116 - 10 - 



Measurenents with the piezo-electric ana other gaujes give the following mean values for T.N.T, 

 p = U.6 X lo' (M^'^/r) dynes/cm^ 



= 7.5 X 10* m'^'^ sec"' 



(52) 



where M is the mass of the charge in granynes and r is the distance from the charge in centimetres. 

 The value of r at the centre of the plate is X. Values of « and M /x(7) appropriate to the 

 middle of the plate were calculated from (62) and are taOulated in columns 9 ano 10 of Table 2. 

 Values of 5 at the -moment the pressure on the plate becomes zero (or strictly the hydrostatic 

 pressure at the depth oonsiOereo) are given in column 11, The kinetic energy of the middle 

 part of the plate is « (p steel) 5^ per c.c. 



When X is larger than a, i.e. than 3 feet, the velocity g of the plate might be expected 

 to be nearly constant over the surface because sin 5 is not very different from 1.0 anfl r is nearly 

 equal to X. &t closer distances, however, the outer parts of the plate will receive from the 

 pressure wave less energy than the middle. This effect has been discussed by Fox in the report 

 •The reflection of a spherical wave from an infinite plate" who finds that the formulae (50) and 

 (51) are sufficiently accurate for many purposes if applied to elements of the spherical wave. 

 To calculate the mean value of ^ over the plate using the expressions (50) and (5l) at all points 

 of the plate using the appropriate values of r and 5 would be extremely laborious. An 

 approximation can be calculated in the form of a factor F by which the value of ^ at the centre 

 must be reduced to get the mean value over the plate. 



Consider a circular plate of radius R and suppose that p is proportional to 1/r = IVR +X 



ition to take the effect of oOl Iquity on g as 



It can be shown that it is a fairly good approxima 



reducing it in the ratio sln^ : 1 below its value for normal incidence. 



expresses the ratio of the djean value of 5 to the value ^ 



The factor F which 

 at the centre of the plate ney therefore 



(53) 



(53a) 



To apply (53a) to the rectangular plate we may take R as the mean of a and b. Thus R = 2S feet. 

 The mean value of the kinetic energy given by the Shockwave to the plate may now be taken approximately 

 as 



I = ^ (p steel) F^2 



(5U) 



The values of t, using p steel = 7.8, F from (53a) and the values of ^ from column 11, Table 2, 

 are given in column 12. If the whole of the energy of the plate were communicated during the early 

 part of the pulse when the pressure is positive it would be expected that W would be equal to t. 

 Values of w /I are given in column 13. It will be seen that only in shots 107 and 108 can the 

 energy be attributed mainly to this cause. Shots 107 and 109 ^ive values of w /T less than 1 but 

 In these two cases the permanent dishing was very small. It seems certain that elastic rxovery 

 would be comparable with the small values of 7, namely .Hi inches and 0,58 inches, obtained In 

 these cases. In all other cas-'s the work aone by the pressure is considerably greater than T. 



4t least three possible explanations of this divergence from the theory of the report 

 "The pressure and impulse of submarine explosion waves on plates' can be investigated, 



(1) The duration of the actual pressure on the plate before it falls to zero may be greater 

 than the calculated value becauss the plate is fixed at the edges so that the rapid cutting off 



of the pressure by motion uf the plate does not happen close to the edge. . ,_ .... 



to extend only a short way inwards from the edge because the duration of the positive pressure 

 calculated in most of the trials to be less than -j^th 0' a millisecond. In this time sound 

 travels 6 inches, so that diffraction from the edge would only have time to affect the pressure 

 over a small part of the total area of the plate. 



This effect is 1 ikely 



■ posit ive pressure is 



In this time sound only 



(2) 



I 



