Destructive Effects of Nuclear Weapons

Blast damageThermal damageRadiation damageEM-pulse

q The generation of a mechanical shock through sudden increase of pressurecauses mechanical damages

q The generation of a heat wave expanding with the shock causesincineration

q The distribution of radiation throughShort range and atmospheric falloutcauses short term and long termradiation sickness effects

q Electromagnetic shock leads to break-down of communication systems

The mechanical shock0.10 ms

0.24 ms

0.38 ms

0.66 ms

0.52 ms

0.80 ms

0.94 ms

pressure

shock velocity: vssound speed: csspecific heat: γ=1.4peak pressure: pair pressure: p0=15 psiwind velocity: vwdynamic pressure: q

( ) ppp

ppp

q

ppc

pp

pp

ppcv

pp

cpp

cv

ssw

sss

+⋅⋅=

⋅−+⋅⋅=

⋅+⋅⋅=

⋅

⋅++⋅

⋅⋅=

⋅+⋅=⋅⋅+

+⋅=

−

0

2

0

2

00

2/1

00

00

75.2

12

86.01715.0

211

86.012

11

γγ

γγ

γ

γγ

Example

ppp

q

ppc

pp

v

pp

cv

sw

ss

+⋅⋅=

⋅+⋅⋅==

⋅+⋅=

0

2

00

0

75.2

86.01715.0

83.01

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 anddynamic pressure p0 vs vw q

psi m/s m/s psi1000 2777 2309 2262500 1981 1619 1033300 1552 1240 556200 1285 999 328100 946 680 12250 718 448 4030 603 321 1720 537 241 810 461 141 25 418 78 13 400 49 02 390 33 01 380 17 0

Shock characteristics

Shock on flat surface causesreflection which is expressedby reflected overpressure pr!

( )

pp

pp

pppp

pqpp

r

r

r

2

8

747

2120

0

≈

≈

++

⋅=⋅++= γ

for large dynamic pressure

for small dynamic pressure

Example shock front against house

example

peak pressure reflected pressure

p0 pr pr/p0

psi psi1000 7430 7500 3479 7300 1933 6200 1187 6100 493 550 197 430 100 320 59 310 25 35 11 23 7 22 4 2

( )pppp

pqppr ++

⋅=⋅++=0

0

747

212 γ 250 kT blast Nevada 1953effect on houses in differentdistance from center of blast

2.65 miles

5.3 miles

The American Home

Shock expansion

Shock expands radially from explosion center.Amplitude decreases, but after time t5 the pressurebehind shock front falls below atmospheric pressure,Under-pressure which causes the air to be sucked in.

Pressure conditions with transversing shock

1. Shock hits2. generates strong wind3. Shock decreases4. Underpressure5. Wind direction changes6. Normal air pressure7. Wind calms down

Pressure induced wind effects

Peak over pressure as function of distancefor a 1kT blast

Distance Effects

3/11 WDD ⋅=

Scaling for blast intensities

e.g. the effect which occursfor a 1 kT blast at distanceD1 occurs for a 100kT blastat distance D. D1=10,000ftðD=24,662ft

100 kT

1 kT

Scaling laws for blast effectsShock/blast expands over volume ~d3, the following scaling law can be applied for estimating distance effects between different blast strengths

3/1

00

3

00

=⇒

=

WW

dddd

WW

3/11 Wdd ⋅=

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

Distance effects of airburst

0

3/1

0

0

3/1

0

3/1

00

35.1200500

7.1200

1000

dd

ddWW

dd

⋅=

⋅=

⋅=

⋅=

⋅= damage comparison for

a 1000 kT and a 500 kT bomb using the scaling lawwith respect to 200 kT bomb

Scaling in Altitude

1

3/1

11 dd

WW

hh

=

=

Similar scaling relation for altitude dependence of blast effects.For altitudes less than 5000 ft (1700 m) normal atmosphericConditions can be assumed. For higher altitude effects changesaltitude dependence of air pressure and sound speed need tobe taken into account.

often scaledto W1 = 1 kT

1

3/1

1 dd

Whh

==

Peak overpressure in height & distance

Suppose you have 80 kT bomb at 860 ft height, what is the distance towhich 1000psi overpressure extends? Normalization: W1=1kT

ftWdd

ftW

hh

47580110

20080860

3/13/11

3/13/11

=⋅=⋅=

===Corresponding height for 1kT burst(or scaled height)

Distance of 1000 psi overpressure

Surface burst versus airburst

Suppose you have 500 kT bomb at 1.1 mile height, what is the distance towhich 2 psi overpressure extends and compare with ground zero detonation.Scaled height for 1 kT bomb; h1 = h/W1/3 = 0.14 miles ˜ 765 ft. This correspondsto d1 = 3800 ft = 0.69 miles. The distance for the 2 psi overpressure on the ground from the 500 kT blast would be d = d1·W1/3 = 0.69·5001/3 = 5.5 miles.Surface burst: d1=2500 ft=0.45 miles, d = d1·W1/3 = 0.45·5001/3 = 3.6 miles.

Blast effects on humans

Thermal effectsApproximately 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 everything within expansion radius. The thermal radiation from a nuclear explosion can directly ignite kindling materials. Ignitable materials outside the house, such as leaves, arenot surrounded by enough combustible material to generate 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.

Fallout10%

Blast50%

Thermal35%

Initial Radiation

5%

Thermal Energy Release

24 rS ⋅= π

412124 1036.1; −−−−⋅=⋅= degscmcalTJ σσ

For a fireball with radius r the heat emitting surface is:

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

Total thermal energy emission from fireball is therefore:

seccalrTrTJSP /1071.14 24724 ⋅⋅⋅=⋅⋅⋅=⋅= −σπ

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 termsof maximum power Pmax (scaled power) and in termsof scaled time tmax which corresponds of time of themaximum thermal energy release from the fireball.

secWt

secktWP

max

max

44.0

56.0

0417.0

/18.3

⋅≈

⋅≈

0.64sect

secktP

max

max

=⋅≈

=⋅≈

44.0

56.0

5000417.0

/10350018.3

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)

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

The total amount of thermal energy emitted at t=1sec is:

seccal.seckTPP

PP

tt

max

maxmax

/10860/8.6010359.059.0

;59.0;56.164.01

12⋅==⋅=⋅=

===

Hiroshima firestorm

Fires can result from combustion of dry, flammable debris set loose by the blast or from electrical short circuits, broken gaslines, 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

dtherm ed

WQ ⋅−⋅

⋅= κ

π 24

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 theexpansion would follow an exponential law with the radiation absorption parameter κ. The heat exposure at distance d would be:

For turbulent firestorms empirical approximations are used to describe transmittance of heat in terms of the transmittance factor τ (empirical factor for visibility) and f the thermal heat fraction of total energy release(f ˜ 0.35-0.42 depending on altitude).

22

1222 /

410

44cmcal

dWf

dWf

dW

Q therm

⋅⋅⋅

⋅=⋅

⋅⋅=

⋅⋅

=π

τπ

τπ

τ

Transmittance

Ignition of combustibles

22

9

212

212 /

108.24

01.01035.010

410 cmcal

dddWf

Q⋅

≈⋅

⋅⋅=

⋅⋅⋅

⋅=ππ

τ

combustibles

Distance [m]

0.001

0.1

10

1000

10 100 1000 10000

heat

rel

ease

cal

/cm

2

Threshold ignition for combustibles2113.0 /5.3 cmcalWQT ⋅≈

10 kT

Fire expansion

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

Hiroshima

EyewitnessesA 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 armsRed flesh exposedPeople were staggering with vacant eyesExtending their arms forwardLike ghostsSuddenly they fell, stumbling over somethingNever to get up again

People burning

Victims

Victims