BALLISTIC RESEARCH LABORATORY
MEMORANDUM REPORT NO. 139
SC/mo
Aberdeen Proving Ground, Md.
April 15, 1943
OPTIMUM HEIGHT FOR THE BURSTING OF A 105MM SHELL
1. The statement of the problem and its solution: It is required to find the height at which it is most advantageous to have a 105mm shell burst in order that the maximum injury may be inflicted on personnel.
It is found (as a result of the calculations to be presented) that the height at which it it most advantageous to have the shell burst is 75 feet.
2. Basis for the calculations: The experimental data on which the calculations were based are those of Mr. Tolch who has analyzed both the angular distribution of the fragments when a 105mm shell bursts and the distribution in weight of these fragments.
Regarding the angular distribution it appears that the greater proportion of the fragments in the lateral spray is confined to an annular cone with semi-angle of 7-1/2. We shall see later that the precise value of this semi-angle defining the angular width of the spray has no special influence on our results.
Regarding the distribution with mass of the fragments, Mr. Tolch's results can be relied upon for the heavier fragments (), while for the smaller fragments the reliability becomes steadily less on account of the necessary incompleteness in the recovery of these fragments. In order, therefore, to obtain a reasonable extrapolation of the distribution for the smaller masses, the total mass contributed by the fragments in the various mass groups was plotted against the mass of the fragment and from a smooth curve drawn through these points, a distribution was derived which formed the basis of further calculations. The observed and the derived distributions are compared in Table I. From this table, Table II giving the number of fragments in the downward lateral spray with masses greater than a given value was derived.
