Stability and Control — Page 301, Lesson 356

Let's pick up with the fin — the vertical stabilizer — because it's the major source of directional stability for the aeroplane. I want you to picture the fin as a wing mounted vertically on the tail. In a sideslip, the relative airflow comes at the aeroplane from an angle, and the fin experiences a change in angle of attack. That change in angle of attack produces a change in lift — which, for a vertical surface, we call side force. That side force acts at the fin, and because the fin is a long way behind the centre of gravity, it creates a yawing moment about the centre of gravity. That moment tends to yaw the aeroplane back into the relative airflow — that's the restoring action that gives directional stability. Now, the magnitude of the fin's contribution to static directional stability depends on two things: the change in fin lift, and the fin moment arm — the distance from the centre of gravity to the fin. The moment arm is a powerful factor, because moment is force times distance. So even a modest side force, acting through a long arm, produces a strong yawing moment. The fin's contribution also depends on its ability to produce changes in lift for a given change in sideslip angle. That contribution is a direct function of the fin's area. So if you need more directional stability, you can increase the fin area. But there's an obvious disadvantage: increased surface area means increased parasite drag. So you pay a drag penalty for a bigger fin. Now, the lift curve slope of the fin — that's how sensitive the surface is to a change in angle of attack. It's desirable to have a high lift curve slope for the fin, so that a small change in sideslip produces a good change in side force. But a high aspect ratio surface — a tall, narrow fin — is not necessarily practical or desirable. There are practical constraints: bending loads, a lower stalling angle, and hangar roof clearance. The stall angle of the fin surface must be sufficiently great to prevent stall and the subsequent loss of effectiveness at the sideslip angles you'd expect in service. And here's the key trick: sweepback or low aspect ratio increases the stalling angle of attack of the fin. So a swept or low-aspect-ratio fin is less likely to stall at high sideslip angles. One more thing about the fin: the flow field in which it operates is affected by other components of the aeroplane, as well as by power effects. The dynamic pressure at the fin could depend on the slipstream of a propeller, or the boundary layer — the excerpt cuts off there, but the point is that the fin doesn't operate in clean air; the rest of the aeroplane and the powerplant influence the airflow it sees. Now, before the fin, I want to bring in the dorsal and ventral fins, because they're closely related. These are small auxiliary vertical surfaces — the dorsal fin is on top of the fuselage, the ventral fin underneath. At small sideslip angles, the side force they create is very small. Why? Three reasons: they're at a low angle of attack, they have a small surface area, and their aspect ratio is very low, which results in a small lift curve slope. So at small sideslip angles, a fuselage that is unstable in yaw will remain unstable even when fitted with dorsal and ventral fins. But here's the important part: dorsal and ventral fins become more effective at relatively high sideslip angles. Because of their low aspect ratio, they don't tend to stall at any sideslip angle an aircraft is likely to experience in service. So their effectiveness increases with increasing sideslip angle. That means the combination of a fuselage with a dorsal or ventral fin is stable at large sideslip angles — the fin kicks in just when the basic fuselage is most unstable. Now, there's a crucial difference between the two. Dorsal and ventral fins contribute in exactly the same way to directional static stability — that's yaw stability. But in lateral static stability — that's roll stability — they differ: a dorsal fin contributes positively to lateral static stability, while a ventral fin is destabilizing in that mode. For this reason, the dorsal fin is much more common. So if you see an aircraft with a fin on top of the fuselage but not underneath, that's why — the dorsal fin helps both yaw and roll stability, while the ventral fin would hurt roll stability. Let me tie this together with the figures. Figure 10.59 shows the contrast between a low aspect ratio surface — or a swept one — and a high aspect ratio surface, and how that affects the lift curve slope. And Figure 10.61 shows the fin in a sideslip: the relative airflow, the arm from the centre of gravity, the change in fin lift, and the resulting tail moment. That's the whole mechanism of directional stability in one picture. So the complete picture is this: the fin is the primary source of directional stability, working through its area and its moment arm. The dorsal and ventral fins are supplementary — they're ineffective at small sideslip angles but become effective at large ones, and the dorsal fin is preferred because it helps lateral stability too. And the fin's design — its aspect ratio and sweep — is a compromise between sensitivity, stalling behaviour, and practical constraints like drag and hangar clearance.