Stability and Control — Page 273, Lesson 328

Let’s pick up right where the elevator deflection and trim lift coefficient meet. I want to walk you through what happens when you hold the elevator in different positions and how that ties to the centre of gravity. First, the key idea: as the elevator is held in various positions, equilibrium — that’s trim — will occur at various lift coefficients. So each elevator position gives you a particular trim lift coefficient, and you can plot that relationship. That’s Figure 10.32, the trim versus elevator deflection graph. On that graph, the vertical axis is the trim lift coefficient, CL, and the horizontal axis is elevator deflection, with UP and DOWN marked. The graph shows a family of lines, each labelled with a CG location — 10% MAC, 20% MAC, 30% MAC, and 40% MAC. MAC stands for mean aerodynamic chord, and the CG location is expressed as a percentage of that chord. There’s also a marker on the graph labelled NEUTRAL POINT. Now, the relationship: when the CG position of the aeroplane is fixed, each elevator position corresponds to a particular trim lift coefficient. So for a given CG, you get one line on that graph. As the CG is moved aft — that is, towards the rear — the slope of this line decreases. And here’s the stability story: the decrease in stability is evident because a given control displacement causes a greater change in trim lift coefficient. In other words, with the CG further aft, the same elevator movement produces a bigger change in trim CL. That is evidence that decreasing stability causes increased controllability, and, of course, increasing stability decreases controllability. So there’s a direct trade-off: more stability means less control response, less stability means more control response. Now, if you move the CG aft until the line of trim CL versus elevator deflection has zero slope, you get neutral static stability. That’s the boundary — zero slope means the trim lift coefficient no longer changes with elevator deflection, and that’s the definition of neutral static stability. One important note from the text: a change in elevator position does not alter the tail contribution to stability. The elevator deflection changes the trim condition, but it doesn’t change how the tail contributes to the stability of the aeroplane. Now let’s move to Figure 10.33, which is trim airspeed versus elevator deflection. Since each value of lift coefficient corresponds to a particular value of dynamic pressure required to support an aeroplane in level flight, trim airspeed can be correlated with elevator deflection. So instead of plotting CL against elevator deflection, you plot equivalent airspeed against elevator deflection. On that graph, the vertical axis is equivalent airspeed, and the horizontal axis is elevator deflection, again with UP and DOWN. There are two lines: one labelled STABLE and one labelled UNSTABLE. Here’s the key concept: if the CG location is ahead of the neutral point, and control position is directly related to surface deflection, the aeroplane will give evidence of stick position stability. Let me unpack that. Stick position stability means the aeroplane requires the stick to be moved aft to increase the angle of attack and trim at a lower airspeed, and to be moved forward to decrease the angle of attack and trim at a higher airspeed. So, to go slower, you pull back; to go faster, you push forward. That’s the stable behaviour. It is highly desirable to have an aeroplane demonstrate this feature. Why? Because if the aeroplane were to have stick position instability, it would require the stick to be moved aft to trim at a higher airspeed, or to be moved forward to trim at a lower airspeed. That’s backwards — pulling back to go faster, pushing forward to go slower — and that’s the unstable case you want to avoid. Now let’s bring in the trim tab and stick force. There is an increment of force dependent on the trim tab setting, and that force varies with dynamic pressure, or the square of equivalent airspeed. So the trim tab force grows with the square of airspeed. Figure 10.34 shows the variation of stick force with airspeed and illustrates the effect of tab setting on stick force. On that graph, the vertical axis is stick force, with PULL and PUSH marked, and the horizontal axis is equivalent airspeed, EAS. There are three curves, labelled 1, 2, and 3, all for a CG at 20% MAC. Here’s how it works. To trim the aeroplane at point (1), a certain amount of up elevator is required, and zero stick force is obtained with the use of the trim tab. So the trim tab is what cancels the stick force. To trim the aeroplane for higher speeds corresponding to points (2) and (3), less and less aircraft nose-up tab is required. So as you speed up, you need less nose-up trim tab. Now, the important observation: when the aeroplane is properly trimmed, a push force is required to increase airspeed, and a pull force is required to decrease airspeed. In this manner, the aeroplane would have positive stick force stability with a stable “feel” for airspeed. So the pilot feels a push as the aeroplane speeds up, and a pull as it slows down — that’s the stable feel you want. So, to tie it all together: you have trim lift coefficient versus elevator deflection, which shows how CG position affects stability and controllability. Then you have trim airspeed versus elevator deflection, which shows stick position stability. And finally, you have stick force versus airspeed, which shows stick force stability and how the trim tab sets the zero-force point. Each of these is a different way of looking at the same underlying stability picture.