The Nature of the Blast

**The** **Nature** **of** **the** **Blast**

**Blast**—40-60% **of** total energy

**The**rmal 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

**The**rmal 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