164 - 2 - 



PART I . 



Summary of Approximation Formulae. 



Two non-dimensional variables define the size, position and motion of the OuDble at any time t, 

 viz:- the radius of the bubble a and the depth z of the centre of the bubble measured from a point 

 3 3 feet above sea level . 



A parameter c appears in the equations, in their non-dimensional forms, which is related to 

 the potential energy in the gas; the value of c for T.N.T. is given by:- 

 1 

 C = 0.075 M^ (2) 



where A is in lbs. 



The period of the first oscillation - T (seconds) 

 1 



(3) 



where Z is the depth of the charge in feet below a point 33 feet above 

 sea level. 



' is thp charge weight in lbs. 



The period is the time taken for the bubble to expand and contract again to its minimum radius. 



At a distance a non-dimensional units from a free or rigid surface the period T is altered to 



0.21 a 

 -!- = (l T _ — [D_) (r.h.S. non-dimensional) (3a) 



where the upper sign is for a free surface, the lower for a rigid surface, and 

 a is the maximum radius (see equation {«)). 



The maximum radius of the bubble - a_ 



a = Tti^ — (l - c a " ) (non-dimensional) («} 



'"0 



z being the non-dimensional depth of the charge at detonation; a is 

 plotted in Figure 2 against z^. 



The vertical momentwn constant - m. 



The non-dimensional constant m is involved in several equations and is given by: 



0.7 a ^ 

 m = — (nor»-dimensional) (5) 



At a distance d non-dimensional units below a free surface or above a rigid surface the 

 vertical momentum constant is changed to m* where 

 5 

 3 , 5 



(5a) 



This value of m' must be used in all subsequent equations involving m If the surface effect 

 Is appreciable in the case considered. 



