DYNAMICS OF PACKAGE CUSHIONING 375 



The displacement direction does not necessarily coincide with the acceler- 

 ation direction. The angle d between them is given by 



where A' is defined by equation (1.7.16). 



The spring characteristics may be made the same in all directions and the 

 displacement direction may be made to coincide with the acceleration 

 direction by setting 



. _ / _ " _ 



Xo — Xq — Xq — /— 



and 



C= t' = t" 



(see Fig. 1.7.1). This makes b = b' = b", c = 0.828 and k/K = 0.274 

 in the calculations of the next section. 



1.8 Procedure for Designing Tension Spring Packages 



The design of a tension spring package, as contrasted with the analysis of 

 one, must proceed without initial knowledge of values for the parameters ko 

 and r, since these cannot be known until the springs are designed. There- 

 fore equations (1.5.4) and (1.5.6) cannot be used directly. For design pur- 

 poses they are transformed to the following set of formulas: 



Vc = |/^V^^ - 1 (1.8.1) 



^ = vh^. - ^ //( v:v + VNTsy + f (1.8.2) 



:^^ = V2(-i 4- \/r+^) (1-8.3) 



M' = N = ^^ = I (1 + 5)(_1 + VTT^) (1.8.4) 



~-b= -1 + ^i^^J^\ (1.8.5) 



These formulas have been converted to design curves which are given in 

 Figs. 1.8.1 to 1.8.5. The curves are for use in connection with the following 

 routine procedure which has been found useful in designing the springs for 

 tension spring packages. Reference should be made to Table I. 



