F = resistance force encountered by the front of the object 

 as it moves through the soil 



F = force produced in accelerating the fluid or soil 

 around the object 



In the first phase of the analysis, equations involving powers of 

 velocities and displacements were assumed as approximate representations 

 of Equation 2. These were in turn analyzed statistically to determine 

 which constant parameters would cause the proposed equations to fit 

 the data best. The forms of the equations were determined by assuming 

 the nature of the forces acting on the object. For example, a general 

 penetration equation should contain pure hydrodynamic forces. These 

 would take the form of a constant force due to weight and buoyancy 

 and a velocity-squared term due to water drag. As the testing device 

 enters the soil, additional forces are encountered, such as viscous 

 resistance of the soil (a function of velocity) and soil shear strength 

 which changes with depth of penetration (a function of displacement) . 

 The form of the first proposed equation was as follows: 



F = (m + c) a = A' + B'v^ + C'v + D'x (3a) 



net 



where F is net force on object 

 net -^ 



m = mass of object 



c = "added mass" 



a = acceleration 



V = velocity 



X = displacement (penetration) 



A',B', C',D' = coefficients reflecting physical factors 



This force equation can be transformed into an acceleration 

 equation: 



a = A + Bv^ + Cv + Dx (3b) 



where A = A' /(m + c) 



B = B' /(m + c) 



C = C /(m + c) 



D = D' /(m + c) 



