Is an increase in induced drag always caused by an increase in the angle of attack?

Question

In this video at 2:57 they increase the AoA to maintain lift, which normally also increases the drag. Now, imagine that we don't increase the AoA: the drag will not increase but we will not have enough lift to maintain level flight. If we want to keep the same lift and fly in level flight we must increase the AoA and only then will the drag increase.

So induced drag is just caused by a larger AoA, so basically this is a type of pressure drag.

Do you agree that if we don't increase the AoA as described in the video then the drag will not increase as well?

Answer 1

At 2:58, the video says "To replace the lift lost by the increased upwash and downwash, the wing must be flown at a higher-angle-of-attack than would otherwise be necessary."

This statement is true no matter what angle-of-attack the wing is "feeling" and no matter how much lift it is making, as long as the amount of lift it is making is not zero.

For example, let's say at a given instant in time, with a given angle-of-attack and airspeed, when the instantaneous flight path is horizontal, the wing would be making Lift equal to Weight if it weren't for the upwash and downwash effect, but because of the upwash and downwash effect, the wing is only making a force equal to 90% of Weight.

Forces are not in balance, and the flight path is curving downward. In the next instant in time the flight time will no longer be horizontal. Yet despite the fact that we aren't actually replacing the "missing" lift, it is still true that that "To replace the lift lost by the increased upwash and downwash, the wing must be flown at a higher-angle-of-attack than would otherwise be necessary." If we were happy to settle for a lift force equal to 90% of weight at that instant in time, and the upwash and downwash effect were not there, we could fly at an even lower angle-of-attack.

More practically, we normally don't want to allow the flight path to curve (accelerate) downward, so we do keep lift close to weight, or very close to it, except during the brief transition (pushover) from a climb to level flight or from level flight to a descent. The reduction of lift that happens in a steady-state descent (or climb), compared to in level flight, is very small for moderate climb or descent angles. For more, see a What produces thrust along the line of flight in a glider? and Does lift equal weight in a climb? .

Only if the wing is mounted inside a wind tunnel, where the connection between Lift and Weight is completely severed, does it really make any sense to ask "What happens if we decide not to replace the missing lift?". In that case, indeed, the upwash/downwash effect does not force the wing to be flown at a higher angle-of-attack than would otherwise be necessary.

Answer 2

It is hard to understand the video in my opinion and also it is hard to understand the induced Drag mechanism thoroughly. I would like to recommend chapter 5 of Adams's "Fundamentals of Aerodynamics" book or other Aerodynamics book to understand in detail.

I will try to explain it as well as I can by myself. Lift (C_L) is the result of a pressure Difference (cp_down - cp_up) between the upper and lower surface. Because of this pressure difference, the air is trying to go from the high pressure lower surface to the low-pressure upper surface. When reaching the tip of the wing it has to curl around, which creates the Vortex. Therefore, Higher Lift results from higher pressure difference and results in higher vortex strength at the tip. The pressure difference/Lift coefficient is usually higher for higher AoA, and lower for AoA. When you fly slower, you need a higher CL, which results in a multiple Times higher CDi. Which means high induced Drag at slow flight.

Unfortunately, there are more ways to explain the induced Drag. Because of the vortex at the tip, a downwash (velocity in the z-direction) is generated. This downwash is changing the local effective aerodynamic AoA, which is different from the local geometric AoA(you can see the difference in the video 7:05). Because the, resulting aerodynamic force is always perpendicular to the air velocity(which has now an additional z component), the Lift vector has then an additional x component. This additional x-Component is the induced Drag(video 3:03).

Another way to understand the induced Drag would be: The 2D Flow is being changed by the vortex in a 3D flow, which is changing the pressure distribution of the wing in such a way that a pressure Difference in front and behind the wing exists. So it is a "pressure Drag".

Is an increase in induced drag always caused by an increase in the angle of attack? Drag = Drag Coefficient * dynamic Pressure * Wing surface No! The induced Drag can rise with higher velocity or higher density, too(if AoA is constant). But usually the needed Lift coefficient is sinking with higher dynamic pressure and therefore the Drag Coefficient too.