An explosion unleashes a sphere of pressure over normal air pressure that damages whatever is in its radius. The pressure in excess of normal atmospheric pressure generated by an explosion is called over pressure. In the case of a nuclear bomb at 2-psi over pressure, approximately 45 per cent of the population is injured, 5 per cent of the population is dead, smaller buildings are destroyed and larger buildings are damaged. Over pressure is useful in calculating a blast radius, especially for nuclear bombs, since certain levels of over pressure consistently produce certain levels of destruction.

Scale the height of the burst for a 1-kiloton explosion. Divide the height at which the bomb was exploded by the cube root of the yield. For instance, with a 43-kiloton explosion at 500 feet, the value will be 142.9 feet. This is the height at which a 1-kiloton bomb must be exploded, in order to have the same over pressure as the original bomb.

Read the graph of the over pressure of a 1-kiloton explosion to obtain the 2-psi distance using the value scaled. A 1-kiloton bomb exploded at 142.9 feet has a 2-psi over pressure extending to 2,700 feet.

Convert the 1-kiloton values back to the values for the actual yield. Multiply the value read in the graph by the cube root of the yield. At 2,700 feet with a 43-kiloton bomb, the distance for a 2-psi over pressure is 9,450 feet.

Convert to miles. Divide the converted value by 5,280, the number of feet in one mile; 9,450 feet would be 1.79 miles.

Calculate the blast radius. Square the distance of the blast and multiply it by pi (3.14). With a 1.79 mile distance, the blast radius of a 2-psi over pressure would be 10.1 square miles.

#### Tip

To calculate a blast radius for a smaller explosion, obtain an over pressure graph of a smaller explosion.

#### Tips and warnings

- To calculate a blast radius for a smaller explosion, obtain an over pressure graph of a smaller explosion.

### Things you need

- Yield of the bomb
- Height at which the bomb was exploded
- Graph of the over pressure of a 1-kiloton explosion

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#### References

- The Nuclear Weapon Archive; Effects of Nuclear Explosions; Carey Sublette; May 1997
- PBS; American Experience; Nuclear Blast Mapper
- Loyola Marymount University; Assignment #4; Weapons of Mass Destruction; J. R. Mureika
- Federation of American Scientists: Introduction to Naval Weapons Engineering --- Warheads
- Defense Technical Information Center; Nuclear Weapons Effects Seminar; Oklahoma City Air Logistics Center; April 1987