The Nature of the Blast

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The Nature of the Blast

The Nature of the Blast

Blast—40-60% of total energy

Thermal radiation—30-50% of total energy

Ionizing radiation—5% of total energy

Residual radiation (fallout)—5-10% of total energy

The results of the weapons test programs

Efficiency of explosion

Kind and shape of blasts

Blast effects, range & damage

Thermal effects

Radiation effects


Classifications of blasts

Surface Blast:

fireball in touch with surface

vaporization of surface structures through blast

and firestorm, immediate radioactive fallout

High Altitude Air Blast:

fireball > 100,000 ft (>3000m)

interrupts satellite based communication

through electromagnetic pulse (EMP)

Low Altitude Air Blast:

fireball < 100,000 ft (without touching ground)

generates shock waves, pressure difference

artificial for large areal damage, sea battle

Subsurface Blast:

Underwater burst

generates surge


Surface Blastthe fireball

Central temperature: ~10,000,000 K

Immediate vaporization of material!

Central pressure: ~33000 atm

Radiation release & absorption in surrounding

matter generates red-glow intense luminosity.

Expansion of fireball through internal pressure

Fireball rises like hot air balloon

Stokes

August 1957

1500 Foot Balloon

19 kt


p ⋅V

T

1

p

p

2

1

Fireball expansion

∝ T;

≈ 300 K,

T


T

2

1

Pressure evolution

within the fireball:

V

p

1

≈ const

≈ 1atm,

T

1,000,000


300

2

≈1⋅10

6

K

≈ 3300 atm = 50,000 psi

Sedov Taylor approximation (valid of first 0.1s)

allowed Russians to estimate the power of the

Trinity bomb from the expansion time conditions

temperature

pressure

E = K ⋅ ρ ⋅ r

r ≈ 950⋅

ρ ≈ ρ ⋅

0

1ktTNT

() t

P

P

0

E ≈ K ⋅ ρ ⋅

0

5

2/5

⋅t

P

P

0

E ≈ 10ktTNT

2/5

[ m]

⋅7.74⋅10

= 4.18⋅10

12

K ≈ 1, ρ = 1kg

/ m

J

14

⋅t

0

8/5

3

≈ 4.04⋅10

13

J

( t

= 1ms)

t r

0.1 ms 24 m

0.4 ms 42 m

0.7 ms 52 m

0.9 ms 60 m


Expansion speed

Initial expansion speed v (T≈1,000,000 K)

c s

is the speed of sound in the vaporized gas

γ is the specific heat ratio of the gas

R is the gas constant: 287 [J/kg K]; T is temperature [K]

2⋅cs

v = cs

= γ ⋅ R ⋅T

≈ 20 km / s;

γ ≈ 1.5

γ −1

2⋅

20

v = = 80 km / s ≈

1.5 −1

240,000 ft / s

Cool-down to T≈3,000 after 15 ms due to radiation losses

Fully ionized plasma

v

v

2⋅cs

= cs

= γ ⋅ R ⋅T

≈ 1km

/ s;

γ ≈1.25

γ −1

2⋅1

= = 8km

/ s ≈ 24,500 ft / s

1.25 −1

Ideal gas


The shock front development

After ~10 second the fireball expands with constant

rate of ~300 ft/s

After ~ 1minute fireball has cooled and radiation emission ceases!


6ms

90 ms

16 ms

109 ms

18 ms

15.0 s


Analysis of Fire ball

Sedov-Taylor Blast analysis

R

=




K

E

⋅ ρ

0




1/5

⋅t

2/5

Valid as long as shock is super sonic: K≈1

Approximation allowed Russian scientists

to estimate the power of US Trinity bomb.


Evolution of Mushroom cloud


General Features – the mushroom





the emergence of the mushroom shape

Absorption of cool air

triggers fast toroidal

circulation of hot gases

and causes upward

motion forming the

stem and mushroom.

Condensation of

water changes red

brownish color of

cloud towards white!

Strong upward wind

Drags dirt and debris

Into the cloud mixing

with radioactive material

Cloud rises in height

with ~ 440 ft/s


Model


Dirt


Cloud Altitude

Maximum altitude for cloud

rise is reached after ~ 4min.

RATE OF RISE OF THE

RADIOACTIVE CLOUD FROM

a I-MEGATON AIRBURST

Height Time Rate of Rise

(miles) (min) (mph)

2.0 0.3 330

3.0 40.7 270

4.0 61.1 220

5.0 102.5 140

6.0 123.8 27

Cloud height & cloud radius

depend on the magnitude of

the explosion, increase of

both radius & height scales

with explosion yield.


Chimney effect again!

v = 0.65⋅

2g


H





T

i

−T

T

i

o




v=wind velocity in m/s

g=9.8 m/s 2 earth acceleration

H=height of heat column in [m]

T o =outside temperature, K

T i =inside temperature in K

For typical firestorm:

H ≈ 10,000 m

T i ≈ 1,000,000 K

T o ≈ 300 K

➱ v ≈ 288m/s = 647 miles/h

Hurricane speeds ~100 miles/h

Conventional firestorm ~220 miles/h

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