Offset Gimbal Stability

mceagle

Gold Member
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Oct 31, 2003
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1,239
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Sunshine Coast, Qld, Australia
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Eagle Rotorcraft
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600 hrs
A question for the gurus. I have flown a some gyros that can be flown with little or no head spring tension, and the stick becomes neutral at a certain airspeed. Eg. low airspeed requires back pressure, cruise neutral, and higher speeds require forward pressure. There are many popular "stable" gyros out there that are like this - most notibily those with nose cone and higher teeter towers and minimal head "offset". This is easily explained.

For the stick to require forward pressure for straight and level flight then the rotor thrust vector must be ahead of the pitch pivot. My question is if this is the case, then wouldn't this situation give the offset gimbal head a de-stabilizing effect instead of the desired automatic stabilizing effect?
Couldn't this situation be potentially fatal for new pilots when first exploring their higher speed envelope?
 
Tim, you’re asking for stuff that’s hard to quantify.

Shortly after I became involved with gyros, I began using Hughes-269 rotorblades and reduced the rotorhead pitch offset from Bensen’s standard of 1” down to 5/8” to get rid of that annoying trim spring (annoying on the ground) and had not given much thought to its effect on stability.

My sorta Bensen had a large horizontal stabilizer mounted directly under the vertical tail and a seatback fuel tank so that it was nearly CLT.

It didn’t seem unstable to me but a friend, Pete Johnson from Swainsboro Georgia, flew my gyro everytime we held a flyin and told me the reduction of offset had made it unstable.

Pete was a pretty bright guy in spite of being from Georgia. He was the person that called my attention to the stabilizing effect of offset; before that, I hadn’t given it much thought.

I also flew a 3-blade rotor with feathering cyclic control on this gyro without difficulty.

Years later, in the 1980s, I bought a load of gyro junk that included a Benson B-7 airframe. I already had a Rotax-447 so mounted it with engine inverted on this airframe, gearbox prop shaft rotated away from the sparkplug end and with the seat mounted nearly on the keel. It did not have a horizontal stabilizer.

This thing was viciously unstable but flyable because of the offset gimbal head.

Ernie Boyette, David Sease and I flew this machine for quite a few hours but it was obviously a pistol with a hair-trigger.

Inverted Rotax engines are 3-way dumb; (1) the contribution to low CG, (2) oil drains into the sparkplugs and makes starting difficult, and (3) the internal oiling system for the main bearings is defeated.

We flipped the engine right side up for a slight reduction of instability.

I later installed a Bell-47 type of no feedback rotor on this machine which made it almost impossible to fly. It was all I could do to keep it right side up.

This old B-7 as I had configured it was a horrible flying machine but it was an education in stability.

So back to your original question; the passing of the rotor thrust vector forward of the pitch pivot is destabilizing but the overall effect depends upon the stability of the airframe. I imagine an RAF-2000 without horizontal stabilizer would be virtually impossible to fly with a helicopter type rotorhead.

A picture of the B-7 with engine flipped upright is attached. That’s Ernie flying it.
 

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Tim, what if you got rid of the offset altogether and went with a straight gimbal (or the old spindle head)? As you flew faster, the rotor "blowback" would increase the inclination of the rotor thrust line. This would amount to a sort of pseudo-stability with respect to airspeed, in that the stick would require forward pressure at ANY airspeed above zero. It would not be UNstable, in that it would always try to return to a certain status quo, but the "status quo" in this case would be a vertical descent.

The OFFSET gimbal head (without spring) does a couple things to alter the picture. First of all, it builds a bias into the flapping/blowback/airspeed relationship. This turns the pseudo-stability w/ respect to airspeed into a more conventional or useful stability. Depending on the offset and the other dimensions of the head, there's an airspeed (now above zero) at which the stick will not be constantly trying to move aft. IOW, the head (with no spring) has a "natural" trimmed airspeed. Above that trimmed airspeed, the flap/blowback principle reasserts itself and creates the same old tendency to return to trimmed airspeed -- which is simply another way of saying you have to hold forward pressure to maintain that higher airpseed. That doesn't seem unstable to me. Instability would mean you had to pull back on the stick to prevent speeding up.

The offset gimbal head also introduces stability w/ respect to angle of attack. Without the offset, at any airspeed above zero, an increase of AOA increases the ever-present tendency of the stick to move aft. This, in turn, tends to increase AOA some more, resulting in a classic case of instability. The offset gimbal employs the increased thrust of the rotor as AOA increases to pull the back of the torque bar up, muting the effect of the jump in AOA. This feature works best if you hold the stick lightly enough for the head forces actually to move the head (floating the stick).

The spring allows us to use extra offset which, combined with the varying spring pull at different airspeeds, increases the airspeed stability already provided by the flap/blowback effect. It seems to me that the spring and the flap/blowback effect work in the same direction -- both contribute to airspeed stability.

The spring also makes the head's trimmed airspeed easily adjustable, without the need to change the actual offset distance.

Finally, the spring becomes a double-edged sword once airframe stability is figured in. If the spring is fixed to the back side of the mast, it is affected by pitching movements of the airframe.* A nose-up pitch relative to the rotor tightens the spring; a nose-down one loosens it. The result is that the spring makes the torque bar and spindle tend to follow the inclination of the airframe. This is a very good thing if the airframe is stable with respect to AOA and airspeed. It's a very bad thing if the airframe is unstable; in a severe case, this linkage could entirely un-do the good work of the gimbal head.

*This is one reason why the mantra "fly the rotor, not the airframe" can keep a student from realizing that a given gyro is simply unstable.
 
Hello All.

Thank you for the awesome info.
Another question for the gurus.....with due respect.

What happens if the trim spring breaks in flight. How will the AC 582 NCTL
and the pilot react to this.

Greetings.
Rehan Janjua.
 
An offset gimbal rotor head that doesn't need any spring tension for a given hands-off trim speed is AOA, or G-load, unstable at any airspeed higher than the trim airspeed. That is because, as Tim said, the RTV is passing ahead of the pitch pivot. As long as the pilot has to hold forward stick pressure, the RTV is passing ahead of the pitch pivot. The rotor is airspeed stable, but AOA unstable.

Having a stable airframe may help a little but without a trim spring there is no airframe-rotor feedback. The only link is the pilot holding the stick - and, as we know, you don't want to count on the pilot for stability.

Yeh, I agree with Tim this could be unsafe for inexperienced pilots.

Udi
 
How do we figure the optimum offset and trim spring pressure?

Does a very large, say 2" offset with appropriate strength springs to compensate, have more stability than say a 5/8" offset and the appropriate strength springs?

Without considering the stick load in the ground of course.

I had a new trim spring break on my s X s A/C training. Both student and I just held the stick tighter. I asked the student why he gave to stick a nit forward and he asked me why I did. He though I was giving him some sort of emergency!!!!!

The stick pressure was quite severe so I just reduced power and almost flew onto the ground without overly flaring. Prior to this happening I had my hand resting on my knee to give the student some confidence. I had just placed my fingers back in front of the stick as we turned base. It was rare for me not to have my fingers in front of the stick due to about the only way a student could kill me was a sudden push forward on the stick.

Now with the stable trainers I seem to have an eternity of time to correct a student’s mistake with pitch control.

Aussie Paul.:)
 
There is a maximum allowable pressure on the stick in the event of trim failure, in our two seat standards. Not only spring tension but also spring rate, can have a bearing on stability.

One well known brand of gyro had an adjustable spring on the front of the joystick to hold it forward. This would create negative stability because the head would react the wrong way with gusts.
 
The same Pete Johnson that first called my attention to the stabilizing effect of offset balanced with a trim spring experimented a good bit with offset and trim springs of various rates.

His conclusion, as best I recall was that Bensen’s 1” offset was best, combined with a very low rate spring.
 
Here’s another way of skinning the cat.

The monkey motion pictured below was an attempt to eliminate rotor feedback to the stick on my B-7 airframe.

The links for pitch control were on a line that converged at the teeter bolt. The point of intersection is the virtual center.

A good illustration of how dumb it is to begin cutting metal before considering all the consequences.

The virtual center changes with pitch input, scribing an inverted “U”. The machine flew fine at an airspeed of 40 mph when the teeter bolt was at the top of the “U” (depends upon the mounting angle of the rotorhead) but any other speed required a good bit of stick force, either fore or aft.
 

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You do not need a spring in an offset gimbel to provide the correct stick force cues wrt speed. Without a spring though, as Doug has pointed out, you are stuck with a fixed trim speed.

As for the AOA stability benefits of the offset gimbal, I have a slightly different take. The notion that the rotor 'blows back' after an increase in AOA is often quoted and accepted as a fact. But strictly speaking this is only true for a helicopter where rotor RPM is maintained constant. In a gyro (at least one with a inertia-less rotor) the rotor is free to change speed, and so any increase in AOA will result in increase in rotor RPM, which will in turn cause a 'blow forward' ( reverse of blow back) rather than blow back. So a gyro rotor may well exhibit g- load stability without an offset gimbal though it may not be much.

How does a typical gyro rotor behave to AOA disturbances- blow back, blow forward or neutral? My guess (based on very crude calculations) is a gyro rotor on its own is in fact very nearly stable wrt AOA. Large thrustline offsets in HTL machines of course overcome this intrinsic stability of the rotor and cause the behaviour we have come to expect from these machines.

Any thoughts?
 
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Raghu, unfortunately most of my experience has resulted in "dirty" data.

I recall that my Air Command in the no-HS, inverted engine config was unstable w/r/t airspeed at high speeds, and w/r/t AOA at all speeds.

At high airspeeds, the nose tucked so low (thanks to a high thrustline) that the trim spring probably slacked off instead of tightening with airspeed as it should. (The spring supplied with the gyro was a single 6" long spring, which gives a fairly high spring rate, compared to some of the longer springs I've seen and used.) The subjective impression was that the machine badly wanted to flip forward once you got it up to 80+ mph. OTOH, a friend always flew an identical machine at that speed and seemed not to care.

Thermal turbulence brought out the aircraft's very poor AOA stability. The initial "hit" from an updraft resulted in a nose-up pitch (HTL again) and a bump in the seat. This was followed a split second later with a second "balloon." The trim spring was taut thorughout; I suspect that a combination of the wrong-way airframe pitch and the tail-heaviness of the McCutchen blades caused this second jump. "Floating" the stick reduced, but did not eliminate, the ballooning. The sound of RRPM increasing was very noticeable.

In this case at least, the RRPM increase did not overcome the AOA instability, although Udi's theory may apply (or be made to apply) to other blades. It's pretty obvious to me that, in this particular gyro, the gimbal-head-and-Udi-effect together were not able to overcome entirely the de-stabilizing effects of tail-heavy blades and a HTL airframe.
 
The G-load instability I mentioned earlier is a result to rotor head geometry, not aerodynamic, as Raghu pointed out.

The first drawing (left) shows the location of the RTV relative to the rotor head pitch pivot in a "normal" rotor system using a no-spring offset gimbal. The reason this kind of rotor head is airspeed stable is because the rotor disc is tilting relative to the rotor head, as a function of airspeed. We call it blow-back As the rotor disc tilts back, the RTV is moving forward relative to the pitch pivot.

At zero airspeed, there is no blow-back, and the rotor is perfectly perpendicular to the rotor head. In this condition, the RTV is passing behind the pitch pivot, causing a nose down pitching moment on the rotor head (and pulling the stick forward). Maintaining this position requires back pressure on the stick. If the pilot lets the stick move forward, the rotor will tilt forward and the gyro will gain airspeed. Airspeed stable.

As the gyro gains airspeed, the rotor disc tilts back, or blows back, in relation to he rotor head, due to flapping. At some airspeed, the RTV is passing right through the pitch pivot. This is the trim airspeed. To fly faster than this airspeed, a forward stick pressure is required, because the RTV will be passing ahead of the pitch pivot.

This configuration is G-load (AOA) unstable any time the RTV is passing ahead of the pitch pivot. The reason this configuration is G-load unstable is because any increase in G-load would cause the rotor head to pitch up - further increasing the G-load. That is an unstable reaction of the rotor head.

The second drawing shows a spring supported rotor head. This head uses more offset, so the RTV never passes ahead of the pitch pivot. The trim airspeed is the airspeed in which the spring moment is equal to the moment created by the RTV force multiplied by the distance of the RTV from the pitch pivot.

The optimal offset, in inches, will depend on height of the teeter bolt over the pitch pivot bolt, and the particular blow-back properties of the rotor.

Udi
 

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The distinction Raghu was making, Udi, was between a constant speed rotor (helicopter) and variable speed rotor (autogyro).

Here’s what Shapiro (Principles of Helicopter Aerodynamics) has to say on the subject:

“In order to realise that the effect of r.p.m. variation can indeed be large, let us mention the autogyro rotor, treated on the assumption that the rotational inertia of the rotor is small enough to ensure “instantaneous” adjustment to the zero driving torque condition (instantaneous in terms of the natural period of the oscillations of the machine). The rotational speed of an autogyro rotor varies with the thrust and with forward speed in such a way that the autogyro rotor with low inertia behaves, from the point of view of its stability derivatives, much more like a fixed wing than a helicopter rotor.

An increased rotor incidence leads to an increased tip speed, the longitudinal flapping is reduced and a nose-down moment is exerted on the machine if it was previously in trim. The nose-down moment is even larger on account of the increase in thrust with an increase in rotor incidence. In this simplified picture the autogyro is therefore statically stable with regard to attitude.

On the same assumption, so long as the rotor incidence remains constant, the tip speed also remains approximately constant and so does cyclic flapping, which means that the moment equilibrium in the pitching plane is undisturbed. We obtain a neutral static stability with regard to forward speed. The real autogyro rotor will behave in a manner between that of the inertialess rotor and the constant-speed rotor.”

Whatever the case, if the rotor thrust vector passes forward of the gimbel pitch pivot, an unstable force is applied to the control system
 
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C. Beaty said:
The distinction Raghu was making, Udi, was between a constant speed rotor (helicopter) and variable speed rotor (autogyro)
I understand the distinction Raghu was making, but I don't think he understood mine... ;)

Udi
 
Udi said:
I understand the distinction Raghu was making,... ;)

Udi

I am afraid I don't think so ;) . Here is why:
If you buy the idea that an autorotating rotor blows forward rather than back when its AOA is changed, then it does not matter (within limits ) if the RTV passes fore or aft of the pivot, you still will get the correct stick pressures wrt AOA disturbances.

Consider, as in your diagram, the RTV ahead of the pivot, i.e the pilot is flying at a speed higher than trim and is holding forward pressure on the stick. If there is an increase in AOA the G-load will increase but in addition the RTV will blow-forward causing the RTV to get closer to the pivot. The direction of the resulting moment depends if the RTV blows-forward enough to offset the increase in G-load or not. As long as the RTV is not way ahead of the pivot before the disturbances, you will find the blow-forward will in fact overpower the g-load increase and cause a reduction in stick pressure

There is of course a point ahead of the pivot where the g-load increase will dominate over the blow-forward and you will get unstable stick forces.

The same thing also applies to the stick fixed scenario wrt CG of the craft. Similarly, you do not get AOA instability as soon the RTV moves forward of the CG.

How much forward? I made some calculations a while back for a 600 lb. AUW gyro, with 23 foot rotor, 300lb. prop thrust, and rotor hub 3 feet above CG. It turned out, in fact the golden prop thrust-line guideline of 2-inch fit exactly. Beyond 2-inch thrusline offset the gyro is unstable wrt AOA. Of course this number does vary depending on the height of the hub, but the offset is not far of 2-inches for typical gyros. I was surprised to get exactly 2 inches for the above case (coincidence I am sure), seemed to fit too well with the Glasgow studies. I will try and post some graphs later when I can track my calculations.
 
I think there are several reasons for the differences between observation and theory.

(1) There is no such thing as an inertialess rotor. All rotors have a finite time constant in response to gusts. There will be as a minimum an initial impulse applied to the stick in an unstable direction if the RTV leads the pitch pivot.

I flew Hughes rotorblades for a good many hours and the lag of rotor rpm vs. “G” load was particularly noticeable. A landing flare required an extended roundout to allow the rotor speed to catch up. Otherwise, a pop flare that worked for low inertia Bensen metal blades would cause the machine to thump in. Hughes-269 blades had 5 lb. brass slugs in the tips.

(2) Some rotors have excess reflex which tends to make them constant speed (a nose up pitching moment coefficient). Bensen wood blades had a positive pitching moment coefficient of ~0.05 and were very soft in torsion.

(3) Tail heavy rotors; those with center of mass aft of the aerodynamic center tend to twist nose up in response to upward gusts. This was particularly evident with Skywheels rotors.
 
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Doug Riley said:
Raghu, unfortunately most of my experience has resulted in "dirty" data.

Thermal turbulence brought out the aircraft's very poor AOA stability. The initial "hit" from an updraft resulted in a nose-up pitch (HTL again) and a bump in the seat. This was followed a split second later with a second "balloon." .

Thanks Doug! Your experience is certainly in line with what you would expect in an HTL machine. It is a good example of the lagged response of a gyro. I presume the second bump in the seat (g-load) was larger than the first?

If we ignore the tail heaviness of the skywheel rotor for a minute, the first (small) bump is due to thermal causing a change in rotor AOA. The second bump is due to the pitch rate caused by HTL. The maximum G-load occurs a short time after the first bump once the pitch rate has stabilized. This lagged response is what makes control of HTL gyros hard.
 
Raghu, my buttockial G-meter is not sensitive enough to tell you which surge was stronger. They overlapped in time, with a relaxation of the G's in between. The whole sequence took maybe two seconds. Back then, I attributed the second pulse to increased RRPM -- especially since it coincided with a lot of rotor "whooshing" noise. I didn't know about the tail-heaviness of Skywheels.

Skywheels are relatively massive, and they don't change RPM quickly for this reason alone. The under-balancing may make this tendency worse. They are therefore far from Shapiro's model of the rotor that changes RPM instantly.

Whether the second kick was because of frame pitching or a lagged increase of RRPM, or a little of both, it's clear that other factors prevented the gimbal head from providing full AOA stability. Simply adding the Air Command HS, and changing nothing else, made quite a profound difference, so frame pitching certainly was one factor.
 
Thanks Chuck B. In general I (understand :)) agree with your post. Just to emphasize a few points:

Inertia of rotors:
It is of course true that all real rotors have inertia and hence a time constant in their response. But if this time constant is small enough compared to the phenomenon we are investigating, we can assume the rotor to be inertialess. For example, if we are modelling the long period (phugoid) oscillation which typically has a time period of 12-14 seconds, we can most likely ignore rotor inertia. Similarly, the short period mode has a period typically between 4 to 8 seconds. It may well be possible to ignore rotor inertia ( at least in the case of light rotors) in this case as well.

Helicopter references such as Johnson's "Helicopter theory" mention that auto-rotating rotors, unlike helicopter rotors, are found in practice to be AOA stable. But unfortunately he gives no empirical evidence or supporting calculations. I have tried to make the calculation myself based on rotor inertia but so far the only results are very crude and rough. Any ideas?

Rotor response during a flare:
1. Stability derivatives such as AOA stability (M-alpha) are only applicable for small deviations from trim as the underlying models are non-linear. Hence these derivatives are invalid for abrupt maneuvers such as flares.

2. In addition to rotor inertia the time to load a gyro to a specific g-load depends on the stability of the gyro- more unstable machines will attain a higher g-load per unit stick deflection because the higher pitch rates augmenting the g-load. Was the Huges rotor gyro more stable in pitch?
 
Raghu, the time constant of Hughes blades with tip weights was in the range of seconds. By watching the rotor tach after tossing my gyro into a tight turn, the rotor rpm could be seen to creep up over a time interval of several seconds before stabilizing. Chopping the power and simultaneously rolling out of the turn would allow the machine to play helicopter with the stored energy for a couple of seconds before the rotor slowed to 1 G speed.

One showoff trick was land after rolling out of a tight turn and chopping the throttle to bring the gyro to zero airspeed at a height of 2 or 3 feet. The machine would hover for a couple of seconds before slowly settling down.

My general impression was that Hughes blades with tip weights gave a better ride in turbulence at the expense of a less whippy control response.

Many of the users of Hughes blades would saw off the outer 8” or so of the tips, which would remove the weights and then reinstall the end plugs.

I’ve flown Hughes blades both ways but preferred the tip-weighted blades after getting accustomed to them.

The US Army used a militarized version of the Hughes-269 as a trainer at Fort Rucker Alabama. They ran out a lot of rotor blades during the Vietnam war which could be purchased surplus for little more than the price of aluminum scrap.
 
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