Subsonic Airflow — Page 63, Lesson 67

Let's pick up right where the airflow over the wing starts to do its real work. We're looking at the subsonic airflow over an aerofoil, and I want to walk you through what happens as we change the angle of attack. First, let's set the scene with the small angles, from 0° up to about 8°. Compared to the free stream static pressure — that's the undisturbed air pressure far ahead of the wing — there is a pressure decrease over the upper surface. And over most of the lower surface, there's also a decrease, but it's a lesser decrease. So the upper surface sees a bigger drop in pressure than the lower surface. Now, here's a key point for a cambered aerofoil — that's an aerofoil with a curved upper surface and a curved lower surface, not a symmetrical one. Because of that camber, you get a small amount of lift even at small negative angles of attack, from about -4° up to 0°. So even when the wing is slightly nose-down relative to the airflow, the camber alone is still generating a little lift. Now let's increase the angle of attack, from 0° up to about 16°. As you increase the angle of attack, the lift force increases. Why? Because the acceleration of the airflow over the top surface is increased. And that acceleration is increased because of a reduction in the effective cross-sectional area of the local streamtube. Let me unpack that. A streamtube is an imaginary tube of airflow, and as the wing tilts up more, the air over the top has to squeeze through a narrower effective passage. When a fluid is forced through a narrower passage, it speeds up. Faster airflow means lower pressure, by Bernoulli's principle. So more acceleration, more pressure drop, more lift. There's another detail here. The reduced pressure 'peak' — that's the point of lowest pressure on the upper surface — moves forward as the angle of attack increases. So as you pitch the wing up, that low-pressure point creeps toward the leading edge. And one more important fact: the greatest contribution to overall lift comes from the upper surface. The upper surface does the heavy lifting, not the lower surface. Now, let's talk about the pressure gradient, because this is the concept that ties it all together. A pressure gradient is a change in air pressure over distance. The greater the difference in pressure between two points, the steeper the gradient. So if you have a big pressure difference over a short distance, that's a steep gradient. There are two kinds we care about. A favourable gradient is when air pressure is falling in the direction of airflow. That's what you see over the front part of the upper surface, where the air is speeding up and pressure is dropping. An adverse pressure gradient is when air pressure is rising in the direction of airflow. And the classic example is between the point of minimum pressure on the top surface and the trailing edge. After that minimum pressure point, the air has to slow down again, and pressure rises as it flows toward the trailing edge. That rising pressure works against the airflow — it's adverse. Now, here's the critical relationship. The higher the angle of attack, the steeper the pressure gradient. And at angles of attack higher than approximately 16°, something dramatic happens. The extremely steep adverse pressure gradient prevents the air flowing over the top surface from following the aerofoil contour. The air can't make the turn; it doesn't have enough energy to push against that rising pressure. So the previously smooth streamline flow separates from the surface. And when that happens, the low pressure area on the top of the section suddenly collapses. Any pressure differential that remains is due only to the pressure increase on the lower surface. That condition — that sudden collapse of the upper-surface low pressure — is known as the stall. We'll describe it in detail in Chapter 7, but for now, understand that the stall is fundamentally a pressure-gradient phenomenon, not just a loss of speed. So let me tie the whole picture together. At low angles of attack, you have a pressure decrease over the upper surface and a smaller decrease over the lower surface, with camber giving you lift even at small negative angles. As you increase angle of attack up to about 16°, lift increases because the airflow over the top accelerates more, the low-pressure peak moves forward, and the upper surface contributes the most to lift. But the pressure gradient steepens with angle of attack, and past roughly 16°, the adverse gradient becomes so steep that the flow separates, the low-pressure region collapses, and you stall. That's the complete story of subsonic airflow over the wing as the angle of attack changes.