- 7 - 



TABLE 1. 



213 



For a long pulse (q small) from a distant source we see from Table 1 that the maximum 

 unbalanced Impulse is small compared with the total incident impulse; physically, this is due to 

 equalisation of pressure round the sphere when the pressure is maintained for a time long compared 

 with that taken by a pressure wave to travel round the sphere. 



For a short pulse from a distant source, however, the maximum unbalanced impulse is of the 

 same order of magnitude as the incident impulse, corresponding in the case of a fixed sphere to an 

 overall reflection factor of 1.29. A point specially worthy of notice, which is seen from equation 

 (3") with X -• 00^ is that the unbalanced impulse tends to zero with increasing time showing that, 

 however short the pulse. Its impulsive effect is eventually diffracted behind the sphere. 



A similar effect is responsible for the fact shown by Table 1 that for short pulses from 

 close sources (x -• l) the maximum unbalanced impulse ts much greater than the directly incident 

 impulse. In such cases the major contribution to the maximum unbalanced impulse comes from 

 diffraction of the incident pulse on to the part of the front of the sphere which is In the shadow 

 and not from the small portion subjected directly to the incident pulse. 



it snould be noted that the values foi- X = l have been given In Table 1 to show the limits 

 for small values of X - i; such small values are possible for large q without invalidating the 

 conditions discussed in paragraph (l) above. 



(3) 



Effect of fixing . 



In view of present interest in the possible difference in damage sustained by a fixed and a 

 suspended target, it is of value to see what evidence can be obtainsd from the present analysis 

 comparing the two cases of k = 1 (fixed) and k = 3/2 (buoyant). 



Comparing on the basis of unbalanced impulse It is seen from Table 1 that this is from 1/3 

 to 1/2 greater when the sphere is fixed. For long pulses from distant sources, however, the 

 unbalanced impulse is small relative to the incident pulse whether the sphere be fixed or buoyant. 

 Thus in this case, corresponding to a relatively large explosion at a large distance the main 

 effect of the pressure pulse is a uniform impulse all round sphere which is large compared with 

 any local increase, due to fixing, of the unbalanced impulse. 



For short pulses from oistant explosions, however, the unbalanced impulse is of the same 

 order as the incident impulse and the possibility of appreciable effect of fixing cannot be dismissed 

 on the present analysis. 



The same is at first sight true of short pulses from near explosions but, on the other 

 hand, in practical examples of this type the damaging effect tends to be concentrated in intensity 

 over the portion of target close to the explosion. 



In order to consider the effect of fixing on tnis near portion it is necessary to note that 

 the complete solutions, of form equation (2), for the two cases of fixed and buoyant sphere differ 

 only in the second term j = 1 which is also the term responsible for the total net force and the 



unbalanced 



