Let, F'apx = 6K (dmin) cos45 (3.35)
If F'apx is greater than Fapx then the values of Kj and dmin remains the same and if
F'apx is smaller than Fapx the values of Kj and dmin should be accordingly altered. The
maximum possible value for the minimum deflection of the spring is given as a
percentage (P) of the working deflection of the spring dw Hence dmin = P dw
Let, F"apx= 6Kj dmin cos45 (3.36)
IfF"apx is greater than Fapx the values of Kj and dmin may remain the same as in
equation (3.36) or the value of dmin is further optimized to a lower value such that F"apx is
equal to Fapx. If F"apx is smaller than Fapx then the value of Kj should be altered.
F
6Kj p (3.37)
dmn
Maximum deflection of the spring,
dmax = dmin + (Lmax-Lmin) (3.38)
Total length of the spring,
LS= Lmin +dmin (3.39)
Hence, the stiffness, minimum deflection, maximum deflection and the total length
of the spring is determined. The Matlab program "PROG1M" as shown in the appendix
A, is used to perform this calculation.
3.5 Numerical Example
Given:
Height of the mast when deployed H= 2m
Length of rectangular plates Lp = 1 m
Height of every single level Hi = 1 m
Mass of each plate Mp = .2 kg