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The principles of regenerative soaring with a dual-role propeller and windmill, or “windprop,” are described. Emphasizing the aerodynamic design and performance of the vehicle and windprop, principles of regenerative flight are derived. Approximate models of atmospheric updraft velocity are suggested. Regenerative aircraft total energy is defined, and the rate of change thereof is studied. We find that regenerative soaring appears both feasible and attractive in relation to classical soaring. In addition, the study reveals good efficiency for both propeller and windmill modes.

The flight mechanics of dynamic soaring are described to explain how the albatross can sustain soaring flight over a waveless sea in any net direction, including upwind, by extracting energy from the wind velocity gradient with cyclic zoom maneuvers. A dynamic soaring force is postulated to be represented by a wind-aligned vector providing energy gain during both upwind ascent and downwind descent in the wind profile. Maneuver angles are specified consistent with both a dynamic soaring rule and the desired net progress over the water. The equations of motion for coordinated maneuvering in the wind profile are derived and numerically integrated for a range of trajectories as perceived by the albatross, and also as perceived by a stationary observer.

A new implementation of the vortex step method for predicting subsonic propeller blade aerodynamic loading is described. The analysis, taking advantage of the classical work by Rankine, Betz, and Glauert, also accounts for the effects of an axisymmetric nacelle in both the vector boundary condition and Glauert velocity diagram. Wake-induced velocities are examined, including effects of wake extent and “observer” position. A certain “equivalence” is demonstrated for the classical results of Betz, Glauert, Goldstein and Theodorsen for the optimum-wake-induced velocities. The effects of wake continuity and rollup are studied, relative to a simple helical wake. Thrust loading calculations are compared to NACA wake-pressure-derived test data. Rationale and methods for geometry “math modeling” are shown and illustrated. Finally, geometric and aerodynamic models are integrated for the preliminary design of a new propeller.

The familiar “vortex step” method for calculating the lift slope, spanwise distribution of lift, and aerodynamic center position is reviewed and enhanced to more accurately locate the wing aerodynamic center and to accommodate arbitrary spanwise variations of sweep, chord, twist, camber, flaps, and dihedral. Lifting and downwash line position and shape are adjusted to account for semi-empirical effects of planform and airfoil properties. Vector and matrix methods are then applied to solve for the spanwise distribution of lift normal to the spar, or for the required twist to obtain a prescribed loading. For induced drag, an “apparent downwash” method is proposed to reveal the negative induced drag of winglets. Then, predicted 2D and 3D wing characteristics are compared to test data. Finally, the methods are applied to the design and analysis of unique wing configurations.

New and powerful methods of characterizing existing and new airfoil geometries with mathematical equations are presented. The methods are applicable to a wide range of airfoil shapes representing traditional, cusped, reflexed, flat-bottom, laminar, transonic, and supersonic designs. With the emphasis on low-speed airfoils, several existing airfoils are first closely matched with the math-modeling methods. Then, to support the design of new airfoil geometries, a new interpretation of Theodorsen's potential flow method is outlined for the calculation and presentation of surface velocity in inviscid flow. Also, a vector approach is introduced for the calculation of pitching moment. Finally, new math-modeled airfoils are proposed for conventional and unique aircraft configurations.