DYNAMICS OF PACKAGE CUSHIONING 



391 



Cubic elasticity will give a (/,„ somewhat more or less than 2h/Gm depending 

 upon whether the parameter r is positive or negative. 



It is seen that a factor of almost four can be gained, in the linear dimensions 

 of the cushioning space required, by replacing the tangent type of cushioning 

 with the hyperbolic tangent type. 



There are several ways of obtaining a load-displacement curve with a 

 shape similar to the hyperbolic tangent curve. One of the most interesting 

 is suggested by the fact that the load-displacement curve of a strut has 

 approximately this shape. Hence a bristle brush has the proper 

 characteristics. 



TABLE II 







1 



2 



3 



4 



5 



6 



7 



8 



9 



10 



11 



12 



13 



Gn 



Pn 



11.1 



15.7 



22.2 



31.6 



39.5 



51.4 



74.0 



91.0 



121.0 



141.5 



173.0 



1.15 Nltmerical Method for Analyzing Class F Cushioning 

 The numerical method to be described is one that has been adapted from 

 a graphical one used by the Committee on Packing and Handling of Radio 

 \'alves of the British Radio Board. The method has advantages of sim- 

 plicity in concept and ease of application, especially when the load-displace- 

 ment curve of the cushioning does not resemble closely one of the Classes A 

 to E described above. It has the disadvantage that it does not yield, 

 directly, numerical factors by which the spring rate or depth of cushioning 

 should be changed in the event that the analysis reveals inadequate or more 

 than adequate protection. 



The method is based on the fact that the area under the load-displace- 

 ment curve of the cushioning represents the energy stored in, or absorbed 

 by, the cushion. The total amount of energy that must be transferred is 

 equal to the product of the weight (IFo) of the suspended item and the 

 height (//) of drop. By finding the abscissa (xn) and its ordinate (P) which 



