Stability and Control — Page 306, Lesson 364

We're starting a new part of the chapter now — the high angle of attack effects on directional stability, and then we're moving into lateral stability. Let's pick it up right where the material gets interesting. First, the high angle of attack problem. When the aeroplane is at a high angle of attack, we can anticipate a decrease in static directional stability. Look at Figure 10.64 in your mind's eye — a high angle of attack reduces the stable slope of the curve of Cn versus β. Now, Cn is the yawing moment coefficient, and β is the angle of sideslip. The stable slope is the gradient of that curve, and when it gets less steep, the aeroplane is less able to resist a yaw disturbance. The decrease in static directional stability is due in great part to the reduction in the contribution of the fin. Here's the mechanism: at high angles of attack, the effectiveness of the fin is reduced because of the increase in the fuselage boundary layer at the fin location. The boundary layer is the slow-moving layer of air next to the fuselage skin; at high angle of attack it thickens, and the fin sits in that sluggish, less energetic air, so it produces less sideforce and less restoring yawing moment. The decay of directional stability with angle of attack is most significant for an aeroplane with sweepback, since this configuration requires a high angle of attack to achieve high lift coefficients. Swept wings need more angle of attack to generate the same lift, so they hit this fin-effectiveness problem sooner. Now, the remedy — the ventral fin. Ventral fins may be added as an additional contribution to directional stability, as shown in Figure 10.65. A ventral fin is a small fin mounted on the underside of the rear fuselage, and it adds yawing stability. But there's a catch: landing clearance requirements may limit their size, may require them to be retractable, or may require two smaller ventral fins to be fitted instead of one large one. The reason is that a big fin hanging below the fuselage could strike the runway on rotation or touchdown, so designers either shrink it, retract it, or split it into two smaller ones. Now, the most critical demands of static directional stability will occur from some combination of four effects: high angle of sideslip, high power at low airspeed, high angle of attack, and high Mach number. Let me unpack each. High angle of sideslip means the aeroplane is yawed well off its heading, demanding maximum restoring moment. High power at low airspeed — the slipstream and propeller effects can be large. High angle of attack, as we just discussed, degrades fin effectiveness. High Mach number — compressibility effects change the flow. Now here's the contrast: the propeller powered aeroplane may have such considerable power effects that the critical conditions may occur at low speed, while the effect of high Mach numbers may produce the critical conditions for the typical transonic, jet powered aeroplane. So a prop aircraft is most stressed at low speed with high power, a jet at high Mach. In addition, the coupling of lateral and directional effects may require prescribed degrees of directional stability — meaning the rolling and yawing motions interact, so you can't size the fin in isolation. Now we shift into a new topic: lateral stability and control. The static lateral stability of an aeroplane involves consideration of rolling moments due to sideslip. Here's the logic. If an aeroplane has favourable rolling moment due to a sideslip, then a lateral displacement from wing level flight produces a sideslip, and the sideslip creates a rolling moment tending to return the aeroplane to wing level flight. By this action, static lateral stability will be evident. So the chain is: disturbance → sideslip → rolling moment → recovery. Of course, a sideslip will produce yawing moments depending on the nature of the static directional stability, but the consideration of static lateral stability will involve only the relationship of rolling moments and sideslip. So we deliberately separate the rolling response from the yawing response for this analysis. Now the definitions, and these are precise. The axis system of an aeroplane defines a positive rolling moment, L, as a moment about the longitudinal axis which tends to rotate the right wing down. So positive roll is right wing down. As in other aerodynamic considerations, it is convenient to consider rolling moments in the coefficient form so that lateral stability can be evaluated independent of weight, altitude, speeds, etc. The rolling moment, L, is defined in the coefficient form by the equation: L = Cl Q S b, or rearranged, Cl = L divided by Q S b. Let me define each symbol. L is the rolling moment, positive to the right. Q is the dynamic pressure — the pressure due to the air's motion. S is the wing area. b is the wingspan. And Cl is the rolling moment coefficient, positive to the right. So the coefficient form normalises the raw moment by dynamic pressure, wing area, and span, which lets you compare stability at different speeds and altitudes. Finally, the angle of sideslip, β, has been defined previously as the angle between the aeroplane centre line and the relative wind, and is positive when the relative wind is to the right of the centre line. So if the air is coming from the right of the nose, β is positive. That sign convention matters because it ties directly into the sign of the rolling moment coefficient we just defined. That's the foundation of lateral stability — the rolling moment coefficient, its equation, and the sideslip angle convention. We'll build on this as we go.