A military planner wants to design a targeting strategy to maximize the number of prompt casualties in metropolitan areas by using twenty 1 Mt bombs. The main cities in the enemy country have the following characteristics:

• City 1: (30,000 people/sq. mi
• City 2: (16,000 people/sq. mi)
• City 3: (10,000 people/sq. mi)
• City 4: (6,000 people/sq. mi)

How would you distribute the twenty bombs, and how many casualties would such an attack produce?

use p = 25 Y / R³
p = peak overpressure in psi
Y = yield in megatons
R = slant range in miles

Hint: An overpressure of 5 psi will kill 50% of the population.

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Targeting Exercise Solution

p = 25 Y / R³

R = 5 ^1/3

R = 1.709 miles

The area enclosed by the 5 psi ring is: 1/4 R² = 9.18 sq. miles.

To maximize the radius R, the bombs should be exploded as ground bursts.

1 bomb on:

City 1: (30,000 people/sq. mi) x (9.18 sq. mi) x (.5) =137,791 killed/bomb

City 2: (16,000 people/sq. mi) x (9.18 sq. mi) x (.5) = 73,440 killed/bomb

City 3: (10,000 people/sq. mi) x (9.18 sq. mi) x (.5) = 45,900 killed/bomb

City 4: (6,000 people/sq. mi) x (9.18 sq. mi) x (.5) = 27,540 killed/bomb

It is clear to see that the best targeting strategy would be to attack City 1 until the area is covered. 300 sq. mi/ (9.18 sq. mi/bomb) = 32.6 bombs

Since your arsenal consists of only twenty bombs, they should all be targeted on City 1. Any bombs on the other cities would produce fewer casualties. Although a more realistic targeting plan would factor in the radiation effects. This would allow for fewer bombs on City 1.

A possible strategy is:

City 1: 14-15 bombs

City 2: 4-5 bombs

City 3: 0-2 bombs

City 4: 0 bombs