The Effect of Wing Sweep on Torsional Divergence

One of the rare benign effects of wing sweepback, aside from its function in reducing transonic drag and instability, is the virtual elimination of the possibility of wing torsional divergence. A wing that is swept back bends under lift loads in a direction that reduces or washes out incidence at the wing tips. This provides automatic load relief.

By the same token, a wing that is swept forward bends under lift load in the opposite sense, increasing the wing tip incidence and load. This adds to the wing-bending deflection and the load in the classic feed-forward sense, producing torsional divergence at sufficiently high airspeeds. Thus, although swept forward wings are free of the premature tip flow separation problems mentioned in Chapter 11, “High Mach Number Difficulties,” they had for many years been dismissed from consideration for new high-speed airplanes.

A classic paper gave the first published account of the effects of sweepback and sweep – forward on wing torsional divergence (Pai and Sears, 1949). A striking aspect of this early paper is the statement of the fundamental equation of aeroelasticity in matrix form. This is an integral equation for the local, or section lift, coefficient. The choice of aerodynamic theory is left free. In 1949, the choices were strip theory, which neglects aerodynamic induction; Prandtl theory; and Weissinger’s approximation.

The advent of composite materials as aircraft structural elements has reopened the door to the sweptforward wing. In 1972, Professor Terrence A. Weisshaar at Purdue University studied the divergence and aeroelastic optimization of forward-swept wings, under a NASA grant. His student, a returning Vietnam veteran fighter pilot named Norris Krone, proposed a PhD thesis on fighter sweptforward wings.

With additional help from Professor Harry Schaeffer, Krone proposed building swept- forward wings in which layers of fiber-plastic composites are oriented to increase greatly torsional stiffness. Such wings could have torsional divergence speeds well out of the flight range. Later, as an official in the Defense Advanced Research Projects Agency, Krone had the unusual opportunity to help turn his research into a practical airplane, the successful Grumman X-29A research airplane.