An Efficient Formation Flight Simulator with Extensions to Unsteady Maneuvers

Abstract

A quasi-steady formation flight simulator is implemented in MATLAB by following a previously published methodology for calculating aerodynamic influence among lifting surfaces. The methodology extends Prandtl’s lifting-line theory both to multiple lifting surfaces and to lifting surfaces with complex geometries. The simulator presented herein is capable of calculating the forces acting on multiple lifting surfaces and on those with various geometric properties, including taper, sweep, and dihedral. A description of the simulator’s implementation is offered, as are several demonstrations of its correctness. Numerous examples of its practical uses are then provided. The quasi-steady model’s use of the section lift coefficient then allows it to be hybridized with an empirical Theodorsen model for unsteady pitching, which in turn allows us to formulate an expectation for the manner in which the unsteady, sinusoidal pitching of a leading wing affects a trailing wing. The pitching motion is found to reduce the trailing wing’s efficiency appreciably, but the reduction behaves asymptotically. Though not implausible, this result would need to be validated by experiment, offering one of many opportunities for further work. Computational efficiency is central to both the quasi-steady and hybrid methodologies. The former only depends on the geometry of the formation flight scenario, thereby avoiding calculations at points between the wings, and the latter similarly avoids the the usual requirement of calculating vortex panel dynamics.