AN ALGORITHM FOR CALCULATING THE AERODYNAMIC DERIVATIVES OF A SUPER-SONIC MISSILE

Determination of the aerodynamic derivatives is considered as an essential procedure when analyzing the flight path trajectory. This trajectory is determined by the aerodynamic forces and moments; which are functions of these derivatives. So, as accurately these derivatives are calculated as accurately the flight path trajectory will be determined. Thus, calculation of the aerodynamic derivatives is necessary for a six-degree-of-freedom missile trajectory simulation. Aerodynamics is part of the missile's airframe subsystem, the other major parts being propulsion and structure. The aerodynamics is closely related to the autopilot and controls that, in turn, form a part of the overall guidance loop. To evaluate the guidance, control, and autopilot behavior, it is required to achieve the three-dimensional representation of the aerodynamic forces and moments coefficients. The intent of the three dimensional representation of aerodynamics is to be able to analyze the missile performance throughout its potential operational regime and not just in the neighborhood of the trim points. The six-degree-of-freedom trajectory simulation, using these three dimensional data, can be used to predict missile performance against maneuvering targets and to troubleshoot flight problems by reconstructing the flight trajectory from on-board measurements of missile parameters. This paper presents an algorithm for calculating the aerodynamic derivatives of a supersonic missile. This algorithm depends on many parameters such as missile aerodynamic configuration shape and dimensions, atmospheric data, positions of center of gravity and center of pressure, angle of attack, side slip angle, control surfaces deflections, and a set of the aerodynamic based data and NASA curves. The atmospheric data are the air density, pressure of the air, the air viscosity and speed of sound. A mathematical model is provided. Software package in the MATLAB environment is developed to calculate the aerodynamic coefficients. The intent from determination of these coefficients is to calculate the aerodynamic forces and moments that affect on the missile during its flight in order to determine the missile trajectory and evaluate the missile control and guidance systems. The effect of the aerodynamic derivatives on the flight path trajectory is analyzed. This effect is discussed in two cases: the simplified case and the complete case. In the simplified case these derivatives are calculated in the supersonic speeds and estimated in the subsonic and transonic ranges. In the complete case these derivatives are calculated in the subsonic, transonic and supersonic speeds. The results show that the complete case is the better case from the viewpoint of the flight parameters (smallest miss distance and smallest normal acceleration).