CONELDENdEdfeks INTRODUCTION In order to estimate the proportion of a city’s population that will be casualties of a thermonuclear weaponit is necessary to construct a model of the bombing of a city. With the resultant casualties as a measure, the effectiveness of various courses of action open to the belligerents can be examined and assigned numerical values, so that the desirability of one course over another can be determined. There are three independent components of the problem: the aiming point or points selected by the aggressor, together with the errors inherent in his aim — in short, the frequency distribution according to which the bombs are laid down; the proportion of casualties as a function of distance from Gz for any given bomb — in other words, the performance of the individual bombs; and the geographical distribution of the population of the city. The last factor contains time as one of its parameters when evacuation is considered. A mathematical model of this problem should extract from each of the components somecharacteristic or characteristics, preferably numbers (rather than graphs, for example), and afford a way of combining these to obtain the measure of effectiveness. In this way each of the components can be varied separately, and the interactions of the components can be determined without resetting every component every time. It would be en- lightening to know the likeliest Jevel of casualties as well, and even more to know the function by which the casualty levels are distributed; but if a single number is required, the expected level is the most natural one to take. This expected value is obviously an idealization. Theraid,if it occurs at all, will only occur once. Suppose the expected level of casualties has been determined to be 40 percent, yet the actual raid kills 50 percent of the population. This fluctuation would not be sur- prising, since 40 percent is only a mean valueandit is reasonable to expect a certain amount of fluctuation (although a fluctuation to 10 percent or 90 percent might be cause for alarm). In brief, the situation being investigated here is one in which no more than a rough index of what may happen can be asked for. Inlight of this it would be pointless to develop tedious and laborious equations or to calculate to very great accuracy. It is felt that the method presented here fulfills the requirements of both flexibility and simplicity. The most time-consuming step in the process is the reduction of the popu- lation data, but once the prerequisite map study has been made, the reduction can be performed on an ordinary desk calculator in a few hours at the most, and of course need not be redone until the population distribution undergoes a marked change. The formulas developed can be quickly evaluated on a slide rule equipped with a scale of negative exponentials. It is hoped that these features will recommend the approach developed here to both local civil defense authorities and sac. 71 ORO—R—-17 (App B) CONEIDENTHAt we. “OY would prove casualties; this proportion is called ‘“‘the expected level.” + the following manner: if the same raid, under precisely the same conditions, were mounted a very large numberof times, then on the average a certain proportion of the population yore The formulas and approach should be as simple and time-saving as is consistent with a realistic analysis. Here a word is in order about the statistical milieu of the problem. The expected level of casualties that an air raid will inflict on a city is determined in e