A new method has been developed for predicting and controlling the ground range of an unpowered reusable launch vehicle. The key feature is the use of the quasi-equilibrium glide condition to create a database of range-togo versus energy for different values of the glide-efficiency factor. Downtrack range to runway touchdown is predicted by performing a two-dimensional table lookup of the range-to-go database. Unlike most predictorcorrector guidance methods, the proposed ground-range guidance scheme does not require onboard numerical integration of the governing equations of motion. Another key element is the coupling between the latter stages of the traditional terminal area energy management phase and the entire approach and landing phase, where the flare-to-touchdown maneuver is concisely parameterized by an exponential altitude profile. Numerical simulations demonstrate that this new method can accurately and reliably guide the vehicle to the desired touchdown conditions despite large errors in the initial states, large errors in the initial downtrack distance to the runway, and aerodynamic drag dispersions.
Nomenclaturelbf E = energy height, ft g = 32.174 ft∕s 2 , Earth's gravitational acceleration h = altitude, ft K = lift-induced drag coefficient parameter K H = altitude error gain, 1∕ft K HD = altitude rate error gain, s∕ft K γ = flight-path angle error gain K q = dynamic pressure error gain, ft 2 ∕lbf L = lift force, lbf M = Mach number m = vehicle mass, slug q = dynamic pressure, lbf∕ft 2 R = ground range, ft R go = range-to-go, ft S = vehicle reference area, ft 2 s = downtrack distance relative to runway touchdown, ft t = time, s V = airspeed, ft∕s x = downtrack position along runway centerline, ft γ = flight-path angle, rad η = glide-efficiency factor ρ = atmospheric density, slug∕ft 3 σ = exponential decay constant for flare maneuver, ft Subscripts 0 = initial value ALI = approach and landing interface EG = equilibrium glide F = start of flare maneuver flare = flare maneuver max = maximum QEG = quasi-equilibrium glide TD = touchdown Superscript * = maximum lift-to-drag ratio