DYNAMICS OF PACKAGE CUSHIONING 581 



' As an example of the calculations, Table I contains the entries for the 

 design of springs for a 21 pound article (including \ the estimated spring 

 weight) which is to be packaged so as not to exceed 35g in a five-foot drop, 



TABLE I 



Computation Form for Tension Spring Packages 



1. W2 (lbs.) 21 



2. // (ins.) 60 



?>. G„, 35 



4. xo (ins.) 5 



5. I (ins.) : 7.07 



6. 6 



7. Calc. xq/( 0. 707 



8. Find Vc from Fig. 1.8.1 0.91 



9. Calc. h/y/c (G,n = L 0.269 



10. Find N from Fig. 1.8.2 1 .265 



11. Calc. W^CnyiliN = K (lbs/in.) 169.0 



12. Calc./ = 3.13 (K/Wo^i (cyc./sec.) 8.9 



13. Find k/K from Fig. 1.8.3 0.274 



14. Calc. k = K ■ k/K (lbs/in.) 46.5 



15. Calc. B = IWih/Kcf 0.368 



16. Find d,„/Vc I from Fig. 1.8.4 0.575 



17. Calc. djC = Vc • d,n/y/a 0.518 



18. Calc. d,n = t ■ djt (ins.) 3.68 



19. Calc. dm/t + xo/t 1 .220 



20. Find efC from Fig. 1.8.5 and line 6 0.580 



21. Calc. /^™ = ^ • e/^ • ^(Ibs) 191.0 



12. Coil diameter (ins.) 1 .40 



23. Wire diameter (ins.) 0.207 



24. Number of turns 19 



25. Fiber Stress (Ibs./sq. in.) • lO'^ 80 



26. Length of Coils (ins.) 3.93 



27. Length inside hooks (ins.) 7.07 



1.9 Cushioning with Tangent Elasticity (Class C) 



This is one of the most frequently encountered classes of cushioning since 

 it includes a very common type of bottoming (Figs. 1.4.3 and 1.4.7). The 

 load-displacement function (equation (1.4.3)) takes into account the fact 

 that the cushioning can be compressed only to a definite amount db . 



To find formulas for maximum acceleration and displacement, we pro- 

 ceed as follows. Substitute equation (1.4.3) in (1.2.15) and perform the 

 integration, obtaining 



^Mogcos"^= -W,h, (1.9.1) 



IT- Mb 



which may be written as 



