Which wing stalls first in a level coordinated turn?

Question

I was told that in a level coordinated turn the inside wing stalls first because it has a higher angle of attack (AoA).

Now, I have always thought that in a level coordinated turn, the wings must have the same AoA and so if stalled the nose will just drop.

I know the differences in AoA in climbing and descending turns and which wing stalls first. I also know that in a level turn the outer wing must travels faster and so will generate more lift.

Is it because since the outer wing has more lift one would need to stop the overbanking tendency by holding 'counter aileron' input, (roll right to hold a left turn), so the inside wing now has a higher AoA overall?

Edit: after some more thoughts on this, I think I have figured it out! Since the outer wing produces more lift due to travelling faster, the inner wing will need to have a higher AoA in order for lift to be the same from both wings (hence the counter aileron inputs). Is this correct?

Answer 1

Since the outer wing produces more lift due to travelling faster, the inner wing will need to have a higher AoA in order for lift to be the same from both wings (hence the counter aileron inputs). Is this correct?

Yes, it is. Technically, the AoA is the same left and right in coordinated flight, but the aileron input reduces the stall margin on the side of the down aileron. But not every airplane needs to add aileron input in a steady turn. For some, the uprighting inertial moment is enough.

Where you DO find a difference in AoA over span is in a climbing or descending turn.

To answer your question: In almost all cases it is the inner wing which stalls first. The lower speed and Reynolds number already lower the stall margin a bit and some trailing-edge-down aileron deflection to compensate for the lower lift from lower dynamic pressure there will make sure that this wing will stall first.

Answer 2

...the outer wing produces more lift because it is traveling faster

Let's take a 2000 lb plane in a level 45 degree turn at 100 knots. Radius of turn is:

R = V$^2$/(11.26×Tan bank angle) = around 900 feet

My aircraft has a 55 foot wingspan. Draw it to scale, or calculate the Radius of the outer and inner wing tips in that circle:

Since the bank is 45 degrees, the horizontal distance between wing tips is 0.707 × 55 feet = around 40 feet

Turn Radius inner wingtip: 880 feet
Turn Radius outer wingtip: 920 feet

Wingtip velocities:

Inner: 100 knots × 880/900 feet = 97.8 knots
Outer: 100 knots × 920/900 feet = 102.2 knots

How does one design an aircraft not to roll uncontrollably into a turn?

First, we can calculate the roll torque created by the lift differential of the inside and outside wings:

Vertical lift required: 2000 lb
Total lift at 45 degrees: 2000/.707 = 2800 lb

Difference in lift (excluding fuselage and wingtip effects):

Average speed of inside wing (tip to fuse): 99 knots
Average speed outside wing: 101 knots.

Lift is proportional to V$^2$

99 knots$^2$ = 9800
101 knots$^2$ = 10200

Lift outside wing = 10200/20000 × 2800 = 1428 lbs
Lift inside wing = 9800/20000 × 2800 = 1372 lbs

Lift differential = 1428 - 1372 = 56 lbs
Roll torque = 56 × 55/4 (wing midpoint to CG) = 770 foot/pounds

The one obvious asymmetrical part of the aircraft is the vertical stabilizer. Combined with the rudder, it forms an airfoil which imparts roll torque on the aircraft. In a properly coordinated turn, rudder into the turn should be providing sufficient roll torque away from the turn to counter-act differences in lift.

Let's plug in some numbers to see if this is possible:

Vertical fin/rudder height: 6 feet
midpoint = 3 feet
"lift" required by Vertical airfoil: 770 foot/pounds ÷ 3 feet = 256 lbs

Lift is proportional to Area

Even with the same coefficient of lift, wing lift roll torque differential can be balanced with a vertical surface less than 10% of the total wing area!

This is in addition to the rudder's primary job of countering adverse yaw created not only by the ailerons, but also by the velocity differential of the wings. Alas, more lift = more drag.

As mentioned by Peter Kampf, a turning aircraft will also try to "flatten", or roll away from a turn due to "centrifugal" forces.

What if my plane has an overbanking tendency?

Seek out expert advice specific for that type of aircraft. It may come down to a choice of evils. Aileron away from a turn, in addition to increasing the AoA of the inside wing, also creates proverse yaw. Now you have to reduce rudder or the plane will skid.

Another option, particularly with aircraft that have very large wings and small tails, is to nudge to nose to the outside enough to use the dihedral effect of the entire aircraft to control the roll. But these are both compromises to a properly coordinated turn.

The greatest evil of all is to turn at a dangerously low airspeed. This is where all the other sins rear their ugly heads, and is why any flight technique other than coordinated should be tried first at least "2 mistakes high".

Finally, we all must consider one non-aerodynamic factor which may influence aileron and rudder input in a turn: forces created by the engine and prop. It is entirely possible that additional inputs must be made to control these forces, even if the aircraft is aerodynamicly coordinated. Strong evidence of this is the fact that power must be increased to hold level flight in a turn.

The proof for best control inputs for the lowest drag in a turn is to see if the aircraft climbs, holds, or loses altitude for each setting tried at a constant power setting.

Answer 3

"I was told that in a level coordinated turn the inside wing stalls first because it has a higher angle of attack (AoA)."

Lift is not just about AoA, it is about AoA and airspeed so I am sorry, but you were told the wrong thing. The inside wing stalls first because it is generates less lift (at the same AoA) as a result of moving slower then the outside wing.