023 180 0203 198 4049 216 8550 235 3699 253 9486 291 2936 328 8832 366 7105 404 7688 443 0518 481 5533 520 2673 559 1880 598 3097 637 6270 711 8559 786 72• 6 862 1898 9182 7939 6854 5083 3742 2732 1976 1414 0998 0694 0472 0313 0201 7 3506E-03 1 2709E-03 -1 2823E-03 3 0283 3 7123 3 7670 3 8217 3 8765 3 9312 4 0338 4 1364 4 2390 HORIZONTAL DYNAMIC IMPULSE PSI-SEC 6192 186 Table 6 DYNAMIC PRESSURE AND IMPULSE VERSUS TIME BASED ON PEAK OVER PRESSURES FROM BRODE 1970 YIELD HEIGHT OF BURST GROUND RANGE PEAK OVERPRESSURE 40 KT 684 KFT 2 977 KFT 8 6363 PSI FREE AIR TIME OF ARRIVAL 1193 9169 MSEC PEAK OP T TA 15 2102 PSI PEAK DYNAMIC PRES 4 8969 PSI PEAK HORIZ COMPT 4 8969 PSI DYNAMIC POS PHASE 813 3632 MSEC TIME MSEC 1198 3112 1202 7104 1207 114-4 DYN IMPULSE HORIZ TIME-TOA DYN HOF IZ COMPT PSI -MSEC MSEC PSI 1255 8724 2L1675 41 6717 61 5320 80 7676 117 4336 151 8161 184 0494 214 2600 242 5673 126-4 7983 1282 7051 269 0843 3 17 1426 1300 6844 1318 7350 1336 8560 1355 0464 1373 3052 · 1391 6314 1410 0241 1428 4823 1447 0050 1484 2 -06 1521 7238 359 2439 396 0838 428 2810 456 3852 480 8848 502 2129 520 7537 536 8474 550 7954 573 2328 589 9118 1211 5232 1220 3552 1229 2063 1238 0763 1246 9651 1559 4-477 1597 4055 1635 5907 1673 9971 1712 6137 1751 4494 1790 4836 1829 7158 1903 7911 1978 5100 2053 8406 602 2123 611 2026 617 7060 622 3537 625 6274 627 8924 629 4242 630 4291 631 3764 631 6575 631 6341 4 3943 8 7934 4 7383 4 5846 4 4357 4 2913 4 0159 1'3 1975 17 6063 26 4383 35 2894 44 1593 53 0481 3 7572 3 51-44 3 2865 3 0727 2 8720 2 5072 2 186•i1 9045 1 6570 1 4400 1 2498 61 9555 70 881-4 88 7882 106 7674 124 8181 142 9391 161 1295 179 3883 197 7145 216 1071 234 5653 253 0881 1 0833 9376 8104 6993 5182 3812 2782 290 3237 327 8069 365 5307 403 4885 441 6737 480 0802 518 7017 557 5324 596 5667 635 7988 709 8742 784 5931 859 9236 2011 1437 1014 0704 0479 0318 0203 7 4461£-03 1 2894£-03 -1 2916£-03 SHOCK G F t FT 2 9838 2 9906 2 9975 3 0043 3 0180 3 0317 3 0453 3 0590 3 0727 3 0864 3 1137 3 1411 3 1685 3 1958 3 2232 3 2505 3 2779 3 3053 3 3326 3 3600 3 4147 3 4694 3 5241 3 5789 3 6336 3 6883 3 7430 3 7977 3 8525 3 9072 4 0098 4 1124 4 2150 H0RI'Z0NTAL DYHAMI C IMPULSE PSI-SEC 6316 187 Table 7 DYNAMIC PRESSURE AND IMPULSE VERSUS TIME BASED ON PEAK OVERPRESSURES FROM BRODE 1970 YIELD HEIGHT OF BURST 40 KT 684 KFT GROUND RANGE 2 282 KFT 13 9840 PSI FREE AIR 776 1969 MSEC 24 9958 PSI 12 2128 PSI 12 2128 PSI 833 5149 MSEC PEAK OVERPRESSURE TIME OF ARRIVAL PEAK OP T TA PEAK DYNAMIC PRES PEAK HORIZ COMPT DYNAMIC POS PHASE TIME MSEC 779 9936 783 7974 787 6081 791 4259 799 0822 806 7661 81-4 4773 822 2158 829 9813 837 7736 853 4379 869 2071 885 0796 901 0540 917 1289 933 3027 949 5740 965 9414 982 -4034 998 9539 1032 34-42 1066 0869 1100 1765 1134 6032 1169 3572 1204 4291 123 8098 1275 4906 1-11 i • j • • 'o- 1347 7183 1H6 4'327 1486 0641 1556 5647 1627 8898 DYN IMPULSE HOF IZ TIME-TOA DYN HORIZ PSI-MSEC MSEC PSI 45 4760 89 2991 131 5297 172 2258 249 2235 320 7290 387 1344 448 8026 506 0706 559 2504 654 ·i-192 736 4600 807 1620 868 0686 920 5127 965 M56 1004 4627 1037 8246 1066 4760 1091 0611 1130 0755 1158 6281 1179 4223 1194 4805 1205 3136 1213 04-81 1218 5213 1222 3538 1225 0038 1226 8080 1228 6865 1229 4780 1229 7436 1229 7752 3 7967 7 6004 11 4112 15 2289 22 8852 30 5691 38 2804 46 0189 53 7844 61 5767 77 2409 93 0101 108 8826 124 8571 H0 9319 157 1057 173 3770 189 7444 206 2065 222 7619 256 1473 289 8899 323 9796 358 4062 393 1602 428 2321 463 6129 499 2936 535 2659 571 5213 640 2357 709 8671 780 3677 851 6928 11 7471 11 2993 10 8687 10 4548 9 6740 B 9519 8 2839 7 6660 7 0943 6 5652 5 6222 4 8140 4 1212 3 5270 3 0174 2 5802 2 2053 1 8836 1 6078 1 3713 9949 7188 5169 3695 2624 • 1849 1290 0891 0606 0406 0179 6 8352£-03 1 7402E-03 -3 5055E-04 COMPT G R KFT SHOCK 2 2888 2 2956 2 3 25 2 3093 2 3230 2 3367 2 3503 2 3640 2 3777 2 3914 2 4187 2 4-461 2 4735 2 5008 2 5282 ' C -C' c C J J JJ 2 5829 2 6103 2 6376 2 6650 2 7197 2 7744 2 829l 2 8839 2 9386 2 9933 3 0480 3 1027 3 1575 3 2122 3 3148 3 4174 3 5200 3 6226 HOiUZONTAL DYN MIC IMPULSE PSI-SEC 1 2297 188 Table 8 DYNAMIC PRESSURE AND IMPULSE VERSUS TIME BASED ON PEAK OVERPRESSURES FROM ERODE 1970 YIELD HEIGHT OF BURST 40 KT 2 394 KFT B 065 KFT GROUND RANGE PEAK OVERPRESSURE 1 5272 PSI IFREE AIR TIME OF ARRIVAL 5489 1631 MSEC PEAK OP T TA 4 9991 PSI PEAK DYNAMIC PRES 5790 PSI PEAK HORIZ COMPT 5790 PSI DYNAMIC POS PHASE 1167 9601 MSEC TIME MSEC 5494 6581 5500 154 5505 6507 5511 1482 5522 1459 5533 1469 5544 15 12 5555 1590 5566 1700 5577 1844 5599 2230 5621 2748 5643 3395 5665 4171 5687 5075 5709 6106 5731 7262 5753 8543 5775 9948 5798 1475 58-42 4-893 5386 8789 5931 3156 5975 7986 6020 3272 6064 9006 6109 5180 6154 1789 6198 8825 6243 6281 6327 6372 6411 7876 6496 0751 6580 4959 6665 0462 DYN IMPULSE HORIZ TIME-TOA DYN HO UZ COMPT MSEC PSI-MSEC PSI 3 1428 6 2095 9 2016 12 1209 17 7468 23 1001 28 1928 33 0363 37 6419 42 0200 50 1323 57 4527 64 0521 69 9956 75 3431 80 H94 84 4648 88 3355 91 8036 9-4 9074 100 1525 104 3250 H 7 6279 110 2287 112 2649 113 8492 115 0734 116 0120 116 7253 117 2619 117 9155 118 2689 118 4427 118 5131 118 5271 5 4949 10 9908 16 4875 21 9851 32 9827 43 9837 54 9881 65 9958 77 0069 88 0212 110 0599 132 1116 154 1763 176 2540 198 3444 220 4474 242 5631 264 6912 286 8316 308 9843 353 3261 397 7158 442 1525 486 6355 531 1640 575 7374 620 35 49 665 0157 709 7193 754 4650 838 4741 922 6244 1006 912 1091 3328 1175 8830 5649 5511 5376 5244 4989 4745 4512 4290 4077 3874 3496 3151 2837 rirc-_ J Jj 2294 2060 1847 1655 1481 1324 1055 0836 0659 0517 0403 0312 0240 0183 0138 0103 5 7673E-03 2 9888£-03 1 3591E-03 4 4597E-04 -3 1660E-05 SHOCt G R KFT 8 0718 8 0786 8 0855 8 0923 8 1060 8 1197 8 1333 8 1470 8 1607 8 1744 8 2017 8 2291 8 2565 8 2838 8 3112 8 3385 8 3659 8 3933 8 4206 8 4480 8 5027 8 5574 8 6121 8 6669 8 7216 8 7763 8 8310 8 8857 8 9405 8 9952 9 0978 9 2004 9 3030 9 4056 9 5082 HORIZONTAL Dn AMIC IMPULSE PSI-SEC 1185 189 Table 9 DYNAMIC PRESSURE AND IMPULSE VERSUS TIME BASED ON PEAK OVERPRESSURES FROM BRODE 1970 YIELD HEIGHT OF BURST 40 KT 2 394 KFT GROUND RANGE PEAK OVERPRESSURE TIME OF ARRIVAL PEAK OP T TA PEAK DYNAMIC PRES PEAK HORIZ COMPT 4 346 KFT 3 6289 PSI FREE AIR 2703 1845 MSEC 14 9972 PSI 4 7693 PSI 4 7693 PSI DYNAMIC POS PHASE 1025 5963 MSEC TIME MSEC - ' - 2707 7280 2712 2748 2716 8249 2721 3783 2730 4949 2739 6246 2748 7672 2757 9227 2767 0910 2776 2721 2794 6720 2813 1221 2831 6216 2850 1700 2868 7668 2887 4-114 2906 1032 2924 8418 2943 6266 2962 4570 3000 2529 3038 2254 3076 3706 3114 68·' -8 3153 1641 3191 8051 21 3921 42 2540 62 5974 82 4340 120 6288 156 9293 191 4202 224 1828 255 2954 284 8331 339 4521 388 6008 432 7787 472 4 45 508 0192 539 8888 56 8 4065 593 8952 616 6499 636 9394 671 0278 697 9280 719 0438 735 5261 748 3148 758 1733 3230 6041 765 7193 3269 5578 3308 6628 771 4500 775 7637 778 9780 782 8434 784 9034 785 096 786 3248 3347 9159 · -• • •· DYN IMPULSE HORIZ TIME-TOA PSI-MSEC ttSEC 3421 9036 3496 381 3571 3287 3646 7288 3722 5638 786 4271 3798 817 2 786 3781 DYN HGRIZ COMPT PSI 4 5435 9 0903 13 6404 18 1938 27 3104 36 4401 45 5827 5-4 7382 63 9065 73 0875 91 4875 109 9375 128 4371 146 9855 165 5823 184 2269 202 9187 221 6573 240 4421 644 7313 718 7191 793 1964 868 1442 943 5443 1019 3793 1095 6327 HORIZCPH L 4 6479 4 3528 4 3596 4 4133 4 3001 4 0815 3 8731 3 6743 3 4848 4 3665 4 3733 4 3870 4 4007 3 3043 2 5225 2 2601 2 0228 1 8085 1 6151 1 4407 1 2838 1 1426 1 0157 7998 6266 4883 • 373 i 2914 2229 1693 1275 0951 0702 0383 0195 8 8636E-03 3 0753E-03 1 5430E-04 -1 1451E-03 4 4143 4 4280 4 4417 4 4554 4 4827 4 5101 4 5375 4 5648 c-n J7 4 6195 4 6469 4 6743 4 7016 4 7290 4 7837 4 8384 4 8931 4 9479 5 0026 5 0573 5 1120 5 1667 5 2215 5 2762 5 3788 5 4814 5 5840 5 6866 5 7892 5 8918 DYNAMIC IMF'ULSE PSI-SEC 7863 190 G F KFT 4 5292 3 1322 2 8124 259 2725 297 0684 335 0409 373 1861 411 5003 449 9796 488 6205 527 4196 566 3732 605 4783 SHOCK lc 1 U Lt -V DYNAMIC PRESSURE AND IMPULSE VERSUS TIME BASED ON PEAK OVERPRESSURES FROM BRODE 1970 YIELD HEIGHT OF BURST 40 KT 2 394 KFT GROUND RANGE 1 521 KFT PEAK Ol ERPRESSURE 9 9411 PSI FREE AIR TIME OF ARRIVAL 1192 6267 MSEC PEAK OP T TA 25 0019 PSI PEAK DYNAMIC PRES 12 2183 PSI PEAK HORIZ COMPT 7 7627 PSI DYNAMIC POS PHASE 800 3640 MSEC TIME MSEC 1195 2194 1197 8216 1200 4334 1203 0547 1208 3257 1213 63-44 1218 9808 1224 3646 1229 7856 1235 2436 1246 2700 1257 -4424 1268 7592 1280 2190 129L8202 1303 5615 1315 4413 1327 -4-582 1339 6107 1351 8973 1376 8672 1402 3561 1428 3527 1 5-4- 8455 1481 8232 1509 2748 1537 1892 1565 5556 1594 1312 1618 3710 1665 2592 1713 9298 1764 2804 1816 2177 1869 6558 1n l i c-1r 7 7 - • J I Ji 1980 7243 2038 135 DYN IMPULSE HORIZ TIME-TOA F'SI-MSEC MSEC 19 9819 39 7507 59 3081 78 6555 116 7271 153 9794 190 4263 2 6 0816 260 9595 295 0738 361 0627 424 1574 -484 4544 5-42 0392 596 9842 649 3484 699 1784 746 5114 791 3785 833 8093 911 4865 979 9036 1039 5755 1091 1700 1135 4512 1173 2112 1205 2160 1232 1732 1254 5409 1269 9945 1291 90-46 1306 7830 1316 5786 132 2 7291 1326 2847 1328 0342 1328 5894 1328 4' 258 2 5926 5 1948 7 8066 10 4279 15 6989 21 0076 26 3540 31 7378 37 1588 42 6168 53 6432 64 8156 7li 1324 87 5922 99 1934 110 9347 122 81-45 134 8314 146 9839 159 2705 184 2404 209 7293 235 7259 262 2187 289 1964 316 6480 3H 5624 372 9288 401 5044 425 7442 472 6324 521 3030 571 6536 623 5909 677 0290 731 8889 788 0975 845 5868 D'i'N HDRIZ COMF'T PSI 7 6518 7 5423 7 -4343 7 3278 7 1192 6 9164 6 7192 6 5276 6 3414 6 1604 5 8136 5 -4856 5 1746 4 8788 4 5965 4 3258 4 0655 3 8143 3 5716 3 3371 2 8930 2 4848 2 1162 1 7892 1 5036 1 2566 1 0445 8631 7082 5730 3790 2448 1528 0899 0473 0195 2 5371£-03 -6 5993£-03 G R KFT SHOCK 1 5278 1 5346 1 5415 1 5483 1 5620 1 5757 1 5893 1 6030 1 6167 1 6304 1 6577 1 6851 1 7125 1 7398 1 7672 1 7945 1 8219 1 8493 1 8766 1 9040 1 9587 2 0134 2 0681 2 1229 2 1776 2 2323 2 2870 2 3417 2 3965 2 4512 2 5538 2 6564 2 7590 2 8616 2 9642 3 0668 3 1694 3 2720 HOF IZONTAL DYNAMIC IMF'ULSE PSI-SEC 1 3284 191 Table 11 DYNAMIC PRESSURE AND IMPULSE VERSUS TIME BASED ON NEW EM-1 PEAK OVERPRESSURES YIELD HEIGHT OF BURST 40 KT 0 KFT GROUND RANGE PEAK OVERPRESSURE TIME OF ARRIVAL PEAK OP T TA PEAK DYNAMIC PRES PEAK HORIZ COMPT 5 201 KFT 3 3500 PSI FREE AIR 2728 1284 MSEC S 0001 PSI 5792 PSI 5792 PSI DYNAMIC PDS PHASE 1043 8417 MSEC TIME MSEC 2733 5275 2738 9281 2744 3302 2749 7339 2760 5460 2771 3643 2782 1886 2793 01 1 2803 8556 2814 6980 2836 4009 2858 1273 2879 8770 2901 6498 2923 4452 2945 2630 2967 1030 2988 9649 3010 8483 3032 7532 3076 6258 3120 5208 3164 6162 3208 7299 3252 9203 3297 1854 3341 5235 3385 9329 3430 4120 3474 9592 3558 6630 3642 5908 3726 7331 3811 0810 DYN IMPULSE HORIZ TIME-TOA DYN HOfUZ COMPT PSI-MSEC MSEC PSI 3 0845 6 0856 9 0053 11 8456 17 2951 22 4500 27 3247 31 9331 36 2884 40 4034 47 11572 54 6882 60 6787 66 0036 70 7309 74 9224 78 6340 81 9162 84 8149 87 3712 91 5938 94 8486 97 3412 99 2365 100 6663 101 7356 102 5272 103 1065 103 5245 103 821• 104 1472 104 2928 104 3418 104 3429 5 3990 10 7996 16 2018 21 6055 32 4176 43 2358 54 0602 64 8906 75 7271 86 5696 108 2724 129 9989 151 7486 173 5213 195 3167 217 1345 238 9745 260 8364 282 7199 304 6247 348 4974 392 4524 436 4877 480 6015 524 7918 569 0569 613 3950 657 8045 i02 2836 746 8307 830 5346 914 4624 998 6047 1082 9526 5634 5480 5329 5183 4900 4632 4377 4135 3905 3687 3284 2921 2595 2303 2041 1807 1597 1410 1243 1094 0844 0647 0493 0373 0279 0207 0152 0110 7 9276E-03 5 5586E-03 2 6540E-03 1 0638E-03 2 4443£-04 -1 3809E-04 SHOCK G R KFT 5 2078 5 21-46 5 2215 5 2283 5 2420 5 2557 5 2693 5 2830 5 2967 5 3104 5 3377 5 3651 5 3925 5 4198 5 4472 5 4745 5 5019 5 5293 5 5566 5 5840 5 6387 5 6934 5 7481 5 8029 5 8576 5 9123 5 9670 6 0217 6 0765 6 1312 6 2338 6 3364 6 4390 6 5416 HORIZONTAL DYNAMIC IMPULSE PSI-SEC 1043 192 Table 12 DYNAMIC PRESSURE AND IMPULSE VERSUS TIME BASED ON NEW EM-1 PEAK OVERPRESSURES YIELD 40 KT HEIGHT OF BURST 0 KFT GROUND RANGE 2 8415 KFT PEAK OIJEF PRESSURE 9 9064 PSI FREE AIR TIME OF ARRIVAL 1009 5443 MSEC PEAK OP T TA 15 0011 PSI PEAK DYNAMIC PRES 4 7716 PSI PEAK HORIZ COMPT 4 7716 PSI DYNAMIC POS PHASE 800 5105 MSEC TIME MSEC 1013 9024 1018 2659 1022 6347 1027 0088 1035 7728 1044 5578 1053 3635 1062 1898 1071 0366 1079 9037 1097 6982 1115 5720 1133 5239 1151 5528 1169r6574 1187 8366 1206 0893 1224 4143 1242 3105 1261 2769 1298 4159 i '7C _ _J h ri n ' 1 0 J-- 1373 4903 1411 4100 1449 57 45 1487 97 68 1526 6097 1565 4666 1604 5409 1643 3264 1712 0346 179 -2 9256 1868 4634 DYN IMPULSE HO UZ TIME-TOA DYN HORIZ COHPT MSEC PSI PSI-MSEC SHOCK G R KFT 4 3581 8 7216 13 0904 17 4645 26 2285 35 0135 43 8192 52 6455 61 4923 70 3594 88 1539 106 0277 123 9796 142 0085 160 1131 178 2923 196 5450 2 8483 2 8551 20 4267 4 1586 59 2184 77 6282 112 5769 145 1722 175 5664 203 9018 230 3121 254 9224 299 1781 337 5509 370 7884 399 5463 424 3997 445 8525 464 3464 480 2680 493 9553 505 7044 524 3354 537 9238 547 7561 554 8063 559 8083 563 3129 565 7314 567 3690 568 4510 569 1424 569 7634 569 9242 S69 8874 4 6038 4 4416 4 2850 4 1338 3 8466 3 5787 3 3288 3 0958 2 8785 2 6759 2 3109 1 9939 1 7187 1 4799 1 2729 1 0936 9384 8041 214 8700 2 8620 2 8688 2 8825 2 8%2 2 9098 2 9235 2 9372 2 9509 2 9782 3 0056 3 0330 3 0603 3 0877 3 1150 3 1424 3 1698 3 1971 233 2662 6881 251 7326 288 8716 326 2788 363 9460 5880 4272 3082 2205 401 8657 1563 3 4434 440 0302 478 4325 1095 0757 0515 03-1-2 0221 0137 4 6447E-03 3 4981 3 5528 517 0654 555 9223 594 9966 634 2821 708 4903 783 3813 858 9191 5 2273E-04 -1 0712E-03 3 2245 3 2792 3 3339 3 3886 3 6075 3 6622 3 7170 3 7717 3 8743 3 9769 4 0795 HORIZONTAL DYNAMIC IMPULSE CPSI-SECl 5698 193 Table 13 DYNAMIC PRESSURE AND IMPULSE VERSUS TIME BASED ON NEW EM-1 PEAK OVERPRESSURES YIELD GROUND RANGE PEAK OIJERPRESS JRE TIME OF ARRIVAL PEAK OP T TA PEAK DYNAMIC PRES HEIGHT OF BURST 40 KT 0 KFT 2 2275 KFT 16 0127 PSI FREE AIR 642 9149 MSEC 25 0000 PSI 12 2165 PSI PEAK HORIZ COMPT 12 2165 PSI DYNAMIC POS PHASE 867 9666 HSEC TIME MSEC 646 6980 650 4886 654 2869 DYN IMPULSE HORIZ TIME-TOA DYN HORIZ CGMPT PS -MSEC MSEC CPSI 1001 8550 1036 7937 1072 0671 1107 6650 1143 577 6 1179 7953 1216 3088 1285 5381 1355 7202 1426 80 5 11 7 9729 11 8 5503 11 8 7612 14 8 73 6 11 S 8l J2 3 7831 7 5737 11 3720 15 1777 22 8117 30 4754 38 1686 45 8911 53 6427 61 4230 77 0694 92 8283 108 6981 124 6771 140 7635 156 9557 173 2521 189 6510 206 1508 222 7500 256 2402 290 1097 324 3468 358 9401 393 8788 429 1522 464- 7501 500 6627 536 8804 573 3939 642 6232 712 8053 783 8876 855 8207 1571 47 2 11 8 7962 928 5583 658 0926 665 7266 673 3903 681 0835 688 8060 696 5576 704 3380 719 9843 735 7432 751 6130 767 5920 783 6784 799 8706 816 1670 832 5659 849 0657 865 6649 899 1551 933 0246 967 2617 45 2335 88 6521 130 33• 3 170 3395 245 6057 314 9805 378 9336 437 8956 492 2614 542 3938 631 1895 706 7211 770 9764 825 6387 872 1354 911 6736 9 -5 2983 973 8710 998 1428 1018 7496 1050 9496 1074 0562 1090 5734 1102 3256 1110 6417 1116 4885 11 0 5680 11 3 3891 11 5 3192 I I 'II - 11 c o 1 11 7025 11 2108 10 7403 10 2901 9 4470 8 6745 7 9666 7 3175 6 7223 6 1762 5 2152 SHOCK G R KFT 2 2343 2 2 11 2 2480 2 2548 2 2685 2 2822 2 2958 2 3095 2 3232 2 3369 2 3642 4 4051 2 3916 3 7216 2 4190 2 4463 2 4737 2 5010 2 5284 2 5558 2 5831 2 6105 2 6652 2 7199 2 7746 2 8294 2 8841 2 9388 2 9935 3 1444 2 6568 2 2446 1 8959 1 6010 1 3514 1 1402 8102 5739 4050 2845 1987 1379 • 0949 0647 0436 0290 0128 5 0808E-03 1 5751E-03 1 2949E-04 -3 6565E-04 3 0432 3 1030 3 1577 3 2603 3 3629 3 4655 3 5681 3 6707 HORIZONTAL DYNAMIC IMPULSE PST-SECl 1 1287 _ 194 Table 14 DYNAMIC PRESSURE AND IMPULSE VERSUS TIME BASED ON NEW EM-1 PEAK OVERPRESSURES YIELD 40 KT HEIGHT OF BURST 684 KFT GROUND RANGE 5 562 KFT PEAK 01JERPRESSURE 2 9550 PSI FREE AIR TIME OF ARRIVAL 3087 6669 MSEC PEAK OP T TA 4 9995 PSI PEAK DYNAMIC PRES 5791 PSI PEAK HORIZ COMPT 5791 PSI DYNAMIC POS PHASE 1070 2484 MSEC TIME MSEC DYN IMPULSE HORIZ PSI-MSEC 3093 0866 3098 5077 3103 9302 3109 3541 3120 2059 3131 0632 3 0965 6 1109 9 0452 11 9012 17 3857 3H1 9260 27 4966 32 1504 36 5538 40 7190 48 3787 3152 7942 3163 6678 3174 5467 3196 3205 3218 1153 3239 9309 3261 7670 3283 6234 3305 4999 3327 3963 3349 3123 3371 2477 3393 2023 3437 1681 3481 2081 3525 3206 3569 5039 3613 7567 3658 0772 3702 4641 3746 916 3791 4313 3836 0087 3919 7543 4003 7053 4087 8537 4172 1918 22 5795 55 2203 61 3241 66 7633 71 6043 75 9076 79 7282 83 1160 86 1161 88 7692 93 1708 96 5842 99 2150 101 2290 102 7596 103 9133 104 7750 105 4117 105 8763 106 2103 106 5866 106 7633 106 8306 106 8417 TIME-TOA MSEC 5 4197 10 8408 16 2632 21 6871 32 5390 43 3963 54 2591 65 1273 76 0008 86 8798 108 6535 130 4483 152 2639 174 1000 195 9565 217 8330 239 7294 261 6454 283 5807 305 5353349 5011 393 5411 437 6536 481 8370 526 0897 570 4103 614 7972 659 2490 703 7643 748 3418 832 0874 916 0384 1000 1868 1084 5249 DYN HORIZ COMPT PSI SHOct G F KFT 5636 5 5688 5485 5 5756 5 5825 5338 5194 4917 4653 -4402 4164 3937 3722 3323 2964 5 5893 5 6030 5 6167 5 6303 5 6440 5 6577 5 6714 5 6987 5 7261 • 26-40 5 7535 2349 2087 5 7808 5 8082 1852 5 8355 1642 5 8629 5 8903 5 9176 5 9450 5 9997 6 0544 6 1091 6 1639 6 2186 6 2733 6 3280 6 3827 6 4375 1-454 1285 1135 0881 0680 0521 0397 0300 0225 0166 0122 8 8608E-03 6 3038E-03 3 1270E-03 1 3497E-03 4 0651E-04 -5 4616E-05 6 4922 6 5948 6 6974 6 8000 6 9026 HORIZONTAL DYNAMIC IMPULSE PSI-SEC 1068 195 Table 15 DYNAMIC PRESSURE AND IMPULSE VERSUS TIME BASED ON NEW EM-1 PEAK OVERPRESSURES YIELD 40 KT HEIGHT OF BURST 684 KFT GROUND RANGE 2 9759 KFT PEAK 01 ERF'RESSURE 8 6-420 PSI FREE AIR TIME OF ARRIVAL 1193 2107 MSEC PEAK OP CT TA l 14 9985 PSI PEAK DYNAMIC PRES 4 7701 PSI PEAK HOR Z COMPT 4 7701 PSI DYNAMIC POS PHASE 813 2707 MSEC TIME MSEC 1197 6042 1202 0026 1206 4058 1210 8139 1219 6-444 1228 4939 1237 3624 1246 2496 1255 1555 126-4 0799 1281 9838 1299 9601 1318 0079 1336 1261 1354 3138 1372 5698 1390 8933 1409 2833 1427 7389 1446 2591 1483 4896 1520 9679 1558 6870 1596 6401 1634 8209 1673 2 2 1711 8402 1750 6668 1789 6969 1828 9252 1902 9935 1977 7056 2053 0298 DYN TIME-TOA DYN HORIZ COMPT PSI-MSEC MSEC PSI 20 6103 40 5640 59 8810 78 5803 4 3935 8 7919 13 1951 17 6032 26 4336 35 2832 44 1517 53 0389 61 9448 4 6132 4 4612 4 3139 4 1713 3 89943 6443 3 4051 3 1808 2 9706 2 7735 2 4159 2 1020 1 8269 1 5859 1 3751 1 1907 1 0297 8891 IMPULSE H0RIZ 114 1954 147 5566 178 7987 208 0484 235 4257 261 0432 307 3949 347 111 383 2847 414 1307 440 9944 464 3589 484 6520 502 2522 517 4937 530 6721 551 7 60 567 4234 578 8926 587 2342 593 2384 597 5080 600 5002 602 56 603 9458 604 8501 605 6964 605 9451 605 9245 70J8692 88 7731 106 7494 12-4 7972 142 9154 161 1031 179 3591 197 6826 216 0726 234 5282 253 0484 290 2789 327 7572 365 4763 403 4294 441 6102 480 0122 518 6295 557 4561 596 4862 635 7145 709 7828 784 4949 859 8191 OO 6601 -4868 3564 r SHOO G r- KFT 2 9827 2 9895 2 9964 3 0032 3 0169 3 0306 3 0442 3 0579 3 0716 3 0853 3 1126 3 14 0 3 1674 3 1947 3 2221 3 2494 3 2768 3 3042 3 3315 3 3589 3 4136 3 4683 2588 3 5230 1861 1324 0929 3 5778 3 6325 3 6872 3 7419 3 7966 3 8514 3 9061 4 0087 4 1113 4 2139 0642 0435 0287 0182 6 6195E-03 1 1351E-03 -1 1251E-03 HORIZONTAL DYNAMIC IMPULSE PSI-SEC 6059 196 Table 16 DYNAMIC PRESSURE AND IMPULSE VERSUS TIME BASED ON NEW EM-1 PEAK OVERPRESSURES YIELD 40 KT HEIGHT OF BURST 684 KFT GROUND RANGE 2 8415 KFT PEAK OVERPRESSURE 9 3882 PSI FREE AIR TIME OF ARRIVAL 1107 8909 MSEC PEAK OP T TA 16 3732 PSI PEAK DYNAMIC PRES 5 6191 PSI PEAK HORIZ COMPT 5 6191 PSI DYNAMIC POS PHASE 803 9413 MSEC TIME MSEC 1112 1854 1116 4-852 1120 7901 1125 1002 1133 7259 1142 3 20 1151 0685 1159 7651 1168 4-818 1177 2183 1194 7505 1212 3605 1230 0472 1247 8095 1265 64-63 1283 5565 1301 5392 1319 5932 1337 7175 1355 9112 1392 5026 1429 3596 1466 4748 1503 8410 1541 4511 1579 2983 1617 376 1655 6778 1694 1976 - n nr J J J •7 7J DYN IMPULSE HORIZ TIME-TOA DYN HORIZ COMPT PSI-MSEC ttSEC 23 7219 4 2945 8 5942 12 8992 17 2093 25 8449 34 5011 43 1775 51 8742 60 5908 69 3274 86 8595 104 4695 122 1562 139 91-85 157 7553 175 6656 193 6482 211 7022 229 8266 248 0202 46 6723 68 8751 90 3534 131 2205 169 4511 205 2070 238 6403 269 8943 299 1038 351 8595 397 8665 437 94-38 472 8154 503 1211 529 4254 552 2267 571 9642 589 0248 603 7492 627 2896 644 6470 657 3461 666 5553 673 1661 677 8555 681 1347 683 3880 684 9021 685 8898 1306 1029 686 8161 879 9649 1954- 481 687 0940 687 0808 SHOCK G R KFT 5 4299 5 2468 5 0696 4 8982 4 5718 4 2663 3 9804 3 7128 3 4624 3 2281 2 8041 2 4334 2 1094 1 8266 1 5799 2 8483 2 8551 2 8620 2 8688 2 8825 2 8962 2 9098 2 9235 2 9372 2 9509 2 9782 3 0056 3 0330 3 0603 3 0877 3 1150 3 1424 3 1698 3 1971 3 2245 3 2792 3 3339 3 3886 3 4434 3 4981 3 5528 1 3648 1 1775 1 0146 8729 7500 5509 4018 2907 2084 284 6116 321 4687 358 5839 395 9500 433 5601 471 4073 509 4850 547 7869 586 3067 625 0385 698 2120 772 0739 846 5900 I PSI 1478 1034 0713 0482 0317 0202 7 3724 -03 1 3607E-03 -1 1082E-03 3 6075 3 6622 3 7170 3 7717 3 8743 3 9769 4 0795 HORIZONTAL DYNAMIC IMPULSE PSI-SEC 6870 197 Table 17 DYNAMIC VRESSURE AND IMPULSE VERSUS TIME BASED ON NEW EM-1 PE AK OVERPRESSURES 40 KT YIELD HEIGHT OF BURST 684 KFT GROUND RANGE 2 2913 KFT PEAK OVERPRESSURE 13 8800 PSI FREE AIR TIME OF ARRIVAL 781 3609 MSEC PEAK OP T TA PEAK DYNAMIC PRES PEAK HORIZ COMPT DYNAMIC POS PHASE TIME MSEC 785 1672 788 9805 792 8007 796 6279 804 3029 812 0055 819 7353 827 4922 835 2759 843 0863 858 7864 874 5909 890 4982 906 5070 922 6156 938 8227 55 1268 971 5265 988 0205 1004 6073 1038 0542 1071 6565 1106 0041 1140 4871 1175 2958 1210 4208 1 _ iC - -- _ J OJ 1281 5341 1317 6 50 1 353 9078 1422-7073 1492 4194 1562 66 163-4 43 DYN IMPULSE HORIZ PSI MSEC 45 6056 89 5459 131 8819 172 6720 249 8249 321 4456 387 9292 449 6421 506 9244 560 0912 655 1625 737 0284 807 4963 868 1254 920 2616 965 0677 1003 5482 1036 5713 1064 8876 1089 1462 1127 5459 1155 5500 1175 8691 1190 5262 1201 0277 1208 4935 1213 7528 1217 4183 1219 9401 1221 6480 1223 4111 122--1- 1437 1224 3838 1224 4081 TIME-TOA MSEC 3 8062 7 6195 11 4397 15 2669 22 9420 30 6445 38 3743 46 1312 53 9149 61 7253 77 4254 93 2299 109 1373 125 1460 141 2546 157 4617 173 7658 190 1656 206 6595 223 2464 256 6932 290 4955 324 6432 359 1261 393 9348 429 0598 464 4922 500 2231 536 2440 572 5468 641 3464 711 0584 781 6356 853 0333 25 0015 PSI 12 2179 PSI 12 2179 PSI 831 8676 MSEC DYN HORIZ COMPT PSI SHOC - G R KFT 11 7501 11 3003 10 8679 10 4521 9 6679 8 9428 8 2721 7 6517 7 0778 2 2981 2 3049 6 5468 5 6007 4 7904 4 0961 3 5012 2 9914 2 5545 2 1802 1 8594 1 5847 1 3494 9757 7025 5032 3584 2534 • 1778 1235 084-8 0575 0382 0167 6 2595E-03 1 5288E-03 -3 7616E-04 2 3118 2 3186 2 3323 2 3460 2 3596 2 3733 2 3870 2 4007 2 4280 2 4554 2 4828 2 5101 2 5375 2 5648 2 5922 2 6196 2 6469 2 6743 2 7290 2 7837 2 8384 2 8932 2 9479 -3 0026 3 0573 3 1120 3 1668 3 2215 3 3241 3 4267 3 5293 3 6319 HORIZONTAL DYNAMIC IMPULSE PSI-SEC 1 2244 198 Table 18 DYNAMIC PRESSURE AND IMPULSE VERSUS TIME BASED ON NEW EM-1 PEAK OVERPRESSURES YIELD 40 KT HEIGHT OF BURST 2 394 KFT GROUND RANGE 7 004 KFT PEAK OVERPRESSURE 1 8733 PSI FREE AIR TIME OF ARRIVAL 4648 3869 MSEC PEAK OP T TA 4 9996 PSI PEAK DYNAMIC PRES 5791 PSI PEAK HORIZ COMPT 5791 PSI DYNAMIC POS PHASE 114-4 2719 MSEC TIME MSEC 4653 7243 4659 0629 4664 4027 4669 7437 4680 4292 4691 1195 4701 8145 4712 5142 4723 2187 4733 9278 4755 3599 4776 8104 4798 2792 4819 7660 48-41 2708 4862 7933 4884 3335 4905 8910 4927 4659 4949 0579 4992 2926 5035 5940 5078 9609 5122 3922 5165 8867 5209 4434 5253 0610 5296 7387 5340 4753 5384 2699 5466 5375 5548 9990 5631 6483 5714 4797 5797 4875 nm TIME-TOA DYN HORIZ COMPT IMPULSE HORIZ PSI-MSEC 3 0528 6 0310 8 9360 11 7696 17 2233 22 4199 27 3562 32 0486 36 5081 40 7451 48 5898 55 661 62 0288 67 7574 72 9056 77 5275 81 6725 85 3859 88 7090 91 6796 96 6901 100 6659 103 8050 106 2702 108 1952 109 6888 110 8398 111 7199 112 3868 112 8872 113 4944 113 3214 113 9817 114 0468 114 0605 PSI MSEC 5 3373 10 6759 16 0157 21 3567 32 0422 42 7325 53 4275 564-8 5509 C • J 5239 4980 4734 l J nri • 77 4274 406 3855 64 1273 74 8317 85 5408 106 9729 128 4234 3474 3127 2812 2526 149 8922 171 3790 192 8838 214 4063 235 9465 257 5041 279 0789 300 6709 343 9056 387 2070 430 5739 474 0052 517 4997 561 0564 604 6741 6 8 3517 692 0883 735 8829 818 1505 900 6120 983 2614 1066 0927 1149 1005 HDF IZONTAL DYNAMIC 2267 2033 • 1820 1629 1455 1299 1032 Of315 0641 0501 0389 0301 0230 0175 0132 9 8457E-03 5 4571E-03 2 8158E-03 1 2788E-03 4 2474E-04 -1 7862E-05 IMPULSE PSI-SEC 199 G R KFT SHOCK 7 orna 7 0176 7 0245 7 0313 7 0450 7 0587 7 0723 7 0860 7 0997 7 1134 7 1407 7 1681 7 1955 7 2228 7 2502 7 2775 7 3049 7 3323 7 3596 7 3870 7 4417 7 4964 7 5511 7 6059 7 6606 7 7153 7 7700 7 8247 7 8795 7 9342 8 0368 8 1394 8 2420 s 3446 8 4472 1140 Table 19 DYNAMIC PRESSURE AND IMPULSE VERSUS TIME BASED ON NEW EM-1 PEAK OVERPRESSURES 40 n HEIGHT OF BURST 2 394 KFT GROUND RANGE 3 5092 KFT PEAK OVERPRESSURE 4 7466 PSI FREE AIR TIME OF ARRIVAL 2175 6770 MSEC PEAK OP T TA 15 0008 PSI PEAK DYNAMIC PRES 4 7715 PSI PEAK HORIZ COMPT 4 7715 PSI DYNAMIC POS PHASE 957 3576 MSEC YIELD TIME MSEC 2179 7305 2183 7887 2187 8518 2191 9197 2200 0697 2208 2386 2216 4264 222-4 6329 2232 8579 2241 1014 2257 6432 2274 2575 2290 ' ·t33 2307 6998 2324 526 234L•t210 2358 3841 2375 4143 2392 511 2409 6731 2444 1908 2·t78 9612 2513· 9782 2549 2359 2584 7285 2620 4506 · •· 2656 3967 2692 5615 2728 9401 2765 527-4 2834 6746 2904 5084 2975 0001 3046 12 3117 8488 3190 1552 DYN IMPULSE HOF IZ TIME-TOA PSI-MSEC MSEC 19 1032 37 7606 55 9810 73 7733 108 1066 140 8303 172 0117 201 7132 229 9967 256 9216 306 9097 352 1272 392 9784429 8384 463 0546 492 9483 519 8150 543 9369 565 5760 584 9639 617 7710 643 9040 664 6067 680 912 693 6754 703 5988 711 2584 717 1233 721 5739 724 9171 728 9847 731 1886 732 2375 732 7575 732 8888 i32 B531 Dnl HOF IZ COMPT PSI 4 0534 4 6547 8 1117 12 1748 4 5405 4 4288 4 3195 4 1081 3 9059 16 2427 24 3927 32 5616 40 7494 48 9558 57 1809 65 4243 81 9662 98 5805 115 2663 132 0228 148 8489 165 7440 182 7071 199 7373 216 8339 233 9961 268 5138 303 2842 338 3012 373 5589 409 0515 3 7126 3 5279 J 3514 3 1828 2 8682 2 5816 2 3210 2 0841 1 8692 1 67-4-3 1 4977 1 3391 1 1959 1 0667 8457 6670 5232 4081 3163 2435 444 7736 480 7197 516 8845 553 2631 589 8504 658 9975 728 8314 799 3230 870 4-452 942 1718 1014 -4782 SHOCK G R KFT 3 5160 3 5228 3 5297 3 5365 3 5502 3 5639 3 5775 3 5912 3 6049 3 6186 3 6459 3 6733 3 7007 3 7280 3 7554 3 7827 3 8101 3 8375 3 864-8 3 8922 3 9469 4 0016 4 0563 4 1111 4 1658 1860 4 2752 1410 4 3299 4 3847 4 4394 4 5420 1058 0786 0434 0224 0104 3 8223E-03 •L4219E-04 -1 0941E-03 4 6446 4 7472 4 8498 4 9524 5 0550 HORIZONTAL DYNAMIC IMPULSE PSI-SEC 7328 200 Table 20 DYNAMIC PRESSURE AND Il1PULSE VERSUS TIME BASED ON NEW EM-1 PEAK OVER PRESSURES 40 KT YIELD HEIGHT OF BURST 2 394 KFT GROUND RANGE 1 4645 KFT PEAK OVERPRESSURE 10 1451 PSI FREE AIR TIME OF ARRIVAL 1171 5790 MSEC PEAK OP T TA 25 0000 PSI PEAK DYNAMIC PRES 12 2166 PSI PEAK HORIZ COMPT 7 4733 PSI DYNAMIC POS PHASE 799 7040 MSEC TIME MSEC 1174 0919 1176 614-4 1179 1467 1181 6887 1186 8017 1191 9533 1197 1432 1202 3713 1207 6374 1212 9412 1223 6616 1234 5310 1245 5479 1256 7108 1268 0182 1279 4688 1291 0609 1302 7931 1314 6639 1326 6719 1351 0936 1376 0463 1401 5186 1427 4988 1453 9756 1480 9378 1508 3741 1536 2736 1564 6254 1593 3516 1639 2109 1686 9132 1736 3508 1787 4253 1840 0471 1894 1335 1949 6031 2006 4002 DYN IMPULSE HORIZ TIME-TOA DYN HORIZ COMPT PSI-MSEC MSEC 18 6514 37 1198 55 4053 73 5075 109 1622 144 0838 178 2729 211 7307 244 4592 276 4608 338 2948 397 2649 453 4105 506 7785 557 4225 605 4021 650 7825 693 6334 734 0285 772 0451 84-1 2431 2 5128 5 0353 7 5676 10 1097 15 2227 20 3742 25 5641 30 7922 36 0583 41 3622 52 0825 62 9519 73 9688 85 1317 96 4392 107 8897 119 4818 131 2140 143 0848 155 0928 179 5145 204 4672 229 9395 255 9197 282 3965 309 3587 336 7950 364 6945 393 0463 421 7726 467 6318 515 3341 564 7717 615 8463 668 4681 722 5544 778 0290 834 8212 901 9128 954 7382 1000 4085 1039 6051 1072 9912 1101 2035 1124 8451 1144 4811 1161 3552 1182 3629 1196 9555 1206 373 1212 0088 1215 0785 1216 5191 1216 9961 1216 95' ' 8 HDRIZDNTAL IIY AMIC SHOCK G R PSI KFT 7 3717 7 2709 7 1709 7 0717 1 4713 1 4781 1 4850 1 4918 1 5055 1 5192 1 5328 1 5465 1 5602 1 5739 1 6012 1 6286 1 6560 1 6833 1 7107 1 7380 1 7654 1 7928 1 8201 1 8475 1 9022 1 9569 2 0116 2 0M 4 2 1211 2 1758 2 2305 2 2852 2 3400 2 3947 2 4973 2 5999 2 7025 2 8051 2 9077 3 0103 3 1129 3 2155 6 8756 6 6828 6 4932 6 3068 6 1238 5 9442 5 5949 5 2591 4 9368 4 6281 4 3328 4 0508 3 7819 3 5260 3 2828 3 0520 2 6266 2 2472 1 9108 1 6145 1 3551 1 1294 9343 7669 6287 5444 3777 2434 1464 0813 0403 0162 3 0B31E-03 -3 3292E-03 IMPULSE PSI-SEC 1 2169 201 REFERENCES Brode Harold L Height of Burst Effects at High Overpressu res The Rand Corporation RM-6301-DASA 1970 DASA report 2506 ----- Theoretical Desc'Piption of the Blast and Fireball for a Sea Level Megaton Explosion The Rand Corporation RM-2248 1959 Needham Charles E Martin L Havens and Carolyn S Knauth Nuclea r Blast Standa Pd 1 kT Air Force Weapons Laboratory Report AFWL-TR-73-55 rev April 1975 202 APPENDIX NEW ANALYTIC FIT FOR REVISED EM-1 CURVES The new fit takes advantage of the similarities evident in the family of HOB curves from 1 0 to 10 000 psi The behavior along the x-axis zero HOB is that of a surface burst for which overpressure can be expressed as a simple function of ground range PD 6 48 1 2518 X 3 9727 2 924 psi A 1 X Along the vertical axis zero ground range the behavior is approximated by PK y 11 049 1 3069 6 0481 y 3 4793 psi A 2 in which x and y are in kft kT113 Along a curve through the maximum horizontal range for each isobar y RA in Fig A l the pressure is expressed by 8 7266 PE 1 7934 441 830 x · x3 4227 1 28 242 x9 661 S RA 2 2643 4 8336 - 0 21915RA A 3 1 1 0453 RA where the curve Y RA 0 00009686 x 2 · 045 0 6857 x 0 · 4906 0 1176 XQ 01869 3 962 - 0 02255 1 296 5 X • 203 A 4 _ y Region III y RM x N 0 -1 -- RF y AA Region r X Figure A 1 Typical isobars and fit regions Along a curve through the relative minimum above the knees y RM in Fig A l the pressure is approximated as RI 3 71 RI l 45 0 7555 - 2 317 y 0 3074 RF 4 106 y 1 291 2 236 1 006 y 2 286 1 0 171 0 056 _-_4_ _ PJ 14 35 y A 5 RI 4 716 ' 10 3 -y 1 · 803 1 230 8 y 2 · 132 0 5642 • A 6 Interpolating between the pressures along the four curves y 0 x 0 y RA x and x RF y defines peak overpressure for any height of burst y and range x The interpolation is not linear and differs in each region region I between y M s 0 and y In RA 1 - FC PD FC •PE A 7 where FC FB 0 433 l OllFB 1 0 444 FB 5 and FB i__ RA In region II between y RA x and x RF y SP s ° ' FO •PL 1 - FP • FC •PE 205 A 8 where FO 0 7717 FN 2 743 0 2283 FN o 7 y y - RA FN RM RM - RA ' FP FO 1 0 00594 1z2 2 565 4 y 4 x PL ' 1 - FH PK FH • PJ FH 0 _09284 FG l 0286 7 696 FG 2 513 1 7 4836 FG 2 · 151 FG _ _ RF and RM -0 09175 1 -0 3896 X 0 00 3582 31 31 x 3 · 106 0 6907 0 4597 X 0 005963 1 - 0 2021 x 0 · 4696 x1 · 106 In region III D P s --PL A 9 This fit provides a continuous analytic approximation to the new and improved peak overpressure curves recommended for EM-1 206 CHAPTER 8 CAVITY DECOUPLING OF UNDERGROUND NUCLEAR EXPLOSIONS Robert M Henson Eugene T Herrin William E Ogle Frank J Thomas 207 DECOUPLING FACTOR Two definitions for the seismic decoupling factor are as follows • Experimental The decoupling factor is the ratio of the amplitude of the teleseismic p-wave from a tamped shot to that from a cavity-decoupled shot of the same yield both signals observed at the same distance from the source • Theoretical The decoupling factor is the ratio of the re- duced displacement potential RDP for an equivalent elastic source for a tamped shot to that for a cavity-decoupled shot The RDP is the proper measure of source strength for gener- ating teleseismic p-waves based on the theory of elasticwave propagation The log to the base 10 of the RDP is directly proportional to the teleseismic magnitude 1 of the event The optimum decoupling ratio the ratio for a fully decoupled shot is defined as the decoupling ratio obtained when the following two conditions are met -·---------------- From calculations that assume an ideal granite medium and experimental results in a salt dome the optimum decoupling ratio · _J L--·-- -- -_________________J The shape of the curve relating decoupling ratio to scaled cavity radius is based on calculations for ideal granite and is shown in Fig 1 208 At practical depths of about 1 km the required cavity sizes are as follows where R is the cavity radius required for optimum decoupling and W is the yield in kilotons In Fig 1 for ideal granite the ordinate is the RDP or equivalent source size for generating teleseismic waves -------------------------- -·-------------- _ -Figure l Final RDP vs scaled initial source size 209 SIGNIFICANCE OF CAVITY DECOUPLING TO TREATY VERIFICATION To calculate the pertinent yields for possible evasion of a Comprehensive Test Ban Treaty CTBT using cavity decoupling we assume that - -ffl i ----------------•---- _ __ ---• --- d' --J The above conclusions are illustrated in Fig 2 which shows the e relation ships between yield magnitude and cavity radius for optimum decoupling Reducing the cavity size or increasing the yield beyond the given values would result in a higher detection probability and might be unacceptable to a careful evader Miningc in salt is a major undertaking j - I j -_ - -- l• l-_ __ _ l' ' - -• i l i - _ _ _ _ w -- •• -- • -7-- -••_J We conclude from the stated assumptions and criteria that a yield _ ___ ---- --- could be fired in a decoupling cavity in salt 210 r I i l l Figure 2 Magnitude-yield relations for tamped and decoupled explosion_s 211 with an acceptable probability of seismic detection depending on the time and effort expended in constructing the cavity j----- ---- --- NONSEISMIC TECHNIQUES Electromagnetic Pulse EMP A decoupling cavity is likely to enhance the electromagnetic signal from an underground nuclear test That is the EMF source should be larger than that from a tamped explosion with the same We conclude that this subject requires additional theoretical analysis and perhaps numerical calculations for realistic salt dome models but that no requirement currently exists for an underground nuclear explosion in order to study the phenomenon Ionospheric Shock The surface motion directly above an underground test in a decoupling cavity and its effect on the ionosphere should be subject 212 Figure 3 Schematic of decoupling cavity in a sa1t dome to decoupling factors s i J nilar to those associated with teleseismic signals It is expected that the ground surface displacements for an optilnrnn decoupling cavity will be reduced below those for a normal L_____________ -•----- ---·-_l rh - · --· probably be studied at reasonable cost by adding on experiments to future underground nuclear tests coupled nuclear experiment in salt--or any other medium--should not 213 significantly change that conclusion We make the following specific recommendations 1 DNA should not invest in a nuclear cavity decoupling experiment at this time 2 DNA should support and cooperate with DARPA in highexplosive tests directed toward understanding the phenomenology of earth motion from decoupled shots 3 Should DNA field an underground nuclear test to explore coupling of near-surface bursts add-on experiments should be included that relate particularly to nonseismic techniques that might improve our capab lity for detecting decoupled explosions 214 CHAPTER 9 TESTING ·RESPONSE TO FIREBALL ENVIRONMENTS NEEDS AND TECHNIQUES Harold L Brode 215 PREFACE Many structures military systems and vehicles are targeted for nuclear attack yet few have been exposed to nuclear explosions-though most have clear vulnerabilities to blast and thermal effects In no case has a complete system been demonstrated as hardened -able to resist the full impact at design levels of a nuclear threat Hardened elements are nevertheless associated with all strategic systems such as the silos that protect land-based missiles and the communication links for control and connnunications centers High levels of protection are required for all egresses and communications for underground command centers and they would be important for superhard reserve missile storage sites Many aspects of air defense and antiballistic missile defense systems also require hardening In virtually all cases designs for survival of surface elements remain untested in the nuclear environment Such a heavy dependence on theory and hypothesis in ensuring the nuclear hardness of vital military equipment or structures has no precedent in other military nonnuclear systems Ample field-testing and realistic exposure to threat weapons is the least we can expect in the certification process for a nonnuclear system Generally passive survival for systems with exposed elements depends on hardening and wide separation between redundant elements that is system survival depends on dispersal and numbers as well as on hardness While the number and separation of elements whether missile silos or communications tie-points to a superhard center are both important the achievable hardness for individual elements usually governs system feasibility and cost With regard to surviv- able communications for a facility deep underground if antennas Some suggested basing modes particularly the MX concept rely on location uncertainty as a partial substitute for dispersal and hardness even so appreciable hardness is necessary to limit the deployment area An ordinary transport vehicle or truck can be damaged at 2 psi 14 kPa and it is within current Soviet capabilities to cover the entire western United States with more than 14 kPa 216 cable tie-ins or repeater stations cannot be hardened at or near the surface to the 1000 psi 7 MPa level but can be guaranteed only to the 100 psi 700 k Pa level then wider separations requiring much longer connections tunnels or cable drill-holes must be constructed the consequent system costs rise significantly Longer tunnels and drill-holes increase the chances of crossing major earthquake faults or other abrupt geologic discontinuities accompanied by a greater chance of gross displacements that can cause tunnel disruption and cable breaks In the end however it is important to ensure that all the hard-surface tie-points are at least as difficult to destroy as the central sometimes deep facility How can we test surface features As the overpressure levels rise from hundreds to thousands of pounds per square inch blast simulation with high explosives rapidly becomes impractical and ultimately impossible At present only a shock tube driven by a large volume of exceedingly high-temperature air appears able to create a nuclear fireball environment on a scale appropriate for fullscale or even scaled-down model structure exposures A nuclear explosive device promises the only known practical means of providing an adequate volume of air plasma at temperatures and pressures high enough to simulate blast waves from a nuclear fireball The response of structures in fireball environments is complex and theoretical treatments are too sketchy to be credible without experimental verification Exposures on past nuclear tests have been too limited to extrapolate to relevant materials and configurations No proposed simulators driven by chemical explosives can hope to create either the high dynamic pressures or the high fireball gas temperatures of a nuclear explosion but a nuclear-driven shock tube in an underground tunnel could generate a realistic large-yield high· • overpressure blast environment It remains to be demonstrated that such a facility could function adequately Questions of containment and safety are of paramount importance Massive wall losses and early tunnel collapse could pre- clude useful tests Adequately designed and tested instrumentation must be available to accurately record both fireball phenomena and 217 structure response Such instruments and techniques have not yet been verified What follows is a paper first prepared more than 12 years ago and subsequently rewritten at least twice drafted to support the concept of an underground nuclear test for fireball exposures need continues and the techniques are now better known tion we address here is What are the current prospects 218 The The ques- SECTION 1 INTRODUCTION Many modern military systems are intended to withstand the effects of nuclear bursts The present missile-basing systems and most ICBMs are designed to survive at very high blast and radiation levels Current missile silos already provide protection from hundreds to thousands of pounds per square inch at megapascal levels of peak overpressure from nuclear blasts Some follow-on missile systems have been planned or designed to withstand thousands of psi We also conceive of active defense systems that can continue to operate during a nuclear attack and believe they must have an appreciable degree of protection from nuclear effects High-level nuclear attack survival is particularly pertinent to command and control facilities and other military contexts in which hardness counts because opportunities for redundancy or mobility are limited It is important that communication links and intelligence facilities be made to survive along with the commanders and communicators who will operate the surviving weapon systems Even tactical systems in a nuclear warfare environment must often rely on high-level protection to gain survivability In all these military systems some surfacesstructures and some near-surface mechanisms or connections must be designed to withstand exposure to close-in nuclear weapon effects often at megapascal blast levels thousands of psi At short range they will also experience thousands to tens of thousands of calories per square centimeter of thermal or X-ray radiation 20 to 40 cal cm 2 of thermal radiation will ignite most combustibles and tens of thousands to millions of radians of nuclear radiation 450 rads is a lethal dose for man They may also be subjected to megapascal blast-wind pressures and to impacts with fast-moving debris or crater ejecta Ground motion may be violent with displacement of as much as a meter velocities of many meters per second and permanent damage 219 At the same time much of the equipment must remain operative and undamaged during exposure to extreme electromagnetic transients running to fields of tens of thousands of volts per meter Surviving high levels of blast pressure from a nuclear explosion means withstanding a fireball environment Current hardened missile- basing systems principally the Minuteman have been examined long and carefully to determine if there is any reason to doubt the design level for survival A direct and convincing test using a series of nuclear explosions on a complex of silos launch-control centers and connected facilities was once planned but it has not been possible to carry out the test since the atmospheric test-ban treaty went into effect However much of the nuclear environment has been reproduced and applied piecemeal to operational or scaled test structures Nu- clear radiation and electromagnetic pulse EMP sources have been provided £or testing systems Overpressure loads have been simulated using the high-explosive simulation test HEST technique and have been applied to full-scale hardened structures Such simulations are very helpful and have contributed impressively to our understanding of and confidence in the survival of hardened facilities Some of these tests are however very expensive a nuclear test would not necessarily be much costlier or more timeconsuming than a simulation test Of course only underground nuclear tests are currently possible so even such tests can provide only partial atmospheric burst environments More important piecemeal simulation of specific effects no matter how well done will leave unanswered many questions about combined effects EMP without ground shock or nuclear radiation may miss some vulnerabilities Structure response to overpressure loads without accompanying drag forces may be misleading • Unfortunately none of the simulation techniques offers complete verisimilitude In some cases the nuclear phenomena are not known well enough to be sure what to simulate e g direct ground shock or debris characteristics Some phenomena still defy simulation at all especially the very intense blast and thermal regime of the nuclear fireball 220 Below in support of further investigations of the effects of fireball exposure we briefly review close-in nuclear burst phenomena the fireball environment and the expected effects on exposed structures We list outstanding close-in vulnerability questions compare alternative fireball simulation and investigation techniques and suggest advantages and disadvantages of each concept is given particular attention The nuclear-shock-tube The use of get-lost holes for disposing of nuclear fission products from nuclear explosive devices is proposed as a feasible method of reducing postshot radiation hazards thus aiding reentry and the recovery of experimental information 221 SECTION 2 FIREBALL ENVIRONMENT Since successful designs for survival inside nuclear fireballs must rely on our incomplete knowledge of close-in phenomenology they must demonstrate an insensitivity to the expected variations in fireball features Test observations from earlier atmospheric bursts com- bined with theoretical calculations of radiation transport and dynamic motions have provided a fairly detailed and presumably accurate picture of free-air bursts yet those descriptions of close-in phenomena are by no means complete In most cases the greatest uncertainty lies not in the phenomena themselves but in the response of exposed materials and in the mechanisms by which damage is done For example free-air fireball temperatures and pressures may be fairly well predicted by detailed calculations and confirmed from observations made during previous atmospheric tests but the responses of such material as concrete and steel to high heat and stress loads are not well known because they are so hard to calculate and difficult to measure In fact few of the boundary phenomena at surfaces--of either earth or structures-are understood or can be predicted More important the basic reflec- tion phenomena from bursts on or near the earth's surface are only partly understood The table below suggests some levels of environmental effects within a fireball in the absence of surface interaction complications The levels represent exposures generally not achievable using conventional nonnuclear simulation techniques even for small-scale model structures or instruments Reproduction of the indicated pressures temperatures and flow rates becomes essential in testing to confirm the survivability of structures or facilities within fireballs--that is for peak overpressure exposures above l MPa As an example consider what can be expected a quarter mile 0 40 km from a l MT burst The peak overpressure is around 1600 psi 222 Close-in weap0n effect levels Effect N N w 1 4 mi Range 1 2 mi Range 1 mi range Yield surface burst 100 kT 1 MT 10 MT 100 kT 1 MT 10 MT 100 kT 1 MT 10 MT Peak overpressure psi 130 1 600 15 000 32 224 1 900 7 3 38 270 Overpressure impulse psi-sec 12 70 320 5 27 160 2 2 11 60 Blast duration sec 0 43 1 3 3 2 0 53 1 2 8 1 1 1 2 1 Peak wind velocity ft sec 3 000 9 300 28 000 1 000 3 400 10 000 300 900 3 700 Peak dynamic pressure psi 250 4 800 70 000 18 370 6 000 1 1 23 430 Drag impulse psi-sec 7 4 28 95 2 3 17 5 62 0 32 6 40 Wind duration sec 1 2 2 4 5 2 1 3 2 5 5 2 1 3 2 8 5 4 Shock-temperature rise °C 600 3 800 15 000 130 770 4 300 34 150 860 Maximum air temperature rise °C 2 400 5 5 5 4 5 5 43 000 3 5 7 130 3 700 2 3 6 50 000 3 1 8 34 580 150 3 8 4 4 800 7 2 6 4 s 6 110 000 4 l g 4 5 7 1 7 5 1 7 6 100 1 000 10 000 U CL 1 25 3 5 10 8 0 62 1 4 3 9 0 44 0 66 1 5 Maximum vertical acceleration g 21 180 1 700 2 1 25 220 0 52 2 4 31 y-ray dose R a Neutron dose rnd a 3 5 4 1 7 4 Soil CL 400 ft sec Maximum vertical velocity ft sec 2 3 20 180 2 1 2 8 24 0 52 2 4 3 4 Maximum vertical displacement ft 0 13 1 3 12 0 14 0 33 3 3 0 036 0 36 0 83 Maximum horizonta displacement ft 0 07 0 7 6 0 14 0 17 1 6 0 036 0 36 0 4 Rock CL J 000 ft nee Us CL 0 25 o 70 2 15 0 12 0 28 0 78 0 09 0 13 0 3 Maximum vertical acceleration g 1 6 7 6 334 0 4 1 9 9 0 0 10 0 48 2 2 Maximum vertical velocity ft sec 1 2 5 7 27 0 31 l 4 6 6 0 08 0 35 1 6 Maximum vertical displacement ft 0 08 0 85 1 8 0 02 0 21 2 0 005 0 05 0 5 Maximum horizontal displacement ft 0 08 0 85 0 9 0 02 0 21 2 0 005 0 05 0 5 8 Hot day 97°F near sea level or cold day 46°F at 3 600 ft pa 1 1 kg m3 11 MPa with a positive phase impulse of about 70 psi-sec 0 5 MPasec lasting 1 3 sec a peak blast wind of 9300 ft sec 2 8 km sec a peak dynamic pressure of 4800 psi 33 MPa and a drag impulse of 28 psi-sec 0 2 MPa-sec over 2 4 sec of positive blast wind The shock-temperature rise at this range 1 4 mi from 1 MT is 3800°C increasing to 43 000°C as the fireball expands beyond that range A gannna-ray dose of about 35 million R 350 thousand grey and a neutron dose of around 4 5 million rad 45 thousand grey can be expected Ground motions in soil of 180 g 20 ft sec 6 m sec maximum vertical velocity and vertical displacements of 1 3 ft 40 cm are possible Each explosive level listed in the table occurs within one or two seconds so that as high pressures are applied high temperatures large ground motions and high doses of nuclear radiation are experienced Combined effects may be more serious than any single ex- posure so that the integrated environment should be contemplated in assessing response and possibly in designing simulators 224 SECTION 3 QUESTIONS ABOUT SURVIVAL AND OPERATION IN FIREBALL ENVIRONMENT There have been exceedingly few attempts to measure the blast heat radiation and debris impacts inside the fireball In contrast about 70 nuclear tests have carried blast measurements at peak levels below 100 psi 700 kPa outside the fireball during the more than 20 years of atmospheric testing Consequently many questions about the survival of equipment and installations at the close fireball ranges remain unanswered As noted the strong shock of the fireball can be well described for a free-air burst Unfortunately the fireball blast cannot be so accurately described when it strikes the ground and its features are even less predictable when the burst itself is on near or under the surface The lone good record of a blast near 1000 psi 7 MPa from a megaton surface burst Meszaros et al 1962 is not so good that it can be definitely compared with calculations Although some kiloton-yield records extend into thousands of pounds per square inch there are very few time-histories above a megapascal Ellis and Wells 1966 and very few peak values have been recorded near 1000 psi 7 MPa The lack of data does not stem from a lack of interest in the high-pressure region rather the nearest gauges were often destroyed in nuclear tests before records could be made Although the old test reports catalog the reasons for the failures the unhappy fact is that early equipment performed poorly at high levels Extreme heat enormous dynamic forces violent ground motion paralyzingly high voltages EMP and deadly flying debris combined to destroy or invalidate records from even the most rugged blast gauges One gains little assurance of the survival of extensive complex structures in a region where simple measurements of the environment have proven so difficult 225 It is true however that the very high pressures 10 MPa of c · underground cavity experiment were measured with slightly more success the results lending some credence to the claim that future nuclear tests could provide more J and better measurements of blast pressures in the tens of megapascals However the very low yield - · should be recognized as caus- ing small displacements and thus making gauge survival easier A number of sophisticated calculations agree on predictions of temperatures densities and velocities as well as pressures in an air-burst fireball but there are only indirect experimental observations mostly photographs for confirming or checking the predictions More important calculations for surface bursts or low heights of burst have not yet proven realistic or reliable Direct measurements of dynamic pressure temperature sound speed and other free-field fireball phenomena pertinent to hard-site survival do not yet exist Instrumentation for the ranges in question grow out of simulator efforts but the lack of success on nuclear events leaves some question as to their survivability or reliability The response of structures and materials to the fireball environment has been observed for only a few tests and for even fewer exposures of materials For all test objects exposure was influenced by blast interactions with nearby surfaces--interactions of uncertain nature and extent This old evidence contained many surprises and mysteries not completely understood or resolved even_today 20 to 30 years later Much careful calculation of both the fireball environment and the material response for each exposure must precede any confident understanding of the few observations On the basis of such confirmation we may be able to predict what other materials might do in other locations on other shots using improved and extended calculations But as always ex post predictions lack the credibility of verified true predictions without further confirmation through realistic testing therefore the former will remain quite uncertain At a half-mile from 10 MT see the table above overpressure is 1900 psi 13 MPa but peak dynamic pressure is 6000 psi 41 MPa and 226 peak wind velocity 10 000 ft sec 3 km sec In such a dynamic flow can any projecting structures no matter how small survive Will doors footings or collars forced up above the surface a few inches--or even only a fraction of an inch by differential ground motion --experience loads for which they were not designed At a 13 MPa 2000 psi level the shock temperature is 4600°K but the hot air behind the shock makes the temperature at that range rise to a maximum of 50 000°K in less than 0 10 sec and persist at that level for another fraction of a second The combined high-speed airflow and high rates of material vaporization at such elevated temperatures make the response of sizable exposed surfaces doubly difficult to predict No currently envisaged laboratory or chemical- explosive test facility can reproduce such a high-pressure high-flowrate high-temperature environment over any useful area Since superhot gas flows themselves constitute the blast load simulating the static overpressures alone cannot--even when given the expected time-history of pressure relief--create the same blast environment that a silo door hardened antenna or intake valve would be exposed to at the 10 or 20 MPa level in a nuclear fireball At such high levels of blast and heat exposure only installations wholly below ground--having no surface appurtenances openings closure mechanisms plenums pop-up antennas etc --can be assured of survival without more careful testing Even for the below-grade portions of surface installations lesser questions about the influence of the superhot fast-flowing air of the fireball on structure and contents may not be answered without testing What will be the effect of high-temperature fireball gases intruding into cracks temporarily opened by the passing ground shock Could the fast-flowing gas lubricate the cracks to reduce shear resistance in large rock joint systems thereby amplifying the hazards of block motion These and related questions peculiar to survival in fireball environments could be answered much more confidently by means of a nuclear test Only underground testing is currently possible but a fireball-sized underground chamber is impractical Can a shock-tube configuration driven by the superheated air from a cavity nuclear explosion provide the 227 -------------------------- - appropriate fireball environment -- -- Is a nuclear-driven shock tube practical in both construction time and cost Carpenter Gilmore and Mills 1976 examined both mechanical and thermal mechanisms that might lead to serious failures following exposure to a fireball Mechanical or structural failures included seal blowout by airblast seal ports opened by structural distortion leak ports opened by cracking and eroding of material inadequate geometrical expansion for leakage and insufficient shielding from hot jets through cracks torching Thermal mechanisms were closure weldup and The enlarging effect of erosion and ablation on a crack or hole through which hot gases penetrated was also considered Their report did not answer all the important questions however and further resolution by means of experiments with a 100 MW plasma arc was recommended along with renewed study of the nuclear-driven shock tube 228 SECTION 4 SIMULATION FOR SYSTEM AND COMPONENT TESTING The atmospheric test-ban treaty precludes direct testing of hardened systems in nuclear fireball environments High-explosive simulation of fireball environments has been attempted successfully with a number of different techniques however The high-explosive simulation test HEST --which uses distributed charges of primacord or other distributed explosives that are arrayed tamped and detonated over a structure so as to reproduce the early portion of a static overpressure blast history--has been used successfully up to 35 MPa A kind of self-destructing high-explosive-driven shock tube the DABS facility creates not only the overpressure but also the dynamic flow for pressures up to perhaps 3 MPa The DABS has serious limitations in both cost and accuracy of simulation however since the high-explosive products are blown over the test structures The so-called BOSS or shaped-charge simulator uses a converging wedge configuration of high explosives without a metal liner to shocksqueeze the contained air to very high temperatures and high velocities The BOSS also unfortunately cannot be used to test full-scale structures without exposing them to a later flow of explosion products In addition its use of explosives is extremely inefficient and it becomes very expensive on a large scale It does however create higher temperatures and higher pressures than can ordinarily be obtained with simple charges of high explosive Physics International 1968 If the loading due to very high blast pressures is understood then it is possible to recreate the loads using a shaped HEST or distributed charges of explosives arrayed over the surfaces of a test structure The high temperatures could be simulated on a small scale with a plasma torch so that some studies of ablative erosion and boundary-layer behavior could be carried out--but the simultaneous pressure and velocity of flow effects would be lacking 229 r Again however high-explosiv gases do not behave like air and none of the flow of fireball hot gases is adequately simulated by a shaped HEST To simulate ground motion either as induced by the air blast or directly caused by cratering it is possible to use a set of explosive charges buried in a line or an array in the ground--what is known as the DI-HEST concept If the actual cratering motions are to be recreated the Mine-Throw concept applies in which the detonation of a distributed high-explosive charge simulates the actual earth stresses leading to nuclear-cratering motions Of all these possibilities only the BOSS concept with a shaped charge creating superheated airflows comes close to recreating the fireball environment accompanying megapascal shocks Even it falls short of reproducing the hot air and temperatures in the tens of thousands of degrees Kelvin at high velocities that follow such shocks and it showers test structures with the expanding explosion products Superheated airflow could be the critical factor in causing damage or malfunctioning in the blast valves plenums delay lines closure seals antenna ports or exposed·faces of any hardened structure Failure to simulate the full high-speed high-temperature plasma flows means less than full credibility in the simulation or testing of structural survivability at fireball levels under megapascal pressures A sure way of obtaining the required fireball temperatures and pressures is to explode a nuclear device in an underground cavity However the cavity required for any reasonable explosion would be inordinately large But there is still the possibility of driving the hot air created by a nuclear explosion down a tube section describes such a nuclear-driven shock tube 230 The next SECTION 5 NUCLEAR-EXPLOSION SROCK TUBE The most direct way of achieving air temperatures up to 100 000°K-predicted in a nuclear fireball at the 70 MPa 10 000 psi peak over- C JU-- pressure distance--is with a nuclear explosion Nuclear bursts in large undergr und cavities have been successfully contained c _ _ _J LPJC-½ C J Furthermore the restraining walls of a rock cavern leading into a tunnel are not unlike the geometry of a conventional shock tube which allows testing at considerable distances from a source of high pressure and makes it easier to generate the long durations typical of large-yield explosions In fact the shock-tube configuration with an explosively loaded driver section and a controlled test section has long been a useful blast-simulation technique A nuclear-explosive driver is however an innovation--neces- sary in this case to generate a large volume of driver gas air at elevated temperatures 10 eV One possible mechanism would detonate a small-yield nuclear device in an air-filled cavity to pressurize and heat the air That hot high-pressure volume would represent a shock-tube driver section When allowed to blow into a tunnel with a variable possibly expanding cross section the hot air could create the flow time-history typical of the strong blast from a large-yield weapon A large-yield environ- ment might thus be provided using a small-yield nuclear source An increasing number of successful tests suggest that a valid structure-response test can be conducted when the scale of test structures as well as the scale of the blast is substantially reduced In that case the overall facility need not be on a scale of a full multimegaton burst Structural design -construction and analysis have reached a point where modestly reduced dimensions still allow dynamic similitude in structure response For instance model silos and hardened structures in high-explosive simulations when scaled down to one-quarter all dimensions reduced to one-fourth 0£ those 231 of the original structure have responded dynamically almost like a full-scale structure Johnson et al 1965 Obviously if quarter- scale tests can be convincing then the requirements for an underground test facility can be dramatically reduced With all dimen- sions reduced by 1 4 the blast energy--and hence the yield to be simulated--is reduced by 1 4 3 or l 64th so that a 16 kT yield represents the effect of 1 MT on a quarter-scale structure In addition by channeling the blast energy do-wn a tunnel just a fraction of the 16 kT yield is needed to develop the blast timehistory Simply the requisite fraction of energy can be estimated as the fraction of total solid angle formed by the tunnel cone interacting with a spherical driver section Thus a test section 80 ft wide at a distance of 250 ft from the 16 kT burst 3000 psi would subtend a solid angle of 0 080 sr or 0 0064 of the total sphere That fraction of the 16 kT yield is 100 tons It is far less diffi- cult or costly to build a cavity to contain 100 tons of nuclear yield than it is to build one for a yield of several kilotons Many questions arise in developing this concept the driver section be to avoid gross wall motions How big must If a spherical driver chamber blows into a conical test section will the adjacent walls shear off in the driver chamber and spoil the shock-tube geometry or cause excessive debris Must the driver section have a volume com- parable to the shock-tube volume Must the tube be conical to produce a decaying blast wave Some of those questions have been previously investigated by the Defense Nuclear Agency with answers encouraging enough to make the concept's general feasibility apparent Lewis 1968 The design becomes more uncertain when effects additional to the high-level blast wave are to be modeled simultaneously It is conceivable to simultaneously create prompt radiation direct and air-induced ground shock and even EMP and thermal radiation with the same or another nuclear source But to do so would require further modification as well as much more sophisticated analysis and theoretical calculations in support of planning 232 Our first objective in investigating the feasibility of a nuclear shock tube has been to show that some reasonable configuration should produce the desired blast history Although many further improvements are likely the simplest configuration for calculation is a nearly spherical driver chamber feeding a cylindrical or conical tube and test section The first calculations were for a driver chamber about 11 min radius centered on a 100-ton-yield nuclear device a spherical model Subsequent calculations investigated the effects of yield and cavity-size changes While more calculations followed sponsored by DNA at The Rand Corporation and Physics International Physics International 1968 the feasibility of a facility to test component and structure response to a true fireball environment seemed already established The concerns sometimes raised over the rate of growth of boundary layers and the consequent choked flow in the test section were allevi- - ' J 19 I l l - - r- _ _ J nl _ _- 'Zl- v o JF- tl - i r l i 9 1 - -•• • - 1w - l ' - 1 -' S' l 3 l -• _ - r _ J r 'l» W 't 1f l1'i 'i W _• - JrC'° i- • 233 SECTION 6 PRETESTS Serious questions arise concerning the novel nuclear test configuration proposed To answer some of them we suggest that a small preliminary nuclear shot in a similar geometry be considered and a study be made of the most questionable features and the potential difficulties identified Some questions to consider not necessarily in order are How serious is wall ablation effect of wall smoothness on strong shock propagation What is the Row can the test section be protected from rock failures upstream in the shock tube or in the driver chamber shot room How can the upstream walls rock be controlled and kept from interfering with the fireball exposure experiments downstream Further questions are Would lining and rock-bolting add measurably to rock control ·o would they contribute to the hazards What late-time problems exist for stemming or for preventing cavity collapse or further extraneous damage to the test section Can the shock propagation and radiation flow reproduce the predicted environment in the test section expected What reflected shock perturbations can be How well can the radioactive debris be prevented from contaminating the test structures What are the problems in ensur- ing reentry into and postshot examination of the test sections In addition what measurements can be made Can overpressure dynamic pressure velocity and temperature measurements be made with sufficient accuracy to improve our understanding of fireballs What ins-trument development and testing is necessary or desirable Clearly the experiment would be of limited use if the data derived from it were no more accurate or reliable than previous measurements or the results of detailed calculations However even a poorly instrumented test promises to provide a benchmark for theoretical work on both e - - r s_ · -· - I 234 Since the earlier efforts at measuring fireball levels much has been accomplished in instrument development and verification calibration--virtually all relevant to the concept of underground-cavity nuclear tests Questions remain however Can we expect signifi- cantly improved knowledge of the fireball environment Can the re- sponses be measured accurately enough to justify the expense and effort involved 235 SECTION 7 TEST OBJECTIVES The obvious goal of a nuclear-shock-tube test is to expose scale-model or prototype missile shelters or silos and surface elements of similar superhard systems to nuclear effects A more gen- eral but perhaps equally valuable set of test objects would include blast valves doors or closures antennas sensors plenums and delay lines for any hardened system hopeful of survival and operation at high blast levels Basic response tests should be considered for various types of metal rock metal rock interfaces concrete moving parts and bearing surfaces and components requiring controlled dimensions such as radar or communications antennas and some types of sensors Of additional great value would be experiments on the physical effects of heat and pressure on both natural and constructed materials--experiments that lead to extreme temperature and pressure transient loads The physics of fireballs--particularly in the presence of surfaces and solid objects--is uncertain and could be studied in such a test In fact some measurements might be carried out quite re- liably and simply underground outside the burst chamber down the shock-tube drift Such measurements have proven extremely diffi- cult in above-ground tests • ' • • 236 SECTION 8 METHODS FOR REDUCING RADIOACTIVE CONTAMINATION OF TEST SECTION Twenty-three years ago it was common to conceive and carry out atmospheric tests for both weapon development and research on weapon effects However the problems in modeling atmospheric bursts are formidable and underground nuclear tests have been used for only limited simulations mostly of exoatmospheric X-ray effects A full- scale nuclear surface burst is best for simulating the ·effects of a nuclear surface burst but a nuclear surfac·e burst in an underground cavity requires such a large excavation that it is impractical One possible mechanism for making such an underground cavity test - -- - ---·---- ---- more useful and more appropriate for e ig2os_i ng_s tn1ctJJTes-in-E n- -a-d -a-c----e±1nctt -----shock tube would be to include a get-lost hole --a tube or drill-hole behind the nuclear device into which most of the radioactivity can be driven and within which it can be contained The rudimentary concept was demonstrated r-•• - -- - -- - 7 -·- in which a drill-hole below an underground test accepted and trapped a great fraction of the radioactive debris from the device The con- cept can be elaborated to the extent that a special test device can be designed to not only produce a nuclear explosion but direct most of the radioactive fission fragments into a pipe that leads below ground The pipe can then be closed by techniques already common in down-hole or vertical line-of-sight open-hole experiments The task of containing the debris and a small fraction of the energy of a nuclear blast--with the bulk of the energy already outside ··· to assist in closure--should be much simpler than that of closing off conventional explosions where most of the explosion energy works to blow out the closures Obviously an underground demonstration of such a device is desirable before its use as a surface-burst simulator is approved An underground test with backup containment could further confirm the feasibility of the get-lost hole concept and 237 demonstrate the adequacy of instrumentation as well as verify theoretical calculations A successful test of the get-lost hole in connection with a shock-tube test would ensure an uncontaminated test section and allow earlier reentry and data recovery The design details of such a device are the proper business of Department of Energy weapon designers Preliminary discussions with Lawrence Livermore Laboratory staff some of whom originated the get-lost hole concept suggest that a special design is within present capabilities and could be worked out in timely fashion if desired that is if money and official sanction were forthcoming Beyond its considerable importance to a nuclear-shock-tube test a surface-burst simulation capability with reduced residual radiation could lead directly to repeated and simultaneous testing of many structures in fireball environments More important it offers an otherwise unattainable opportunity to simulate the prompt nuclear radiation and the close-in EMP fields important aspects of which are not now calculable The return currents in the ground and the dynamics of intense close-in nuclear radiation heating with induced activity or n y reactions in solid and construction materials need experimental investigation and confirmation Not all aspects of cloud rise dust debris and ejecta phenomena from nuclear bursts can be simulated with chemical-explosive bursts At the same time realistic calculations are extremely dif- ficult to both formulate and accomplish--yet are usually incomplete and unreliable Such phenomena are beyond the simulation ability of current underground test concepts The cratering from an underground nuclear device cannot be said to reproduce the initial conditions of an operational weapon delivery or a real warhead Even so it will yield radiation levels and reproduce energy densities much more like those of a real burst than any high-explosive charge could generate X-rays can be made to shine from such a source device and hundreds to thousands of megabars of pressure can be delivered to the g·round surface in the immediate vicinity Any chemical explosive is limited to fractions of a megabar and to temperatures of a few thousand 238 degrees Although detailed replication of yields masses and geom- etries of interest to coupling studies is thus unlikely the general features of nuclear bursts important to coupling can be reproduced and studied in greater realism than by any other simulation short of full-scale operational weapon tests 239 BIBLIOGRAPHY Air Force Systems Command Systems Applications of Nuclea l' Technology Effects of Air Blast Ground Shock and Cratering on Hardened Struc-tu res Air Force Systems Command Manual AFSCM 500-8 1 March 1967 Brode H L A Review of Nuclear Explosion Phenomena Pertinent to Protective Construction The Rand Corporation R-425-PR May 1964 Review of Nuclear Weapons Effects Ann Rev Nuc Sci Vol 18 1968 Carpenter H J F R Gilmore and A F Mills Sealing Facilities against Nuelea P Fireball Effects R D Associates RDA Report TR-2006-007 November 1976 Ellis P A and P B Wells High Pressure Surfae e Airblast Phenomena Kaman Nuclear KN Report 66-207 R 13 May 1966 Glasstone S and P J Dolan eds The Effects of Nuclear Wecrpons 3d ed U S Department of Defense and U S Department of Energy -197J ------- Johnson J E et al Simulation of Air-Blast-Induced Ground Motions Phase II Vol II Air Force Weapons Laboratory AFWL Report TR65-26 May 1965 Lewis J Defense Atomic Support Agency personal collllil unication 1968 Meszaros H et al Airblast Phenomena and Instrumentation of Structures Oper Hardtack Ballistic Research Laboratory Report WT-1612 16 July 1962 Moulton J F Jr ed Nuclear Weapons Blast Phenomena Defense Atomic Support Agency DASA Report 1200 March 1960 Physics International informal discussions and papers for the Defense Atomic Support Agency 1968 Sauer F M 3d Nuclear Geoplosics Vol IV Empirical Analysis of Ground Motion and Craterir q Defense Atomic Support Agency DASA Report 1285 May 1964 C 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