A digital computer program was available to perform a regression 

 analysis on the proposed equation . Since the data were available in 

 digital form, it was an easy matter to input values of acceleration and 

 respective velocity, velocity-squared, and displacement for each of 

 the tests. The output of the regression analysis consisted of values 

 for the coefficients, A, B, C, and D and statistical information for 

 each test. 



After performing the regression analysis, Equation 3b was found to 

 be a weak duplication of the test data. Consequently, several other 

 euqations were proposed and analyzed until reasonable correlation 

 resulted. The following equations were analyzed, in succession, and 

 were all found to have weak correlation: 



a = A + Bv + Cx (4) 



2 2 



a = A + Bv + Cv + Dx + Fvx + Fx (5) 



2 2 3 3 



a = A + Bv + Cv + Dx + Exv + Fx + Gv + Hv x (6) 



o 2 3 3 4 



a = A + Bv + Cv + Dx + Exv + Fx + Gv + Hx + Iv (7) 



Equation 8 was found to duplicate the data from any given test with 

 high correlation: 



o 2 3 3 4 2 



a = A + Bv + Cv + Dx + Evx + Fx + Gv + Hx + Iv + J(vx) 



+ K(vx)3 (8) 



Because of the complexity of Equation 8 and because the regression 

 analysis revealed that several terms were insignificant, a modification 

 to Equation 8 was formulated and analyzed. Its form was: 



a = A + Bv^ + C(vx) + D(v^x) (9) 



(It should be emphasized that even though the constant coefficients, 

 A, B, etc., appear several times in the above equations, these 

 coefficients do not symbolize the same value from equation to 

 equation.) The results of the regression analysis on Equation 9 

 were as follows: 



10 



