Research Ideas

From lifting-line theory we can prove that for a given amount of lift and wingspan, the optimum lift distribution to minimize induced drag is the elliptic lift distribution. However, this is in part due to the fact that the induced drag is being computed from only a single vortex sheet. In ground effect, you can model the aerodynamics using a reflection plane. The lift distribution changes along the wing due to the presence of the ground, and it's possible that the optimum lift distribution to minimize induced drag also changes and becomes a function of height above ground. In any case, the optimum twist distribution to achieve minimum induced drag will change in ground effect. This can all be studied from the numerical lifting-line algorithm presented by Phillips and Snyder. It may also be possible to develop an analytic infinite-series solution, but this would take a bit of work.

Related Papers:

Phillips, W. F. and Hunsaker, D. F., "Lifting-Line Predictions for Induced Drag and Lift in Ground Effect," Journal of Aircraft, Vol. 56, No. 4, pp. 1226-1233, July-August 2013, DOI: 10.2514/1.C032152

Traditional thin airfoil theory also assumes small angles of attack. This results in a linear relationship between lift, pitching moment, and angle of attack. These linear relationships are often assumed in aircraft design. However, from conformal mapping we can show that the lift and pitching moment are not exactly linear functions of angle of attack, even for angles of attack below stall. From thin airfoil theory, if we drop the small-angle approximation, the solution for the lift as a function of angle of attack matches that from conformal mapping. However, I have not yet been able to prove that the pitching moment from thin airfoil theory without the small angle approximations matches that from conformal mapping. It seems straight forward, but I haven't cracked it yet.

The concavity of the locus of aerodynamic centers of an airfoil as a function of angle of attack switches direction when you go from a cambered airfoil to a symmetric airfoil. Not sure why but would be interesting to figure out.

Related Papers:

Hunsaker, D. F., Pope, O., Taylor, J., and Hodson, J., "Aerodynamic Centers of Arbitrary Airfoils Below Stall", Journal of Aircraft, Vol. 56, No. 6, pp. 2158-2171, 2019, DOI: 10.2514/1.C035579

Can the ideal flap effectiveness of a leading-edge flap be computed from thin airfoil theory? It seems rather straight forward, but I haven't seen it done.

Related Papers:

Hunsaker, D. F., Reid, J. T., and Joo, J. J., "Geometric Definition and Ideal Aerodynamic Performance of Parabolic Trailing-Edge Flaps," International Journal of Astronautics and Aeronautical Engineering, 4:026, 20 pages, 2019, DOI: 10.35840/2631-5009/7526

The parabolic flap has a higher ideal flap effectiveness than a traditional flap. Is there a way to find the optimum flap deflection distribution that maximizes ideal flap effectiveness?

Related Papers:

Hunsaker, D. F., Reid, J. T., and Joo, J. J., "Geometric Definition and Ideal Aerodynamic Performance of Parabolic Trailing-Edge Flaps," International Journal of Astronautics and Aeronautical Engineering, 4:026, 20 pages, 2019, DOI: 10.35840/2631-5009/7526