Mathematical relationship between mean cable tensions and structural parameters of deployable reflectors

The main purpose of the paper is to investigate the effects of structural parameters of deployable reflectors on their mean cable tensions. The proportional relations between spatial and plane cable nets are firstly explored on the basis of projection principle. By the means of obtained proportional relations, the analytical expressions between the mean spatial cable tensions and structural parameters of deployable reflectors including aperture, subdivision number and focal length are then derived. In the following, a modified plane projection method is proposed for pretension design of offset reflectors. Finally, numerical simulations are taken to verify the analytical expressions, as well as the modified plane projection method. The results show that the mean spatial cable tensions are predicted accurately by the analytical expressions, and uniform tension distribution is obtained by the modified plane projection method. With the applications of the analytical expressions and the modified plane projection method, the cable tensions can be controlled more flexible and convenient in engineering applications.