Estimation Technique of Minimum Energy Required for Complete Deployment of Folded Fin Under Gust Requirement (II): Considering Time Constraint

Abstract

A previously developed estimation technique, of the minimum energy required for complete fin deployment under an operational requirement of gust speed, was modified to consider time consumed for fin unfolding as an additional requirement, which might lead to an increase of the required energy. Some modifications were made such as non-zero kinetic energy of unfolding fin when completely deployed and its monotonically increasing angular speed during unfolding motion having a profile of square-root function which helped to properly evaluate elapsed time for fin unfolding and to combine the additional time constraint with the fin folding motion equation including external moments of aerodynamics, gravitation, and friction, while, in the previous study, zero energy and bell-shaped speed profile had been used. Demonstrations of this estimation technique considering the time constraint additionally to the gust speed requirement were carried out with the same unfolding fin system and torque profiles used in the previous study and showed that unfolding systems equipped with energy estimated by this technique met all the given gust requirement and time constraint, irrespective of their torque profile, in terms of elapsed time for fin unfolding and allowable wind speed denoting the maximum speed of gust against which in every direction fin could deploy.