Subsonic Airflow — Page 63, Lesson 68

Let’s start with the Centre of Pressure, because it’s the idea that ties the whole aerofoil together. Every part of the wing’s surface contributes to lift, but we don’t want to track a million little forces. So we define a single point along the chord — the line from the leading edge to the trailing edge — where all that distributed lift is effectively concentrated. That point is the Centre of Pressure, usually shortened to CP. Now, where does the CP sit? It’s not fixed. Its location depends on two things: the camber of the aerofoil — that’s the curvature of the mean line between the upper and lower surfaces — and the section lift coefficient, which is essentially the angle of attack. So as you change angle of attack, the CP moves. Here’s the behaviour you need to remember. As the angle of attack increases from 0° up to 16°, the upper surface’s ‘suction’ peak moves forward. That suction peak is the point of lowest pressure, the strongest lift contribution on the top of the wing. Because that peak shifts forward, the CP — the point where lift is concentrated — also moves forward. So increasing angle of attack moves the CP forward, and at the same time the magnitude of the lift force increases. That continues until you reach the stall. At the stall, the lift force decreases abruptly, and the CP generally moves back along the chord. And here’s a key detail: the CP is at its most forward location just before the stall, at the point of maximum lift coefficient, which we call CL MAX. So the sequence is: CP moves forward as you increase angle of attack, it’s furthest forward right at CL MAX, then at stall the lift collapses and the CP jumps back. Now let’s move to the Aerodynamic Force Coefficient. First, what is a coefficient? It’s a dimensionless number — no units — that expresses the degree of magnitude of something. An aerodynamic force coefficient is a common denominator for all aircraft, whatever their weight, size, or speed. That’s the whole point: it lets you compare the aerodynamic behaviour of different aeroplanes on the same scale. The formal definition: an aerodynamic force coefficient is a dimensionless ratio between the average aerodynamic pressure and the airstream dynamic pressure. Dynamic pressure is the pressure you feel from the moving airstream, the kinetic energy of the flow. From that definition, we get the specific coefficients. The lift coefficient, CL, is the ratio between lift divided by the wing planform area, and dynamic pressure. The drag coefficient, CD, is the same idea: drag divided by the wing planform area, over dynamic pressure. So both are normalised by the wing area and the dynamic pressure. Why do we need these coefficients at all? Because the force coefficient is an index of the aerodynamic force that is independent of area, density, and velocity. It’s derived from the relative pressure and velocity distribution. And it’s influenced only by the shape of the surface and the angle of attack, since those two factors determine the pressure distribution. So if you change the wing shape or the angle of attack, the coefficient changes; but if you just fly faster, or at a different altitude, or in a bigger aircraft, the coefficient stays the same — that’s what makes it so useful. Let me show you the movement of the centre of pressure on the diagram. So to pull it together: the CP is where lift acts, it moves forward with increasing angle of attack up to CL MAX, then jumps back at the stall. And the coefficients CL and CD are the dimensionless tools we use to describe those forces independent of size, speed, and density.