SHOCK WAVE MEASUREMENTS 237 



The general agreement is excellent, even to the shape and position of the 

 bump at t/W^'^ = 225 ^isec./lb.^^^. The differences in pressures at 

 later times are to be attributed to experimental inaccuracies rather than 

 to failure of similarity. 



The agreement among results for the 3 charge weights can also be 

 shown by comparison of values for peak pressure and reduced values of 

 time constant, impulse, and energy density. The reduced values are 

 obtained by dividing by W^'^, this being necessary to make the values 

 comparable as all depend linearly on time, which scales as W^'^. The 

 results in Table 7.1 are seen to be in excellent agreement except for 

 the impulse (integrated to 6.7^), the difference in this resulting from 

 the discrepancies in the tails of the measured curves. 



The following parameters are functions only of the ratio W^'^/R: 

 Peak " ■ . 



E/W 



Peak pressure Pm, reduced time constant d/W^'^, reduced impulse I/W^'^, reduced energy density 



Table 7.2. Functional dependence of shock wave parameters on charge weight W 

 and distance R required by similarity. f(x) represents an undetermined function 

 of the argument x. The last column gives the limiting acoustic law for a spher- 

 ical wave. 



A natural question is whether the verification of similarity for 

 spherical charges is also obtained for other charge shapes. There ap- 

 pear to be no direct experiments establishing similarity in such cases, 

 but indirect evidence gives no reason to doubt the validity of the prin- 

 ciple, nor does the hydrodynamical theory. The results of Fig. 7.3 

 and Table 7.1 thus provide a good experimental basis for accepting the 

 principle as generally valid for shock waves, and this acceptance is fur- 

 ther justified by less direct tests described in the following. 



B. Similarity curves for spherical charges. The principle of simi- 

 larity, as developed in section 4.1, leads directly to simple predictions of 

 the functional dependence of shock wave parameters on distances from 

 the charge and its dimensions. These predictions are summarized in 

 Table 7.2, and follow simply from the basic proposition which can be 

 stated: pressures for the same value of W^'^/R are the same at equal 

 values of t/W^'^. To show how this is fulfilled in practice, values of the 

 various reduced parameters listed in Table 7.2 can be plotted as func- 

 tions of W^^^/R for different values of both W^'^ and R. If similarity is 

 in fact realized, all the points for each reduced parameter should lie on 



