# RAND Bombing Probability Computer

This computer/calculator was produced by RAND for the United States Air Force.  It allowed USAF planners to calculate the probability of hitting a target [or landing within a certain distance of a target] with one or more bombs. I think it could have been used for both nuclear and conventional bombs, and for devices delivered by missile or bomber,

To understand its function imagine that a U-2 flight has discovered a missile silo east of the Urals.  It can be assumed to be hardened and contain an ICBM. The missiles payload and target would be unknown; it could be a city or a SAC base.  If USAF target planners assumed that the target was a US city they would have to decide how many missiles might be needed to give, say,  a 80-90% probability of disabling the silo before it could launch.

[Note – going for a high probability kill could be overdone. In 1991 the new head of SAC looked at the US Single Integrated Operational Plan. The SIOP was the list of targets that would be attacked in the event of a nuclear war with the Warsaw Pact. He found hundreds of warheads aimed at Moscow, including dozens targeted on a single radar installation outside the city.]

Before using the calculator a planner would have needed to have access to CEP [circular error probability] data derived from missile firings  on the Pacific test ranges. The CEP is defined as the radius of a circle, within whose boundary 50% of the bombs [or other projectiles] could be expected to land.  They would need to know the accuracy they could expect from their delivery system [missile or bomber].   An accurate bomb delivery system  would have a lower CEP than an inaccurate one.

For example, if you fired a missile from a base in the USA against a target in the Soviet Union and you thought from your missile tests that the CEP would be two miles. There would be a 50% chance that the missile warhead would detonate within two miles of the target. A further 43% between two and four miles, and  7% that it would land between four and six miles. The chance that the missile would land more than six miles away would be less than 0.2%.

If the target was a hardened silo containing a missile targeted on a US city then that degree of accuracy might not have been acceptable. The Bombing Probability Computer allowed planners to calculate the effect of increasing the number of missiles sent against that target. The calculator assumes a multivariate normal distribution of hits.

The US Single Integrated Operational Plan [SIOP] identified 3,729 targets in the Soviet Union, China, North Korea and Eastern Europe. These were grouped into more than 1,000 ground zeros and would be attacked by 3,423 nuclear weapons. About 80% were military targets and the rest civilian.  Approximately 220 million people would have been killed.

The plan called for a probability of at least 75% that a target would be destroyed. A higher percentage was specified for some targets. One target was scheduled to be hit by a Jupiter missile, a Titan missile, an Atlas missile and hydrogen bombs dropped by three B-52s.

The normal distribution might be appropriate for missiles but not for conventional bombs delivered by an aircraft. In that scenario a plane would be flying in a line over a target and releasing bombs in sequence. For that kind of attack it would be more sensible to assume a elliptical distribution. The Bombing Probability Computer could be used for elliptical and linear distributions.

The calculator is made of plastic and is 6″ [152mm] in diameter. It was manufactured by Perrygraf and copyrighted in 1961.

For more posts about Cold War calculators click on the Cold War Calculators category on the right.