time taken to fully deploy any layer in the structure remains a constant. This is an
approximation method and the solution obtained is not accurate.
Let the stiffness of the springs for any layer be Kj. During the deployment of a
layer the time taken (ti) over any position interval Xi to Xi+l is known. For some position
interval Xi to Xi+l the time taken (ti) would be the least when compared to the time taken
by the layer to deploy through any other position interval. Let this value of time be
assigned to the variable LT. Then, from equation (2.19)
Time taken for the structure to deploy from
Xo to X1 = LT lo = ti
X1 to X2 = LT 112 = t2
X2 to X3 = LT 123 = t3
Xn-1 to Xn = LT l(n-1)n = tn (2.23)
Where lot, 112, 123, ...... l(n-1)n are variables.
From equation (2.21),
LT (lo+ 112 + 123 + 134 +................... l(n-l)n)= TT (2.24)
LT' (loi+ 112 + 123 + 134 +.................. l(n-l)n) = GT (2.25)
Where, GT is the new 'time' within which the layer should completely deploy and LT' is
the new 'least time' for some position interval Xi to Xi+i. In both equations (2.24) and
(2.25), (lo + 112 + 123 +134 +................... + l(n-1)n) remain the same since the time taken
to deploy through any two corresponding position interval in two different layers is
proportional. The pattern at which the instantaneous time changes at every position
interval is always the same for layers with different spring stiffness. From equation
(2.25)