Bodies of Maximum Lift-to-drag Ratio in Hypersonic Flow
Maximizing lift-to-drag ratio of slender body in hypersonic flow investigated by calculus of variations
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Maximizing lift-to-drag ratio of slender body in hypersonic flow investigated by calculus of variations
Optimizing lift-to-drag ratio of slender, flat-top wing of given planform in hypersonic flow by using variational calculus methods
Lift-drag ratio attainable by slender flat-top body at supersonic speeds, considering Newtonian pressure distribution and constant skin friction
Two-dimensional wings of maximum lift-drag ratio in hypersonic flow
Lift to drag ratios of slender, conical bodies flying at hypersonic speeds, and effects of geometric parameters on aerodynamic stability
Maximum lift-drag ratio of slender, flat top, hypersonic body assuming modified Newtonian pressure distribution and constant surface averaged skin friction coefficient
Slender wing maximum lift-drag ratio at hypersonic speeds obtained assuming modified Newtonian pressure distribution and skin-friction drag
Maximum lift-drag ratios for slender flat-top homothetic bodies flying at hypersonic speeds
An investigation has been made to determine the effect of ground proximity on the aerodynamic characteristics of aspect-ratio-1 airfoils. The investigation was made with the model moving over the water in a towing tank in order to eliminate the effects of wind-tunnel walls and of boundary layer on ground boards at small ground clearances. The results indicated that, as the ground was approached, the airfoils experienced an increase in lift-curve slope and a reduction in induced drag; thus, lift-drag ratio was increased. As the ground was approached, the profile drag remained essentially constant for each airfoil. Near the ground, the addition of end plates to the airfoil resulted in a large increase in lift-drag ratio. The lift characteristics of the airfoils indicated stability of height at positive angles of attack and instability of height at negative angles; therefore, the operating range of angles of attack would be limited to positive values. At positive angles of attack, the static longitudinal stability was increased as the height above the ground was reduced. Comparison of the experimental data with Wieselsberger's ground-effect theory (NACA Technical Memorandum 77) indicated generally good agreement between experiment and theory for the airfoils without end plates.
Lift-to-drag ratio attainable by slender, homothetic body at hypersonic speeds, assuming Newtonian pressure distribution and constant skin-friction coefficient
Lift to drag ratio attainable by slender conical bodies flying at supersonic velocities
Lift to drag ratio by slender conical body flying at hypersonic speeds
Variational calculus used in obtaining lift drag ratio attainable by slender conical body at hypersonic speeds
Variational approach to conical bodies having maximum lift drag ratio at hypersonic speeds, assuming Newtonian pressure distribution and constant friction coefficient
The influence of the maximum lift-to-drag ratio on the turning performance of an Orbital Transfer Vehicle is analyzed. Chapman's variables are used to formulate the equations of motion which are valid for both atmospheric flight and flight in a vacuum in a Newtonian gravitational field. Of the six adjoint variables involved in the variational formulation, four exact integrals and two approximate relations are obtained. This leads to an approximate but explicit control law for the lift and bank control. The control law is tested numerically for a whole range of entry speeds, from parabolic entry to near-circular entry with several values of maximum lift-to-drag ratio. The extensive numerical results, which are very accurate as compared to the exact optimal values, show that the maximum plane change for any speed ratio V(entry)/V(final) is simply proportional to the maximum lift-to-drag ratio, and depends solely on this parameter.
Similarity laws for bodies maximizing lift-to-drag ratio at hypersonic speeds, considering longitudinal and transversal contours
A wind-tunnel investigation has been conducted to determine the effect of ground proximity on the aerodynamic characteristics of thick highly cambered rectangular wings with aspect ratios of 1. 2, 4, and 6. The results showed that, for these aspect ratios, as the ground war, approached all wings experienced increases in lift-curve slope and reductions in induced drag which resulted in increases in lift-drag ratio. Although an increase in lift-curve slope was obtained for all aspect ratios as the ground was approached, the lift coefficient at an angle of attack of 0 deg for any given aspect ratio remained nearly constant. The experimental results were in general agreement with Wieselsberger's ground-effect theory (NACA Technical Memorandum 77). As the wings approached the ground, there was an increase in static longitudinal stability at positive angles of attack. When operating in ground effect, all the wings had stability of height at positive angles of attack and instability of height at negative angles of attack. Wing-tip fairings on the wings with aspect ratios of 1 and 2 produced small increases in lift-drag ratio in ground effect. End plates extending only below the chord plane on the wing with an aspect ratio of 1 provided increases in lift coefficient and in lift-drag ratio in ground effect.
An investigation was made to determine the aerodynamic characteristics of tapered and rectangular wings with partial-span plain flaps. Two Clark Y airfoils equipped with center section and with tip-section flaps were tested. The results showed that the aerodynamic characteristics of partial-span plain flaps were, in general, similar to those of split flaps of the same span, but that the lift and the drag were less for the wing with plain flaps than for the wing with split flaps of comparable size. For the rectangular wing with center-section plain flaps, the maximum lift and the lift-drag ratio at maximum lift were greater and the drag at maximum lift was less than for the wing with tip-section plain flaps of the same size. The maximum lift of the tapered wing varied in the same manner as that of the rectangular wing but the drag and the lift-drag-ratio relationship were opposite.