A theory of velocity limitation is developed on the basis of a simple analytical model of a returning space probe. The limiting velocity is the lowest atmospheric entry speed for which the heat-protection material of the probe is entirely consumed. The geometry treated is a family of slender blunted cones moving in the direction of the axis. The face of the cone is assumed to be continuously vaporized by the flow. The entry speed is presumed to be so high that a large fraction (or all) of the vehicle volume is consumed in the entry. The entry speed is also high enough for the dominant mode of heat transfer to the vehicle to be through radiation from the hot gas cap at the nose. In the regime of radiation dominance, a second-order nonlinear differential equation is found which describes the geometric and dynamic history during atmospheric entry. By means of solutions of the basic size-altitude equation the velocity limit is traced out. With a limiting form of the heat-input function, explicit formulas for the limiting velocity of the family of truncated cones are developed. The limiting velocity is found to be independent of the size of the probe but dependent on the shape. Pointed cones yield the highest limiting velocities for the class of probes considered. However, flat-faced cylinders yield values nearly as high. The proportions of the cylinders do not reflect the limiting velocity, and therefore long rods and thin wafers have the same values. Only the altitude of the high-mass-loss region shifts with the probe size or with the cylinder proportions.The face of the cone is assumed to be continuously vaporized by the flow. The entry speed is presumed to be so high that a large fraction (or all) of the vehicle volume is consumed in the entry.
|Title||:||A Theory of Space-probe Entry Under Conditions of High Mass Loss|
|Author||:||Frederick Clifton Grant|