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 Blast – the 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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