# Contribution of wing vertical location to roll stability

Recently, I was reading about the factors that contribute to roll stability of an aircraft and came across a point stating that the wing's vertical location (Distance of wing from CG) contributes to the roll stability of the aircraft. I cannot comprehend this statement completely and even if it did, How much of an effect does it truly cause when compared to having features like a wing dihedral? Any information and explanations would really help me understand this concept.

• – user
May 16, 2019 at 10:54
• The Center of Gravity of aircraft is not a vertical measurement, it is a horizontal measurement from the datum point of the aircraft, or expressed as a percentage of the mean aerodynamic chord. High wing or low wing is not a contributing factor to roll stability, but the wing's dihedral angle is. May 16, 2019 at 10:55
• @JuanJimenez There is a vertical CG, although until you have the height of a 747 it's typically ignored during load planning. But it's there, and designers are aware of it, even if crews don't have to be (given how little they can affect it).
– Ralph J
May 16, 2019 at 13:24
• Voting to leave open, since nothing in the other answer really addresses the OP's question other than to say "aerodynamics matter more". Okay, that's great, but these effects seem worth discussing, even if they're less influential than the other.
– Ralph J
May 16, 2019 at 13:27
• @JuanJimenez As far as physics and everyday usage are concerned, an object's centre of gravity is a point. May 16, 2019 at 14:45

## 2 Answers

An aeroplane in a pure co-ordinated turn has a deflection of both the ailerons and the rudder. This is cumbersome however, much easier to only deflect the wheel, tilt the lift vector, and let the aircraft sway into the turn. The vertical tail will then experience a slip angle, which will point the nose into the direction of the turn at the expense of a small sway velocity: sideways.

So now the question is: how does the aeroplane react to a sideways incoming airstream. What we want is that if the pilot deflected the wheel to the right, he has to keep the wheel to the right to maintain the right hand turn. So upon an un-coordinated turn, without touching the pedals, we want the aircraft to try to level itself again upon an incoming sideways velocity.

If we look at what happens to a low wing aircraft first, we see that the incoming sideways stream sees little resistance when streaming over the fuselage top, but gets caught in the wing/fuselage intersection and builds up pressure there. So the sideways velocity introduces a rolling moment in the direction of the turn, which the pilot has to compensate for by turning the wheel the other way. This is not the behaviour that we want.

In order to correct for that, we can introduce wing dihedral: now the incoming sideways air stream wants to level the aeroplane again, and the pilot needs to keep the wheel deflected into the turn, which is what we want.

And of course, with a high-wing aeroplane the above is valid vice-versa: the sideways stream wants to level the aircraft, so the roll behaviour is naturally how we want it to be already. Depending on the wing/fusleage shape and many other factors, the aeroplane can be too stable and we'll need to implement anhedral, wings pointing down.

• Draw a vertical line through the center of lift in the undihedralled low wing at a bank and you will see the displacement of CG from Clift. In a large aircraft this is what causes the roll to continue before side slip even starts. -20, I Don't care. This is why top heavy is unstable. May 16, 2019 at 14:55
• Lift goes through the CoG though. At a bank angle, lift is not vertical. And dihedral fixes roll instability... May 16, 2019 at 15:03
• With respect, vertical lift vectors hold the plane up. Yes, total lift and CG are still "centered" WRT "top" and "bottom" of aircraft, but they are displaced WRT gravitational field in a roll. At 500 mph this matters little, but should not be forgotten. Displacement of lift (dihedral) or weight (hang glider) becomes important as one slows down, and as Juan pointed out, is critical in spins. And please don't forget what slip does to a tall upright vertical tail. Regards, Bob May 16, 2019 at 16:05

High-wing airplanes are usually designed with less dihedral than low-wing airplanes because of the various different ways that a high wing placement enhances roll stability.

Several of these are addressed in this answer-- Why do low wing aircraft have higher dihedral than high wing aircraft?

For any of this to make any sense, it is imperative that we understand that when an aircraft is banked, it tends to turn (i.e. the flight path tends to curve), and in a turn, there tends to be sideslip, unless the pilot is using the rudder to eliminate it. Sideslip is the fundamental driver behind nearly all the dynamics at play with regard to roll stability. The actual reasons for the sideslip are not obvious and are related to the fact that in a steady turn, the wingtips are moving at different airspeeds, which tends to create a yaw torque. Also, if the vertical fin is tangent to the curving flight path through the airmass, then the fuselage centerline at a more forward location on the aircraft cannot be tangent to the curving flight path through the airmass, so there is no way for the fin to completely eliminate sideslip in the absence of a rudder input. In fact, in some cases the vertical fin can be said to actually be causing sideslip. (Imagine a very long fuselage and a small radius of curvature of the flight path.)

Therefore a non-level bank attitude causes a turn which causes sideslip which can create a roll torque towards wings-level via dihedral, "pendulum effect", and other aerodynamic effects.

Note that in a high-wing aircraft, the wing's drag vector, acting above the CG of the aircraft, will tend to contribute a stabilizing roll torque (tending to roll the aircraft toward wings-level) in a sideslip even in the absence of any significant aerodynamic sideforce. This is an example of what is often called a "pendulum effect".

The "pendulum effect" is tremendously strong in paragliders, and plays a significant role in hang gliders as well. In hang gliders, when the pilot exerts no muscle force, the pilot's weight acts as if it is located where the flexible hang strap connects to the aircraft structure. Raising or lowering this point of attachment affects the aircraft's pitch and roll stability dynamics. Some older hang gliders had the "hang point" located several feet below the wing, creating a strong stabilizing "pendulum effect".

Consider the difference in flight characteristics of a model airplane with a heavy weight attached to the end of a thin strut projecting high above the aircraft, versus a model airplane with a heavy weight attached to the end of a thin strut projecting far below the aircraft. It's clear the flight characteristics would not be identical in each case. It's also clear that if both aircraft were trimmed for a steady glide, the aircraft would be much more stable in both pitch and roll in the latter case than in the former.

See this answer for a more extended discussion of hang glider dynamics and other issues related to the "pendulum effect" and roll stability: Does "pendulum effect" apply to hang gliders or any aircraft?

• "the wing's drag vector, acting above the CG of the aircraft, will tend to contribute a stabilizing roll torque" – that you need to explain. Drag points backwards (per definition). How can it produce a roll? Due to its backward orientation, it should only be able to cause yawing and pitching moments. What would be the effect for causing a rolling moment? That would require either sideways or vertical drag. Those forces are, however, called side force and lift, respectively. Jul 7, 2019 at 17:02
• @PeterKämpf if we define roll as motion around the aircraft's longitudinal axis, then when the aircraft is yawed to point in a different direction than it is moving through the air, a drag force acting above or below the CG will create a roll torque. Jul 7, 2019 at 17:04
• So this is a sideslip-induced rolling moment. It has several contributors, and drag is only a small part of it. It is dominated by dihedral. And a pendulum is really not involved. Jul 7, 2019 at 17:17
• Lovin' the dv's as always. This was actually one of my better answers ever. Short, to the point, and only lightly edited! Feb 22, 2022 at 22:37