Analysis of potential small satellite launch operations at the Denel Overberg test range.

Abstract

One of the primary objectives of the South African First Integrated Rocket Engine (SAFFIRE) programme of UKZN’s Aerospace System Research Group (ASReG) is to develop the capacity for orbital injection missions to Low Earth Orbits (LEOs) from South Africa. The most likely launch site for these missions is the Denel Overberg Test Range (OTR) near Cape Agulhas in the Western Cape. In order to determine the suitability of OTR as a launch site, it is imperative to gain an understanding of the performance, mechanics and structural loads of a vehicle entering orbit. The goal of this dissertation is to analyse the performance of a variety of modern two-stage launch vehicles as they travel along orbital injection trajectories into LEOs from OTR. This study considers solutions for the ascent-to-orbit trajectory for various launch vehicles. The primary method was to utilise trajectory optimisation methods and this was achieved by developing an optimal control solver, which makes use of direct Hermite-Simpson collocation methods, and a sequential quadratic programming solver. In order to improve the robustness and speed of the solver, formulae for the first order analytical derivative information of direct Hermite-Simpson collocation were developed. The optimal control solver was then validated using various linear and nonlinear examples from literature. The optimal control solver was used to analyse the performance of various hypothetical missions conducted by the following established launch vehicles: Rocket Lab’s Electron, SpaceX’s Falcon 1, SpaceX’s Falcon 9, and ASReG’s proposed small satellite launch vehicle, CLV. As a baseline comparison, all vehicles were launched from OTR into various LEOs. The payloads, trajectories, control histories and structural loads of these vehicles for injection were investigated. Finally, the effect of perigee altitude, inclination, and eccentricity of orbits on the extracted results was studied. The payload performance of the launch vehicles considered were relatively similar to that provided by each vehicle’s corresponding payload user guide. On all missions, the altitude of the Electron, Falcon 9 and CLV would constantly increase with range, however the Falcon 1 would tend to rise, dip, and then rise once more on missions to orbits with a perigee altitude of 200 km. Such trajectories are referred to as lofted trajectories and are common among vehicles with a low upper stage thrust to weight ratio (Patton and Hopkins, 2006), such as the Falcon 1. The tangent yaw and pitch of the thrust direction was highly linear for all analysed missions. This result allows for a reasonable control law which can be used to determine trajectory solutions using indirect optimal control methods. This study demonstrates the viability of the Denel Overberg Test Range as a competitive base of operation for space launch missions to LEO.