CONTFIVENTTA L The treatment is meant to be indicative rather than exhaustive. It should perhaps be stated explicitly that the annex aims to be clear enough to be applied by those who are not particularly interested in the details and detailed enough to be of interest to those who are not specifically concerned with the applications. BOMB DISTRIBUTION It is commonly assumed that bombing errors follow a binormal distribution; i.e., that in a suitably chosen coordinate system the number of bombsfalling in a rectangle dx by dy situated at (x, y) is proportional to (1/2meg75) exp [— (2°/205) — (y*/278)], (Al) where og and 7, are the standard deviations, the distribution has been rotated to remove the cross-product term, and the origin has been taken at the mean. If, as seems verylikely, the errors are the resultants of a great number of independent causes, then Eq. Al is in fact a consequence of the Central Limit Theorem. Of course there may be several distributions corresponding to Eq. Al and having different means; e.g., the various aircraft on a bombing mission might be given their own aiming points in an attempt not to overkill at the center of the city. There is no need to consider a covariance term in these dis- tributions unless it is anticipated that an attack might be mounted against the city from several directions simultaneously, a situation that for simplicity will be disallowed in this discussion. Similarly there is no a priori reason for supposing that the attacker’s accuracy of aim would vary from point to point in a massed attack. It is therefore assumed that Op and Tg, remain constant from distribution to distribution. Indeed, later in the analysis, it will be further assumed that og = rg, and Tz will be suppressed in later equations. BOMB EFFECTIVENESS Examination of any atomic-weapon curve showing proportion of people killed or injured at ‘ground r’’ (i.e., distance r from Gz), indicates that the eurve might be adequately approximated by a suitably scaled normal distribution. curve werereally given by Suppose in fact that the e- exp [— (A/2)r?]. (A2) Here c is a scalar, the proportion of casualties at Gz, and » is measured in inverse squarefeet andis in fact the reciprocal of the variance. Thus a small value for A represents a spreadout distribution and indicates a bombeffective out to a large radius; large \ indicates an ineffective bomb. Perhaps the clearest way of characterizing these parameters is through oot as the concept of lethal area. The lethal area of the weapon described by Eq. A2 is (A3) see nae: Rr e- exp [— (A/2)r?]r dr d@ = 2ae/X. What remainsis to fit the empirical curve by a curve of the form of Eq. A2. This is done by the method of moments. Indeed, for Eq. A2 yo = f° c- exp (— (4/2)r*] dr = V7) - (c/2%, aa ps =f c- exp [— (A/2)r%2 dr = VGr/8)- (6/4), and solving for c and A gives Result 1. 72 ORO-—R-17 (App B)