Do twin engine airplanes have increased roll stability?

Do twin engine airplanes with counter rotating props have increased roll stability?

Imagine a gust of wind hitting the airplane from the front right quarter.

The gust hitting the front of the plane first would yaw the plane to the left, before the rear vertical stabilizer can counter the yaw, the airplane will then roll to the left as the right wing sees more lift.

With a twin engined aircraft, the left engine would counter that yaw.

If less yaw, would that mean less roll, and therefore more roll stability?

Is this correct thinking?

If not, what can be done to increase roll stability besides using a maximum dihedral of about 6 deg and the addition of ventral fins, and wing sweep?

• It is not clear which direction you are imagining the wind gust coming from when you say "45 degrees to the right". Also, in the non-counter-rotating case, couldn't possibly make a difference which side the wind gust was coming from? Sep 15, 2020 at 17:23
• Question or three. If the wind were coming from the right at 45° (in other words, a quartering headwind coming from the right), wouldn’t the aircraft weathervane (yaw) to the right? While airborne, would there be any tendency to roll since there would be a lack of ground friction? Wouldn’t the aircraft just have a different ground track and groundspeed versus heading and airspeed? In the absence of uncoordinated flight, would there be a lift differential to cause a rolling moment? If there was a rolling moment to the left, wouldn’t the yaw to the right balance it out? If not, please explain. Sep 15, 2020 at 17:44
• @Fred, could you explain what you mean by "would counter the yaw". Are you thinking about gyroscopic effects, or moment ("weight") effects, or aerodynamic effects, or force effects ?? It's really unclear at the moment. Sep 16, 2020 at 11:54

You're imagining the wind coming from the right, pushing the nose to the left. That doesn't happen. In fact, this is much more likely to push the nose to the right, because the vertical stabilizer, being a large panel that's far from the center of mass, creates a larger torque. This phenomenon is called "weathervaning", and is a huge concern for tailwheel planes and seaplanes particularly.

But, to get to the actual question: You are correct in thinking that, if a plane is yawing to the left, the outside wing is going to generate more lift, causing it to roll left. But, no, having multiple engines on an airplane will not stabilize it in either roll or yaw. For all the thrust from the left engine is doing to counter the yaw, the right engine's thrust is balancing it out, so a twin engine will not be any more stable than a single engine, all else being equal.

• What about a larger moment of inertia conferred by weight displaced from the centerline of the craft? Is that at all significant, at least for large engines? Sep 16, 2020 at 3:53
• I see no basis for this answer TBH, more weight on the wings should increase roll inertia, which will have an effect on stability. Do you have any sources to back this up?
– GdD
Sep 16, 2020 at 8:10
• @Vroomfondel would seem to be perfectly correct, and in general, unfortunately this answer totally confuses me on a physics level. It's not even clear which point it is addressing? (since the question is so confusing!) Sep 16, 2020 at 11:55
• @Vroomfondel I wasn't talking about gyroscopic effects at all. The OP mentioned that they thought the left engine, specifically, would compensate for yaw. I took that to mean that they were talking specifically about the torque from the thrust of the left engine, which is, in fact, compensated for by the thrust from the right engine. I'll add a bit to my answer to make that more clear. Sep 16, 2020 at 14:03
• @user2647513 Yes, having weight farther from the centerline would increase the moment of inertia, which would resist rolling slightly more. But the question (at least, as I understood it) was specifically about thrust, so that's what I addressed. Sep 16, 2020 at 14:15

If one goes to an indoor arena with no wind and tosses gliders from the bleachers, 2 things will work: dihedral and pendulum.

Dihedral provides roll stability by keeping the center of vertical lift in line with the CG. This concept is easily seen in the relationship of wing and horizontal stabilizer/elevator (or stabilator) on the pitch axis.

Pendulum works the same way as in a parachute. One may picture this mechanism as a parachute/glider that also moves horizontally. It is lift (or drag) up, weight down.

Dihedral effect comes into play when you move outdoors and experience variable wind, or gusts, that are enough to perturb the aircraft so that it must "right" itself.

Now, we consider, the "dihedral effect" of wing sweep, wing dihedral, upright vertical stabilizer, fuselage side area above or below the CG, ventral fins, etc. that effect roll once the plane is slipping and the relative wind is no longer directly from ahead.

This is where we generally throw away the "low pendulum", now aerodynamic forces around the CG are critical to good handling characteristics in a crosswind gust. The wing dihedral is balanced with "anhedral effect" of side area below the CG, which can include big solid disc fixed gear, slab sided fuselage, and downward pointing vertical fin.

Adding perimeter weight towards the wingtips with 2 engines or fuel tanks will increase roll inertia, which is helpful for passenger comfort in a transient gust. Higher wing loading also contributes.

But wing dihedral is a weak stabilizing force in a crosswind, and adding more will not work nearly as well as properly balancing side area above and below the CG. The Cessna 172 is a living testament to this design.

Yes, twin engines will have increased roll stability compared to a single engine, all other things being equal.

As others have mentioned in comments, roll stability is directly impacted by moment of inertia. To be specific, it is determined by roll moment of inertia. For a derivation of the relationship see sections 4.3 (Representation of Aerodynamic Forces and Moments) and 4.3.1 (Longitudinal Stability Derivatives) of this publication. Moment of inertia is a product of mass and the square of its distance from the axis of rotation. Increase in mass or distance increases the moment and thus the stability.

Suppose we have two airplanes that are identical apart from the placement of the engines. Assume the mass, aerodynamics, and mass distribution (apart from engine) are identical. Let the engines of the first plane be very far from the longitudinal axis and the engines of the second plane very close to the longitudinal axis.

The equations indicate that the first plane will have a higher roll moment of inertia and higher roll stability than the second plane. Consider a force acting on the plane that causes some amount of roll. How much force would be required to rotate each plane by angle θ? While both planes would rotate by the same angle, the engines would move different distances, resulting in different amounts of work required. To move the first plane the same as the second, you need either an increase in force or time.

With respect to the relationship between yaw and roll, I can't speak to it but check out this paper on Longitudinal Static Stability. As best I can tell, it seems to me that there is a positive relationship between roll and yaw as described by "roll-yaw inertial coupling".

Any tendency for divergence in pitch is resisted by the much larger longitudinal static stability. This form of inertial coupling is known as ‘roll-yaw inertial coupling’.

• this is very well presented, but you may want to dig a little deeper. Roll inertia affects roll rate, but whether or not it wants to roll or not depends on the dihedral (which can help if wings so not perfectly match)(and, of course, the ailerons). Dihedral stability is an interaction between center of vertical lift and CG. Also, pitch stability is on a different axis than yaw or roll. Sep 16, 2020 at 19:48
• That's not the definition of roll stability. Roll inertia is just that...inertia. Stability is about restorative force (static stability).
– JZYL
Sep 16, 2020 at 20:17
• $restorative force$, like it. Sep 16, 2020 at 20:45