In most tests, the identification of soil entry was difficult to 

 determine. The technique used was to examine the forces on the object 

 in the water as opposed to the forces on the object in the soil. A 

 plot of velocity-squared versus acceleration is necessary, and its 

 rationale begins with the following hydrodynamic force equations. 



(m +c) a = -mg (-^^ -) + C^ (-|) A v^ (la) 



c 



P - P C p „ 



m+c p m+c Z p 



c 



where a = acceleration, feet per second per second 



g = acceleration of gravity, feet per second per second 



m = the mass of the object, slugs 



p = the average mass density of the object, slugs per 

 cubic foot 



p = the mass density of water, slugs per cubic foot 



w 



C = coefficient of drag, dimensionless 



A = profile area, square feet 

 P 



V = velocity, feet per second 



c = "added mass" associated with accelerating water around 

 an object, slugs 



The left hand side of Equation la represents the net force on the 



object (ma) plus the "added mass" associated with accelerating an 



object through a fluid. The first term on the right is buoyancy and 



weight lumped together to represent the driving force. The second 



term is the drag force. 



By dividing through by (m + c) , Equation lb is derived. The 



form of the relation between a and v is a straight line with slope, 



C„ p P - P 



D w . , 1 ^. • ,. ^ mg c w 



, ; , — ;- A and acceleration intercept, — y — 7 — . . 



(m + c) 2 p '^ ' (m + c) p 



