Swept Wings and Effective Dihedral
by Bill and Bunny (B2) Kuhlman
RC Soaring Digest, January - March 2000
Swept Wings and Effective Dihedral
One facet of tailless aircraft performance has always intrigued us Ñ the ability of swept wing tailless sailplanes to travel at high speed without exhibiting Dutch roll, yet demonstrate excellent spiral stability whilethermalling. This differs from what is seen in high performance conventional tailed sailplanes. The designer of a conventional cross-tailed competition F3B machine must very carefully balance wing dihedral and vertical stabilizer surface area. There is a tendency to Dutch roll at high speed, and opposite aileron must be applied during thermal turns to prevent a spiral dive, even when the aircraft isoptimized. Since both vertical stabilizer area and geometric wing dihedral are held constant during ßight, what is it about swept wings which allows them to Òviolate the rulesÓ? To begin, we need to go over the fundamentals, and so Parts 1 and 2 of this four part series will be devoted to explaining effective dihedral itself Ñ how it is derived and how it inßuences aircraft stability. Pitch, Yaw, and RollDiagrams of aircraft in which the three rotational axes are noted can be found in most aerodynamics textbooks. Our rendition is included here as Figure 1. In simple terms, the nose of the aircraft can move up and down through an axis which parallels the wing span (pitch, Y axis), and it can move right and left through a vertical axis which passes down through the fuselage in the region of thewing (yaw, Z axis). The aircraft can be also be made to rotate around an axis which roughly goes through the nose and tail cone (roll, X axis). Elevator deßection changes the camber of the horizontal tail (stabilizer and elevator), increasing lift in the direction opposite to elevator deßection. By moving the elevator up or down, the aircraft tail may be lowered or raised, thus raising or loweringthe nose. This is a change in pitch (Y axis). The size of the elevator and the distance between the center of gravity (CG) and the elevator determine elevator power. The larger the elevator surface area and the larger the distance between the CG and the elevator, the more elevator power. If the elevator is deßected upward, the aircraft tail is pushed downward and the nose is thus raised. It must beclearly understood that the elevator controls the wing angle of attack, that is the angle of the wing to the freestream airßow. A larger upward deßection of the elevator will place the wing at a higher angle of attack. However, when elevator deßection is neutralized, the wing will return to its ÒnormalÓ angle of attack. This is because the horizontal tail acts as a longitudinal stabilizer. Therudder, when deßected, pushes the tail either right or left. Rudder deßection changes the camber of the vertical tail, increasing lift in the direction opposite to rudder deßection. When the rudder is deßected to the right, for example, the tail swings to the left and the nose swings to the right, inducing yaw, a rotation around the Z axis.
r + FLIGHT DIRECTION CG YAWv u +
w Y + Z
p ROLL X
Axis X (roll) Y (pitch) Z (yaw)
Linear velocity u v w
Angular displacement f q y
Angular velocity p q r
Figure 1, rotational axes Larger deßections of the rudder will result in greater yaw angles, but the aircraft will return to zero degrees yaw when the rudder is neutralized. The vertical tail thus acts as a directional stabilizer. Ailerondeßection changes the camber of the wing in the region of the aileron. Upward deßection reduces lift, and further deßection may cause negative lift. As one aileron deßects upward, the opposite aileron deßects downward. Downward deßection increases wing lift in the region of the aileron. These changes in lift promote the lifting of the wing for which the aileron is deßected downward, and the...