Stability and Control — Page 293, Lesson 355

Let’s pick this up right where the fuselage leaves us in trouble. I want to walk you through the dorsal and ventral fins, because these are the design fixes for a problem we just saw: the fuselage itself is unstable in yaw. Here’s the situation. When an aircraft is yawed — that is, its nose is rotated sideways relative to the flight path — the fuselage, seen in plan view, acts like a weathervane pointing the wrong way. The aerodynamic force generated on the fuselage acts ahead of the centre of gravity, and that produces an unstable yawing moment. In other words, the fuselage wants to make the yaw worse, not correct it. That’s the instability we’re overcoming. So to fix it, the designer can add dorsal or ventral fins. Let me define each precisely. A dorsal fin is a small aerofoil, of very low aspect ratio, mounted on top of the fuselage near the rear. A ventral fin is mounted below — underneath the fuselage, also near the rear. Aspect ratio, by the way, is the ratio of span to mean chord; a very low aspect ratio means the fin is short in span and relatively long in chord — stubby, in other words. Both fins are shown in Figure 10.58, a side view of the fuselage with the dorsal fin on top and the ventral fin below. Now, how do they work? Let’s take the case where the aircraft is yawed to the right. The dorsal and ventral fins will create a side force to the right. Think about that: the fin surfaces are now angled into the airflow because of the yaw, so they generate a sideways aerodynamic force. The key point is the line of action of this force. It’s well aft of the aircraft’s centre of gravity — the CG. Because the force acts so far behind the CG, it produces a yawing moment to the left. And that left yawing moment is opposite to the right yaw we started with, so it’s a stabilizing effect. The fin is pulling the nose back toward the flight path. But here’s the limitation, and it’s an important one: at small angles of yaw, these fins are ineffective. Why? Because at very small yaw angles, the fin surfaces are barely angled into the airflow, so they generate almost no side force. The instability of the fuselage is most pronounced at small yaw angles, and that’s exactly where the dorsal and ventral fins give you the least help. So they’re a partial fix — they help at larger yaw angles, but they don’t cure the small-angle problem. Let me tie that back to the figures. Figure 10.57 shows the unstable yawing moment on the fuselage in plan view — the force, the flight path, and the unstable yawing moment all labelled. Figure 10.58 gives you the side view with the dorsal fin on top and the ventral fin below. So when you look at those, you’re seeing the problem and the two-part solution. That’s the dorsal and ventral fins: small, low-aspect-ratio aerofoils near the rear of the fuselage, top and bottom, generating a side force aft of the CG to create a stabilizing yawing moment — but only effective once the yaw angle is large enough.