Is this explanation of adverse yaw correct?

Question

It is explained here that adverse yaw is caused by the difference in induced drag due to the difference in lift being generated by each wing.

I've also seen a couple of websites (including Wikipedia) that argue that this explanation is wrong. They explain the cause of adverse yaw as being the change in the direction of the lift vector during a roll, or what some refer to as the "twisted lift" concept. They usually have a diagram like the following:

source

The twisted lift explanation discounts a difference in induced drag due to a change in the amount of lift. They contend that lift and drag remain the same but they twist in different directions. The descending wing has a slightly higher local AoA and the rising wing slightly lower. Since lift is perpendicular to the local airflow the lift vector rocks forward on one wing and aftward on the other.

This explanation seems flawed to me.

• First of all, in the diagram they show the force on each wing being the same. If that were the case the aircraft wouldn't roll at all, it would ONLY yaw.
• Second, the vector of lift being perpendicular to the airflow is correct, but that is really just an arbitrary division of the total aerodynamic force. The yaw axis of the plane is not dependent on airflow. It would be dependent on the portion of the force vector parallel to the wing chord, aka the axial force. As shown in another question, depending on a number of factors the force vector in relationship to the wing does not necessarily move forward with an increase in AoA.
• I can't come up with solid numbers, but trying to figure this out for normal flight speeds it would require a very fast roll to even make a 1° difference in local AoA. I ran numbers for a 3° per sec roll at 120 KTAS on a 36ft wingspan (C172) and came up with a change in AoA of about .27°, and that Is only at the wingtip. It would decrease the closer it got to the fuselage. It doesn't seem like it would be enough to cause a significant change in vector and a resulting yaw moment. Or at least it would be secondary in magnitude to the difference in the drag due to reduction of lift.

Since the changes in lift are being created either by changing the effective camber of the wings (ailerons) or by altering the trailing edge flow (spoilerons) rather than a change in AoA I don't think it's quite so simple to predict that the direction of the aerodynamic vectors will necessarily move in opposite directions as this theory assumes.

If this explanation is correct can someone show me what I'm missing?

Answer 1

First of all, in the diagram they show the force on each wing being the same.

In a steady roll, i.e. when the roll rate is constant, the forces are the same. A non-zero moment causes angular acceleration, so when the aircraft is rolling with constant rate of roll, the moment must be zero, which means the lift on both wings have to be equal.

That rules out difference in magnitude of lift as the source of the difference and leaves the difference in angle as the only plausible explanation. The explanation is correct.

---

When you first deflect ailerons, the wing with aileron down does indeed start to produce more lift and the wing with aileron up less lift. This difference causes rolling moment, which causes the roll rate to increase. It already starts causing adverse yaw due to the difference in magnitude of lift too.

However as the roll rate builds up, the angle of attack increases lift on the wing going down and decreases it on the wing going up until the lift equalizes and the roll rate stabilizes. At that point the lift is the same and the adverse yaw is caused by different direction of lift due to different angle of attack.

The fact that ailerons are deflected throughout the roll might lead you to think that there is still difference in lift. But there isn't. The aileron deflection just changes the roll rate in which the forces are in equilibrium.

Also while the angle between realtive wing and the total aerodynamic force (which corresponds to the relation between lift and induced drag) is in general not constant, in this case all the factors it depends on — wing span, air speed and density — are (almost) the same for both wings, so the difference in angle of attack is the main factor for the direction of the resulting force.

And last, but not least: How It Flies is very reliable regarding the physics (and most other things too). I would be very surprised to find an incorrect explanation there.

Answer 2

Both explanations in the OP are correct to the overall phenomenon of adverse yaw.

There are three sources of adverse yaw:

1. Difference in induced-drag due to ailerons: down wing aileron reduces lift while the up wing aileron increases lift, which generates a difference in induced drag in each wing. This yaw moment counters the desired yaw motion. This is manifested through the control derivative $C_{n_{\delta a}}$.

2. Yaw-roll damping: as roll rate builds up to steady-state, the down wing experiences a larger flow incidence while the up wing experiences a smaller flow incidence due to the rolling motion. This is the twisted-lift concept mentioned in the OP: because of the difference in the local AOA, the lift and drag vectors are twisted. As Jan Hudec correctly pointed out in his answer, at steady-state roll, the total lift on each wing is equal, so the yaw moment really comes from the twist. This is manifested through the stability derivative $C_{n_p}$.

3. Converted sideslip: if there is a non-zero AOA, the rolling motion will convert some of the AOA into sideslip; this sideslip is opposite to the direction of the turn. This effect is especially pronounced when the roll rate is large. Some high performance FBW systems will address this by implementing stability-axis roll instead of body-axis roll, especially on fighter jets whose roll rates are high.