Optimal ascent trajectories of the horizontal takeoff single-stage and two-stage-to-orbit launchers

Abstract

w = earth rotation rate, radlsec (.) = time derivative Optimal ascent trajectories of the rocket-powered, horizontal-takeoff, single-stage and two-stage-to-orbit launchers have been determined using FONPAC, a trajectory optimization program that uses the nonlinear programming and collocation technique, The single-stageo = initial state to-orbit configuration was that of the Reusable Aerodynaf = final state mic Space Vehicle, while the two-stage-to-orbit launcher consists of two "almost" identical stages which were mated in the piggyback configuration at launch. Solutions to these optimization problems require the determination of coefficients of the polynomials that represent the control variables and values of the state variables at nodes delimiting trajectory segments to maximize the injected weight or payload subject to the dynamic pressure, normal and axial load, and the heating limit constraints. A simple sizing algorithm which determines thrust and weight also was implemented in FONPAC for the two-stage configuration. This approach eliminates the usually tedious process in which several iterative steps normally are required between configuration design and trajectory optimization. SubscriprsResults obtained from FONPAC indicate that the use of the collocation technique is a superior method in assessing performance capability of new and unconventional launchers. h = r = g = & ( = v = gz = T = L = D = 9 " m = Az = Y = e = Is, = a = o = + = Nomenclature altitude, ft vehicle radius vector, ft vehicle relative velocity, f p s gravitational constant (32.174 fls2) gravitational acceleration component along the radius vector, f/s2 gravitational acceleration component in the latitude direction, €Is2thrust, lb engine specific impulse, sec lift, lb drag, Ib dynamic pressure, psf vehicle mass, slug relative azimuth angle, rad angle of attack, rad relative flight-path angle, rad longitude, rad bank angle, rad geocentric latitude, rad This work was supported by the U. S. Air Force Space Systems