Let me unpack that — Page 119, Lesson 141

I want to walk you through the concept of induced drag, because this is the drag that is born directly out of the production of lift itself. And as the text says, it's the production of lift that actually reduces the magnitude of the lift force being generated. Let me unpack that. When a wing generates lift, it deflects the airflow. Ahead of the wing, the air is pushed up — that's the upwash. Behind the wing, the air is pushed down — that's the downwash. Now, the tip vortices — those swirling masses of air that spin off the wingtips — they increase both the upwash over the outer portions of the span and the downwash over the outer portions of the span. So the effective airflow over those outer sections is no longer the same as the relative airflow far from the wing. It's angled. Here's the key consequence: this increased upwash and downwash reduces the effective angle of attack over the outer portions of the span. The wing is still at the same geometric angle to the relative airflow, but the local airflow it actually sees is tilted, so the effective angle of attack is smaller. And because the effective angle of attack is reduced, the lift vector itself gets inclined rearwards. That rearward inclination of the lift force is what we call induced drag. Let me be precise about the geometry, because the figure labels it clearly. We have the relative airflow, which is the airflow far from the wing, undisturbed. Then we have the effective airflow, which is the airflow actually seen by the wing section, tilted by the downwash. The angle between the relative airflow and the effective airflow is called the induced angle of attack, labelled i. And the angle between the effective airflow and the chord line is the effective angle of attack, labelled e. So the lift force, which is perpendicular to the effective airflow, gets tilted rearwards relative to the relative airflow. That rearward tilt is the induced drag component, labelled Di. Now, the angular deflection of the effective airflow is a function of two things: the strength of the tip vortices, and the True Airspeed, TAS. And the vertical velocities in the vicinity of the wing — the upwash and downwash — are a function of tip vortex strength. So to replace the lift lost by that increased upwash and downwash, the wing must be flown at a higher angle of attack than would otherwise be necessary. And that higher angle of attack increases drag. That extra drag is induced drag. Now let's look at the factors that affect induced drag, because there are three of them, and each has a specific relationship. First, the size of the lift force. Because induced drag is a component of the lift force, the greater the lift, the greater the induced drag. In level flight, lift must equal weight, so induced drag depends on the weight of the aircraft. Higher aircraft weight means greater induced drag. Now, certain manoeuvres require the lift force to be greater than the aircraft weight. The relationship of lift to weight is known as the Load Factor, or 'g'. For example, during a steady turn, lift is greater than weight, so induced drag is higher during a steady turn than in straight and level flight. So induced drag increases as the Load Factor increases. And here's the precise relationship: induced drag increases in proportion to the square of the lift force. Second, the speed of the aircraft. Induced drag decreases with increasing speed, for a constant lift force. Why? Because as speed increases, the downwash caused by the tip vortices becomes less significant. The rearward inclination of the lift is less, and therefore induced drag is less. The precise relationship: induced drag varies inversely as the square of the speed. So if you double the speed, induced drag drops to a quarter. Third, the aspect ratio of the wing. Aspect ratio is the span of the wing relative to its chord. The tip vortices of a high aspect ratio wing affect a smaller proportion of the span, so the overall change in downwash is less, giving a smaller rearward tilt to the lift force. So induced drag decreases as aspect ratio increases, for a given lift force. And the induced drag coefficient is inversely proportional to the aspect ratio. Let me just make sure you've got the full picture of how these three factors interact. Induced drag is a penalty you pay for making lift. It's proportional to the square of the lift force, so heavy aircraft and high-g manoeuvres pay a heavy price. It's inversely proportional to the square of the speed, so slow flight is expensive in induced drag. And it's inversely proportional to aspect ratio, which is why high aspect ratio wings — like those on gliders — are so efficient at reducing induced drag. One thing I want to flag: the text references page 121 for a detailed explanation of the speed relationship. We'll get to that in due course, but for now, hold the inverse-square relationship in your mind. Let me also point you to the figures, because they show this beautifully. Figure 6.8 shows the effective airflow versus the relative airflow, and how the tip vortices increase upwash and downwash over the outer portions of the span, reducing the effective angle of attack. Figure 6.9 shows the upwash and downwash as vertical velocities in the vicinity of the wing, functions of tip vortex strength, and how the angular deflection of the effective airflow is a function of both vortex strength and True Airspeed. And Figure 6.10 shows the geometry of induced drag itself — the relative airflow, the normal downwash, the effective airflow, the effective angle of attack e, the induced angle of attack i, and the lift inclined rearwards, with the induced drag component Di. So the core idea to take away: induced drag is not a separate friction or pressure drag. It is the rearward component of the lift force itself, created because the tip vortices tilt the effective airflow and reduce the effective angle of attack, which tilts the lift rearwards. And it's governed by those three relationships — square of lift, inverse square of speed, and inverse of aspect ratio.