Destructive Effects of Nuclear Weapons

q The generation of a mechanical shock through sudden increase of pressure causes mechanical damages Blast damage Thermal damage q The generation of a heat wave expanding with the shock causes Radiation damage incineration EM-pulse q The distribution of radiation through Short range and atmospheric fallout causes short term and long term radiation sickness effects q Electromagnetic shock leads to break-down of communication systems 0.10 ms The mechanical shock

0.24 ms shock velocity: vs sound speed: cs specific heat: g=1.4 0.38 ms peak pressure: p

air pressure: p0=15 psi wind velocity: vw 0.52 ms pressure dynamic pressure: q

0.66 ms g +1 p p vs = cs × 1+ × = cs × 1+ 0.86× 2×g p0 p0

0.80 ms -1/ 2 c × p æ g +1 p ö p c v = s ×ç1+ × ÷ = 0.715× × s w ç ÷ g × p0 è 2×g p0 ø p0 1+ 0.86× p p0 0.94 ms p2 p2 q = = 2.5× 2×g × p0 + (g -1)× p 7 × p0 + p Example Depending on the peak pressure (atmospheric pressure 15 psi) and the speed of sound (cs=330 m/s in atmospheric gas) you receive the following values for shock and wind velocity and dynamic pressure p0 vs vw q psi m/s m/s psi 1000 2777 2309 2262 p 500 1981 1619 1033 v = c × 1+ 0.83× s s p 300 1552 1240 556 0 200 1285 999 328 100 946 680 122 p cs vw == 0.715× × 50 718 448 40 p0 1+ 0.86 × p p0 30 603 321 17 20 537 241 8 p2 q = 2.5× 10 461 141 2 5 418 78 1 7× p0 + p 3 400 49 0 2 390 33 0 1 380 17 0 Shock characteristics

Shock on flat surface causes reflection which is expressed

by reflected overpressure pr!

7p0 +4p pr = 2p +(g +1)×q = 2p× 7p0 + p

pr »8p for large dynamic pressure

pr » 2p for small dynamic pressure Example shock front against house example

7p0 +4p 250 kT blast Nevada 1953 pr = 2p +(g +1)×q = 2p× 7p0 + p effect on houses in different peak pressure reflected pressure distance from center of blast

p0 pr pr/p0 psi psi 1000 7430 7 500 3479 7 300 1933 6 200 1187 6 100 493 5 50 197 4 30 100 3 2.65 miles 20 59 3 10 25 3 5 11 2 5.3 miles 3 7 2 2 4 2 The American Home Shock expansion

Shock expands radially from explosion center.

Amplitude decreases, but after time t5 the pressure behind shock front falls below atmospheric pressure, Under-pressure which causes the air to be sucked in. Pressure conditions with transversing shock

1. Shock hits 2. generates strong wind 3. Shock decreases 4. Underpressure 5. Wind direction changes 6. Normal air pressure 7. Wind calms down Pressure induced wind effects Distance Effects

Scaling for blast intensities 1/3 D = D1 ×W

100 kT e.g. the effect which occurs for a 1 kT blast at distance 1 kT D1 occurs for a 100kT blast at distance D. D1=10,000ft ðD=24,662ft Peak over pressure as function of distance for a 1kT blast Scaling laws for blast effects Shock/blast expands over volume ~d3, the following scaling law can be applied for estimating distance effects between different blast strengths

3 1/ 3 W æ d ö æ W ö ç ÷ ç ÷ = ç ÷ Þ d = d 0 ç ÷ W0 è d0 ø èW0 ø

Normalized to a standard 1kT blast the following expression can be applied:

1/3 d = d1 ×W Distance effects of airburst

1/3 æ W ö 1000 1/3 ç ÷ æ ö d = d0 ×ç ÷ = d0 ×ç ÷ =1.7 × d0 damage comparison for W è 200 ø è 0 ø a 1000 kT and a 500 kT 1/3 æ 500 ö bomb using the scaling law = d0 ×ç ÷ = 1.35× d0 è 200 ø with respect to 200 kT bomb Scaling in Altitude

1/3 h æ W ö d h 1/ 3 d = ç ÷ = often scaled = W = ç ÷ to W = 1 kT h1 èW1 ø d 1 1 h1 d 1

Similar scaling relation for altitude dependence of blast effects. For altitudes less than 5000 ft (1700 m) normal atmospheric Conditions can be assumed. For higher altitude effects changes altitude dependence of air pressure and sound speed need to be taken into account. Peak overpressure in height & distance

Suppose you have 80 kT bomb at 860 ft height, what is the distance to

which 1000psi overpressure extends? Normalization: W 1=1kT h 860 Corresponding height for 1kT burst h1 = 1/3 = 1/3 = 200 ft (or scaled height) W 80 1/3 1/3 Distance of 1000 psi overpressure d = d1 ×W = 110 ×80 = 475 ft Surface burst versus airburst

Suppose you have 500 kT bomb at 1.1 mile height, what is the distance to which 2 psi overpressure extends and compare with ground zero detonation. 1/3 Scaled height for 1 kT bomb; h1 = h/W = 0.14 miles ˜ 765 ft. This corresponds to d1 = 3800 ft = 0.69 miles. The distance for the 2 psi overpressure on the 1/3 1/3 ground from the 500 kT blast would be d = d1·W = 0.69·500 = 5.5 miles. 1/3 1/3 Surface burst: d1=2500 ft=0.45 miles, d = d1·W = 0.45·500 = 3.6 miles. Blast effects on humans Thermal effects Approximately 35 percent of the energy from a nuclear explosion is an intense burst of thermal radiation, i.e., heat. Thermal effects are mainly due to originated heat from blast which expands with wind velocity and incinerates Thermal everything within expansion 35% radius. The thermal radiation Blast from a nuclear explosion can 50% directly ignite kindling materials. Ignitable materials outside the house, such as leaves, are Initial Fallout not surrounded by enough Radiation10% combustible material to generate 5% a self-sustaining fire. Fires more likely to spread are those caused by thermal radiation passing through windows to ignite beds and overstuffed furniture inside houses. Thermal Energy Release

For a fireball with radius r the heat emitting surface is: S = 4p ×r 2

Total energy emitted per cm2 and second is described by the Stefan Boltzmann law

J = s ×T 4 ; s = 1.36×10-12 cal cm-2s -1deg -4

Total thermal energy emission from fireball is therefore:

2 -7 4 2 P = S × J = 4p ×s ×T4 ×r =1.71×10 ×T ×r cal / sec

With radius r in units m and temperature T in Kelvin The thermal power of the fireball changes with time. Thermal energy release should be expressed in terms of maximum power Pmax (scaled power) and in terms of scaled time tmax which corresponds of time of the maximum thermal energy release from the fireball. For air bursts below 15,000 ft altitude the maximum power Pmax & the maximum time tmax are related to the bomb yield W (in kT)

0.56 Pmax » 3.18×W kt / sec

0.44 tmax » 0.0417×W sec

e.g. for a 500 kT burst in 5000 ft altitude:

0.56 Pmax » 3.18×500 =103 kt / sec

0.44 tmax » 0.0417×500 = 0.64sec The total amount of thermal energy emitted at t=1sec is: t 1 P = =1.56; = 0.59; tmax 0.64 Pmax

12 P = 0.59× Pmax = 0.59×103 = 60.8kT / sec = 60.8×10 cal / sec Hiroshima firestorm

Fires can result from combustion of dry, flammable debris set loose by the blast or from electrical short circuits, broken gas lines, etc. These fires can combine to form as terrible firestorm similar to those accompanying large forest fires. The intense heat of the fire causes a strong updraft, producing strong inward drawn winds in which fan the flame, take away oxygen so it is difficult to breath, and destroy everything in their path. The expansion of firestorms

Different scaling laws apply for calculating the heat and incinerating effects from bomb yield. Fire advances by wind driven heat propagation. In a uniform atmosphere without turbulent or convective processes the expansion would follow an exponential law with the radiation absorption parameter k. The heat exposure at distance d would be: W Q = therm ×e-k ×d 4p ×d 2 For turbulent firestorms empirical approximations are used to describe transmittance of heat in terms of the transmittance factor t (empirical factor for visibility) and f the thermal heat fraction of total energy release (f ˜ 0.35-0.42 depending on altitude). W ×t f ×W ×t f ×W ×t Q = therm = =1012 × cal / cm2 4p × d 2 4p × d 2 4p × d 2 Transmittance Ignition of combustibles

f ×W ×t 0.35×10×0.01 2.8×109 Q =1012 × =1012 » cal / cm2 4 d 2 4 d 2 d 2 1000 p × p × 10 kT 2

10 combustibles

0.1 heat release cal/cm

0.001 10 100 1000 10000 Distance [m] 0.113 2 Threshold ignition for combustibles QT » 3.5×W cal / cm Fire expansion

Fire expansion is driven by shock driven winds which develop rapidly turbulences due to temperature Differences. Fire spreads with rapid Speed, leaving no chance to escape.

Hiroshima Eyewitnesses

A bright flash and explosion at the same time; I could not see an inch ahead Is it smoke or dust? It all happened in a moment Hiroshima was engulfed in a sea of flames. Those who got burns were fleeting here and there, crying in pain “Help!" With screams, a wave of people come rushing toward me. Kojin-machi, Burn wounds

Peeled skin was dangling like seaweed from their arms Red flesh exposed People were staggering with vacant eyes Extending their arms forward Like ghosts Suddenly they fell, stumbling over something Never to get up again People burning Victims Victims