Stability and Control — Page 301, Lesson 360

Let’s pick this up right where the sideslip discussion left off. We’ve been looking at what happens when an aeroplane sideslips — the forward, right wing meets the relative airflow at a greater inclination than the rearward wing. That means more lift on the right side, and with more lift comes more induced drag on that same side. I’ll come back to the lift side of that when we get to lateral static stability, but for now the key point is the drag. Because the right wing has more induced drag than the left, you get a yawing moment to the right. And that yawing moment tends to eliminate the sideslip — it swings the nose back around into the relative airflow. That is a stabilizing effect, and it can become quite important if the sweepback angle is large. Now I want to walk you through how directional stability actually builds up in a real aeroplane. Figure 10.63 shows a typical breakdown — it separates the contribution of the fuselage from the contribution of the fin. The graph plots yawing moment coefficient, Cn, against sideslip angle, β. Let me define those two symbols clearly, because they carry the whole story. Cn is the yawing moment coefficient — it’s the non-dimensional measure of the moment that tries to rotate the aeroplane about its vertical axis. β, beta, is the sideslip angle — the angle between the aeroplane’s longitudinal axis and the relative airflow. On that graph, the fuselage alone gives a destabilizing contribution — it actually pushes the aeroplane further into the sideslip. But notice this: that instability decreases at large sideslip angles. The fin alone, on the other hand, is highly stabilizing — right up to the point where the fin surface begins to stall. And that’s the crucial constraint. The fin’s contribution has to be large enough that the complete aeroplane — the wing-fuselage-fin combination — shows the required degree of stability overall. So the problem is clear: the fin is the main stabilizer, but at large sideslip angles the fin can stall, and once it stalls it loses its stabilizing authority. That’s exactly where the dorsal fin comes in. The dorsal fin is that small extension running forward along the top of the fin, blending into the fuselage. It has a powerful effect on preserving directional stability at large sideslip angles — the very angles that would otherwise produce stall of the fin. Let me give you the two mechanisms by which the dorsal fin does this, because they’re quite different. The first, and the least obvious but most important, is a large increase in the fuselage stability at large sideslip angles. Remember, the fuselage alone was destabilizing — the dorsal fin changes that character at high sideslip, making the fuselage contribution much more stabilizing. The second mechanism is that the dorsal fin reduces the effective aspect ratio of the fin. Aspect ratio, remember, is the span squared divided by the area — for a fin, it’s a measure of how long and slender the surface is. Reducing the effective aspect ratio increases the stall angle for the surface. A lower aspect ratio fin stalls later, at a higher angle. So the fin can tolerate a larger sideslip angle before it loses lift. So by this twofold effect — boosting fuselage stability at high sideslip, and delaying fin stall by lowering the effective aspect ratio — the dorsal fin is a very useful device. And there’s one more point worth noting: if the fin itself is swept back, that also helps. A swept-back fin has a decreased lift curve slope — the lift builds up more gradually with angle — and that decreased slope also decreases the tendency for the fin to stall at high sideslip angles. So sweep on the fin and a dorsal fin work together to keep the fin flying and keep the aeroplane directionally stable right through the large sideslip regime.