Control of the yawing moment about the z-axis is provided by means of the rudder. The rudder is a movable surface that is hinged to a fixed vertical stabilizer. The rudder is the vertical counterpart to the elevator, and its effectiveness is determined in the same way. Referring to Figure 8.26, the vertical tail is shown at zero sideslip angle with the rudder deflected positively through the angle Sr. The rudder produces an increment in the vertical tail lift (or side force) that results in an increment in the yawing moment, given by
AN = -1, ALv
The increment in the tail lift is given by
A Lv = r),qSvavT S,
Figure 8.26 Rudder control.
so that in coefficient form, the rate of change of CN with respect to the rudder angle becomes
Сщ = ~ViVvavr (8.91)
The subscript r is dropped on S, since it should be obvious that 5 refers to the rudder when considering CN. т is the effective change in the angle of the zero lift line of the vertical tail per unit angular rotation of the rudder and is estimated in the same manner in which т was obtained for the elevator.
As an example in the use of the rudder, suppose the airplane pictured in Figure 8.25 lost power on its right engine. If each engine is located a distance of Ye from the fuselage centerline, the resulting asymmetric thrust would produce a yawing moment about the center of gravity equal to TYe. In steady
trimmed flight the thrust, T, must equal the drag and N must be zero. Therefore,
DYe + qSbCNs 8r — 0
Given the airplane and rudder geometry and CD as a function of V, one can then calculate the vertical tail volume necessary to keep 5r within prescribed limits, usually a linear operating range.