34 
This maximum displacement is independent of the target properties, being 
in fact simply twice the displacement associated with the pulse in mid-water 
with no target present. It indicates, for example, that at 50ft. froma 
charge of 300 lb. T.N.T. the maximum deflection of the plating would only 
be about 0.4 in. #$This is certainly too small in comparison with observed 
damage to single-hulled surface vessels having plating about 1/4 in. thicke 
In general, therefore, the assumptions of this case seem unlikely to be 
relevant in the practical problem of damage. 
Water exerts no tension on plate but does not cavitate 
89 The solution given by equation 30 is now valid only for the initial 
period t, in fig. 16 during which the pressure on the plate is positive. 
At t = t,. the plate will leave the water and will subsequently be brought 
to rest by the resistance kx. Putting p = 0 in equation 31, the time t, 
is given by 
nt, = pai log & eee ece eee eee eee (34) 
and thence by use® of equation 30 the velocity v, of the plate at this 
time is 
ail 
Vo = 22 gb oe eee eee coe eee eee (35) 
fe 
this is the velocity with which the plate leaves the water. Whilst it may 
be permissible under most relevant practical conditions to neglect the 
stiffness term kx during the time t, in order to derive equation 35, 
it is essential to introduce this resistance during the subsequent motion 
since it is then the only mechanism which brings the plating to rest. 
The subsequent maximum displacement x,,,, is easily obtained from the energy 
equation 
eye ip e 
B nox = 3m, eee eee eee eee eee (36) 
The maximum displacement given by equations 35 and 36 will be greater than 
that given by equation 33 for case 1, the stiffness k being restricted to 
values small enough for it to be neglected, as assumed in deriving both 
equations 33 and 35. For example, with 1/4 in plate and typical 
stiffness, the explosion of 300 lb. T.N.T. at a distance of 50ft. would 
produce a deflection of about 1-2 in. on the assumptions of case 2 as 
compared with the estimate of 0.4 in. for case 14 The damage (as indicated 
by maximum displacement) estimated on the assumptions of case 2 is still, 
however, on the small side in comparison with observed damage in many 
Cases. It is desirable, therefore, to see whether the remaining case 3 
will lead to greater estimates of damage. 
* Equation 35 is obtained by differentiating equation 30 with 
respect to time that is, 
