Study of spacecraft hover and translation modes above the lunar surface

Abstract

Hover and translation in the absence of a finite atmosphere, such as with the lunar environment, preclude the use of aerodynamic lifting devices and require the use of rocket thrust. Three modes of thrust application and vehicle orientation through which this may be achieved are analyzed. Particular application is to lunar landing; however, equations are derived in a general form, applicable to any case where aerodynamic effects can be neglected. Performance of the modes is optimized and compared on the basis of propellant consumption and total system weight. The optimum mode is one in which the thrust vector required for translation is obtained by tipping the vehicle and aligning the engine with the vehicle centerline. Optimum values of vehicle tilt angle and translation time have been found to exist; these values are a function of translation requirements. Nomenclature a = acceleration, ft/sec 2 Fh = horizontal thrust vector, Ib F r = resultant thrust vector, Ib F v -vertical thrust vector, Ib g c = Earth gravity constant, ft/sec 2 g = local acceleration of gravity, ft/sec 2 a P = propellant specific impulse, Ib-sec/lb /tot = total impulse, Ib-sec $ 3 = total distance translated, ft T = design thrust of engine, Ib ttot = total hover and translation time, sec ti = acceleration time, sec tz = time-to-start of deceleration, sec 1 3 = total translation time, sec VQ = initial velocity, fps WF = weight function, Ib-sec/lb Wip = propulsion system inert parts weight, Ib Wo = vehicle weight, Ib W p = propellant weight, Ib W r = propulsion system weight, Ib T^eng = engine weight, Ib B = thrust vector angle, deg