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.
An Efficient Formation Flight Simulator with Extensions to Unsteady Maneuvers.
Retrieved from the University of Minnesota Digital Conservancy,
Content distributed via the University of Minnesota's Digital Conservancy may be subject to additional license and use restrictions applied by the depositor.