The following (long) article is the compilation of a set of messages sent to the RCSE mailing list both reviewing the aerodynamics of roll control and stability, and some reaction to various recent postings to the list on the topic.
Basics of Roll Control and Stability
There's apparently a lot of misinformation floating around on this subject of roll control and stability, judging by the discussion on this thread so far. I thought I covered the basics at least partially in some of my other posts, but apparently some of you might like something a bit more detailed. I'll review the general topic, then address a sampling of some of the recent posts. I will leave off the names of the posters, since it is not my intent to impune anyone in particular (on the contrary, I strive to be an "equal opportunity impuner").
I expect that most or all of you are familiar with the basic forces on an aircraft in unaccelerated level flight. The horizontal forces of thrust and drag balance each other, as do the vertical forces of lift and weight. However, as soon as we bank the aircraft into a turn, some profound changes occur.
Viewed from behind, lift is approximately perpendicular to the wings. When the wings are banked, the lift vector is no longer parallel to the weight vector. A portion of the lift vector (its "vertical component") is acting upwards to oppose the weight, but there is now also a horizontal component pulling the aircraft to the side. This is what actually turns the aircraft. In a so-called "coordinated turn", the centrifugal force caused by the turn exactly opposes the horizontal component of lift, so that all forces are once again in balance. The curious side effect of this is that since the vector sum of the weight and centrifugal force ("CF") vectors are exactly parallel, equal and opposite to the lift vector, THE AIRCRAFT HAS ALMOST NO WAY TO KNOW IT'S IN A TURN!
This is why instruments are required for flying full scale aircraft inside of a cloud. Your inner ear cannot tell the difference between CF and gravity any more than the wings can, so neither you nor the airplane can tell which way is level flight. Without a gyroscope or some other way to determine which way is "right side up", you can't keep the wings level.
This also is why you can't steer an aircraft the way you steer a car. A "properly designed" aircraft, in a coordinated turn, with the fuselage parallel to the airflow (i.e.: zero yaw angle) generally WILL NOT roll out of a bank by itself if you center the controls. In fact, once it is stabilized in the turn, the controls will probably (other than some exceptions which I'll get to in a moment) be nearly centered already! To turn an aircraft, you apply aileron (or rudder, as the case may be) to roll into the bank, center the controls at the desired bank angle (other than the SMALL amounts that might be required to keep the bank angle constant), then, once the desired turn is nearly complete, apply OPPOSITE aileron or rudder to roll the wings back to level.
In case you missed it, here it is again: centering the controls to roll out of a turn will NOT work satisfactorily in most cases. You tell the plane to start turning with ailerons or rudder, you center the controls while you allow the aircraft to complete the desired turn, then you apply opposite aileron or rudder to roll out of the turn.
Expecting the aircraft to steer like a car, and to roll out of a turn without you telling it to, is NOT a valid way to judge the "quality" of a design, rather, it's a refusal to accept the laws of physics.
While all of this is going on about the roll axis, some other interesting side effects are occurring about the pitch axis. Since some of the lift of the wing is now being used to balance CF, that means that the vertical component of lift is no longer as big as the weight of the aircraft. This causes the aircraft to start to descend. Of course as soon as it does, the downward change in the flight path increases the angle of attack on both the wing and the tail. If the aircraft has positive pitch stability it will tend to nose down, keeping the angle of attack of the wing nearly constant. Because of the downward flight path, the aircraft will start to pick up airspeed, which will supply the extra lift required to make the vertical component of the now tilted lift vector once again equal to weight. When the aircraft is rolled back to level flight, the extra speed it now has, coupled with its positive pitch stability, will cause it to zoom up to reduce the airspeed back to normal. If you're seeing a speed increase during a turn, and a zoom coming out, it's probably an indication of two things: 1. Plenty of pitch stability, maybe even more than you need (move the C/G back), and... 2. Incorrect piloting technique. Read on, there's a remedy.
If the aircraft has neutral pitch stability (C/G is at or behind the aft limit), it will not nose down in response to the downward flight path, and the change in flight path will therefore cause an increase in the angle of attack. This will supply the necessary increase in lift to put the whole system back in balance. Of course the down side of this is that this aircraft will demand that the pilot supply all corrections for gusts, etc., refusing to do anything about them by itself. It will also give the pilot little or no feedback in the form of pitch attitude changes when it encounters those disturbances. This is why we don't generally design training aircraft with neutral stability in pitch.
A third possibility is that the aircraft has positive stability in pitch, but the pilot, realizing that extra lift is required to keep airspeed constant in the turn, pulls just enough up elevator while in the turn to supply the necessary extra lift through angle of attack increase. The pilot smoothly releases this extra up elevator as he or she rolls the aircraft out of the turn, and the model arrives back at wings level with the same pitch attitude and airspeed it had before entering the turn. This is called "finesse".
If our models were expected to do all the flying themselves, including reading the pilot's mind, this would be called "Free Flight", not "Radio Control".
The airflow past the aircraft in a turn is not straight anymore, it's curved by the turn. If the turn is coordinated, this means that it's parallel to the fuselage at the wing, but blowing outward and downward on the nose, and inward and upward at the tail. On most models this effect is minimal, because the radius of the turn is very large compared to the dimensions of the model. However, on very lightly loaded models with long tail moments, this effect can become quite significant. The upward flow at the tail tends to push the tail up and the nose down, which increases the amount of up elevator required to keep the airspeed constant. In effect, the tail is "cracking the whip". On R/C HLG's this effect can be extremely pronounced; for example, on our Monarch R/C HLG's, a maximum performance, minimum radius turn can require more than twice as much up elevator to keep airspeed constant than it takes to fully stall the model in level flight! Of course, you must instantly back off on the up elevator if a gust or other disturbance momentarily causes the turn to widen, increasing the turn radius and reducing the curvature of the airflow. It's a lot like playing a fish on the end of a line, and to watch a master perform this art is to observe true poetry in motion. There's nothing quite like watching a 1.5 meter model roll into a 50 degree bank 1.5 meters off the ground, start making one meter diameter, perfectly round circles with its inside wingtip, and proceed to "speck out" from a thermal about the size of a picnic table!
The effect of the curvature of the flow acting on the fin and rudder is to yaw the model towards the outside of the turn. On an aircraft with no ailerons this can be a good thing, because of another quirk of turning flight. The wing on the inside of the turn has less airspeed than the wing on the outside of the turn, and therefore needs more angle of attack to make the same amount of lift as the other wing. If it doesn't, the aircraft will try to roll into a steeper bank. This is called "overbanking tendency". The yaw caused by the curvature of the flow, if the design has been properly tuned, when coupled with the dihedral of the wing, will increase the angle of attack on the inside wing and decrease it on the outside wing exactly enough to keep their lifts equal and the bank angle constant.
If the aircraft has little coupling between yaw and roll (little dihedral or sweep), the airspeed difference btween the inside and outside wingtips may tend to roll it into a steeper bank unless corrected. It's not uncommon on aircraft like this to need "top" aileron (aileron input opposite from the direction of turn) to correct the overbanking tendency, and "bottom" rudder (rudder input in the same direction as the turn) to counteract the effects of curvature of the airflow in order to keep the turn coordinated. Two examples of this I've seen on full scale aircraft are an Aeronca 7AC "Champion" and a Schweitzer 2-22E sailplane.
This also brings up the subject of tip stall. We're using a lot of small increases in angle of attack here to keep things in balance, and of course there's a limit on how much of that you can do before the airfoil says "ENOUGH!" and quits flying. Because of this, the stall speed increases as you increase the bank angle. It also means that, because it is flying slower in a turn, the inside wing tip is the most likely candidate for a stall in a turn, unless the designer has used airfoil selections, planform changes, etc., to make the center of the wing stall first. The lower speed at the inside wingtip actually exacts a double penalty, because in addition to the lower airspeed, you also get a lower Reynolds number, which increases the drag and reduces the maximum lift coefficient.
Virtually any model can be made to tip stall if the weight is low enough to allow a small enough turning radius. Because of this, contrary to what you might expect, airplanes with very low wing loadings are actually the most at risk for tip stall.
This phenomenon raises its ugly head even higher when you try to roll out of the turn. You need to momentarily increase the lift on the inside wingtip to get the mass of the wing moving back towards level flight. If the inside wingtip is already on the verge of stall, this extra demand for more lift could be just enough to push it over the edge, resulting in a snap roll into the turn, or at least a very sluggish response to your roll command. If your model rolls smartly into the turns, but seems reluctant to roll out, it could be that you're flying too slow. A little down elevator can help here, since it reduces angle of attack, starts increasing airspeed, and also widens out the turn and reduces the curvature of the airflow. All of these things will give that poor, overworked inside wing tip a better chance of doing its job successfully.
"Spiral Stablity and Dutch Roll"
Now let's talk about "Spiral stability" and "Dutch roll". Spiral stability is the tendency of a model to roll out of a turn by itself while the controls are centered. As should be apparent from the above, this is usually near neutral or even slightly negative for most aircraft (i.e.: they want to steepen up the bank angle in a turn). Dutch roll is a tendency to oscillate side-to-side in both yaw and roll, something like a falling leaf. On full scale aircraft it's an excellent way to promote a demand for additional airsick bags from the rear seat passengers. Spiral stability and dutch roll are intimately connected, both controlled by the balance between dihedral and vertical fin. Too much fin or not enough dihedral and you get spiral instability; too much dihedral and/or not enough fin and you get dutch roll. It's very difficult to find that exact balance where you don't get some of one or the other.
So how does spiral stability work? Imagine an aircraft that has just dropped a wing in response to a gust. It hasn't really started turning yet, so there isn't any centrifugal force of significance at this point. The lift vector's horizontal component starts pulling to one side, and its reduced upward component allows the model to begin to descend. In effect, the model looks like it's sliding down along the slope of the tilted wing. At this point a couple of things happen. The sideways motion acting on the dihedral of the wing causes a yaw that increases in angle of attack on the down wing panel, and decreases the angle of attack on the other one. This causes a difference in lift between the two, that tries to roll the aircraft back to level. On high wing models, the yaw can cause a difference in air pressure on the sides of the fuselage, which increases the lift of the down wing panel, and decreases the lift of the other panel. On low wing aircraft the opposite can occur. This is why sometimes a high wing aircraft can get away with less dihedral than an equivalent low wing design.
Meanwhile, the fin and rudder are also reacting to this yaw. They attempt to yaw the aircraft back in line with the new airflow direction, even while the dihedral effects of the wing are trying to roll it back the other way. If the fin and rudder, plus the overbanking tendencies that take hold as the aircraft begins to turn, are powerful enough, their corrections can cancel out the dihedral's attempts to roll the aircraft back towards level flight. The aircraft stays banked, and may even tighten up into an eventual "graveyard spiral", the classic example of spiral instability. On the other hand, if the dihedral effects dominate, then the aircraft will tend to roll back towards level flight. However, if the fin/rudder effects are unable to zero out the yaw as as the bank angle comes back to zero, then the aircraft will continue rolling into a bank in the other direction. This can lead to a chain reaction, with the yaw and roll effects chasing each other back and forth like a dog chasing its tail. This is our old nemesis, "dutch roll".
For trainers, it might seem that shading the balance in favor of more spiral stability might be desireable, for that often advertised (but seldom delivered) ability to roll out level if the controls are released. Unfortunately, the ensuing dutch roll is likely to drive beginners crazy! The exception might be very lightly loaded trainers with very long tail moments (like our new 2-meter Chrysalis), where the curvature of the airflow in the turns can be used to help the spiral stability without getting into dutch roll problems. This generally isn't as effective on aircraft with higher wing loadings because the turning radius is larger for a given bank angle, which reduces the curvature of the airflow. Of course the tail moment must not be TOO long, since too much of a good thing there can make consistent, tight turns very difficult. Some of our competitors' products with unusually long tail moments have been observed to have some trouble in that regard. Everything in an aircraft design influences everything else. If you go overboard trying to fix one problem, you're likely to create new problems in other areas.
Aircraft with aft-mounted Whitcomb winglets (the kind that develop strong lift forces inward towards the center of the wing) such as the Rutan "Vari-eze" and "Long-eze", and the Beech "Starship" also can have very positive spiral stability, provided that they also have reasonably strong yaw-to-roll coupling. The lift of the faster-moving winglet on the outside of the turn is greater than the slower-moving winglet on the inside of the turn, which tends to yaw the aircraft away from the turn, resulting in a roll towards level flight.
In any case, too much spiral stability is not necessarily a good thing, because it can make it more difficult to do smooth turns. Somewhere close to neutral spiral stability is generally accepted as the most desireable setup. On thermal soarers we spend a huge amount of effort in both the engineering and test phase to get a design that will go around and around in perfect circles all day long with an absolute minimum amount of control inputs.
Comments on Recent Postings
Now let's address some of the comments in various postings to this thread:
>...It sure LOOKS like it needs more tip dihedral. Maybe it feels different if you are the one on the sticks, as an observer it appears to yaw a lot before it rolls, that is a sure sign to me of insufficient dihedral on a rudder / elevator plane. <
Yes and no. On a rudder/elevator model, some yaw is required in order to cause a roll response. How much is "too much" is to some extent a matter of opinion. A more important issue is whether or not the model has enough roll response to effectively deal with the typical levels of turbulence the model should reasonably be expected to handle.
One other factor to consider is airspeed. If the pilot has the model at very low airspeed, then control response is likely to be degraded. On large models it's well known that near stall you should expect the controls to be a bit "mushy", but what many folks don't realize is that on small models this degradation often begins well above stall. This is due to the effects of Reynolds number. As you slow down, L/D and max lift coefficient decrease, and drag increases. This not only reduces performance, it also contributes to adverse yaw and therefore degrades roll response.
Yes it is possible to make controls that are powerful enough to overcome this, but that is not always a wise thing to do. It can make the controls overly sensitive at higher speeds, and also removes a means of warning to the pilot that he/she is flying in a poor area of the performance envelope. A model with a designed-in mushiness in the controls that begins just before the model actually gets deep into the poor L/D zone can warn the pilot before any serious performance losses occur.
>Dihedral is PRIMARILY for roll recovery (roll stability). It's only secondarily that it works as a poor-mans aileron. When a rudder-elevator control scheme is chosen on a plane for lightness, simplicity, ease of building, or whatever, you understand that you're sacrificing a true 3-axis control function for a quasi-2-axis system that RESULTS in 3-axis control. <
This is basically true most of the time, although I personally don't like to think of it as a case of one thing being more important that the others. Dihedral can also be used to improve PERFORMANCE in a turn. We've found this in a number of cases on HLG's, and it can be observed on a number of soaring birds.
>You strive to achieve a "feels good" balance between roll recovery dihedral and the dihedral required to get a satisfactory wing roll response once you initiate the rudder. You don't want to overpower one with the other. <
Well, not exactly. The two are not mutually exclusive. You do generally need more dihedral for adequate roll response with rudder than what is required for adequate roll stability alone, but there is no detriment to roll stability from the extra dihedral. You do, however, need more fin area to control the dutch roll behavior. If you're seeing a degradation in handling after an increase in dihedral, it's probably because you didn't also re-size the fin properly.
>What do you mean when you say really stable? If you put it in a 45 degree bank at 250 feet of altitude how high is it when the plane recovers on its own? Does it? If it pretty much holds the bank till it hits the ground it isn't stable ;-).
Oh, contrare, mon ami! If you put a model in a 45 degree bank and it faithfully holds that bank angle all by itself through multiple circles, it sounds pretty stable to me! If it happens to hit the ground in the process because you didn't bother to give it the extra bit of up elevator it needed to replace the lift it's now using to turn (because YOU told it to do so), then I'd say the problem in this case is not with the airframe design, it sounds to me more like trouble with a loose nut on the end of the control stick. What you describe is more in the area of pitch stability, not roll stability.
>Well, this isn't much of a tip dihedral question anymore, it gets into the whole realm of "spiral stability" of which I have TRIED to grasp, but claim no fame to having mastered it or even beginning to understand it! Rudder area is certainly an integral part of the equation. I've toyed with having Darwin put a larger rudder on the Push-E Cats to offset some of the "rudder area" that is up front (namely the nose!) <
The key question here is do you actually have any problems with spiral stability (does the model tend to steepen the bank angle by itself and/or fall out of the turn into a gradually steepening "graveyard spiral)? If so, add some dihedral and/or reduce the fin/rudder area. Does it have a problem with dutch roll? add some fin/rudder area or reduce dihedral. Does it have both? Try increasing the tail moment arm, then go through a re-sizing of the fin/rudder area. Does it require too much yaw to get the desired roll rate? Increase dihedral, but be prepared to also increase fin/rudder area if some dutch roll problems show up.
I've flown Darwin's Pushy Cat, and although I don't have enough stick time to get truly familiar with it, it didn't seem to have any particularly objectionable characteristics from what I could tell. The roll response wasn't as crisp as I personally prefer for my own models, but probably about right for a model that might be flown by a lot of first-time beginners.
>...To be truly stable, a plane should recover in all 3 axis in a "reasonable amount of time". That "time" factor is the key issue in people's perceived stability of a plane.<
Well, no, if it's wing loading is more than in the "very low" category, it will probably have very sluggish self-recovery from roll (if at all) provided the turn is coordinated to begin with. BTW, for exactly this reason, free flight models generally do NOT make coordinated turns. Instead they are set up for a skidding turn, with an excess of "top" aileron input and enough "bottom" rudder to force a turn against the aileron. If the turn was truly coordinated, the model would have no way to detect changes in bank angle (for the reasons I discussed above), and therefore could not hold a specific bank angle. When I was a kid in grade school and first attempting to master FF hand-launched gliders, I watched quite a few of my little creations spiral into the ground until someone explained this principle to me.
And now for the infamous Partenavia discussion:
>...I had a Graupner Partenavia for several years...this plane (built per the plan) had so little roll stability as to be laughable. The roll response with initial rudder application was not too bad, if you did the initial rudder application slowly it would look to an observer like a normal start of a turn. The problem was recovering from the turn! Let go of the rudder and the little bit of elevator required for the turn and the thing would happily slide off to the inside of the turn with no hint of a recovery. At that point application of opposite rudder would cause a 20 degree yaw change on the fuselage and a delayed roll response to level flight...Lot's of [folks] either crashed or had big difficulties flying it because the roll reponse was so out of whack. Being a reasonably proficient pilot I quickly figured out the method required to make it look OK in the air. Ease into the rudder to start the turn so that the fuselage didn't radically yaw off the line of flight, to exit the turn you needed to give opposite rudder before releasing the elevator and as the wing got close to level even ease in a bit of down elevator. <
This doesn't sound as much like a roll stability problem (although the bit about sliding off to the inside of the turn does suggest that the dihedral is a little marginal) as it sounds like a roll authority problem. First of all, as I discussed above, simply centering the rudder is NOT a reasonable way to expect any airplane to roll out of a turn. Some aircraft might actually do that (typically lightly loaded models with very long tails, as I discussed above, but even then they will probably do it very sluggishly), but it is unreasonable to EXPECT that a model behave that way. The real problem here as I see it is that the aircraft didn't roll out of the turn when opposite rudder was applied.
To understand this situation, consider that the Partenavia is a scale model of a full-scale twin-engined aircraft. Granted, it might not be exactly scale, but it must be close enough to scale to at least maintain a general resemblance. This requirement limits the model designer's options in some crucial areas related to handling qualities. First of all, the full scale aircraft was designed to use ailerons as the primary roll control. The dihedral was therefore set to provide adequate roll stability, which in this particular case you don't want to have very much. A twin with strong dihedral effects is likely to get into some major wallowing problems in turbulence, because of all the weight in engines and fuel tanks that are located quite far from the C/G. It's better to let the aircraft tend to ignore momentary disturbances from gusts, etc.. As far as the fin/rudder area is concerned, the main factor determining that on a full scale twin engined aircraft is the rudder authority required to overcome asymmetric thrust in case of an engine failure. These two factors mean that a full scale twin is likely to have minimal dihedral, but gobs and gobs of extra fin/rudder area. This is a perfect recipe for some spiral instability problems when this aircraft is scaled down to model size, and the limited amount of re-sizing possible without destroying scale appearance may not be enough to entirely fix it. It appears to me that the biggest mistake in this model probably was in trying to use rudder instead of ailerons to control roll.
When you make a scale model of a full scale aircraft, it's quite likely that the constraint of scale appearance will force you into compromises in other areas. To some extent it's the nature of the beast. When you heap other constraints on top of that, such as using a control philosophy and setup that is drastically different from the one the original aircraft used (such as using rudder for roll on an aircraft designed for ailerons), you are stacking the deck against yourself.
>Again, I'm not implying the Pushy-cat is anywhere near as bad as this particular plane. I just use it as an extreme example of not enough dihedral. Rudder / elevator planes should be stable and not require great feats of piloting skill to make them look smooth in the air. Rudder /elevator is just another flight control system that should be properly harmonized, that harmony includes the proper amount of dihedral to result in stability. Ailerons are different and require minimal roll stabilty. <
Not necessarily. As I said, I agree the Partenavia sounds like it might not have enough dihedral, but mainly from a roll AUTHORITY standpoint; although low, it sounds to me that the roll STABILITY is not the major failing. The two are not the same at all. I can fly a plane with marginal stability, as long as the controls have enough authority.
As far as ailerons REQUIRING minimal roll stability, this is not necessarily true. If the model has inefficient ailerons that cause lots of adverse yaw, then low dihedral effect is a requirement, since the adverse yaw will tend to cancel out the rolling effect of the ailerons. Unfortunately this is all too common in many aircraft designs, but it is VERY FAR from being a universal axiom. The key thing to remember is that the real problem here is the inefficiency of the ailerons. If you can design ailerons that don't make gobs of drag (and the adverse yaw that goes with it) when they are deflected downward, then you can have as much dihedral as you want. One example of exactly this is our old Monarch 'CX' R/C HLG and Speed 400 electric, the last of the wood-winged Monarchs. This model had very wide chord (and very efficient) flaperons over the entire span of the wing from root to tip. It also had the exact same polyhedral setup as the Monarch 'C', its 2-channel rudder-elevator cousin. This means that the dihedral of the outer wing panels was considerably more than 20 degrees! Since the flaperons were extremely efficient, there was no adverse yaw of significance, and the roll rate with aileron alone (i.e.: ZERO rudder added), and with no aileron differential, was at least as good as the roll rate with rudder alone (those of you who've flown 2 channel Monarchs can vouch for those models' nimble roll response on rudder alone). By coupling in enough rudder to cause some proverse yaw (so that the rudder induced roll augmented the roll from the flaperon deflection), quite spectacular roll rates were possible on the 'CX', plus we had the benefits to circling performance that dihedral can provide.
The 'CX' was an excellent airplane for its time, but the state of the art moved on, and we now have other models that are even better. We did, however, keep those super-efficient ailerons. They live on today in modified form on our Wizard R/C HLG and Speed 400 kits.
>After all, the rule of thumb is the fuselage needs to always point in the direction of flight. <
This is a matter of degree. If you want to control roll with rudder instead of aileron, some yaw is necessary, it won't work otherwise. How much yaw is acceptable is to some extent a judgement call.
>If you can put an aircraft in a flight attitude which requires the fuselage to yaw well off the flight path for recovery - something is wrong. "Well off the flight line" being defined as clearly visible from the ground. All rudder/elevator set ups are going to knock the yaw string off center a bit every time you turn, it is only a few degrees though. <
By that criteria, "something is wrong" with nearly all R/C sailplanes that don't have ailerons! Like I said, it's a matter of degree. There are a lot of other factors that come into play. There are times you don't even want to try to keep yaw at or near zero. In some cases of curved airflow in a turn, the relative wind at the tail can be different from that at the wing, in both the pitch and yaw sense, by considerably more than ten degrees! In this case, the minimum drag might not necessarily occur when the fuselage at the wing is lined up with the local airflow. In any case, if you have no ailerons, you will need some yaw during the turn to counteract the airspeed difference between the inside and outside wingtips.
Although it is a good idea to minimize the amount of yaw required to get a decent roll rate, what really matters is whether or not you get enough roll response to deal with the demands of the maneuvers you fly and the turbulence you fly in.