115 



Value of hi z 



It has been pointed out that the ratio of the maximum deflection v^ of* the plate to its 

 mean deflection z may be expected to bear some relationship either to the degree of concentration 

 of loading towards the centre of the plate or to the sufldenncss of its application. The maximum 

 value to be expected with uniform impulse is 2.57(3) . The minimum for uniform pressure Is 

 2.0«(»). Of the 19 shots analysed in Table 2 (overleaf) only shot 6/1 gives a higher value than 

 this range and then is only U above It. Two shots 107 and 108 give values of \\Jz below 2.06. 



The values of h /r are given In column 6 of Table 2, and are shown in Figure U. In this 

 figure they are plotted with X, the distance of the charge from the plate, as ordinate because the 

 concentration of loading near the middle of the plate must Increase as X decreases. 



If the deflection were due entirely to the impulse supplied by the Shockwave during the 

 snail fraction of a millisecond when the water Is in contact with the plate and acting on it with 

 a positive pressure, the values of h /z might perhaps be expected to be in the neighbourhood of 

 2.U. If, however, the plate is bombarded with spray after losing contact with the water or if 

 the duration of the pressure is prolonged by the pressure of a kinetic wave following the pressure 

 pulse h /z may be expected to approach the value 2.06, appropriate to a uniform static loading, 

 tor large values of x. 



It will be seen In Figure u that as X Increases h /z ooes in fact decrease towards the 

 value 2.06 and that It Increases with decreasing value of X down to X « 31 feet. For nearer 

 explosions at li and 2 feet h /z again decreases, towards the value corresponding with uniform 

 steady pressure. 



Energy used in doing work against jilastic stress in the plate. 



The distribution of plastic strain energy absorption in the plate does not necessarily bear 

 any definite relationship to the distribution of pressure. On the other hand, if the edges of the 

 plate may be regarded as fixed, all the energy put into the plate 5y the pressure over its surface 

 is used in doing work against the plastic stresses. The total energy given to the plate by the 

 pressure distribution is therefore equal to w x (area of the plate), see equation (39), and the 

 mean energy given to unit volume of the plate Is equal to W . The accurate value of w would only 

 be calculated by taking a complete set of distortion measurements. The value given by (39) is the 

 minimum value consistent with a given value of z. Using a = 2 feet 11 inches, P = 20 tons/square 

 inch « 3.09 X 10 dynes/sq.cm., (39) gives 



Wp = 5.76 X 3.09 X lo' {F/35)^ = 1.45 X lo' X z' (U9) 



where w is expressed in ergs/c.c. of steel and z is expressed in inches, as measured. 

 Values of z are given in column 5, Table 2, and of W in column 8. 



Comparison with energy given to the Plate by the pressure iulse ^ 



The velocity with which the plate is discharged from the surface of the water by the pressure 

 pulse has been calculated (5) on the assumption that a plane compression pulse of form p = p c""' 

 strikes the plate. Values of p^^ and n are known for certain explosives, notably T.N.T. The motion 

 of the plate rapidly gives rise tea negative pressure and the motion subsequent to the attairenent 

 of zero pressure depends on whether water can sustain tension either Internally or at the surface 

 of the plate. Tne velocity of the plate at the moment when zero pressure is attained is'6) 



I = \e-^'^~^ (50) 



m 



where « = fximn sin 6, c is the velocity of sound in voter, m= \.{p steel) = 7.8t is the mass per 

 unit area of the plate, p is the density of water, 6 is the angle of Incidence of the wave on the 

 plate. We may use this first to calculate the velocity with which the central portion of the plate 

 is discharged. Her* = 90° so that (50) nay be written 



t ' ^ e-'"-' (51) 



/x 



Measurements 



