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The W31 was an American nuclear warhead used for two US missiles and as an atomic demolition munition.
The W31 was produced from 1959, with the last versions phased out in 1989.
Nike Hercules missile
The Nike Hercules was a surface-to-air or surface-to-surface missile system deployed around US cities and various locations in Europe and Japan. Most, but not all, of these missiles were deployed with nuclear warheads. In South Florida, half of the Nike Hercules missiles of the Homestead-Miami Defense were armed with the T-45 high-explosive warheads.
Three yield variants, of 2, 20, and 40 kiloton yields, were deployed on these missiles starting in 1958 and finally retired in 1989. 2,550 of these models were produced. The 20 kt version of the W-31 was solely used in the Nike Hercules system.
A similar variant, the XW-37, was a high yield version of the XW-31. Development started in January 1956. Three months later, the XW-31 was redesignated XW-31Y1 (for yield 1) and the XW-37 designation was changed to XW-31Y2 (for yield 2).
MGR-1 Honest John missile
The Honest John was a short-range surface-to-surface tactical ballistic missile used by the US Army.
Three yield variants, also apparently 2, 20, and 40 kilotons, were deployed on Honest John missiles from 1959 to 1987. A total of 1,650 Honest John W31 warheads were produced.
Atomic Demolition Munition
Between 1960 and 1965, 300 W31's were stockpiled for use as ground based Atomic Demolition Munitions. Information regarding the destructive yield is sparse, though given the expected mission profile of such weapons, it is likely to have been at the lower end of the range, i.e. 2 kt or less.