Date of Award


Degree Name

MS in Aerospace Engineering


Aerospace Engineering


College of Engineering


Aaron Drake

Advisor Department

Aerospace Engineering

Advisor College

College of Engineering


The bell-shaped lift distribution (BSLD) wing design methodology advanced by Ludwig Prandtl in 1932 was proposed as providing the minimum induced drag. This study used this method as the basis to analyze its characteristics in two wing formation flight. Of specific interest are the potential efficiency savings and the optimal positioning for formation flight. Additional comparison is made between BSLD wings and bird flight in formation.

This study utilized Computational Flow Dynamics (CFD) simulations on a geometric modeling of a BSLD wing, the Prandtl-D glider. The results were validated by modified equations published by Prandtl, by CFD modeling published by others, and by Trefftz plane analysis. For verification, the results were compared to formation flight research literature on aircraft and birds, as well as published research on non-formation BSLD flight.

The significance of this research is two part. One is that the BSLD method has the potential for significant efficiency in formation flight. The optimal position for a trailing wing was determined to be partially overlapping the leading wing vortex core. For a BSLD wing these vortices are located inboard from the wingtips resulting in wingtip overlap and have a wider impact downstream than the elliptical lift distribution (ELD) wingtip vortices. A second aspect is that avian research has traditionally been studied assuming the ELD model for bird flight, whereas this study proposes that bird flight would be better informed using the BSLD.