Single blade rotor - the physics.

[AdamFrisch]

They've been tried and shown to work, but no wider use has been forthcoming. The MBB 109 is as far as I know the only full size experimental. There have been loads of RC heli experiments:

-qhEsuhi1PU

(jump to 4:58 to see just how silent it seems to be).

But, just to satisfy my own curiosity, help me get some basic helicopter blade construction facts straight in conjunction with this design:

I would assume that a single blade (with a counterweight) would work much like a semi-rigid 2-blade would in lead/lag. Meaning, there wouldn't be any need for the blade to lead or lag as it would be "swallowed" by the opposing "blade" (as in the counterweight).

However, the blade would flap. Would this have to be compensated for by a hinge, or would this also be "swalloved", so to speak.

I'm trying to establish if there's a need for any hinges at all in a single blade system?

Thanks for your input.

[TeeS]

Hi Adam

I can't help with the Physics but suspect you meant the Bo-102 and 103 rather than MBB109.

Cheers

TeeS

[AdamFrisch]

I think you're right. My memory isn't very good and I'm far to lazy to do any research:)

[delta3]

Adam

I think the BO-102 was a "hover training device"
I would be very doubtful it would be capable of achieving any speed.

As far as the construction would be:

flap : I can hardly see how a helicopter would be capable of forward flight without cyclic control which means flap...

lead-lag : is a consequence of flap. Since there is no symmetry as there is in a two bladed heli, Coriolis could be a problem depending on the detailed construction.

I think the BO-102 setup is a stiff rotor with one central flapping hinge. This forces symmetry in flapping which is beneficial for Coriolis, but at the expense of bending moments which are 10 times greater than Coriolis forces....

Looks a lot more simple to me to put two blades....

[Phil77]

delta3:
without doubting the validity of your concern, as I know you're quite the theorist ;-)
...but why would flapping be an issue? I mean blades in all fully articulated rotor systems flap independently, therefore lead-lag independently. same goes for cyclic control and even coriolis - as long as it rotates fast enough I suppose.

[delta3]

Phil

My concern is the total lack of symmetry at the hub.

A stiff setup leads to big bending forces between an aerodynamically active blade and a basically dead weight that only sees inertial forces. The magnitude of these bending force depend on the target forward speed and the result flap.

One of the nice things about rotor blades is that generally speaking tend to "compensate forces locally", that is aerodynamic and inertial forces, which reduces forces (at least the first order harmonic forces) drastically, and allows for light efficient blades. This also allows as you suggest articulated setups

In order the let the blade go freely one could allow some elasticity between blade and counter weight, but the dynamics of the two are different.

One can easily setup the math model for this, but "ironing out" all the hurdles created by this set up makes me wonder why one would want to do this to begin with: what is wrong with putting two blades.

As Adam suggested the only possible gain could be less blade vortex interaction.

d3

[Dave_Jackson]

Adam,

Thanks for the video link.

It is said that the single-blade rotor gives the best lift to weight ratio, however it creates severe vibration in cruise.

This may answer your question;
Helicopter - Outside - Single-Bladed Rotor - Complete Rotorcraft (http://www.unicopter.com/B472.html)

This maybe too much; :)
Single-Bladed All Electric Rotor (http://www.unicopter.com/ElectroRotor.html)


Dave

[AdamFrisch]

No tracking, potentially less vibration and if that RC guy's link claim is anything to go by, less power needed.

Help me understand - with cyclic input comes flapping and as it goes around and flapping to equality - would this be true for a single blade system, or does it need the second blade to flap to equality, so to speak?

[delta3]

Dave

The severe vibrations in cruise are produced by the different dynamic behaviors of the two different halves. These differences look nearly impossible to compensate in any reasonable dynamic range, even putting a quite complex head.

d3

[Dave_Jackson]

Hi d3,

Yes, I agree. (http://www.unicopter.com/1496.html)

It's too bad, because it would have been nice to put the weight of the counter-weight to use by making it an electric motor.

Dave

[delta3]

Quote from your link: "Musings on the single-blade rotor and 1P vibration."

This text indeed contains some of the scenario's of what can go wrong, first order oscillations in all directions.

In the horizontal plane because of the non vertical lift,
but also vertically (even if one would allow elasticity or hinges as the text suggest), because even if the system allows easily to construct an inertial equality, by design there is no aeroDYNAMIC equality, so flapping will also create vertical vibrations: there is no blade going down to compensate the up going blade loosely speaking, even a hinge still transmits vertical forces.

Rotors are quite complex dynamic systems....

Looks like a hell of a job to get that fixed...

d3

Added : scaling changes dynamic behavior quite a bit. A RC model will show mostly qualitatively similar effects, but quantitatively quite different because length, mass, surface, weight, strength etc doesn't not scale equally and this will influence resonance and vibrations quite a bit. So at the speeds shown vibrations could be ok for the RC model, but this will no longer be so when going full scale.

[NickLappos]

The Rotordyne had rotor tip ram jet thrusters fed fuel along the blades. The Hughes H 17 (https://en.wikipedia.org/wiki/Hughes_XH-17) used tip jets that were fed air from engines on the fuselage. I think the Rotordyne was the first machine to fly with ram jet tip thrusters, the second was probably the Dutch single rotor blade helicopter (!) the NHI H-3 Kolibrie (https://en.wikipedia.org/wiki/NHI_H-3_Kolibrie) which was relatively successful and flew in the late 1950s. Seated in that picture in Wikipedia is Rene Van Der Harten, a founder of KLM Nordzee, a personal friend and one heck of a pilot. It takes lots of courage to strap yourself into a one-bladed tip jet helicopter in the 1950's!

All these machines had no torque and so no anti-torque devices. I would suppose they would fly quite similarly. They were all reportedly able to extremely efficiently turn fuel into noise.

[meleagertoo]

Kolibri had a single rotor blade???
I wouldn't normally dream of questioning Nick Lappos but all the pics I can find of the NHI H3 clearly show a conventional two-blade configuration.
I do recall a single blade helo from the '50s, with a 'cannonball' counterbalancing the blade. A Bolkow?

Edit: to point out that although it's stated the NH17 and the Kolibrie had "no torque and so no anti torque devices" they both had tail rotors as bearing friction is a factor in the hover and exerts a significant torque reaction to the fuselage and has to be countered, as we know from t/r drive failure practice.

I notice that the Kolibrie had a single-bladed tail rotor which is perhaps where the confusion arose.

The single bladed helo was the Bolkow 103.

[Winemaker]

The single bladed helo was the Bolkow 103.
That's pretty interesting. Found a good photo of it.

https://cimg4.ibsrv.net/gimg/pprune.org-vbulletin/1000x691/bolkow_00ca16d396fe65687c049e08e3c8e0381eadbeba.jpg

[TeeS]

That's pretty interesting. Found a good photo of it.

https://cimg4.ibsrv.net/gimg/pprune.org-vbulletin/1000x691/bolkow_00ca16d396fe65687c049e08e3c8e0381eadbeba.jpg
Except I think that is the Bo102 fixed base trainer Winemaker.
Cheers
TeeS

[Winemaker]

Except I think that is the Bo102 fixed base trainer Winemaker.
Ah! Thanks. I was concentrating on the counterbalanced rotor and didn't look at the base.

[Senior Pilot]

Welcome back, NickLappos and a very Happy Birthday, too 🎂

Off topic re rocket tips as the S-57 was to be air driven tips, but Igor Sikorsky had some research and experiments with single blade helicopters and there is a page dedicated to them here (https://www.sikorskyarchives.com/S-57%20CONVERTIPLANE.php)


https://cimg0.ibsrv.net/gimg/pprune.org-vbulletin/490x227/cfaedb43_5103_44c5_9b82_77b9f732d91f_4b90923f9b734f21b92e7b4 90b304d391ef77e47.jpeg

[megan]

Good to see your return Nick, you have been missed.

[Ascend Charlie]

I cannot understand how the force can be resolved - the blade generates lift, and is sort of based on its CG, which is a distance from the rotor hub. It must generate a rolling moment, which on a two-bladed machine is balanced by the same force from the other side. But without an opposite blade, there would be a force that is moving around the mast 5 times a second.

10 years ago, Adam Frisch asked:
with cyclic input comes flapping and as it goes around and flapping to equality

Flapping to equality only happens if the cyclic is held steady, and it leads to dynamic instability and eventual destruction - move the cyclic in the direction you want to go, and you solve the problem

[MeddlMoe]

Many of the lift and cruise concepts for eVTOLs want to stop the propellers in forward flight. A single blade propeller may be usefull, because it could implement a flapping hinge, while still avoiding divergence of the forward facing non-rotating rotor blade. Implementing a flapping hinge would allow to reduce the mast moments, which can be quite high on a rigid propeller.

@Ascend Charlie: The aerodynamic moment can not be transferred with a Flapping hinge that is located in the rotor center. The moment is reacted by a constant flapping angle (conical rotor blade "disk"). The blade goes up and the counterweight goes down. The centrifugal force acting on these two weights creates a moment that counteracts the moment from the non-central aerodynamic forces.