Where, Fx and Fz are the forces in the x and z direction while F is the resultant force.
Li and 0i are determined from the equations (3.10) and (3.11) depending on the
displacement. The Matlab program "PROG4T" as shown in the appendix A, is used to
perform this calculation.
3.4.5 Velocity and Acceleration with Respect to Position when the Mast is Deployed
in a Single Stage
The instantaneous time with respect to position is the same for all the levels after
the stiffness of the spring is designed as in Case 3.43. The total time taken to deploy the
mast in one single stage is equal to the time taken to deploy a single level, when the mast
undergoes stage wise deployment. The velocity and acceleration of the topmost platform
is,
N(Z,,)- N(Z,, )
Velocity VN N ) (3.33)
tn
Acceleration AN VN VN (3.34)
t
Where, Zn, Zn-1 and tn are determined from equations (3.18) and (3.19). From equations
(3.33) and (3.34) it is evident that the velocity and acceleration of the last vertical
member on any side is N times the velocity and acceleration when the mast is deployed
stage wise. The Matlab program "PROG5M" as shown in the appendix A, is used to
perform this calculation.
3.4.6 Stiffness and Minimum Deflection of the Spring when an External Load is
Applied
Let Fapx be the external force applied in the negative z direction when the mast is
fully deployed, hence when fully deployed the springs should apply a counter active force
in the z direction equivalent to Fapx to prevent any change in the shape of the mast.