Stalling — Page 173, Lesson 207

Let's pick up right where the mathematics of the level turn left off, because this page is where that trigonometry turns into a real operational limit. We just proved that in a 45° bank, lift must be 1.41 times the weight. Now I want to introduce the formal name for that ratio, because it's the single most important number in stall management. It's called Load Factor, given the symbol n, and it's also called 'g'. The definition is simple: Load Factor equals Lift divided by Weight. So if lift is 1.41 times weight, the load factor is 1.41, and we say the aircraft is pulling 1.41 g. Two relationships follow directly from that definition. First, increasing lift in a turn increases the load factor. Second, as bank angle increases, load factor increases. Both of those are just restating the geometry we already did, but now with the proper term attached. Now here's the critical operational consequence. In straight and level flight at the maximum lift coefficient, which we call CLMAX, it would be impossible to turn AND maintain altitude. Why? Because to turn and hold altitude you need more lift, and to get more lift you need more angle of attack. But at CLMAX you're already at the maximum angle of attack before the stall. Trying to increase lift any further would stall the aircraft. So if you start a turn at an indicated airspeed above the stall speed, at some bank angle the lift coefficient will reach its maximum, and the aircraft will stall at a speed higher than the 1g stall speed. That's the key idea: the stall speed goes up in a turn. Now, the increase of lift in a level turn is a function of the bank angle only. And we can calculate the stall speed in a turn using a formula. The stall speed in a turn is given the symbol VSt, and it equals the 1g stall speed, VS, multiplied by the square root of 1 over the cosine of the bank angle. Written out: VSt equals VS times the square root of (1 divided by cos φ). Let's work the example from the page. Our example aeroplane has a 1g stall speed of 150 knots CAS. CAS means calibrated airspeed. In a 45° bank, cos 45° is 0.707, so 1 over 0.707 is 1.41, and the square root of 1.41 is about 1.19. Multiply 150 by 1.19 and you get 178 knots CAS. So the stall speed in a 45° bank is 178 knots. Now let's do a 60° bank. Cos 60° is 0.5, so 1 over 0.5 is 2, and the square root of 2 is about 1.41. Multiply 150 by 1.41 and you get 212 knots CAS. So in a 60° bank the stall speed is 212 knots. Here's the takeaway in percentage terms. The stall speed in a 45° bank is 19% greater than the 1g stall speed. In a 60° bank it's 41% greater. And since these are ratios, this is true for any aircraft, not just our example. The percentage increase is universal. One final point that often surprises people: load factor does not affect stall angle. The angle of attack at which the wing stalls is fixed by the aerodynamics of the wing. What changes in a turn is the speed at which you reach that angle, not the angle itself. So the stall angle stays the same, but the stall speed rises with bank angle. That's the complete picture: load factor is lift over weight, it grows with bank angle, and it drives the stall speed up through that square-root formula.