Store Separation Equations of Motion

Abstract

Combat aircraft utilize expendable stores such as missiles, bombs, flares, and external tanks to execute their missions. Safe and acceptable separation of these stores from the parent aircraft is essential for meeting the mission objectives. The equations of motion for a store in free flight are similar to the conventional aircraft flight dynamics equations prevalent in the literature. However, a careful distinction is necessary due to the relative motion of two neighboring bodies. Of specific interest is the store motion relative to the aircraft; knowledge of which is necessary for modeling the aerodynamic interaction between the store and aircraft. This paper presents an in depth development of the store separation equations of motion with particular emphasis on the motion of the store relative to the parent aircraft. The same framework is used to derive the kinematic differential equations used for flight test trajectory reconstruction based on inertial measurements. The relationship between trajectory reconstruction and the equations of motion leads to a method for estimating the aerodynamic forces and moments directly from flight test data. An example based on separation of a representative store from an F-16 aircraft is presented to demonstrate the efficacy of store separation trajectory prediction and trajectory reconstruction. I. OverviewMathematical modeling and simulation (M&S) is used to reduce the risk, cost, and schedule of aircraftstores compatibility efforts and provides a valuable toolset for the practicing store separation engineer. In a general store separation program, M&S will be used to develop a streamlined and cost-effective wind tunnel test, perform sensitivity and uncertainty analyses to determine best and worst-case predicted outcomes, down select to configurations and flight conditions of interest for flight test, assess the risk of each individual flight test event, and ultimately provide a certification recommendation to the authorizing agency for operational use. A central component of M&S necessary for trajectory prediction is the formulation of the store separation equations of motion.Trajectory prediction involves statement of the rigid body equations of motion and development of mathematical models for each of the relevant components that influence the store during separation. These models may include aircraft maneuvering, ejector performance, 1, 2 constraint mechanisms such as rails or pivots, 3 aerodynamic effects, 4 configuration changes such as deploying wings or fins, 5 and control surface deflections. 6 The rigorous development of each of these models is beyond the scope of the present work; instead, emphasis will be placed primarily on rigid body dynamics and flight test validation. The store separation equations of motion are derived in Section II and the same framework is extended to reconstruction of flight test trajectories in Section III. II. Store Separation Equations of MotionMathematical modeling of store separation is accomplished by dividing the separation event ...