682 - " - 



Tliese laws can be verified yy substitution in (5), (6), (7), (lO) and (ll). The velocity of the 

 waves at corresponding points are in the ratio of n:l. 



The fact that wave heights at corresponding distances are only in sixth root of the charge ratio 

 implips that only relatively modest waves are to be expactod from large surface explosions. 



C ase II. Initial Crater arid Dome , 



Writing as before 



we must first solve the pquation 

 „3 



h^ (h, + 2) 



(15) 



h-J (hj + Z) 

 for the ratio h,/h . Suppose that the solution is 



hj/hj = m (16) 



Then the scaling laws are 



a, /a, = d,/d, = k,/k, = r,/r, = allcrl = t^/tf = m 



'2 '"?' 'r ''1' " "' ''^' 



$2 {m x, /Tt) = m t,^ (x,i) 



The velocities of the waves at corresponding points are in the ratio iMii. 1. 



If a small model experiment is compared with a very large full scale trial we may assure that h, 

 is negligible compared with Z and that Z is negligible compared with h-. Then 



^ - n 3/" (z/hj) ''" 



The results to te expected from large explosions therefore scale up with those from those of a 

 given small explosion in the ratio of the fourth root of the charge ratio, the corresponding distances 

 and depths being in the same ratio. 



The results to be expected from two small scale experiments may be approximated by assuming that 

 h, and h are both negligible compared with Z. Then 



and the wave heiahts, distances and depths scale according to the linear dimensions of the charges. 



Wave System from a Surface ^'xp 1 siov over Deet' "later . 



According to the Cauchy-Poisson theory of gravity surface waves (Lamb's Hydrodynamics Sixth 

 Edition page 432), the surface elevation of radius O) and time t caused by the application of unit impulse 

 downward at the origin at time t = is given by 



G(9t /ai) (18) 



(l») 



