Minimum fuel closed-loop translation

Explicit guidance law for minimum fuel horizontal translation with bounded control.

“…S. SAROA* Indian Institute of Technology, Kharagpur, India T HE problem of three-dimensional boundary-layer flow near a spinning cone for an incompressible viscous fluid was studied by Wu. 1 He showed that with a suitable choice of coordinate axes and a suitable independent variable, the velocity functions can be obtained from the same set of equations as that for a disk rotating in an infinite fluid at rest (Karman's problem), but the pressure distribution is modified. Datta 2 showed that this is also true for Reiner-Rivlin where m is a stress tensor, p is an indeterminate hydrostatic pressure, and vt and a; are velocity and acceleration vectors, respectively.…”

“…A large number of fluids of technical importance can be represented by this constitutive equation. We discuss the aforementioned problem of Wu for an incompressible second-order fluid given by the constitutive equation (1).…”

Study of spacecraft hover and translation modes above the lunar surface

“…Control considerations are beyond the scope of this study; an excellent closed-loop solution is provided in Ref. 3.…”

“…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 Introduction P REVIOUS studies 1 -2 have shown the existence of optimum conditions for minimum propellant consumption during vehicle translation parallel to the lunar surface. This study represents a more graphical approach in which the influence of over-all propulsion system weight is considered along with the effect of operating off of the optimum design points.…”