326 - 6 - 



In equation (5) the coefficients jiven by Bureau of Ships have been increased by about 

 19 per cent to bring them into better .iccord with the jraphs of Report A and with the data 

 obtained from the full numerical integration of the equations of motion. 



The Bureau of Ships formula for f^, Is 



where the quantities In the brackets art non-dimensional and where R is the distance from the 

 Charge in feet, and M the weight In lb. of T.N.T. having the same bubble energy as the actual 

 charge; P is in lb/square inch, Equations (5) and (6) agree within about 5 per cent with the 

 curves in Report A and with the results of the full numerical integration of the equntlohs of 

 motion. It Is to be noted that since both RP^ and a^ are functions of the momentum m equations 

 (5) and (6) can only be used when surfaces are absent. If any surfaces are present which cause 

 an appreciable alteration of the momentum m then the original equations In Report A must be used. 



References , 



(1) The Effect of a Rigid Wall on the Motion of an Underwater Gas Bubole. 

 M. Schiffman. A,M,P. Memo 3 7:1; AMG-NYU, No. 7. July, 19U3. 



(2) On the Best Location of a Mine Near the Sea Bed. A.M. P. Rep. 37!lR, 

 AMG-NYU, No. W. O.S.R.D. 3841. May, 1914. 



(3) In O.S.R.D. 38*1 a relation between the displacement and momentum Is given 

 which becomes, in Taylor units, 



^'z^"^ - 41.26 (mz^l/^) I 1-774 (mz„''^)M 



This relation agrees quite well with tne points obtained ^rom their 



1 1/3 

 numerical integration but deviates markedly for higher values of h z^^ ' from 



the data in Table I. Equation (3) above Is therefore to be preferred, 



(u) The results are collected in Report B. These equations are Crilled 'approximate" 



since, in contrast to Schiffmann's treatment of the-inflnlte rigid plane, they 

 are obtained by neglecting terms of tht- order of a /d and higher powers, d 

 being the distance of the bubble centre from the surface. 



(5) "The Attraction of an Underwater Explosion Bubble to a Rigid Disc". 



(6) Buships 19U4-1. 



