393 



where W Is the weight of the charge in pounds, 



p^ Is the total hydrostatic pressure. Including atmospheric pressure, 



expressed In atmospheres, and 

 H is the rise in feet from the point of detonation to the location of 



the next peak compression. 



The total rise during the first compression and the re-expanslon should be 

 about 2H. The charge may vary from 1 ounce to 1000 pounds, and the depth may 

 be as much as 300 feet for the larger charges. 



In using this formula It must be remembered that If the point of 

 detonation is too close to the surface, the gases will blow through the sur- 

 face, at least in large part, and no typical recompression can occur. This 

 ought almost certainly to be the case if the point of detonation is closer to 

 the surface than the maximum radius attained by the gas globe in its first 

 expansion. 



The formula for H as given by the approximate calculations of the 

 present report may be found by putting By = B^ = 0, c^ = 1 , N^ = and drop- 

 ping the term in B^ In Equation [191. which turns out to be negligible in all 

 interesting cases of purely gravitational action. Then Equations [I'+a], [l6], 

 [19], and [2^] give H = X^ - X„ = U.O VW/p^, in exact agreement with Equa- 

 tion [2U]. 



It will be noted that the rise H up to the first peak compression 

 Increases as the weight of the charge Increases, and also as the hydrostatic 

 pressure decreases. The Increase results partly from the greater buoyant 

 force on a larger gas globe and partly from an Increase in the time occupied 

 by the oscillation. 



An interesting plot given In Reference (8) is reproduced In Figure 

 5. It shows the radius of the gas globe and the upward displacement of its 

 center as functions of the time, for four different values of the initial 

 hydrostatic pressure, as found by numerical integration. The plot applies 

 approximately to any charge at suitable depths; small errors will remain 

 owing to the fact that in the calculations no allowance was made for the gas 

 pressure. It is interesting that at the smallest depth, Zq = 1 , the gravita- 

 tional effect is so large that the radial motion is almost deadbeat, so that 

 no succeeding pulses occur. 



The scales in Figure 5 vary with W, the weight of the charge in 

 pounds. Unity on the axis of ordinates represents L feet, and unity on the 

 axis of abscissas represents T seconds, where L and T are given by the 

 formulas 



L = 10 H^ ^ feet 

 T = 0.55 W 8 seconds 



