RAND Damage Probability Computer for Point Targets with P and Q Vulnerability Numbers


The Damage Probability Computer for Point Targets with P & Q vulnerability numbers was created to provide military planners with a quick way of estimating the outcome of nuclear bomb attacks on overpressure-sensitive targets (PVNs) and  dynamic pressure-sensitive targets  (QVNs).  PVN targets are destroyed by crushing [vertical blast pressure], QVN targets are destroyed by being knocked over [horizontal blast pressure].  A tank might be resistant to overpressure but capable of being tipped over by dynamic pressure effects. A hardened missile silo might be immune to dynamic pressure and have to be destroyed by overpressure.

The computer  was first issued in 1974. A modified version,  with an additional scale for calculating optimum air burst heights, was issued in 1977. The computer shown is the 1977 version.  It is approximately 7 inches in diameter [18 cm] and is made of plastic. It was manufactured by Perrygraf.

At the time the US and the UK had a Single Integrated Operational Plan [SIOP] which listed all potential targets in the Warsaw Pact countries [and some other countries].  Each target was given a vulnerability number [see this post for an explanation of vulnerability numbers] and a desired probability of destruction. The desired probabilty was usually 0.75 but some targets were seen as more important and had higher probability numbers. What constituted ‘destruction’ was also defined for each target. For example, steel surface storage tanks had to be ruptured to be considered destroyed.

A point target is a small target which needs an accurate strike to destroy it. A city would not be a point target, a missile silo would.

Also, at this time the US and UK were introducing multiple independently targetable re-entry vehicles [MIRVs] to replace unitary warheads [a single, usually large, warhead].  The increase in the number of warheads allowed military planners to add a large number of targets to the SIOP.   MIRVs carried more warheads but smaller ones.


The Poseidon Submarine Launched Ballistic Missile [SLBM], introduced in 1972, carried 10 or 14 W68 40 kiloton warheads [the Hiroshima bomb yielded 16 kilotons and the Nagasaki bomb 21 kilotons]. The Minuteman III had three 170 kiloton warheads.  Such warheads could be used for point targets as well as city busting.

The computer only calculates blast effects. Thermal, cratering, ground shock and fallout [or other radiation] effects are not taken into account.

Performing Calculations

Damage Probability Computer noexif  3

The red side of the computer is used for P targets (PVN) and the blue side for Q targets (QVN).

Inputs to the computer are –

1.   The warhead yield. This is entered on scale A.

2.    The K factor adjustment. This is read from scale B. The K factor accounts for the increase in the duration of the blast wave with increasing yield. A higher- yield weapon will have a greater probability of destroying a target at a given pressure than a lower-yield weapon because the blast wave from the higher-yield weapon acts over a longer time.

Damage Probability Computer noexif  2

2.    The adjusted target vulnerability number (PVN or QVN).   Before entering a targets vulnerability number it is adjusted by its K factor.   The computer has different scales for weapon yields under or over 20 kilotons. For yields under 20 kilotons the adjusted value of K is added to the VN number and for yields over 20 kilotons it is subtracted to produce an adjusted K factor. That produces an adjusted vulnerability number that is entered on scales C for an air burst and scale D for a ground burst..

3.   The warhead delivery Circular Error of Probability [CEP].  This is a measure of the accuracy of the delivery vehicle [e.g. bomber, ICBM, SRBM or submarine launched missile]. This is entered on scale E.

The output of the computer is a probability of destruction number. This is read from scale F.  If a target required a 75% chance of single shot destruction and the above calculation only produced a probability of 50% the planner could run the calculation again with a higher yielding warhead or a more accurate delivery system.

For targets with Q vulnerability numbers the optimal airburst height can be read from scale G.

Damage Probability Computer noexif 2

The damage  probability  calculation is based on the sigma-20 damage function  for PVNs, and on the sigma-30 damage function for QVNs, as defined in the  Physical Vulnerability Handbook for Nuclear  Weapons produced by the Defense Intelligence  Agency.

Damage Probability Computer noexif  4

The end of the SIOP

“On January 25, 1991, General George Lee Butler  became the head of the Strategic Air Command. During his first week on the job, Butler asked the Joint Strategic Target Planning Staff to give him a copy of the SIOP. General Colin Powell and Secretary of Defense Dick Cheney had made clear that the United States needed to change its targeting policy, now that the Cold War was over. As part of that administrative process, Butler decided to look at every single target in the SIOP, and for weeks he carefully scrutinised the thousands of desired ground zeros. He found bridges and railways and roads in the middle of nowhere targeted with multiple warheads, to assure their destruction. Hundreds of nuclear warheads would hit Moscow—dozens of them aimed at a single radar installation outside the city. During his previous job working for the Joint Chiefs, Butler had dealt with targeting issues and the damage criteria for nuclear weapons. He was hardly naive. But the days and weeks spent going through the SIOP, page by page, deeply affected him.

For more than forty years, efforts to tame the SIOP, to limit it, reduce it, make it appear logical and reasonable, had failed. “With the possible exception of the Soviet nuclear war plan, this was the single most absurd and irresponsible document I had ever reviewed in my life,” General Butler later recalled. ‘I came to fully appreciate the truth … we escaped the Cold War without a nuclear holocaust by some combination of skill, luck, and divine intervention, and I suspect the latter in greatest proportion.’

Butler eliminated about 75 percent of the targets in the SIOP, introduced a targeting philosophy that was truly flexible, and decided to get rid of the name SIOP. The United States no longer had a single, integrated war plan. Butler preferred a new title for the diverse range of nuclear options: National Strategic Response Plans.”    Schlosser, Eric. 2009. Command and Control. London: Allen Lane.

1974 version of calculator

RAND V1 Damage Probability 1

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

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