The Turn and Slip Indicator — Page 192, Lesson 231

Let’s pick this up right where the physics of the turn indicator gets interesting. I want to walk you through what a balanced turn actually looks like inside the instrument, and then what happens when the pilot gets the bank wrong. We’re looking at a balanced turn to the left — to port. Picture the aircraft in a steady turn. The lift vector L is acting upward through the wings. Now, because the aircraft is turning, there’s also a centrifugal force C pushing outward, away from the centre of the turn. And of course there’s the aircraft’s weight W acting straight down. In a balanced turn, the lift L is equal and opposite to the resultant of weight W and centrifugal force C. That resultant is the single combined force you get when you add the downward weight and the outward centrifugal force as vectors. And note this: the 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 inside the curved tube is also subject to a centrifugal force, and that force also depends on TAS and rate of turn. So the ball rolls outward along the tube until it finds a new equilibrium position. At that point, the reaction of the base of the tube on the ball — the force the tube’s wall pushes back with — is exactly balanced by the resultant of the ball’s own weight W and its centrifugal force C. So the ball just sits there, stable, in that curved tube. Here’s the clever bit. The aircraft and the ball are experiencing the same TAS and the same rate of turn, which means 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. They point in the same direction. 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. That’s the line straight up and down through the aircraft. And 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. Which means it’s in the same line as the lift L. And that is precisely the definition of a balanced turn — lift, weight, and centrifugal force all line up, and the ball sits central. That’s what Figures 14.5 and 14.6 are showing you: the balanced turn to port, with the ball central. Now let’s look at unbalanced turns, and this is where the instrument earns its keep as a slip-skid indicator. Let’s assume the TAS and rate of turn are exactly the same as in the balanced case, so the ball itself hasn’t moved laterally — it’s still in the same position in the tube. The only thing that changes is the bank angle. If too much bank is applied — 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. In a slip, the radius of turn will be less than it should be. The aircraft is being pulled toward the inside of the turn. On the other hand, if insufficient bank has been applied, the instrument indicates that the aircraft is skidding out of the turn. This time the radius of turn is greater than it should be — the aircraft is being thrown toward the outside. So the whole story of this instrument is: central ball means balanced turn, ball toward the inside means slip, ball toward the outside means skid. And the reason it works is that the ball and the aircraft share the same TAS and rate of turn, so their force resultants stay parallel, and the ball’s position in the tube tells you exactly how the aircraft’s force balance sits relative to its vertical.