modification for use with (1) a soil with properties which vary with 

 depth and (2) irregularly-shaped objects. Only a numerical technique 

 such as that of Smith" appears to be directly applicable to these more 

 general situations. However, the technique of Smith should be modified 

 somewhat to more accurately model the penetration process. Several 

 additional force terms should be considered, and the relationship 

 for predicting the penetrating object frontal resistance should be 

 modified. 



The proposed modified prediction technique is based upon 

 Equation 2: 



EF=ma = F^ + F^ + F3^ + Fgp + F^ (2) 



where the terms are as defined previously. Considering each term 

 separately and defining downward forces as positive: 



1. F ~ The driving force is equal to the weight of the object 



in water. 



2. Ftt ~ ^'^^ hydrodynamic drag force is usually expressed by an 



equation of the form: 



^H = -S Pw T- ^P (10) 



where C = drag coefficient 



p = mass unit weight of water 

 w 



v = object velocity 

 A = object cross-sectional area perpendicular to motion 

 For a given object the drag equation may be written more simply as 



^H = -°s^' (11) 



where D = specific drag coefficient 



12 



