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IV. EFFECTS OF PRESSURE WAVES 30 
10. ENERGY-MOMENTUM CONSIDERATIONS 
10. ENERGY-MOMENTUM CONSIDERATIONS 
In designing a structure to resist damage by an explosion wave, it may be 
more helpful to view the effect on the structure in terms of energy and momentum 
rather than in terms of pressure. The energy and the momentum broyght up by the wave 
must be either reflected back into the water or absorbed by the structure. 
If the structure is rigid, the energy is completely reflected. Since, how- 
ever, compressions are reflected as compressions, the particle motion in the reflect- 
ed wave has the opposite direction to that in the incident wave; hence the momentum 
taken up by the structure is twice that brought up by the incident wave. Further- 
more, the process of reflection occurs in this case simultaneously with that of in- 
cidence. Hence the doubled absorption of momentum requires doubled stresses and 
strains in the structure (in addition to a possible further increase due to resonance 
effects). 
To decrease the absorption of momentum, the structure must yield to the 
wave. If it yields, however, a fresh complication arises; for then it will take on 
part or all of the incident energy. Two alternatives are then open. 
The energy may be converted into heat by means of friction and permanently 
retained in this form in the structure. If this is done, perhaps by the use of non- 
elastic materials, the impact of the explosion wave is handled somewhat as is the re- 
coil of a gun, whose energy of backward motion is absorbed in dashpots. 
If, on the other hand, the structure is made resilient, the energy will be 
returned into the water in a reflected wave, accompanied by the usual amount of mo- 
mentum. As in the case of rigidity, therefore, the total amount of momentum ab- 
sorbed by the structure will be twice that brought up by the incident wave. With the 
resilient structure, however, the process of reflection occurs partly or wholly after 
the incidence of the wave. Hence the doubling of the maximum stress is avoided. The 
general concussion of the vessel may be about the same in either case; but with the 
resilient structure the probability of rupture or deformation should be less. This 
“conclusion appears to be illustrated by the case of an ice breaker sheathed with 4 
feet of wood, against which a mine was exploded. The general damage throughout the 
ship was appreciable, but the local damage to the sheathing and to the steel hull was 
negligible. 
As to the desirable amount of yielding, the theoretical answer is, the more 
yielding the better . The results deduced from calculation in the foregoing simple 
cases indicate that as the yielding increases to large values the absorption of en- 
ergy decreases again; the absorption both of energy and of momentum tend ultimately 
toward zero (see Figure 10). The ideal procedure would be, therefore, to make the 
skin of a ship easily movable in‘directions perpendicular to its surface and to sup- 
port it only by means of very flexible springs or by air pressure. Then, as the cal- 
culation for a thin plate shows, the pressure wave would be completely reflected, its 
only effect on the ship's skin being to displace it inward an inch or so. No damage 
would result, and the concussion would be negligible. 
