SHOCK WAVE MEASUREMENTS 229 



Their character is also affected by the shape of the charge, as are fea- 

 tures of other positions of the pressure-time curve. The origin of these 

 humps has not been conclusively demonstrated, but it is reasonable to 

 presume that they arise from internal reflections in the product gases of 

 the rarefaction wave of pressure generated in these products when the 

 initial detonation wave first reaches the surface of the charge. No de- 

 tailed analysis of the complicated dynamics inside the products has 

 been attempted, but the time of appearance in the shock wave in rela- 

 tion to the initial peak is at least of the order of magnitude to be expected 

 from this explanation. 



It is to be expected that charges which do not have spherical sym- 

 metry will give rise to a shock wave which is not symmetrical, and dif- 

 ferences in form of the wave at different points around the charge are 

 in fact observed. An example is the pressure-time curve, shown in 

 Plate VI for the shock wave at one end of a cylindrical charge contain- 

 ing 300 pounds of TNT. In this case, two pressure peaks are observed, 

 the second being higher than the first, and it is evident that approxi- 

 mation of the curve by an exponential is only a crude representation of 

 it. Double peaks of this kind are usually observed at points on or near 

 the extended axis of cylindrical charges, their relative magnitude and 

 displacement depending on the relative dimensions of the charge and 

 distance of the point of observation. These complications are accentu- 

 ated for small charges of insensitive explosives, for which relatively 

 large booster charges of more sensitive materials must be used to insure 

 proper detonation. The explanation of such departures is considered 

 in section 7.7, but can be considered roughly to be the result of a non- 

 linear combination of shock wave pressures from different parts of the 

 charge. 



The conclusion of importance for the present is that, while an ex- 

 ponential curve is a simple and convenient approximation to the form 

 of an underwater shock wave, it is by no means a perfect representation 

 and in some circumstances is a rather poor one. 



7.2. Experimental Shock Wave Parameters 



A complete, explicit representation of experimentally measured 

 shock wave pressure-time curves for any type of charge would be an 

 equation giving the pressure as a function of time after arrival of the 

 initial peak in terms of the charge weight and position of the point of 

 measurement. Even for the simplest forms of charge conveniently 

 realizable, an exact result of this kind would be cumbersome and not 

 readily visualized. On the other hand, a simple functional representa- 

 tion by means of a negative exponential curve is not a fully adequate 

 representation, as the discussion of section 7.1 shows, and some compro- 

 mise between the two possibilities is usually desirable. 



