Rotor Speed - Size and Safety

[freebird]

I have followed several threads about RRPM, decay, etc... It boils down to where I need to use my own figures as examples to get the warm and fuzzy.

My machine is an Aircommand CLT single seater with a nose and a 582. I have the small tail that is farther back than some of the older aircommands.

The rotors are 25' DW's. I weigh about 180lbs. She tries to leave the ground at under 300 rpm and operates at 305rpm at 45mph airspeed. There seems to be a lot of floating with these rotors. I have seen this same arrangement with 250lb pilots.

Given that I have more power than many and my RRPM is a slower than most, am I in danger of Torque roll or pushover? What is not "ideal" here?

I have been telling myself all along that this setup should be ok for me as a beginner because the extra lift could be a good thing. I suspect that I could climb at close to 1500 fpm. I have lots of power.

[PW_Plack]

Free, from what I've read over the years, 305 RRPM on a set of Dragon Wings is too slow, suggesting you have too much rotor. Check with Ernie, but I think he usually wants to see 330 or more, and sizes rotors accordingly. There might be a shorter hub bar available which would get you back in the safe RRPM range.

[GrantR]

Free provide your gyros gross Weight. Ernie will probably pot on here what size rotor blades you need. I am thinking 23' for your gyro.

[MichaelBurton]

As others have stated 300rrpm is too slow. Rrpm is governed by disk loading so you will need a shorter rotor. One of the main dangers is that your forward speed will cause rotor flap problems during take-off. A blade flap event resulting in rollover and possibly injuries is a likely product of such an event. In flight it will limit the forward speed of the gyro. Also as the rotor rpm increased the conning angle is reduced and the rotor can handle more load. If the rotor is overly large it may not have the strength to hold the weight of the gyro and the blades could fail in flight. If the conning angle if not correct then the rotor will have additional shake. There may be other hazards that I have not thought of or addressed. The rotor rpm that you report is not way out of line but caution is advised and a shorter rotor would increase safety and likely reduce your two per rev shake.

[groundhog]

a low wing loading such as you have makes you very sensitive to turbulence or floaty as you say.A shorter wing as suggested will make your machine nicer to fly on rough days and hence safer in my opinion.A shorter hub bar is a good idea or you could carry a "reserve " of fuel somewhere near your optimum centre of mass.

[MikeBoyette]

Freebird,
Give Dad a call and he can tell you what size rotors you should be using based on AUW and density where you fly. His number is 813-634-3370. If you want you can speak to him in person if you plan on attending Bensen Days.

[Aussie_Paul]

Which is more important to know. Rotor RPM or rotor tip steed?

Aussie Paul. :)

[Resasi]

Paul you will no doubt get the experts answering but my guess is that, as always we are dealing with compromises.

Choice between a too low RRPM and a 'good' tip speed, or higher than optimum tip speed with a 'safe' RRPM and reasonable disc loading.

[Passin' Thru]

Paul you will no doubt get the experts answering but my guess is that, as always we are dealing with compromises.

Choice between a too low RRPM and a 'good' tip speed, or higher than optimum tip speed with a 'safe' RRPM and reasonable disc loading.

Good point on dealing with compromises. After some experience, one may find some compromises subjectivly more to their liking. One case in point; on my light weight "toss about" local pea patch fliers, I like shorter blades (higher disc loading) turned a bit faster (less pitch) than optimum effeciency. This gives a faster control response and a more "solid feel" to the machine. Your taste may vary.;)

[ckurz7000]

...One of the main dangers is that your forward speed will cause rotor flap problems during take-off....

Michael, can you explain to me why you think the lower rrpm of a longer rotor is more prone to blade flapping than the higher rrpm of a shorter rotor?

Without thinking about it too deeply, it seems to me that what matters is the ratio of rotor tip speed vs. translational velocity. How you get the tip speed (if by twirling shorter blades faster or having longer blades) doesn't matter.

-- Chris.

[RotoPlane]

With 25' rotors and a tip speed of 412 fps, gives 315 rrpm. Everything I've read says a tip speed of ~400 fps is ideal.

305 rrpm equals ~400 fps. Are Dragon Wings different?

[PW_Plack]

...Are Dragon Wings different?

If I understand correctly, they are more efficient than many blades, but may stall more abruptly at the threshhold. I'd want to maintain the RRPM margin recommended by the manufacturer.

[Resasi]

Peter I went by Ernie's recommended disc loading for the weight band and alt we most commonly expect to be operating it in and ended up with 23's on the DW's.

If I do manage to take it back to Kenya that will be sea level to about two thousand feet and quite warm temps.

If then managed to take it up-country to Nairobi for the occasional visit that would be at around 5,500' AMSL and a density alt of around 7000' and would then have to accept a rather reduced performance.

Find the Bensen and 22' Rotor Hawks very maneuverable. We pitched it down a tad to make patting it up a little easier.

[MichaelBurton]

Michael, can you explain to me why you think the lower rrpm of a longer rotor is more prone to blade flapping than the higher rrpm of a shorter rotor?

Without thinking about it too deeply, it seems to me that what matters is the ratio of rotor tip speed vs. translational velocity. How you get the tip speed (if by twirling shorter blades faster or having longer blades) doesn't matter.

-- Chris.

Rotor speed is in a gyroplane governed by disk loading. Let consider a low disk loading and overly large blades. If we go to the limits we can better see the problem. At 300 rpm we don't have a large problem and with caution we can manage to fly.

What if we use a rotor that only turns at 200 rrpm during flight. At this point the CF is lower and the blades may not support the gyro. When the wheels depart the ground the blades fold and the flight ends.

If we manage to get into flight the rotor tip speed will not be near what it would be with the smaller blades as the rotor will be producing the same amount of lift with a large or small rotor. So our forward speed will be limited. It would be much easier to have a blade flap event during take-off as the forward speed of the gyro is a larger percentage of the tip speed.

If we don't consider profile drag we have create an example where the aerodynamic forces are constant. We will lift the same weight so the forces will be equal. Most of the vertical lift is produced near the tip of the rotor. For our short rotor this area is reduced so the lifting area must move faster. On the longer rotor the area is extended and a much lower speed is required to produce an equal amount of lift. The tip speed will not be equal for the short blades and high rrpm and the long blade with slow rrpm. The long blade will have a slower blade tip speed.

[ckurz7000]

Michael,

I agree with you that the coning angle would increase with a larger rotor diameter until, at some point, the blades would fold. But this isn't the regime I am concerned with and let's assume, for the sake of this discussion, that the blades were infinitely stiff and we don't have to worry about coning.

I also agree with you that the total lifting force must be independent of the rotor diameter and will be produced mainly at the outboard section of the rotor blades.

Let's simplify this problem even more so that we can concentrate on the pertinent issues more clearly: pretend that the rotor consists only of a blade section on the ourboard side that's attached to the mast by a simple rod (i.e., forget the inboard stalled area as well as the driving area of the blade and only keep the lifting area).

In this case the only quantities that determine the lifting force are the angle of attack and the airspeed (keeping the profile the same between the long and short blades). I can't but conclude that the airspeed which the lifting portion of the rotor sees determines the overall lift produced by the rotor (for equal angles of attack).

Which leads me back to my statement that a longer rotor turns by that amount more slowly than a shorter rotor that is required to make the tip speeds come out the same.

That would lead me to conclude that your safety margin for blade flapping is -- in first approximation -- independent of rotor diameter.

-- Chris.

[MichaelBurton]

Michael,

I agree with you that the coning angle would increase with a larger rotor diameter until, at some point, the blades would fold. But this isn't the regime I am concerned with and let's assume, for the sake of this discussion, that the blades were infinitely stiff and we don't have to worry about coning.

I also agree with you that the total lifting force must be independent of the rotor diameter and will be produced mainly at the outboard section of the rotor blades.

Let's simplify this problem even more so that we can concentrate on the pertinent issues more clearly: pretend that the rotor consists only of a blade section on the ourboard side that's attached to the mast by a simple rod (i.e., forget the inboard stalled area as well as the driving area of the blade and only keep the lifting area).

In this case the only quantities that determine the lifting force are the angle of attack and the airspeed (keeping the profile the same between the long and short blades). I can't but conclude that the airspeed which the lifting portion of the rotor sees determines the overall lift produced by the rotor (for equal angles of attack).

Which leads me back to my statement that a longer rotor turns by that amount more slowly than a shorter rotor that is required to make the tip speeds come out the same.

That would lead me to conclude that your safety margin for blade flapping is -- in first approximation -- independent of rotor diameter.

-- Chris.

Chris,

If we make enough assumptions we can come to any conclusion we want. In the two examples you are looking at large vs small rotor the lifting area is not equal. If they were equal you would be correct. The area on the large rotor that is producing a vertical component of lift is much larger. For this larger rotor to produce the same amount of lift it will have a dramatically slower air speed(and tip speed).

[C. Beaty]

Rotor tip speed ~ 66 x square root of blade loading.

Say 22’ rotor of 7“ chord and AUW = 500 lb.

Then blade loading =39 lb/ft² and tip speed = 412 fps and rotor rpm = 358 rpm.

Say 25’ rotor of 7” chord and AUW = 500 lb.

Then blade loading = 34.3 lb/ft² and tip speed = 386 fps and rotor rpm = 295 rpm.

Rotor tip speed sets top speed; a gyro won’t go much faster than ~ 35% of tip speed at which point the stick will be on or near the forward stop.

In the case of the 22’ rotor, rotor limited top speed is 98 mph.

In the case of the 25’ rotor, rotor limited top speed is 92 mph.

Disc loading sets the minimum flight speed; with a disc loading of 1 lb/ft², a gyro of limited power will fly quite slowly but isn’t much fun when the wind puffs. Feels like a sheet of toilet paper in the breeze.

[MichaelBurton]

Thanks Chuck,

I can never figure out how much math to post. I was getting ready to post the formulas but did not know if that would help produce understanding or just confuse the issue. By posting the results of the calculations you have produced simple proof. Don't know why I didn't t think of that.

[C. Beaty]

This is mostly the sort of arithmetic taught in high school, Michael, that most people were taught and then promptly forgot.

I remember learning how to extract square roots by longhand methods in the 7th grade and, having a facility for the arcane, still can but would bet most of my classmates couldn’t. A Japanese girl, many years ago, showed me how to work square roots on an abacus board.

But that’s all pretty silly with even the lowliest electronic calculators having a square root key.

[ckurz7000]

@Michael: Yes, I see now what my mistake was: I didn't account for the differing size of the lifting areas. A larger rotor whose tip speed is the same as that of a smaller rotor would produce excess lift due to its larger lifting area. Hence it needs to to have a lower tip speed.

@Chuck: To satisfy me I will have to see a derivation of the tip speed equation. Without that, it's just "proof by affirmation" :) I'll play around and see if I can come up with one by myself. If not, I'll have to get myself Gessow and Meyer....

Thanks guys for setting me straight, -- Chris.

[MichaelBurton]

I play with the math all the time. My wife Lauren is a math teacher and we attend regular math conferences. Her students and coworkers think we are a bit on the nerdy side. I just like to be able to have an intelligent conversation with her about the things she is doing.

The simple approximation only uses basic math but it does not tell the story. The problem requires multiple iterations on a calculator or a little help from Newton and Leibniz.

Most of my real math experience is ones and zeros. In my former occupation I was a software engineer. I spent 17 years working with ones and zeros. Now I get all the way up to 9.

[StanFoster]

Michael- I idolize you math wizards. I know just enough about it to realize there is a lot more to learn. I have always loved math and I have made a good living just using HS math. I would be dangerous with college level math in my head....:lol::lol:

You guys amaze me,....and its always a pleasure learning from your threads.


Stan

[C. Beaty]

Chris, lift coefficient = 6W/SρVt²

W = AUW, lbs
S = blade area, ft²
ρ = air density, slugs/ft³
Vt = tip speed, fps

DW rotor blades are twisted with a higher angle of attack at stall and are operated at somewhat lower tip speed than other rotor blades. The constant 66 becomes ~71 for the others.

Oops- the factor 6 comes from (½) ρV² and integration along the blade span (1/3). Not all of the blade is moving at tip speed.

[freebird]

Thanks for all the response. I will try to get the accurate weight of the machine and get back to Ernie. Concerning the vibration, the smoothness of my machine is one of the reasons I haven't just traded for smaller blades based on the input I have received. They are very smooth and I am a little afraid that my next set might not be so great.

I have considered the idea of adding more fuel. Of course if I had it, I would burn it and find myself landing in the same condition I am in now.

Thanks again.

[ckurz7000]

Chris, lift coefficient = 6W/SρVt²

W = AUW, lbs
S = blade area, ft²
ρ = air density, slugs/ft³
Vt = tip speed, fps

DW rotor blades are twisted with a higher angle of attack at stall and are operated at somewhat lower tip speed than other rotor blades. The constant 66 becomes ~71 for the others.

Oops- the factor 6 comes from (½) ρV² and integration along the blade span (1/3). Not all of the blade is moving at tip speed.

Hi Chuck, the lift equation to start from is L = (½) CAρV². That relationship is easy to derive, particularly since it is essentially used as a definition for the lift coefficient. As you point out, you need to integrate this along the span taking into account that V=wr (w=angular velocity of blade, r=distance from mast). Also, the infinitesimal planform area of a small blade section of width dr and a cord length of S is equal to dA = Sdr.

With this, the contribution of a small raidal blade section to the total lift force can be expressed as:

dL = (½)Cp Sdr w²r².

Integrating this, I get:

L = (1/6) CpSw²r^3.

This can be regrouped by noting again that Sr = A and wr = V:

L = (1/6) CpAV².

So, yes, I agree with you on the total lift force. What I still need to think about is the statement about the blade tip speed being proportional to the square root of the blade loading. But I wrote yesterdays posting late at night and this one just before breakfast. I surmise it is as simple as noting that L=W and then solving for V. So, just forget my question, I think I answered it myself.

That equation assumes a constant lifting coefficient (i.e., constant AoA) alsong the blade, of course, because C is a function of AoA, right? How valid is this assumption? It's probably OK in a fixed wing. In a rotor, there will always be a point where the blade is stalled, however.

Thanks, -- Chris.

[C. Beaty]

That equation assumes a constant lifting coefficient (i.e., constant AoA) alsong the blade, of course, because C is a function of AoA, right? How valid is this assumption? It's probably OK in a fixed wing. In a rotor, there will always be a point where the blade is stalled, however.

Thanks, -- Chris.Chris, of course lift coefficient varies along the blade span in a complex way. The number I use is based on observation; an empirical mean.

Perhaps someone can write a solvable equation that accounts for skewed flow, Reynolds number, inboard stall vs. μ, etc. I can’t.

[Doug Riley]

Here's another data point: I first flew my tandem Dominator with 28-foot blades (DWs, of course) and a Rotax 618. Solo, the RRPM in level flight was 285. The tip speed was then 418 ft./sec. or 285 mph. At an easy 70 mph cruise, mu was 0.24 -- similiar to a Bensen. The ship would do 100 mph level if pushed, for a mu of 0.35. Damn, right on the money.

With a disk loading of 1.1 lb./sq. ft., the gyro was in the gyrobee disk-loading range -- and felt like it. Rather marshmallowy, but certainly not dangerous for weekend flying and a few yanks/banks. I don't play around with low-G maneuvers, beyond those supplied by Mother Nature on a bumpy day.

[MichaelBurton]

Michael- I idolize you math wizards. I know just enough about it to realize there is a lot more to learn. I have always loved math and I have made a good living just using HS math. I would be dangerous with college level math in my head....:lol::lol:

You guys amaze me,....and its always a pleasure learning from your threads.


Stan

Not a real wizard more like a sorcerers apprentice.

[C. Beaty]

Here's another data point: I first flew my tandem Dominator with 28-foot blades (DWs, of course) and a Rotax 618. Solo, the RRPM in level flight was 285. The tip speed was then 418 ft./sec. or 285 mph. At an easy 70 mph cruise, mu was 0.24 -- similiar to a Bensen. The ship would do 100 mph level if pushed, for a mu of 0.35. Damn, right on the money.

With a disk loading of 1.1 lb./sq. ft., the gyro was in the gyrobee disk-loading range -- and felt like it. Rather marshmallowy, but certainly not dangerous for weekend flying and a few yanks/banks. I don't play around with low-G maneuvers, beyond those supplied by Mother Nature on a bumpy day.There is no magic in rotor rpm. The Kellett KD-1 with 40’ rotor ran at 200 rpm for a tip speed of 419 fps.

[C. Beaty]

For anyone interested in big, slow turning see-saw rotors, here’s a link to the Kellett-Hughes XH-17 heavy lift helicopter. A 130’ rotor turning at 88 rpm.

http://www.aviastar.org/helicopters_eng/mcdonnel_crane.php

[Timchick]

Here's a video on youtube showing it fly. It's around the 2 minute mark in the video.

http://www.youtube.com/watch?v=hvCMrt1JPwo

[Resasi]

No need for a RRPM guage, just count blades.

[L_Butler]

Chuck,

I have noticed that the Tervamaki performance program shows the opposite trend regarding rotor diameter. If you plug in a larger rotor diameter the flying envelope gets bigger, that is, both higher top speed and lower minimum speed.

If I remember correctly, Hollman's program shows the same results although I no longer have a working copy of that program to verify it.

The rotor rpm goes as expected, lower at larger diameter.

Larry

[C. Beaty]

Drag limited top speed would increase with rotor diameter, Larry.

[Gyro_Kai]

This is a great educational thread, I'm loving it.

Kai.

[ckurz7000]

Would be good to know how Jukka models the rotor. Drag is only one thing limiting top speed. Blowback angle (and associated stick travel limits) also come to mind. As are potential stability issues.

-- Chris.

[Passin' Thru]

...Drag is only one thing limiting top speed. Blowback angle (and associated stick travel limits) also come to mind. As are potential stability issues.

For what it's worth, That's my view on it also.
.

[L_Butler]

I'm not connecting the dots.

I don't believe the Tervamaki program considers blowback since it allows rotor pitch up to 15 degrees without problems (perhaps higher, I stopped there). Rotor stability may be included since the curve stops abruptly if the chord gets too large. Drag seems to be a factor since the rate of climb varies with the speed.

Leaving all other things constant and changing only the diameter, the program shows an increase in speed with an increase in diameter. The rotor rpm decreases with an increase in diameter.

I didn't try to do the math since the size of the display is very small and would lead to estimating errors. There is no numerical readout.

I'm confused by your formula (post #17) which seems to me to be at odds with Tervamaki's program.

Larry

[C. Beaty]

Larry, I was saying only that if top speed is limited to 35% of rotor peripheral speed, the point where most gyros will start to run out of forward stick, then naturally the faster rotor will go faster.

A larger diameter, slower turning rotor will have lower drag, both induced and profile and if drag is the only consideration, then yes indeed, the larger rotor will go faster.

Some of the 1930s gyros would go as fast as 50% of rotor peripheral speed because the wings unloaded the rotor.

[ckurz7000]

...I'm confused by your formula (post #17) which seems to me to be at odds with Tervamaki's program...

Larry, the discussion about the formula is just to show a general scaling law, i.e., that the tip speed of the rotor scales as the square root of the blade loading. This is certainly not to be used to infer a top speed of a particular rotor. There are more things than tip speed entering here (rotor stability and rotor drag for instance).

-- Chris.

[L_Butler]

OK, I was trying to infer a larger relationship based on a subset.

Thanks for the explanation.

Larry

[frankjhelms]

Free, from what I've read over the years, 305 RRPM on a set of Dragon Wings is too slow, suggesting you have too much rotor. Check with Ernie, but I think he usually wants to see 330 or more, and sizes rotors accordingly. There might be a shorter hub bar available which would get you back in the safe RRPM range.

This is all good info for us less experienced.

So doing the basic geometry: Tip speed = Pi * Blade Dia. * rot. vel. / 60 sec/min, if I get it.

Then 25' blades at 305RRPM are running at 399.24 fps tip vel.
and
23' blades at 330RRPM are running at 397.41 fps tip vel.

Assuming that the two sets of blades use similar construction and materials, the 25' blades would only mass 1/12 more than the 23's . Since the centrifugal force would be higher in the longer blades, because of their higher tip speed and mass, would the slightly increased lift cause greater blade flex?

I'm amazed that the slightly longer blades would have such a tendency to structurally fail, as was stated earlier.

Can anyone help explain this please?

Thanks for the benefit of your experience again. I know I have a lot more to learn.

[C. Beaty]

Centrifugal force varies as rpm² so the shorter blades will generally have the greater centrifugal force and operate at a shallower coning angle.

CF = W x R x rpm²/2900 (R being the distance from center of rotation to blade CG)

Coning angle is part of the problem with longer blades on lightweight machines. Greater coning requires more undersling and exacerbates shake problems. Extra tip weight is one way out.

[L_Butler]

Chuck,

I have thought that typical blowback angle was about 3 degrees or less. Yet it just occured to me that when the stick is at the forward stop and forward airspeed is low that the blowback angle must be much greater.

What confuses me is how does the rotor assembly maintain adequate airflow so as to maintain flying RPM at low forward airspeed. You have mentioned that in the past you have increased the pitch on your rotor blades. You noted that with a high pitch on your rotor blades you maintained virtually no forward airspeed and only went vertically with changes in throttle.

How literal is vlrtually no forward airspeed?

I have experienced vertical descents and understand how the rotor keeps moving, but I used a lot of forward distance to get up to that point. How do I gain altitude with an unpowered rotor with virtually no forward velocity?



Thanks,
Larry

[C. Beaty]

Blowback/flapping angle, Larry, depends upon the ratio of rotor peripheral speed to forward speed (mu).

The experiments I’ve done were at ~20 mph with the rotor cranked up against the pitch adjustment stops. Unfortunately, I didn’t have much instrumentation at the time so don’t know the exact rotor rpm but it was slow; similar to rotor startup when you’re nearly banging the flap stops.

The gyro was quite nose high even with the stick against the forward stop because the rotor disc angle has to be high to develop the lift at such low airspeed.

Others have performed the same experiments with old Rotordyne and Stanzee blades. EA VanHoten use to say it was like screwing itself up and down with the throttle.

[L_Butler]

Chuck,

OK, 20 mph is virtually no forward speed.

As I experiment with various pitch setting on my blades (when it's warm out, not this time of year), I considered retreating blade stall as the primary pitch limiting mechanism. However on a heavy machine like mine, blade yielding might be a larger concern in adjusting the pitch.

Are you aware of any failures due to material yield on a slow turning blade?

Thanks,
Larry