380 



surface of the plate and the charge center. Because of considerations 

 advanced in Sec, 4, the pertinent solutions for T^ = 3/4 are found by 

 interpolation. 



In Sec, 4, an attempt is made to apply the foregoing results 

 to damage by underwater explosions. In the absence of a detailed solution 

 of the hydrodynamical probleir. associated with loadint:, certain rough sejoi- 

 empirical assumptions are made. It is assu'iied that each element of plate 

 absorbs almost instantaneously in the form of kinetic energy a constant 

 fraction of the energy incident in the solid angle subtended by that ele- 

 ment. This assumption leads ijmaediately to am initial velocity distribu- 

 tion proportional to (R + r )~-^'^; hence the special emphasis on ">'= 3/4. 

 Since the velocity of sound in water is much greater than the velocity of 

 transverse plastic waves in the plate, retardation effects in the explosion 

 wave are neglected. A foraiula is obtained giving the critical weight W of 

 a given explosive necessary to cause rupture when exploding in contact with 

 a plate of thickness a^^. The results of this formula are compared vdth the 

 results of rupture experiments •pmm^immmA at the David Taylor Model Basin, 

 Attention is centered on the values of 2Ct ^^^ fraction of the total energy 

 of explosion delivered to the plate, giving agreement between the theoretical 

 cind experimental results for rupture by contact explosions. The values of 

 y so obtained are scattered in a range of values of reasonable magnitude 

 (0.1 to 0,3). The Y values apparently depend on the plate thickness in a 

 relatively regular fashion, the explanation of which is as yet unclear. 

 Although the results do not appear very satisfactory from the standpoint 

 of predicting rupture, they may be regarded as fairly conclusive evidence 



63 



