Undersling vs Coning angle

[automan1223]

Here is a question that approaches a problem from another angle.

Many rotorsystems suffer from shake due to incorrect undersling. Instead of putting a different teeter block or height at the rotor head could you change undersling by changing the coning angle ?

Is the coning angle a "fixed" dont mess with it kind of thing or could you make minor changes in degree of coning angle and effect undersling that way. This is just a theory question.

Jonathan

[Aussie_Paul]

Jonathon, it is my understanding that the coning angle "finds" its own level no matter what pre set coning angle you have built in to the hub bar.

I think that the only way to change coning angle would be to increase blade pitch and slow the rotors down.

Am I right fellas?

Aussie Paul.:)

[Alan Coats]

Jonathon, it is my understanding that the coning angle "finds" its own level no matter what pre set coning angle you have built in to the hub bar.

I think that the only way to change coning angle would be to increase blade pitch and slow the rotors down.

Am I right fellas?

Aussie Paul.:)

I was going to post the same answer. The other day someone posted a spreadsheet that, among other things, predicted the coning angle as determined by all up weight, rotor weight, and rotor rpm.

Alan

[Crash one]

Jukka Tervamaki has a downloadable programe for performance which looks perfect for this, just tick on boxes for what you want.
Trevor

[Alan Coats]

That's the I was thinking of. Here is a link to it-

http://www.icon.fi/~jtki/gyrocomp.html

Alan

[Master Roda]

I'll go ahead and throw this out there:

Try a 3 bladed system. (I know this isnt a solution for most)
Do all those things you mentioned, taller teeter, less weight, etc.
INCREASING (not decreasing) R.P.M. will bring coning down (less shake)

OR, IMO, you said it best "INCORRECT UNDERSLING"

Also, a stiffer blade tends to have lower coning. Try buying stiffer blades.

Good luck

[Doug Riley]

Some 2/rev rotor shake is NOT cureable with undersling. Picture what an air molecule up ahead of your rotor "sees" as your 2-blade rotor spins. The rotor is effectively foreshortened when it's in the 12 o'clock - 6 o'clock position as compared to when it's at 3 o'clock 9 o'clock.

To make matters more interesting, when in the 12-6 position, the aft blade is foreshortened more than the forward one.

[Master Roda]

All 2 bladed system's have a 2 bump per rev. Simply stated, it can be reduced. This "bumping" also happens at different RPM's. Notice how a 2 blade rotor system will not "bump" when it's unloaded in flight?

Foreshorten? That blade is still the same length. No matter what it looks like. The same amount of air molecules will strike the blade. It just depends on the incidence of the blade that will dictate how it will affect the system as a whole.

Hope that helps.

[Doug Riley]

Of course the blades don't change length.

The fact that, when the rotor is in the 12-6 position, the upwind blade both has a higher angle of attack, and interacts with more air molecules, than the downwind blade, however, is easily and accurately pictured by analogizing with optical foreshortening.

The angle-of-attack part of the effect is also similar to the one encountered when a FW plane with wing dihedral slips sideways upon application of rudder. There's a dissymetry of lift that causes the plane to bank away from the direction of slip unless we cancel it out with aileron.

[Vance]

Hello Doug, Welcome home!

I am reading your explanation and I don’t get it. I am particularly interested in this aspect of rotor dynamics.

I would be grateful if you could find a way to bring it down to my level. Perhaps if you would quantify the magnitude of the phenomenon it would be easier for me to understand.

Thank you, Vance

[Doug Riley]

Vance, I can't quantify but here's a sketch.

You can see that air impacting the upwind blade at any Point A will do so at a greater angle of attack than at any point on the downwind blade, Point B. Blade A will have more lift and drag than Blade B.

From a profile drag viewpoint, the projected, or frontal, area of each blade matters. The frontal area of the upwind blade is (blade chord X Distance #1). The frontal area of the downwind blade is (blade chord X Distance #2).

This simpifies reality quite a bit. The blades are rotating, so the air molecules cross each blade diagonally, at an angle that varies along the span of the blade. This has the effect of "stretching out" the effective airfoil section by increasing its effective chord while holding the thickness constant -- again to varying extents, depending on where you look up and down the span.

It would be a miracle if a simple teeter (or other flapping) hinge could create cyclic pitch changes that would completely eliminate the differences in lift that this process tends to create. Even if it did, you'd still be stuck with variations in drag (compared to drag when the rotor is crosswise to the gyro) that would create some 2/rev.

[Vance]

Thank you Doug!

That helps a lot. I have had the greatest difficulty understanding the two per rev shake. Your explanation is the most plausible that I have yet encountered.

I am still struggling to understand what the hub feels and which way it wants to move. Is this force in line with the rotor thrust vector? Would the movement be in line with the thrust vector? If the head was allowed to move with soft mounts, how would this change the effect?

Does this cause the coning angle to change during a revolution? How much?

Would four blades double the frequency and halve the amplitude?

I am sorry this didn’t come up at Bensen Days. I do believe that many on the forum would like to understand this better. You have touched on something I am particularly confused about.

Thank you, Vance

[Al_Hammer]

A couple of points; not neccessarily in agreement with Doug... :D
True enough, if air is coming at the blade from a somewhat endwise, or spanwise direction, I think you can see that it will pass over the blade on a diagonal rather than perpendicular to the leading edge, thus it will travel a greater chord length.

Doug says that this increase in effective chord length will increase lift. I suppose that if fixed wingers want to increase lift they can start sweeping their wings back for the same benefit. Maybe the wings should be swept back 100 % so the air has to pass over the entire span edgewise for really great lift.
No, the obvious fallacy here is that as the wing or blade is swept back, the spanwise flow increases, but the effective airspeed decreases. That's the real reason for swept back wings(and rotor tips) It reduces the mach number and the wing sees the air coming at a slower velocity. Of course, lift varies as the square of airspeed so the increased chord length is offset by the loss of airspeed.

The upward coned blade does in fact see a very slight increase in angle of attack. Most of the oncoming air , when the blade is pointed over the nose, is pointing spanwise , but a small component is acting vertically. Of course most of the lift comes from the rotational movement of the blade, but there is a small increase in angle of attack at the front and a small decrease at the rear, no argument.

It is not a source of vibration, however, or not much of one, because a little left stick nicely cancels the problem, which, by the way, shows itself as a right rolling tendency.
If the blade sees a bit of increase AOA as the blade goes over the nose, then left stick will rotate that blade down and take it out at the source.

The same thing happens with flapping. Disymmetry of lift is cancelled at the source, so technically there is no disymmetry of lift in flight.

This brings me to my next point, which is that one of the real sources of 2 per rev is , in fact, from the limitations of flapping.
Flapping, as we all know, changes the angle of attack of the blades as they move around the circle and these changes are supposedly whats needed for cancelling the lift variations caused by airspeed variations on the advancing/retreating blades.
Trouble is, that lift varies as airspeed squared. So, as the blade goes from 12 o'clock to 3 o'clock (Rear to broadside) it sees the lift change faster than the flapping can deal with. Flapping can't deal with anything other than a smoothly changing lift that varies as the sine of the angle. The result is that a small remnant of lift changes are left and they have a 2 per rev component, most pronounced near the tips where the lift and airspeed are greatest.
I believe that's why cameras mounted on the blade show the tips dancing up and down at 2 per rev.

Incorrect undersling is another source of 2 per rev, as mentioned. In that case, its from mass being jerked around , not aerodynamic effects.

As for drag variations due to advancing and retreating , I think it is an over simplification to say that drag increases when the blade hits the air broadside.
Remember- the forces of drag and propulsion are balanced in autorotation.
Lift increases on the advancing side, but does autorotative force increase or decrease at that point? Since flapping equalizes lift, does it equalize drag?
Do you see that it starts to get complicated?

I suspect that a plot of drag vs autorotative force around the disc would not show a simple relationship.
I do have such a plot, made by Raoul Haffner in the 30's.(Thanks, Chuck B.)
It shows the net torque , or moment at each position. I added color to the graph. Green shows areas of net propulsion(negative drag) and brown/red areas have net drag. It appears that things are pretty much balanced across the disc at most pints, but not all, but who knows how accurate this really is. Haffner didn't have dsl, or even a computer.

[gyropilot]

Incorrect undersling is another source of 2 per rev, as mentioned. In that case, its from mass being jerked around , not aerodynamic effects.Al,

Would you agree that it's pretty easy to figure out where one-to-one vibrations comes from? Usually it's a balance issue, a tracking error, or possibly the blades don't share identical lift characteristics. If you positively rule out balance issues, then your pretty much left with tracking and/or lift problems to fix.

But is there a way to rule out where a 2-per-rev vibration is (or isn't) coming from in flight tests?

For starters, wouldn't the 2-per-rev vibrations from imperfect undersling pretty much disappear in a power-off vertical descent? If so, wouldn't they reappear even at slow flight (with a high power setting) where the rotor disk angle of attack is high?

If a 2-per-rev vibration doesn't disappear in a vertical descent, what would that be telling us?

Thanks in advance,

John L.

[Al_Hammer]

Well, John, as far as I know 2 per rev should disappear in a vertical descent, since there is no assymmetry of lift and no flapping, etc.
I don't know that thatt is helpful to know. When it comes back in forward flight, finding the source is tricky. An electronic balancer/ vib meter won't help because it can't produce a phase angle like it can with one per rev, only a vibration amplitude.
It will separate 2 per rev from one per rev, using software filters, so you can always know when the mass balance chordwise balance and stringing are correct- now which one is it?

One-per , which is indicative of a mass imbalance of some kind can be tracked down with a balancer in the sense that it does tell you the "clock" angle relative to the blade reference position(over the nose, or wherever.) That tells you which blade is heavy. If its zero degrees, the reference blade is heavy- 90 degrees, the stringing is out(the tips are closer together on one side), but then again you might have a tracking problem. As I understand it , these things are usually done in cycles where you first track, then balance, then rinse and repeat. The one time I used my $1500 balancer on a gyro, it gave confusing results for 2 per rev and 1 per weren't all that consistent.
I have been motivated to the extent that I designed my own balancer. The plans are still on paper, unfortunately. :D

[Vance]

AAAARRRRGGGG!!! Just when I thought I was starting to get it.

Al are you in agreement with Doug that two per rev shake is about the lift changing as the rotor rotates?

Is the two per rev about foward flight?

Is the shake in line with the rotor thrust vector?

I love you chart and the colors are lovely.

Thank you, Vance

[Vance]

Hello Al, I am in more trouble than I thought.

Are you saying that the thrust (lift) happens at the rear and right side of the disk?

Are you saying it sucks on the center left of the disk?

Thank you, Vance

[Al_Hammer]

Al are you in agreement with Doug that two per rev shake is about the lift changing as the rotor rotates?

Only some of it is lift changes. Improper coning will produce mass shaking at 2 per rev.


Is the two per rev about foward flight?

Yes, the problem goes away if there is no flapping and or forward speed.

Is the shake in line with the rotor thrust vector?

Its usually in the form of a lateral shake, plus some vertical shake(cabin hop),usually a tracking problem, which is in line with the rotor thrust. the two per shake means one blade is lifting while the other is lifting less, thus the tendency is for lateral shake.

I love you chart and the colors are lovely.


Thanks, I wanted it to look like a coloring book.

Are you saying that the thrust (lift) happens at the rear and right side of the disk?

The thrust happens everywhere, with only minor variation. The chart shows the in-plane torque and how it changes as the blades enter different sectors.
Usually the plus and minus forces cancel, but as you can see, there are positions where both blades experience net drag. They still may be producing thrust and lift, so try not to confuse the two issues.

Are you saying it sucks on the center left of the disk?
The left of center(green) area is not sucking, its where the blade has net positive torque , overcoming drag. That's what keeps the rotor spinning.
A helicopter needs to provide torque mechanically, a gyro provides it aerodynamically through the blade itself.


AAAARRRRGGGG!!! Just when I thought I was starting to get it.

I know the feeling, Vance.

[Vance]

Thank you Al, You are a good friend and a very nice fellow. I think that helps. It will take me a while to rise up to the new level of confusion.

I am still wondering if a four bladed fully articulated rotor of half the chord would halve the amplitude and double the frequency? Or does something entirely different happen?

I am on a fools errand of building such a rotor with an offset gimble, so I am hoping if I can gain confusion on a high enough level I won’t have to build it, or my rotor test stand.

Thank you so much for the help, Vance

[Al_Hammer]

I am still wondering if a four bladed fully articulated rotor of half the chord would halve the amplitude and double the frequency?

I think you are correct on this one, Vance. The term "N per rev" is often used to indicate that the frequency of vibration goes up with the number of blades.

Thanks for the kind words.

[StanFoster]

Vance: You arent the only one that resembles the RCA dog with his head tilted in bewilderment.:D


These very well explained posts are the meat of this forum. Thanks Doug , Chuck,,Al...and many others for your excellent inputs on so many interesting aspects dealt with here on this forum.


Stan

[Doug Riley]

To clarify: I did not say (nor mean to imply) that the aerodynamic "stretching/thinning" of the airfoil increases lift. Quite the contrary. A flat board wing (like that on a hand-tossed balsa glider) isn't very efficient.

The point is that this distortion of flow over the blade DOES reduce the lift of BOTH blades. This results in a variation in the magnitude of total rotor thrust, producing cabin "hop" and potentially a very slight variation in coning angle.

In an old piece in the PRA mag, Bensen said that the variation in lift on a Bensen B-8M during the orbit of the rotor was on the order of six pounds.

There's also a probably a variation in the DIRECTION of rotor thrust. This would account for some of the fore-aft stick shake that we fight with. (One possible reason that the Beaty/Dominator "slider" head doesn't get rid of all of this shake is that the sliding happens along the roll pivot, which is angled back rather than being parallel to the flight path.)

The weird one to think about is the dissymetries of lift between a 12 o'clock blade and a 6 o'clock blade. The front blade clearly has a higher AOA and more lift and drag. The diagonal flow may also shift the center of lift of the blade spanwise. Given that the rotor will not readily depart from a flat-plane orbital path (i.e. the tips won't track an up-and-down path like a roller coaster), these differences may end up causing the individual blades to bend up or down in a "curling" action. (Films of blades shot by a camera mounted on the rotor hub do show such cyclic "curling.")

[Vance]

Thank you Doug, that helps.

I love the way something that apears so simple is actually so complex.

I think it is remarkable that anyone got it to work.

I have been defeated by less complex development programs.

Thank you, Vance

[Al_Hammer]

Doug, I didn't mean to misquote you- sorry. I think the fact that there is a right rolling tendency shows that there is an increase in lift at 12 o'clock and a decrease at 6. This is complicated in practice by the torque roll tendency of the prop and the need to offset rotor thrust to counteract it.
The pilot nullifies any increased lift at the front from coning effect with a left stick input. Any increase in lift will tend to tilt the disc 90 degrees later, rather than curl the tips- after all, thats how we control the rotor. For this to be true, it must be a cyclic input that varies at a 1 per rev rate. The effect I mentioned where lift varies as a result of airspeed squared actually creates a 2 per rev input and this , rather than tilting the disc, does shake the tips. There isn't much to be done about it short of advanced control mechanisms that operate at higher harmonics.

There may well be a 6 lb cabin hop as Bensen claimed. That's about 1% of rotor thrust, so would be noticeable. One way to know would be to measure it at 1 per rev and 2 per rev settings on an electronic balancer and see what it says. Of course cabin hop can be caused by blade-cabin interference effects, as well as tracking problems, so we still wouldn't know the exact source.

Vance, all this is complicated, but probably no more so than the mechanics of counter-steering on a bike. A subject that's also argued about perpetually on other forums. I found myself investigating for myself the other day when I was out on my bicycle. To turn right you do steer opposite initially, which sets up a lean in the desired direction. Then you steer in the direction of the turn. Proper understanding of counter-steering can make your turns a lot crisper, as I'm sure you are a master of. Sorry to veer off topic.