A Method for Seeking Range of Missing Plane Based on Law of Energy Conservation
Tian-Quan Yun *
School of Civil Engineering and Transportation, South China University of Technology, Guangzhou, 510641, P.R. China
*Author to whom correspondence should be addressed.
Abstract
A method for seeking range of a missing plane based on Law of energy conservation is suggested. The method starts with the final information of the location(s) of the plane A(x,y,z) provided by satellites. A flying path with most far from an origin in same time interval [0,T] is proved. Suppose that the flight flies in non-powered state since A(x,y,z). By the Law of energy conservation, the problems corresponding to two ranges of velocity are reduced to Riccati equation and Volterra equation respectively. The exact solutions of these equations are found, and the seeking range is calculated. Finally, the relative motion in longitude direction due to self-rotation of earth is added to the calculated range. A simple calculation is given for reference.
Keywords: Law of conservation energy, Riccati equation, Volterra integral equation, non-powered flying, lift-to-drag ratio, self-rotation of earth.