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The Semirigid Approach to Wing Torsional Divergence
In the semirigid approach to wing torsional divergence and related problems a reference section of the wing is selected to represent the entire three-dimensional wing. This simplification works quite well for slender wings, that is, wings of high-aspect ratio.
Semirigid analyses of wing torsional divergence are given in a number of textbooks (for example, Duncan, 1943; Fung, 1955). Fung shows a wing section that rotates about a pivot and is acted upon by a lift load. The pivot represents the chordwise location in the section of the wing’s elastic axis, or location where lift loads will not produce twist. The lift load can be taken as acting through the section’s aerodynamic center. The aerodynamic center, near the section’s quarter-chord point, is the point about which section pitching moments are invariant with angle of attack (Figure 19.1).
The wing section will come to a static equilibrium angle at some angle of attack under the combined action of the lift load and a spring restraint about the pivot. The spring restraint represents the wing’s elastic stiffness. If the pivot, representing the elastic axis, is behind
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Figure 19.1 Semirigid model forwingtorsional divergence. Thewingis replacedby atypical section, pivoted aboutapoint that represents the wing’s elastic axis. The spring represents elastic stiffness. Inthis illustration, the wing’s aerodynamic center, where the lift acts, is forward of the pivot point. Increasing airspeed eventually leads to a torsional divergence. The angle of attack a increases without limit. (From Fung, The Theory of Aeroelasticity, Dover, 1969) |
the wing’s aerodynamic center, the equilibrium angle of attack increases with increasing airspeed, which gives higher wing lift loads.
For any eccentricity, or distance of the aerodynamic center ahead of the pivot, and for given spring constants and wing lift curve slopes, or variations of wing lift with angle of attack, there is an airspeed at which the semirigid model diverges. That is, the equilibrium solution fails. Twist angle and angle of attack increase without limit. This is the calculated wing torsional divergence speed.
Wing torsional divergence problems were encountered on the Republic F-84 and Northrop F-89 airplanes, both equipped with large tip tanks (Phillips, 1998). Fixed fins on the outside rear of the F-84’s tanks moved the wing’s aerodynamic center aft, eliminating the problem.
