Derivations of the Formula f = 1 - e - nL

by Robert L. Helmbold

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This study presents two rigorous mathematical derivations and two heuristic "proofs" of a formula often used for the expected fraction of casualties from ordnance fired into an area, and assesses the formula's validity. It is found that the validity of this approximation depends on the target area being large, the distribution of bursts uniform over the target area, and certain independence assumptions. In many cases of practical interest, these limiting conditions are not satisfied --especially for small targets and a relatively high proportion of casualties--and some fairly sizable discrepancies between the approximate and exact fractions of casualties have been observed. It would seem prudent to avoid use of the approximate formula when it is not certain that its basic assumptions are applicable to the situation considered. 11 pp. (MW)

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