I have a quick physics, sort of, question about what controls roll rate. It seems that our models stop rolling quickly when the stick is released. It also seems that on planes capable of several consecutive axial rolls that roll #3 is no faster then roll #2. I assume a specific aileron deflection and velocity will create a torque which implies an angular acceleration -- not a constant roll rate.

Does all this mean that the plane reaches a steady (terminal) roll rate rather quickly?

Carl

The mass moment of inertia about the roll axis is relatively low in relation to the aerodynamic torque that induces the roll, so that maximum roll rate will normally be attained within less than a tenth of a second after the ailerons reach full deflection, after which the roll rate will slow slightly, due to drag of the deflected ailerons.

Terminal velocity is proportional to sqrt(m). Does that mean the roll rate is proportional to sqrt of the roll moment?

The equations are a little different -- Maybe I'm getting old, I use to be able to figure these things out [sm=confused.gif]

Carl

Ahhh, I think I got it. There's the torque which is equal to the drag force caused by the rotation and the moment of inertia does not enter the equation. The inertial term is only important in the start and stop of the roll.


Carl

Right after a fashion. The roll acceleration is a function of the rolling moment due to the ailerons and the roll inertias of the airplane. As mentioned for our average airplane this is farily rapid. The peak rate of roll is a function of the applied moment from the ailerons and the roll damping, the term Clp. That is the rolling moment that is generated opposite to the ailerons and is due to the roll rate. The faster the roll rate the greater the term is to try to stop the rate. It's basically aerodynamic drag in a roll direction.

When the two terms (roll moments due to ailerons and Clp) are equal and opposite you have a constant roll rate.

So you get what you observed, the initial roll acceleration then the steady state roll in the remainder of the first, second and third, etc. rolls. When you release the control input then the roll damping decellerates the roll rate and finally stops the roll.

Ben,

I don't know all the aerodynamics terminology but understand the steady state balance picture. I apologize for being an electrical engineer. In the terminal velocity situation the applied force is m*g so the mass stays in the equation. Steady state is F=mg=drag, drag goes with V^2 so you have a sqrt(m) dependence in Vterm. On the wing the applied torque must be a sum (integral) of the aerodynamic force*distance to the roll axis and there is no Ixx term in the applied torque.

I'm surprised the roll seems to stop on-a-dime when releasing the sticks. The aerodynamic drag in the roll direction should go to zero as the rotation rate slows. You would think it would slowly coast to a stop.

Carl

The aerodynamic torque produced by highly deflected ailerons is enormous, compared to the torque required to accelerate the airplane to full angular velocity in roll in a fraction of a second. If you are flying at say, five times stall speed, the incremental lift per square foot of wing maybe be capable of producing a rolling torque of several hundred pounds-feet on an average .40-.60 model, if the model had some way to resist it for longer than a few milliseconds. My models also stop rolling just about as fast as the servos can move - I can detect no lag. The same torque would similarly be applied to arrest the roll, when the ailerons are returned to center. This can easily be calculated by calculating the effective incremental angle of attack of the wing that is produced by the ailerons, and working out the lift along the wing, and the accompanying moments. I just wish that yaw would damp as fast as roll - it would surely make clean snapping maneuvers a lot easier.

If what you say is so, is there any disadvantage to putting servos in the wings?

Carl

Thinking about it, we must apply some reverse aileron to stop the roll. We don't just let go of the stick. It will not be hard to test!

Now it makes sense to me that the low inertia makes for the very crisp axial roll maneuvers. It also makes the term roll damping make sense. The damping, in a basic physics sense, would control our ability to stop the roll without overshooting or oscillating about the stop point.

Is "roll damping" used in a generic sense to refer to aerodynamic drag in a roll direction?

Carl

To a pilot, "roll damping" is the resistance of the aircraft to roll. If you neutralize the ailerons, the airplane stops rolling. That's as it should be. You'll still need to use aileron to roll out of any bank, but a well-damped aircraft will stop rolling as soon as the input (aileron, gust, etc) is removed.

I don't think I've ever flown a model that didn't stop rolling when you neutralized the controls. You had to roll out of a bank, but you didn't need opposite control to stop a roll.

Think of roll moments and roll inertias. Similar to linear F=ma but angular rates and angular inertias. I don't have my text book handy so won't remember the exact equations or units (I hear cheers of gratitude) but....

The roll acceleration is the rolling moment due to ailerons, Clda x da (rolling moment due to ailerons times aileron deflection) divided by the roll inertia (with proper care taken of the units which I didn't). The roll angular deceleration is due to roll damping, the Clp x p, again the rolling moment that is due to the roll rate (there is a differential angle of attack on each panel due to the roll rate and a corresponding lift differential on each panel) times the roll rate. The roll moment in ft-lbs is those two Cl times a bunch of stuff.

So you start out with the initial ailerons deflections causing a constant angular (roll) acceleration. As the roll rate increases there is an opposing roll moment due to the roll rate. That causes an angular deceleration.

This keeps up until there is a steady state roll rate achieved with the aileron deflection held in - the input moment is equal to the damping moment. Remember that the moments in ft/lbs are a function of rotation speeds, etc.

When the aileron control is released you now only have roll damping and the roll rate.

In a perfect world the deceleration would be initially high but would asymptotically approach 0 - it would take a long time to get to zero - resulting in the need for a little reverse aileron to stop the final little bits of roll rate.

In the model airplane low roll inertia real world the deceleration takes place very quickly and we get to a point where the roll rate is insignificant very quickly. You don't have to use any reverse stick. Usually a bump in the air comes along to jiggle things to require a stick input before the residual roll rate is a problem. So the result is that it looks like all you have to do is release the stick and the roll stops. Also the residual roll isn't a problem as you are turning or doing something else.

In the old days we would calculate on big sheets of paper the roll time history of something like a big transport, not a good way for an engineer to spend his time. There is an approximation to the steady state roll rate that I don't remember but it doesn't tell you how you got to the steady state roll condition - which is important. Now we use a computer. I ran those programs for a couple of years, not all that much fun either as you had to hand plot the results at that time.

Aside from the last bit of gripe stuff is this any help?

Thanks Ben,

The general picture is clear to me now. I grabbed a couple of aerodynamics books from our library at work. Mostly to look up the definitions of aerodynamic terms. It helps communication if I'm not using the wrong terminology. You would think an axial roll with a constant forward velocity would be one of those simplified examples every basic aero text would use. The roll direction derivative Clp must be very complicated since it was only given a hand waving explanation and no equations.

Anyway I did not mean to stray too far from modeling. The reason I asked the question originally was because I wanted to understand the trade-offs for putting servos in the wings of a model. In my case there is a choice of putting two servos in the wings or a single servo on the wing center line with a more complicated mechanical linkage. I estimated the change in roll inertia to be about 7% -- modest -- between the two configurations. The yaw inertia change must be less. I started thinking about how the airplane rolls and was surprised that the moment of inertia did not seem to be very important.

Of course, the axial roll situation may not be a very appropriate analogy for relatively slow-flying barrel-rolling WWI model.

Carl

PS. I use the following units Torque=(I)*(ang. acc.) ==> carats*furlong^2 * radians/fortnight^2

I'm not sure if my explaination is entirly correct but noone else has said it yet (or at least said it in the same way) so i feel i should bring it to the table.

I can supply no specific maths to this but its seem to me that the acceleration from straight and level flight to maximum roll rate is dependent upon the torque supplied from the wings due to aileron deflection and the inertia of the aircraft. I don't think this was actually the original question but it does deal with the issue of weither putting servos in the wings will affect roll rate. It WILL affect acceleration into max roll rate but i very much doubt it will reduce it by anything that you could call noticable.

As for maximum roll rate, i think the best way to explain my point is to look at the 2 extreme conditions

Maximum roll torque will be at the initial situation with the aircraft in straight and level flight and ailerons at full deflection (for simplicity i'm going to assume that there is no lag in aileron movement). The aircraft will obviously begin to roll at this point accelerating at a rate dependent upon the torque from the wing and there inertia.

the other extreme is when the aircraft is at its maximum roll rate. in this situation it is easiest to visualise whats going on if you take a snapshop of the wing at a moment in time. If in this snapshot you could view the angle of attack of the wing due to its rotating movement through the air. In the following i'm talking about the 'upward' going wing with 'downward' going aileron. the combination of rotating wing (moving 'upward' in relation to forward speed) and forward speed will create an angle of attack that would appear to be negative. As roll rate increases the negative angle of attack will increase until the wing (with its increased camber due to down going aileron) will no longer create any lift at all. at this point there will be no rolling torque created any more and it is therefore impossible to roll any faster. In reality this point will not be reached as you will still need torque from the wings to overcome the drag caused by the wings hitting the airflow slightly flat side on. So at some point you will reach an equilibrium between the reducing torque from the wings and increasing drag and at this point you will have reached your maximum continuous roll rate.

when aileron is released the oppersite to the above takes place and the roll will stop and return the wings to zero (normal) angle of attack.

So the 2 main factors affepcting your max roll are forward airspeed and lift prduced by wings at maximum aileron deflection. weight should not have a contibuting factor.

Carl - I thought those unit usage went out when I graduated, I hate trying to get units right. The nice thing about working in the industry today is that everything is computerized and automatically spits out the right answers (if the inputs are the same).

With out models the inertias are so small and control power so large that we start out with excess almost. The servos do increase the inertias but a fraction of a degree of control throw more gives the same roll acceleration. Where inertias start to be a problem is in the full size heavy lifters with engines in pods and fuel everywhere. There rolling takes an appointment. Fighters like the F-15 are of course better but when they are loaded down with external fuel tanks and bomb racks it can slow them down some also. Our models make things a lot easier.

The lifting contests that Paul is involved with can have a lot of problems involved with inertias and control but apparently the biggest problem is in the design teams and student pilots.

Andyede - you have pretty close to the right concept just the wrong terms (at least to me who speaks aerodynamics. What I said in my comment a couple of replys above is the same thing. Between your two extremes is a varying acceleration that is dependent on the roll rate of the airplane.

When you say - the wing will no longer create any lift at all - isn't right. To roll all you have to do is create an imbalance between the two wings. Whether or not the wing goes to no lift depends on the roll rate and initial angle of attack - it takes a lot of roll rate to drive the wing to zero lift. What actually is happening is that the acceleration being produced by the aileron is = to the deceleration due to the roll rate (that angle of attack thing which is called Clp - roll damping due to roll rate). That can occur any time depending on control deflection and does not depend on the wing going to zero lift.

The drag hitting the wings you mention is the Clp term. You actually get to the steady state roll condition very quickly with our models. When looking at anything aerodynamic concerning controls you have the control deflections - da - delta aileron, the efficiency of the controls - Clda - rolling moment due to aileron, damping coefficients - Clp as defined above, and the dynamic pressure due to velocity. You multiply the whole mess together to get the rolling moment in ft-lbs. That moment into the rolling inertia gives the rolling acceleration. The airplane can be analyzed the same way in pitch and yaw. It is all moments, inertias and angular accelerations. In the linear directions it is simpler, you just have the lift, drag and side forces operating thru the mass of the airplane. Do all six at once and you can do a time history of how the airplane should fly. There are short cuts to get to some of the results but to be entirely accurate you need to do the whole ball of wax.

Keep in mind most of the terms are dependent on the geometry of the airplane and mass distribution. Roll inertias won't have an effect of maximum roll rate but weight of the airplane will. I think you meant roll inertia in that comment. Weight will cause a variation in angle of attack - the control effectiveness is a function of angle of attack and the way the airplane rolls depends on the orientation of the roll axis with respect to the airplane velocity vector.

More than you wanted to know?? You have done a reasonably good job of analysis, you just need to convert to our terms :-)

Andyede, an excellent summary of the intuitive understanding I've gained the last few days. Having worked doing physics and electrical engineering for many years the steady state equation

Applied Torque=Drag at Steady State Roll Rate

tells me much about the roll behavior (there are very many systems that follow the same sort of force balance analysis). I sort of worked the problem backwards having an intuitive understanding of the behavior, then trying to understand all the details. The devil is always in the details, so I posted my random thoughts here to keep me honest.


I don't think the stopping of the roll is quite as simple. The rapid angular deceleration when the ailerons are released is close to opposite, but the behavior around zero roll rate is determined by other factors. The standard analogy would be a mass on a spring on a table. The behavior around zero displacement is controlled by the mass, stiffness of the spring, and damping. The system can oscillate or exponentially damp to zero. I'm not sure that the simple spring analogy is very accurate for an airplane. It might be if you put a wing in a wind tunnel, had a constant wind, and restricted motion to only rolling. There is a lot of coupling between forward energy, pitch, yaw and roll in aircraft so the damping and stiffness about zero roll rate appears to be very complex.

Ben is correct, for my Killer Kaos, by the time I complete a few rolls I'm already turning into the next pass and would not notice the roll characteristics as it approaches zero roll rate. I am not a pilot, but my limited full-scale experience says Bax is correct -- stopping roll does not seem to require reverse control input. I don’t remember any planes that tended to oscillate in roll so the damping must be pretty good even at very slow roll rates. I’d be curious if an aerobatic or fighter pilot notices the final roll behavior when coming out of a rip-roaring axial roll.


Carl

i'll take my same snapshot of the wing when you release the ailerons. You will still have the negative angle of attack due to the continued rotation but now you have no aileron the wing will now be producing 'negative' lift which is going to oppose the roatation and apply a torque in the opposite direction. this force will be created only while the aircraft is rotating in roll. So when you release the ailerons you will immediately have an opposing force to the continued roll that will stop as soon as the aircraft returns to non rolling flight. the speed at which the roll stops is going to be related to inertia in the same way as the wing picks up speed.