The Turn and Slip Indicator — Page 192, Lesson 231

Let’s pick this up right where the turn indicator’s theory of operation leaves off — with the balanced turn, and then the two failure modes you’ll be expected to read off that little ball. First, the balanced turn to the left. Look at Figure 14.5. The aircraft is banked, and the lift L is equal and opposite to the resultant of two forces: the aircraft’s weight W, acting straight down, and the centrifugal force C, which acts outward from the centre of the turn. That centrifugal force C is proportional to TAS — true airspeed — and to the rate of turn. So the faster you’re going, or the faster you’re turning, the bigger that outward force gets. Now the ball. The ball in its curved glass tube is also subject to a centrifugal force, and that force also depends on TAS and rate of turn. So in a turn, the ball rolls outward along the tube until it reaches a new equilibrium position. At that point, the reaction of the base of the tube on the ball is again exactly balanced — this time by the resultant of the ball’s weight W and its centrifugal force C. That’s Figure 14.6. Here’s the key insight, and I want you to hold onto it. The aircraft and the ball are experiencing the same TAS and the same rate of turn, so they have the same acceleration towards the centre of the turn. Because of that, it can be proved that the resultant of weight and centrifugal force for the aircraft is parallel to the resultant of weight and centrifugal force for the ball. Parallel — same direction in space. Now, if the ball is laterally central in the tube — sitting between the two etched lines — then the resultant and reaction forces on the ball must lie in the aircraft’s vertical. Since those forces are parallel to the aircraft’s resultant of weight and centrifugal force, that aircraft resultant must also lie in the aircraft’s vertical. And if it lies in the aircraft’s vertical, it’s in the same line as the lift L. That is the definition of a balanced turn — the lift and the resultant of weight and centrifugal force are collinear, so there’s no sideways component. The ball central means balanced. Now the unbalanced cases, and this is the part you’ll actually fly with. Let’s keep TAS and rate of turn the same as before, so the ball hasn’t moved laterally on its own. Suppose you apply too much bank for that TAS and rate of turn. The tube has been rotated too far in the rolling plane. The ball now appears off-centre — no longer between the etched lines — and it correctly indicates that the aircraft is ‘slipping in’ to the turn. The radius of that turn will be less than it should be. That’s Figure 14.7. On the other hand, if you apply insufficient bank for the same TAS and rate of turn, the instrument indicates that the aircraft is ‘skidding out’ of the turn — that’s Figure 14.8 — and this time the radius of turn is greater than it should be. So the rule you’ll fly by: ball central means balanced. Ball toward the inside of the turn — the low side — means slipping in, radius too small. Ball toward the outside — the high side — means skidding out, radius too large. The ball is your sideways-acceleration detector, and it’s telling you whether the lift vector is doing its job of matching the resultant of weight and centrifugal force.