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Your figures seem problematic. For example, the volume of a 10m radius sphere is below 10^4m3, air density at normal conditions is, very roughly, 1kg/m3, so how do you get more than 10^8 N buoyancy force? According to calculations in US patent application 11/517915 (Akhmeteli, Gavrilin, Layered Shell Vacuum Balloons, you can find it at USPTO site or at ...


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It forms a cone because it depends on a shock wave, and the region enclosed by the shock wave appears conical in shape. See, for example, the apparent cones here: They are also visible here: Wikipedia appears to be fairly clear on why vapor cones are related to shock waves. From the introduction to the article about vapor cones: Atmospheric water ...


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The shock wave from a supersonic object is a cone composed of overlapping spherical wavefronts. As individual wavefronts form, they propagates radially outward at speed $c$ (speed of sound) and have a radius $ct$. At the same time the object traveling at speed $v$ moves forward $vt$. The angle of the vertex of the of the shock wave is known as the Mach angle ...



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