extended formation flight, Cart3D, Euler solver, CFD, drag savings, roll trim, transonic flow


Flying airplanes in extended formations, with separation distances of tens of wingspans, significantly improves safety while maintaining most of the fuel savings achieved in close formations. The present study investigates the impact of roll trim and compressibility at a fixed lift coefficient on the benefits of extended formation flight. An Euler solver with adjoint-based mesh refinement combined with a wake propagation model is used to analyze a two-body echelon formation at a separation distance of 30 spans. Two geometries are examined: a simple wing and a wing-body geometry. Energy savings, quantified by both formation drag fraction and span efficiency factor, are investigated at subsonic and transonic speeds for a matrix of vortex locations. The results show that at fixed lift and trimmed for roll, the optimal location of vortex impingement is about 10% inboard of the trailing airplane’s wing-tip. Interestingly, the improvement in drag fraction is relatively robust in the vicinity of the optimal position. Over 90% of energy benefits can be obtained with a 5% variation in vertical and 10% variation in spanwise positions. Control surface deflections required to achieve roll trim reduce the benefits of formation flight by 3-5% at subsonic speeds and 9-11% at transonic speeds. Overall, simulations show peak induced drag saving for the trail aircraft are 54% in subsonic flow and 35% in transonic flow while accounting for trim.

Original Publication Citation

Kless, J., Aftosmis, M., Ning, A., and Nemec, M., “Inviscid Analysis of Extended Formation Flight,” AIAA Journal, Vol. 51, No. 7, Jul. 2013, pp. 1703–1715. doi:10.2514/1.j052224

Document Type

Peer-Reviewed Article

Publication Date


Permanent URL






Ira A. Fulton College of Engineering and Technology


Mechanical Engineering

University Standing at Time of Publication