362 BELL SYSTEM TECHNICAL JOURNAL 



Example: Find the properties of the hnear cushioning required so that 

 the maximum acceleration will be 50g in a 3 ft. drop of a 20 lb. article. 

 From (1.3.4), 



necessary travel, dm = — ^ — = 1.44 inches. 



From (1.3.5), 



^ , 20 X (50)' ._ . „ ,. 

 sprmg rate, k^ = = 694 Ibs/m. 



2 X 36 



From (1.2.16) 



Maximum force P^ = 20 X 50 = 1000 lbs. 



1.4 Cushioning with Non-Linear Elasticity 



In practice it is rarely that a packaging system has linear spring charac- 

 teristics. Departure from linearity may be due to 



Fig. 1.4.1— Linear elasticity. Class A. 



1. Non-linear geometry, such as in the tension spring package described 

 in Section 1.7. 



2. Non-linear characteristics of distributed cushioning materials such as 

 excelsior and rubber. 



3. Abrupt change of stiffness such as occurs if the packaged item can 

 strike the wall of the container. 



For the purpose of developing design formulas it is desirable to have 

 analytical functions to represent load-displacement characteristics. It is 

 not feasible to have only one family of functions with adjustable parameters 

 to fit all possible shapes of load-displacement curves. Therefore, all the 

 practical shapes have been divided into six general classes, most of which 

 are associated with simple functions having one or two adjustable param- 

 eters. The six classes are as follows: 



Class A — Linear Elasticity. This has already been treated. Its load- 

 displacement function is 



P = hx2. (1.4.1) 



