m SURFACE AND OTHER EFFECTS 



exponents are probably appropriate for bubble pulse pressures. The 

 dependence of damage on peak pressure or impulse in limiting cases, 

 with so to speak a fractional utilization of impulse in intermediate cases, 

 is well illustrated by Modugno or diaphragm gauge plates, which for 

 small charges undergo deformations determined by impulse, and for 

 charges of several hundred pounds respond much more nearly to the 

 initial shock wave peak pressure. The dynamical properties of the 

 gauge and its surroundings must of course also be considered. For ex- 

 ample, increased rigidity of surrounding or supporting structures has 

 the effect of increasing the equalizing diffraction pressures, and hence 

 leads to increased deformations. 



If cavitation occurs in the water adjacent to the structure, a some- 

 what different state of affairs occurs in which a large amount of energy 

 can be trapped as kinetic energy of the structure and cavitated water, 

 and later expended in plastic work of deformation. The resultant 

 deformation may then be roughly in proportion to the square root of 

 incident shock wave energy, and hence vary with charge weight and 

 distance roughly as ]V^^^/R. Experimental evidence in some cases in- 

 dicates approximate equality of this energy with plastic work of defor- 

 mation. It is important, however, to observe that the total energy 

 absorbed by a plate of finite area may considerably exceed the incident 

 shock wave energy over the same area, the excess coming from other 

 parts of the wave by the agency of diffraction. 



The various empirical laws as to variation of pressure wave pa- 

 rameters with weight and distance are frequently helpful in analysis of 

 damage, but these laws should not be taken too literally. Observed 

 variations of damage may be determined in part by one parameter more 

 than another, but a considerably different weight-distance law for 

 damage may, and often does, result from the dynamical properties of 

 the structure. Furthermore, the differences in the characteristic laws 

 are not always clear cut. A weight exponent corresponding to defor- 

 mation varying as W^-"^^ may perfectly well be the result of peak pressure 

 proportional to W^-^^, or square root of energy varying as TF° -^ An- 

 other consideration is the fact that shock waves near a charge are propa- 

 gated with considerable energy losses by dissipation, and conclusions 

 valid at greater distances should not be extrapolated to near-contact 

 explosions without careful analysis or supporting data. 



