Diagrams, tables, and photos for theory articles

Last updated September 5 2005

Illustration of the reduction of lift coefficient due to sweep, and the way that this is most pronounced at high angles-of-attack. Source: "Aerodynamics for naval aviators (NAVWEPS 00-80T-80)" by Hugh H. Hurt (1965, Office of the Chief of Naval Operations, Aviation Training Division, for sale by the Supt. of Documents,US Govt. Printing Office). A sideways airflow over a swept-wing aircraft can be viewed as a decrease in sweep of the "upwind" wing and an increase in sweep of the "downwind" wing. Therefore, this diagram is the key to understanding the following idea: when a swept-wing aircraft experiences a sideways airflow, the resulting difference in lift coefficient experienced by the left and right wings is strongest at high angles-of-attack. In other words, the dihedral-like stabilizing effect ("positive coupling between slip (yaw) and roll") created by sweep is strongest at high angles-of-attack. Once we are comfortable with this idea we can go on to make the following observations: a hang glider's overall coupling between slip (yaw) and roll is determined by the competing effects of sweep and anhedral. The destabilizing roll torque ("negative coupling between slip (yaw) and roll") created by anhedral is relatively independent of angle-of-attack, and is usually stronger than the stabilizing roll torque ("positive coupling between slip (yaw) and roll") created by dihedral. As a result of all of these relationships, and especially as a result of the way that the roll torque created by sweep is highly dependent on angle-of-attack, it turns out that the destabilizing, anhedral-driven, "negative coupling between slip (yaw) and roll" that we often encounter in flex-wing hang gliders is always most pronounced at low angles-of-attack. This increased "anhedral effect" at low angles-of-attack is why hang gliders are so responsive to roll inputs at low angles-of-attack, especially with the VG off: adverse yaw is being harnessed to create a helpful roll torque. This increased "anhedral effect" at low angles-of-attack is also why hang gliders are prone to yaw-roll oscillations at low angles-of-attack, including during aerotow, especially with the VG off. See the theory section of this website for more.

Illustration of the yaw torque (weathervane effect) generated by a sideways airflow (sideslip) interacting with a swept wing.  Source: same as above

Defining drawing for the conical Rogallo wing. Source: "The Hang Glider's Bible" by Michael A. Markowski (1977)

Defining drawing for the cylindrical Rogallo wing. Source: "The Hang Glider's Bible" by Michael A. Markowski (1977)

3 graphs: Aerodynamic twist of conical and cylindrical Rogallo wings, Spanwise lift distribution for conical and cylindrical Rogallo wings at L/D max, and Airfoil section lift coefficients during a minimum sink condition for conical and cylindrical Rogallo wings. Source: "The Hang Glider's Bible" by Michael A. Markowski (1977). (Some things on these graphs should be taken with a grain of salt; for example I can't imagine that the lift coefficient would really be so different as M. notes (1.0 vs .4) in the min sink condition (which occurs at max L^1.5 /D) versus the max L/D condition. Also the depiction of the downward lift generated at the washed-out wingtips seems a bit overstated for the case of the conical wing at the max L/D condition.)

Accurate diagram of forces in a "fully coordinated" turn with no sideslip and adequate lift (G-loading), a turn with inadequate lift (G-loading) and no sideslip, and a slipping turn with adequate lift (G-loading)   Source: Steve Seibel

Diagram to accompany "Mathematics of circles in wind"  Source: Dan Tyler

Photos of hang gliders and models to illustrate how billow contributes to the net geometric anhedral of a swept wing:

Photos of models that illustrate how washout or billow contribute to the net geometric anhedral of a swept wing

Photos of hang gliders that illustrate how billow contributes to the net geometric anhedral of a swept wing

More photos that illustrate how billow contributes to the net geometric anhedral of a swept wing -- views of inverted gliders

Model illustrating the "hinge lines" on a wing with billow

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