DYNAMICS OF PACKAGE CUSHIONING 



393 



Column 2. A(x2)n is the increment of displacement between (.V2)„-i and 

 (x-2)n . A(n-2)n = (^^2)71 " (^^^a)^-! , scc Fig. 1.15.2. Note that, 

 as the curve becomes steeper, A(a-2)„ is taken smaller for better 

 accuracy. 



Column 3. (.V2)„ is the displacement associated with the n^' point (see Fig. 



1.15.2). 

 Column 4. P„ is the load that produces displacement (.V2)„ . 



->4-<— 



A(X2)j A(X2)2 A(X2)3 A(X2^ 



X2= DISPLACEMENT 





V 



A(X2) 



Fig. 1.15.2 — Graphical illustration of numerical method of calculating area under load- 

 displacement curve. See Table II. 



Column 5. A^„ = ^A(x2)n{Pn-i + Pn) is the area of the trapezoid with 

 altitude A(x2)n and bases Pn-i and P„ . It is approximately the 

 energy absorbed by the cushioning in displacing from {x2)n-i 

 to (a;2)„ . 



Column 6. ^„ is the sum of all the trapezoidal areas from X2 = to X2 = 

 (.T2)„ . It is approximately the total energy the cushioning can 

 absorb in displacing an amount (x2)„ beginning at zero dis- 

 placement. Note that ^0 is always equal to zero. 



Column 7. /?„ = A„/W2 is the height of fall that will cause the cushioning 

 to displace an amount {x2)n • In Table II, TI^2 = 18.5 pounds. 



Column 8. G„ = -P„/TI^2 is the maximum acceleration experienced by the 

 suspended mass when dropped from a height hn . 



