DYNAMICS OF PACKAGE CUSHIONING 



383 



The ratio G,„/Go is plotted against the ratio db/do in Fig. 1.9.1. It may 

 be seen that the multiplying factor increases very rapidly as the displace- 

 ment ratio (db/di)) falls below unity. For example, if the cushioning, with 

 tangent elasticity, reaches hard bottoming (di,) when only 80% of the 

 required displacement (do) is attained, the acceleration is multiplied by 

 3.5; if only 609o of the required displacement is available, the acceleration 

 is multiplied by 11.5. 



Example: To illustrate with a numerical example, consider the case already 

 discussed in Section 1.3, where we found that a spring rate of 694 lbs/in 

 and a displacement of 1.44 inches were required to limit a 20-pound article 



03 



0.2 

 0,1 



.2 .4 .6 .8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 24 2.6 2.8 3.0 



Fig. 1 .9.2 — Curve for finding maximum displacement for cushioning with tangent elasticity. 



See equation (1.9.5). 



to an acceleration of 50g in a 3-foot drop with linear cushioning. Let us 

 suppose that only 1.15 inches are available, instead of 1.44 inches, and that 

 the cushioning has tangent elasticity starting with a spring rate of 694 

 lbs. /in. Entering the curve of Fig. 1.9.1 at db/do = 1.15/1.44 we find 

 Gm/Go = 3.5. Hence the maximum acceleration will be 175^ instead of the 

 required 50g. This illustrates the wide variations in acceleration that may 

 occur as a result of minor variations of dimensions in high G packages. 



It is not necessarily true that the 17 5 g test is 3.5 times as severe as the 

 50^ test for all elements of the supported structure, since the severity de- 

 pends also on the shape and scale of the acceleration-time relation. The 

 factor may be more or less than 3.5 but it will be very close to this value for 



