DYNAMICS OF PACKAGE CUSHIONING 385 



17 5si if the cushioning bottoms witli tangent elasticity. Now, according to 

 equation (1.10.2), the best initial spring rate for cushioning with tangent 

 elasticity would be 



A'u = = 1690 Ibs/ni. 



In this case, equation (1.10.3) gives, for the maximum acceleration, 



„/ 3.9X36 .^- 

 G. ^ ^^^ = 122g. 



Hence, confronted with a space limitation less than that required for a 50g 

 linear spring, it is better to use an initial spring rate higher than that for the 

 50g linear spring in order to strike an economical balance between displace- 

 ment and bottoming. The best balance, among cushionings having tangent 

 elasticity, is obtained by using equation (1.10.2). 



If no factor of safety is considered, it would be still better not to use a 

 bottoming type of cushion at all. From equations (1.3.5) and (1.3.3) 

 it can be seen that a linear spring with a constant of 1090 lbs/in will give 

 only 63g with a displacement of 1.15 inches. Such a spring, though, would 

 bottom very sharply at a drop slightly higher than 3 ft. and would give 

 an acceleration much greater than cushioning with tangent elasticity which 

 bottoms more gradually. This may be important if there are high-fre- 

 ciuency, brittle elements in the packaged article (see Part III). 



1.11 Procedure for Finding Maximum Acceleration and 



Displacement for Cushioning w'ith Tangent Elasticity 



(Class C) 



To illustrate the use of the equations and curves for Class C cushioning, 

 the same example used for Class B will be used, as it was observed that the 

 experimental load-displacement curve in that example (Fig. 1.6.1) is a 

 border line one which can be treated as either B or C. 



By laying a straight edge along the first part of the curve (Fig. 1.6.1), 

 the average initial spring rate is found to be 305 lbs/in. This value is taken 

 as k() in the present case. 



The next step is to find a value of db such that a graph of P/db vs Xo/db 

 will fall slightly above the curve ko = 30(0) in Fig. 1.4.7; db must be greater 

 than 2 inches, since that displacement was obtained in the experiment. 

 As a trial take db = 2.25 inches and test it at one point, say the experi- 

 mental point P = 300 lbs., x^ = | in. Then P/db = 133 and Xo/db = 

 0.39. The point (0.39, 133) falls below the curve ko = 30(0) in Fig. 1.4.7. 

 Next try db = 2.5 inches. In this case, for the e.xperimental point P = 



