Aerodynamic versus Ballistic Flight
Open Journal of Fluid Dynamics
We consider, compare, and contrast various aspects of aerodynamic and ballistic flight. We compare the energy efficiency of aerodynamic level flight at a given altitude versus that of ballistic flight beginning and ending at this same altitude. We show that for flights short compared to Earth's radius, aerodynamic level flight with lift-to-drag ratio 2 L D > is more energy-efficient than ballistic flight, neglecting air resistance or drag in the latter. Smaller altitude farther if thrown
... er if thrown horizontally against the wind than with it. Then we compare the energy efficiency of surface transportation versus that of both aerodynamic and ballistic flight. Earth (and hypothetically also on Mars) as examples, we consider aerodynamic level flight in rarefied and dense aerodynamic media, respectively. We also briefly discuss hydrofoils. We appraise the optimum range of air densities for aerodynamic level flight. In Section 4 we consider flights of hand-thrown projectiles that are unpowered except for the initial throw. We describe how aerodynamically efficient ones (i.e., with large L D ) such as Frisbees, Aerobies, and boomerangs not only can traverse record horizontal distances, but (along with discuses) also can-since lift exceeds weight at achievable throwing speeds-maintain altitude farther if thrown horizontally against the wind than with it. In Section 5 we compare the energy efficiency of surface transportation versus that of both aerodynamic and ballistic flight. Brief concluding remarks are given in Section 6. Footnotes provide supporting references and some auxiliary information. Supplementary Notes, providing more comprehensive auxiliary information concerning topics discussed in the main text and/or in the cited references including some additional supporting references, are given in the Appendix. In this paper we define "aircraft" as any type of aerodynamic flying machine-for example man-made airplane or sailplane, bird, or flying insect in forward or hovering flight, including hand-thrown aircraft (e.g., discus, Frisbee, Aerobie, boomerang, etc.). Underwater airplanes, which we will briefly consider in Section 3.3.2, and hydrofoils, which we will briefly consider in Section 3.4, should be classified as aircraft because their lift obtains aerodynamically rather than via buoyancy, even though the density of their aerodynamic medium (water) is ≈ 800 times that of air at sea level. By lifting the hull out of water into air, drag on the hull of a hydrofoil at any given speed is reduced ≈ 800 times; only the wings need suffer water resistance as opposed to air resistance. Except for a few very brief parenthetical remarks concerning hovering flight, in this paper we consider only aircraft that obtain their lift by virtue of their translational forward motion, i.e., translational-lift aircraft-for example man-made airplanes and sailplanes, birds and insects that obtain their lift by virtue of their translational forward motion, underwater airplanes, hydrofoils, and hand-thrown translational-lift aircraft (e.g., discuses, Frisbees, Aerobies, boomerangs, etc.). Except for a brief consideration of underwater airplanes in Section 3.3.2, and a brief consideration in Section 3.4 and occasional other even briefer remarks concerning hydrofoils, from among translational-lift aircraft we consider only aerial translational-lift aircraft, which obtain their lift by virtue of their translational forward motion through air-for example man-made airplanes and sailplanes, birds and insects that obtain their lift by virtue of their translational forward motion, and hand-thrown translational-lift aircraft (e.g.