Rapid Analytical Calculation of Maximum Crossrange for Hypersonic Gliding Vehicles

According to lateral maneuver problem for hypersonic gliding vehicles, a novel analytical model of the crossrange is deduced and a rapid method to calculate lateral maximum range is proposed. The analytic solution to the lateral maneuver ability of the hypersonic glide vehicle is an extremely complex problem, because the lateral maneuver variables are heavily coupled with a lot of variables, such as the heading angle, aerodynamic forces, velocity, and other flight variables. First, the non-dimensional centroid dynamic and kinematical equations of the hypersonic vehicle are established, the optimal bank angle with respect to maximum crossrange is obtained by taking the second derivative of latitude. Second, the analytical model for calculating heading angle is deduced and the analytical expression of the lateral maneuver range is described. A rapid calculating method of the maximum crossrange is provided based on the quasi-equilibrium glide condition and extremum principle. Finally, the numerical simulation results with respect to newly proposed analytical method are compared with the maximum lateral range generated by Gauss pseudospectral method, the validity of the new method is completed.