Stalling — Page 173, Lesson 205

We’ve just seen that the stall happens when the wing reaches its maximum lift coefficient, CLMAX. Now I want to show you how we actually calculate the stall speed, and then how weight changes that speed. Let’s start with the lift formula. You know lift equals ½ ρ V² S CL. If we transpose that formula to solve for speed, we get the stall speed formula. It’s written as VS1g equals the square root of L divided by ½ ρ CLMAX S. Let me unpack that. VS1g is the one‑g stall speed — the speed at which the wing stalls in steady, level flight where the load factor is exactly one. L is the lift, which in level flight equals the weight. ρ is air density, S is wing area, and CLMAX is the maximum lift coefficient, the value of CL at the stalling angle. So the stall speed is the speed at which, at CLMAX, the lift just balances the weight. Now, the key point: at CLMAX for one‑g flight, a change in weight requires a change in lift. And you can see from the formula that if weight goes up, lift goes up, and therefore VS1g goes up. Heavier aircraft stall faster. That’s the direct effect. We can quantify this with a ratio formula. The new stall speed equals the old stall speed times the square root of the ratio of new weight to old weight. Written out: VS1g new = VS1g old × √(new weight / old weight). Here’s a worked example. An aircraft weighs 588 600 newtons and stalls at 150 knots CAS. What’s the stall speed if weight drops to 470 880 newtons? We plug in: VS1g new = 150 × √(470 880 / 588 600). That works out to 134 knots CAS. Notice the rule of thumb: a 20% reduction in weight gives roughly a 10% reduction in stall speed. That’s because of the square root — the speed changes with the square root of the weight ratio, not linearly. And the same formula works in reverse for an increase in weight. Now here’s a subtle but crucial point. The angle of attack at which the stall occurs is NOT affected by weight. The stall angle is fixed by the aerofoil. What changes with weight is the speed at which you reach that angle. To hold a given angle of attack in level flight, you must change the dynamic pressure — that is, the CAS — if the weight changes. So weight changes the speed, not the angle. There’s a caveat though: this holds provided CLMAX isn’t affected by speed, which it will be at speeds above Mach 0.4 — that’s a compressibility effect we’ll look at later. Two more points to note. Density altitude does not affect indicated stall speed — because the airspeed indicator reads dynamic pressure, and the stall occurs at a fixed CAS regardless of density. And weight does not affect stall angle, as we just said. Now let’s move to a new topic: the composition and resolution of forces. This is the mathematical toolkit we’ll need for the rest of the chapter. A force is a vector quantity. That means it has both magnitude and direction. We represent it as a straight line passing through the point where the force is applied. The length of the line represents the magnitude, and its direction shows which way the force acts. Because forces are vectors, we can add or subtract them to form a resultant force — the single force that has the same effect as the combination. Or we can do the reverse: resolve a force, splitting it into two or more component parts, simply by drawing the vectors. To actually calculate the components, we use trigonometry. If we know one angle and the length of one side of a right‑angled triangle, we can find the other sides. This is exactly what we do when we resolve a force into its horizontal and vertical components. Here are the three relationships. In a right‑angled triangle, we label the sides: the hypotenuse is the longest side, opposite the right angle. The opposite side is across from the angle we’re using, and the adjacent side is next to that angle. Then: sine of the angle equals opposite over hypotenuse. Cosine equals adjacent over hypotenuse. And tangent equals opposite over adjacent. So SIN = Opp/Hyp, COS = Adj/Hyp, TAN = Opp/Adj. That’s the tool we’ll use to break forces like lift, weight, and thrust into components — which we’ll need when we look at climbing, descending, and turning flight.