# Is induced drag only created by wingtip vortices induced downwash?

In PHAK, I saw that There is two types of downwash

• formed by airfoil shape that necessary(help?) to produce lift
• formed by wingtip vortices

in phak 5-7 It said 'This induced downwash has nothing in common with the downwash that is necessary to produce lift'

My question is Does first type of downwash (necessary to produce lift) also produce induced drag? I keep searching about this and they always say about wingtip vortices induce downwash not that 'necessary to produce lift' downwash.

• "PHAK" is full of garbage. I'll get back to you later with some specific examples. Commented Mar 31 at 19:17

I really don't know why they waste time and effort in the "PHAK" writing and teaching this stuff.

Fundamental in aviation is that the moving aircraft interacts with the air, producing drag. Heavier than air craft must make lift to counter-act gravitional force.

This is done by increasing angle of attack from a zero lift state, AKA D0. Any drag associated with lift production is Dinduced, or Di.

Drag = D0 + Di

Downwash and tip vorticies are the result of lift production. To say they are unrelated is nonsense.

Downwash is flow from the trailing edge. In the simplest explanation, the mass of air pushed down = the weight of air craft pushed up.

Tip vortexes form because increasing angle of attack (creating lift) causes a pressure differential between upper and lower wing.

The lift equation is:

Lift = Area × Density × Lift coefficient (including AoA) × Velocity$$^2$$

When velocity is high and AoA is lower, these tip vorticies can spill harmlessly away from the wing tip and not affect lift or drag. When the plane slows down and AoA increases, the vortex may start to impinge on the upper wingtip surface$$^1$$.

So, the answer is that neither downwash or tip vorticies produce drag. They are the result of the velocity and angle of attack one flys their aircraft at.

The most important concept to grasp is that the best combination of Velocity and Angle of Attack is at Vbg. That's where one wants to be if the engine fails and a safe landing area is available to glide to.

$$^1$$ this has a secondary effect. The aircraft must increase AoA or speed to maintain lift, resulting in more drag, directly translating into more fuel consumption.

There is a very common form of incorrect reasoning on display here. In a steady flow we observe two apparently distinct phenomena A and B. We then ask which is cause and which effect. This is almost always wrong, because usually both A and B are effects of causes that operated before the flow became steady. @Robert DiGiovanni is correct to consider how the flow evolves starting with zero lift. To say that "these tip vortices can spill harmlessly away from the wing tip and not affect lift or drag" is however seriously misleading.

A and B here are what are often called the bound vorticity and the free vorticity. Vorticity is a vector whose direction is the local spin axis of the fluid, and whose magnitude is the spin intensity. Mathematically, the vorticity can be deuced from the velocity, and usually the velocity can also be deduced from the vorticity. They are alternative descriptions of the flow. Therefore we can pretend that either of them is the cause and the other the effect. This will not be a problem as long as we only consider steady flows.

So we can imagine that the trailing vortices, rather than "spilling harmlessly away", "reach back" to affect the velocity on the wing. This is "induced incidence" and is the "cause" of "induced drag". This mechanism is reduced for high aspect-ratio wings and is absent for two-dimensional wings.

The statement in PHAK that "A has nothing in common with B" is completely ridiculous scientifically. Its only possible purpose is to prevent pilots from worrying about things they have no reason to worry about. In fact classical wing theory is a well-established university-level subject that is found hard by many students because it gets quite mathematical, but leads to many fascinating conclusions. For those who are merely curious, a description that I am assuming to be true of @aviii there should still be satisfying explanations. Let me try.

The purpose of a wing is to produce downwash, and the simplest explanation is indeed that "the mass of air pushed down = the weight of air craft pushed up". A fuller analysis of the vertical momentum also includes the pressure, which changes with velocity according to Bernouilli's Law. Just behind the wing, there is "lifting downwash" produced by the pressure difference needed to achieve lift, and also "induced downwash" produced by (or at least associated with) the trailing vortices. In sum, these must combine to conform with the geometry of the wing, so the presence of induced downwash reduces the lifting downwash and therefore reduces the lift. It also results in drag.

I hope this helps but there are better explanations available. I could recommend one if I knew more about your level of interest.

• in all fairness I did mention that, at lower speeds and higher angles of attack, the vortex can affect lift production. I suggest it is in poor taste to mention my name and say my work is "seriously misleading". This type of comment is unnecessary. Commented Mar 31 at 20:17
• If you look at the wingtips of albatross and compare them with eagles you may gain some insight into what wingtip design is best for what combination of velocity and Angle of Attack works best for lowest drag. Eagle wings have slats to gain as much energy from wingtip circulation as possible, whereas as smooth taper serves the albatross well. Wingtip devices such as winglets can add drag at higher speeds (and also indirectly add drag through increased weight). Commented Mar 31 at 20:24
• @Robert DiGiovanni. I thought you did a great job moving things on from the PHAK statement, but to move things on further it really is necessary to recognize that the vortices do much more than trail away. I was sure that you knew this and had simply been a little casual with your phrasing. I apologise for not phrasing this more respectfully. Commented Apr 1 at 2:59
• how much the tip vorticies do (in terms of lift reduction) depends on Velocity, AoA, and tip design. Your answer otherwise makes good reading. The concept of trailing flow "reaching back" (flow reversal) is exactly what happens along the trailing edge as AoA approaches stall, and the tip vortex indeed has a similar effect from the side (at the tip). Downwash at the tips and winglets can reduce this, as does higher AR, as you pointed out. Commented Apr 1 at 10:17

PHAK is actually not totally wrong:

In PHAK, I saw that there are two types of downwash

• formed by airfoil shape that is necessary (help?) to produce lift
• formed by wingtip vortices

This is correct.

In aerodynamics there are indeed two distinct phenomena called with the same name i.e. downwash. The first one is a pure 2D phenomenon while the second one is a 3D phenomenon.

Let's start considering a 2D "wing" i.e. an airfoil. The airflow around an airfoil is well known and looks like this:

(Source)

Schematically, the airflow goes up in front of the airfoil, accelerates on its upper part, goes down behind it and decelerates on the lower part. If the freestream airflow's speed could be subtracted, a "circulation" of air around the airfoil would be visible:

(Source: Daniel P. Raymer, Aircraft Design: A Conceptual Approach)

This circulation of air is what creates lift on the airfoil. The airflow going up in front of the airfoil is termed upwash, while the air going down behind it is called downwash.This is the first downwash and it is jointly-responsible for the creation of lift (together with the upwash, the acceleration on the top and the deceleration on the bottom). Mathematically all this is translated via the famous Kutta–Joukowski theorem:

$$L=\rho V \Gamma$$

where $$\Gamma$$ (gamma) is the mathematical symbol used to represent the circulation.

For the second downwash we have to go 3D and bring into play Newton's third law (action-reaction): in order for the air to push the wing up, the wing must push air down. That means that if well in front of the wing the airflow is basically horizontal, on the back it is slightly going downward. This downward movement is also called downwash and is associated with the induced drag.

Note that in 2D the airflow is horizontal both well in front and in the back of the airfoil, is the circulation (first downwash) around the airfoil that produces the lift and there's no second downwash i.e. no induced drag in 2D (there's only lift).

Does first type of downwash (necessary to produce lift) also produce induced drag?

Yes, they are the two sides of the same coin. It can be demonstrated that the second downwash (the one responsible for the induced drag) is proportional to the spanwise change of lift i.e. the spanwise change of circulation i.e. the spanwise change of the first downwash (the one responsible for the lift). It can also be demonstrated that the induced drag reaches a minimum if the spanwise change of lift is elliptic.

• This is a very well written answer. Could you expound upon "in 2D (there's only lift)? One might say (in a infinitely small 2D cross-section) there is neither lift nor drag. Then it is confirmed that the "first type of downwash also produces induced drag", finishing with elliptic distribution minimizes induced drag. Why are we "beating around the bush" with induced drag when you so well illustrated it simply as a rearward pointing vector combined with the normal lifting force vector (from the aerodynamic force generated by the wing with increased AoA from D0) in a previous answer. Commented Apr 2 at 23:18