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has been cited by the following article:

• TITLE: Aerodynamic versus Ballistic Flight

  AUTHORS: Jack Denur

  KEYWORDS: Aerodynamic Flight, Ballistic Flight, Lift, Drag, Lift-to-Drag Ratio, Air Density, Energy Efficiency

  JOURNAL NAME: Open Journal of Fluid Dynamics, Vol.9 No.4, December 18, 2019

  ABSTRACT: 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 L/D > 2is more energy-efficient than ballistic flight, neglecting air resistance or drag in the latter. Smaller L/D suffices if air resistance in ballistic flight is not neglected. For a single circumnavigation of Earth, we show that aerodynamic flight with L/D > 4π is more energy-efficient than minimum-altitude circular-orbit ballistic spaceflight. We introduce the concept of gravitational scale height, which may in an auxiliary way be helpful in understanding this result. For flights traversing N circumnavigations of Earth, if then even minimum-altitude circular-orbit ballistic spaceflight is much more energy-efficient than aerodynamic flight because even at minimum circular-orbit spaceflight altitude air resistance is very small. For higher-altitude spaceflight air resistance is even smaller and the energy-efficiency advantage of spaceflight over aerodynamic flight traversing the same distance is therefore even more pronounced. We distinguish between the energy efficiency of flight per se and the energy efficiency of the engine that powers flight. Next we consider the effects of air density on aerodynamic level flight and provide a simplified view of drag and lift. We estimate the low-density/high-altitude limits of aerodynamic level flight (and for comparison also of balloons) in Earth’s and Mars’ atmospheres. Employing Mars airplanes and underwater airplanes on Earth (and hypo-thetically 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. We then consider flights of hand-thrown projec-tiles 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. Then we compare the energy efficiency of surface transportation versus that of both aerodynamic and ballistic flight.