1163 
-9- 
Damage to structure supporting the plate 
Though the damage whicn the water pulse will do depends on the strength of the supporting 
structure, so that the actual amount of damage cannot be calculated, the foregoing analysis shows 
that for a given amount of damage the relationship between charge and distance can be determined. 
This will depend on whether (a) the plate remains in contact with the water or (b) it breaks contact. 
(a) The water remains in contact with the plate. 
In this case the plate is moved through a distance ay and is brought to rest by the suction 
of the water. The true value of cae will depend to a small extent on the stiffness of the structure 
out this effect will always be small compared with the effect of water suction in a structure of the 
type used in ship construction. In assessing the damage expected according to (a) it is necessary 
to compare the charges which will produce a given value of (Soe From (24) it witl be seen that 
p 
eo rc — , or, inserting € from (22), 
mn € 
2p, sin ie] 
noc 
(32) 
Snax 
For a given amount of destruction therefore a constant value of Po sin@/n is necessary. The 
maximum pressure at distance r from a submarine explosion of a mass M of explosive is Pin anh /3 7 - 
where A is a constant depending on the composition of the explosive and a number of other factors 
which can be regarded as constant when the relationship between charge-weight and oe fora 
given arount of damage is being considered, The time constant n is proportional to wt 3 so that 
n= 8 thus for a given amount of destruction according to hypothesis (a) 
[#2 sin q wi/3 . 
r 
constant 
(33) 
* 7 2130s. 
or r is proportional to M°'* sin@ 
and for normal incidence r is proportional to w2/3 
(b) The water breaks contact with the plate when the pressure ceases to be positive. 
In this case the plate is discharged from the water with velocity Gy where cae is given 
by (27). In this case inserting the expressions a amt 3 ir, n= BM /3 jn (27) 
a 28 ey 
Set cB) Ge (34) 
To find how r varies with M the case of normal incidence may be considered. in that case € = pc/mn. 
For a given thickness of plate therefore € i's proportional to wt Though (34) shows that for a 
given amount of destruction r is not related to M by any simple power law, yet for practical purposes 
it may be convenient to find the power law which most nearly represents (34) over a limited Ainge. 
Assuming this to ve 
r = (constant) mS (35) 
the valuc of S may be determined by logarithmic differentiation of (35) and (34), thus 
SS (36) 
Bi | 
and 1S om ore [Pee ¢ (37) 
and since € is proportional to yi/3 de /e = 5 (dM/tt). | Hence c mparing (36) and (37) 
Vog , € 
s+ 3-5[ ety |[s- es] oH 
Values esses 
