The Lift Curve — Page 77, Lesson 88

Let’s start with the lift curve itself. Figure 5.4 shows the lift curve of an aerofoil section, with the lift coefficient, \(C_L\), plotted against angle of attack. The first thing that jumps out is that this particular section is symmetrical, because no lift is produced at zero angle of attack. That’s a key clue — a cambered section would produce some lift even at zero angle of attack, but a symmetrical one gives you exactly zero there. The lift curve is a really convenient way to illustrate the properties of various configurations, and we’ll use it extensively throughout these notes. So let’s read it properly. As angle of attack increases, the lift coefficient increases — up to a maximum value, which we call \(C_{LMAX}\). That maximum corresponds to the “Critical” angle of attack. If you keep increasing the angle of attack beyond that point, the airflow can no longer maintain its previous smooth flow over the contour of the upper surface, and lift will reduce. That phenomenon is called stall, and we’ll discuss it in detail later. For now, just hold onto the shape: lift coefficient rises with angle of attack, peaks at \(C_{LMAX}\) at the critical angle, then falls off. Now, the interpretation of the lift curve. This is where we start connecting the curve to real flying. First: to generate a constant lift force, any adjustment in dynamic pressure must be accompanied by a change in angle of attack — and this holds at \(C_L\) less than \(C_{LMAX}\). In other words, if you want to keep the same lift but change your speed, you have to change your angle of attack to compensate. Second: for a constant lift force, each dynamic pressure requires a specific angle of attack. So there’s a one-to-one relationship — a given dynamic pressure gives you a particular angle of attack for a given lift. Third: minimum dynamic pressure is determined by the maximum lift coefficient, \(C_{LMAX}\), which occurs at a specific angle of attack — approximately 16 degrees. So you can’t fly slower than a certain speed, because at some point you run out of lift coefficient. Fourth: the angle of attack for \(C_{LMAX}\) is constant — and that’s true for a given configuration. So for a fixed configuration, the stall angle doesn’t change. Fifth: if more lift is required due to greater operating weight, a greater dynamic pressure is required to maintain a given angle of attack. Heavier aircraft need more speed to hold the same angle of attack. And sixth: the greater the operating weight, the higher the minimum dynamic pressure. So a heavier aircraft has a higher minimum speed. Now, to use the lift formula with specific values, we need to convert each item to SI units. Let me walk you through the example. The mass of the aircraft is 60,000 kg. To convert mass to weight, we multiply by the acceleration of gravity, which is 9.81 m/s². The wing area is 105 m². Density is the ICAO Standard Atmosphere sea level value of 1.225 kg/m³. The speed resulting from the calculation will be in m/s. And for reference, there are 6,080 feet in one nautical mile, and 3.28 feet in one metre. Now the lift formula itself: \[ L = \frac{1}{2} \rho V^2 C_L S \] Here, \(L\) is lift, \(\rho\) is air density, \(V\) is true airspeed, \(C_L\) is the lift coefficient, and \(S\) is wing area. When we transpose the formula to calculate speed, it becomes: \[ V = \sqrt{\frac{L}{\frac{1}{2} \rho C_L S}} \] So to find the speed for a given lift, you take the lift, divide by half the density times the lift coefficient times the wing area, and take the square root. Let me tie this all together. The lift curve gives us the relationship between \(C_L\) and angle of attack. The lift formula lets us convert that into actual speeds and forces. And the interpretation rules tell us how the aircraft behaves — how speed, weight, and angle of attack interact. That’s the core of understanding lift in flight.