Trajectory Control and Analysis for the Vertical Takeoff and Vertical Landing Reusable Launch Vehicle's Upper Stage

Abstract

*Reusable launch vehicles are a promising business for the future. The vertical takeoff and vertical landing vehicle is one example of reusable launch vehicles. However, compared with other types of reusable launch vehicles such as horizontal take off and horizontal landing ones, this type of vehicles typically has a small payload capacity and the ability to provide very small or even zero velocity to the upper stage at the peak of the reusable launch vehicle’s trajectory. This makes the payload difficult to achieve a parking orbit for further orbital transfers. This paper develops a new and intuitive method of the trajectory control, called “energy for altitude and time” (EFAT), which allows an upper stage to achieve low Earth orbit with little initial velocity. This proposed method will be numerically compared with a conventional method (optimal ascent algorithm) combined with two optimization methods (a genetic algorithm and SNOPT). Nomenclature A = upper stage cross section area a a ∆ = maximum available acceleration from the selected engine c t a ∆ = acceleration in the transverse direction c r a ∆ = acceleration in the radial direction n r a ∆ = desired acceleration in the radial direction n t a ∆ = desired acceleration in the transverse direction drag a = atmospheric drag acceleration 2 J a = J2 acceleration D C = atmospheric drag coefficient GA = genetic algorithm 0 g = gravitational constant at sea level n g = desired acceleration of the upper stage sp I = propellant specific impulse 2 J = J2 perturbation coefficient m m � = max mass flow rate of propellant c m = current mass of the upper stage f m = final mass of the upper stage i m = initial mass of the upper stage re m = remaining mass of the upper stage p m = mass of propellant m m = mass of the selected motor s