Does dihedral improve roll stability in gusty conditions?

Question

Against roll instability, should I add more dihedral/a high wing?

I'm trying to build an RC plane that can handle windy conditions. For that I want extraordinary aerodynamic stability. For longitudinal static stability, I make my planes quite nose-heavy, and compensate for that with a greater tail downforce. That works. What doesn't work is lateral stability/roll stability. In theory, if a gust rolls my airplane, I will have a sideslip. Due to a high-wing configuration, and a dihedral angle, I will have a rolling moment that will counteract the original roll angle. Image from avstop.com, modified

So I made my plane attempts have great dihedral/polihedral angles, and a really high wing with a solid surface underneath to further help counteract any rolling.

Any time I went crazy on dihedral and high wings, my planes kept crashing agressively due to very sudden and very powerful side/back flips. At first I didn't understand, as these features should've made my plane almost un-rollable.

However, what I suspect is that these features had the opposite effect. Correct me if I'm wrong, but looking a the first diagram, what I see is that when a plane flying at level flight encounters a sideways gust, it will also make the plane agressively roll over, just as if the sideways gust was from a roll induced sideslip.

Is this a correct assessment? Did these roll stability features make my planes roll around uncontrollably?

Is there a way to have my plane react normally to a sideways gust while having static roll stability? Do I need way bigger vertical stabilizers for these dihedral values?

Answer 1

I think you’re having a classic dilemma of static directional stability vs dihedral effect. There is always a compromise between the two. Increasing dihedral makes spiral mode more stable. But this has a side effect, which is less stable dutch roll. Moreover, in extreme cases, dutch roll may even become unstable. The side flips you are describing sounds like an extreme unstable dutch roll mode, which eventually may end up in uncontrolled flight.

If you are unable to reduce the dihedral effect, one other fix you can apply is to increase the directional stability by increasing the effectiveness of the vertical stabilizer. Even though, that fix makes the aircraft less stable in spiral mode, it’s almost always preferred to have a spirally less stable aircraft than the one that has unstable dutch roll. Because, a pilot can easily stop the effects of an unstable roll by ailerons. However, stopping an unstable dutch roll can get a little bit tricky and even dangerous in large airplanes, especially under stress.

So I recommend initially, reduce the dihedral effect. If that's not possible then increase the vertical tail effectiveness (read: volume) ( volume = v.tail area x distance to cg).

Answer 2

Dihedral does not help roll stability to a side force gust. Quite contrary, a gust will roll the plane into a slip, which then will turn the plane downwind (courtesy of your elevator turned rudder).

Firstly, I would not recommend setting a model plane with excessive "static stability" in windy conditions. You want to be staticly stable, but not so much that a gust will pitch you up into a stall. Higher wing loading also helps.

But roll stability from dihedral is good for cruising flight, but no match for a side gust, especially in a model.

What you must do to keep dihedral is to put side area below the CG. This is known as "anhedralling". Sea gulls lower their wingtips. Cessna put the wing (and fuel) on top. Consolidated built their famous PBY 3 Catalina with the engines on top too! All 3 want to roll into the wind, not away. This is the key.

A fourth design, the common paper airplane, does this with gusto. The side "keel" balancing with the upraised wing around the center of gravity is best for cross wind roll stability.

So you may experiment by raising of lowering your CG, adding side area, and glide testing in a cross wind. Your second model seems to have more of a chance. You may try a shorter and more square vertical stabilizer, and a bit of weight (a coin or two) on top of the wing at the expected Center of Pressure.

Answer 3

Correct me if I'm wrong, but looking a the first diagram, what I see is that when a plane flying at level flight encounters a sideways gust, it will also make the plane aggressively roll over, just as if the sideways gust was from a roll induced sideslip.

That's correct. The "positive effective dihedral" generates a "downwind" roll torque in both cases, in relation to the "relative wind".

Is there a way to have my plane react normally to a sideways gust while having static roll stability?

Just go easy on the dihedral, or on other factors that contribute to "positive effective dihedral" (e.g. high wing placement, low C.G. placement.) "Overdoing" these things, especially in combination, will give you way too much "effective dihedral" which will make your plane much too vulnerable to the immediate effects of strong sideways gusts. And see the comment below about the benefit of reducing the size of the vertical fin.

Do I need way bigger vertical stabilizers for these dihedral values?

I don't believe that that's going to help you. And contrary to another answer, I don't believe that you are experiencing classic "Dutch Roll". I think you are just seeing your plane suffer from the immediate effects of strong gusts, due to excessive "effective dihedral", and likely due to excessive positive longitudinal stability (pitch stability) as well.

For any given desired degree of positive roll stability, you can get away with less "positive effective dihedral" geometry -- specifically meaning that the aircraft will generate less "downwind" roll torque at any given sideslip angle-- if you reduce the size of the vertical fin. This will allow the plane to experience more sideslip in the long run, so that whatever "positive effective dihedral" is present will be more effective at generating a roll torque to roll the plane back to wings-level.¹

Look at it this way-- if you want to increase the plane's degree of positive roll stability, you can either increase the degree of "positive effective dihedral", or you can decrease the size of the vertical fin. Either alteration will help the plane come back to wings-level in the long run.
And to a first approximation, we might think that either alteration also might make the plane have a greater tendency to roll "downwind" immediately after being struck by a sudden side-gust. But that's not really true. In the short run, the effects of the two alterations will have very different effects on the way the plane reacts to a sudden side-gust. Because when the plane is struck by a transient side-gust, it doesn't have time to yaw into alignment with the airflow (relative wind) before the "positive effective dihedral" generates a strong "downwind" roll torque, so an overly-large fin won't do much to minimize the aircraft's immediate (downwind) roll response in this situation.

So for best stability in gusty conditions, keep the vertical fin as small as you can, and go easy on the "positive effective dihedral" as well, only designing in the minimum amount needed to slowly return the aircraft to wings-level after a disturbance. The smaller the vertical fin you can get away with, the less "positive effective dihedral" you'll be able to get way with as well, and still have the plane slowly roll back to wings-level after a disturbance.

Generally speaking, all these factors tend to shift the "effective dihedral" in the positive direction:

Low CG placement relative to overall shape of aircraft

Wing mounted directly on top of fuselage, especially a slab-sided fuselage. (To some extent a similar extent is generated by putting the wing on a pylon of substantial length ("chord").)

Actual dihedral in the wing (or tail)

High-mounted vertical fin

Naturally, an important question that would help you choose from the various different solutions that have been offered in various answers, is "how does the plane fly in smooth air?" True "Dutch roll" instability should manifest itself even in smooth air, especially in response to certain initial control inputs. If you do find that to be occurring, then this answer may not be the right one for your situation.

Footnotes:

1. To understand why "positive effective dihedral" tends to return an aircraft to wings-level after a disturbance, we have to understand that a) all turns tend to involve some amount of sideslip (toward the inside wingtip, so that a "yaw string" would blow toward the outside wingtip), at least in the absence of a "coordinating" rudder input, and b) sideslip interacts with positive effective dihedral"-- no matter exactly what the specific source of the "positive effective dihedral" geometry is -- to create a downwind roll torque, which in the absence of gusts, tends to return an aircraft toward wings-level.