Wing Tip Vortices — Page 89, Lesson 102

I want to walk you through wing tip vortices now — this is where the lift story gets really interesting, because it turns out that producing lift creates a penalty, and that penalty is drag. Let's start with the basic pressure picture. Air flowing over the top surface of a wing is at a lower pressure than the air beneath the wing. That pressure differential is what generates lift. But that same pressure difference has another consequence: the trailing edge and the wing tips are where the airflows from above and below interact. The pressure differential modifies the directions of flow. Specifically, it induces a spanwise vector — a flow component along the wing's span, from root to tip — towards the root on the upper surface, and generally towards the tip on the lower surface. Now, here's the convention you need to lock in: an aircraft is viewed from the rear. From that viewpoint, an anti-clockwise vortex is induced at the right wing tip, and a clockwise vortex at the left wing tip. So you get a pair of counter-rotating vortices trailing off the wing tips. The strength of these vortices depends on angle of attack. At higher angles of attack — which correspond to lower indicated airspeed, lower IAS — the chordwise vector decreases. The chordwise flow is the airflow moving along the chord, from leading edge to trailing edge. When that decreases, the effect of the resultant spanwise flow increases, and that makes the vortices stronger. So high angle of attack, low speed, strong vortices. Now let's look at what these trailing vortices do to the airflow around the wing. They create certain vertical velocity components in the airflow in the vicinity of the wing — both in front of it and behind it. These vertical velocities cause a downwash over the wing. Downwash is the downward deflection of the airflow. And that downwash results in a reduction in the effective angle of attack. Here's the key relationship: the stronger the vortices, the greater the reduction in effective angle of attack. And because of this local reduction in effective angle of attack, the overall lift generated by a wing will be below the value that would be generated if there were no spanwise pressure differential. This is the beautiful paradox of flight — it is the production of lift itself which reduces the magnitude of the lift force being generated. So what do we do about it? To replace the lift lost by the increased downwash, the aircraft must be flown at a higher angle of attack. And flying at a higher angle of attack increases drag. This extra drag is called induced drag. And again, the stronger the vortices, the greater the induced drag. Let me give you the full picture with the terminology from the diagram. The vertical velocities in the vicinity of the wing are a function of tip vortex strength. Upwash increases ahead of the wing, downwash increases behind it. The angular deflection of the effective airflow is a function of both vortex strength and True Airspeed — TAS. So the faster you go, the less the airflow gets deflected for a given vortex strength. Now the angles. We have the relative airflow, and the effective airflow is deflected downward by the downwash. The effective angle of attack is denoted by the symbol epsilon with a subscript e — that's the angle between the chord line and the effective airflow. The induced angle of attack is denoted by epsilon with a subscript i — that's the angular difference between the relative airflow and the effective airflow, the amount by which the effective angle of attack has been reduced. Because the effective angle of attack is decreased, the lift vector is inclined rearwards. That rearward inclination of the lift vector is what produces induced drag, denoted D with a subscript i. So induced drag isn't a separate force — it's the rearward component of the lift vector caused by the decreased effective angle of attack. And this matters far beyond just drag. Wing tip vortices, in particular their influence on upwash and downwash, have a significant effect on several important areas of aircraft aerodynamics, stability and control. We'll be returning to these effects throughout the remaining chapters. So the chain is: pressure differential creates spanwise flow, which rolls up into tip vortices, which create downwash, which reduces effective angle of attack, which reduces lift, which forces a higher angle of attack, which increases drag — and that drag is induced drag. That's the whole story in one loop.