Is it possible to design a helicopter with fixed rotor blades only (no blade angle/flap/pitch)?

Question

I am not familiar with helicopter rotor design but I wonder if it is possible to build a working/flying helicopter with fixed rotors that cannot change the blade angle, flap, pitch or adjust blades otherwise?

I am curious whether the changes in rotation speed would suffice for controlling the aircraft. I guess the cheap RC helicopter models may use such simple design, but is it possible to scale that up to 1:1?

I mean propellers that are solid state and cannot be adjusted in any way except changing their rotation speed, like plastic props used in RC modelling. I do not mind if the whole helicopter design is a traditional main rotor + tail rotor or a coaxial rotor design.

I am interested in 1:1 scale size (at least the Mosquito personal helicopter size). Has anyone tried such simple design?

Also I consider electric propulsion where the RPM changes may be quicker that with internal combustion engines.

Answer 1

Scaling laws are your enemy here.

Model helicopters can be controlled with changes in rotational speed, but for full-sized helicopters the energy needed to quickly change the speed of their rotors relative to the energy needed for lift creation is far too high. In detail:

The moment of inertia of a scaled-up rotor changes with the fifth power of length. The mass of the rotor changes with the cube of the linear scale, and the moment of inertia adds another factor proportional to the square of the linear scale.

A bigger object also needs slower changes, but time scales only with the square root of the linear scale. Next, the engine power available for speed changes will scale with the 3.5th power of scale*.

This still leaves a deficit of one power in the engine power available for speed changes when the helicopter is scaled up.

Lift asymmetries in forward flight can be dealt with by adding a second, counter-rotating rotor, but scaling laws can not be designed out. As Jan Hudec points out, you need to repeat the same trick for forward-backward lift shifting, so four rotors would be the minimum to control this type of helicopter in all directions.

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* Proof: Thrust must exceed weight, so thrust goes up with the third power of scale. Rotor disk area scales only with the second power of scale, so a higher acceleration through the rotor disk is required to create more lift per rotor area. If we look at the power required in the static case $$P_{min} = \frac{\eta_{Prop}}{T_0}\cdot\sqrt{\frac{\frac{4\cdot T_0}{\pi\cdot d^2}\cdot g}{2\cdot\rho}}$$ and insert the scaling factor in all scaleable variables, a power of 3.5 remains for the minimum power $P_{min}$. This is more than the increase in static thrust because the efficiency of the rotors declines with higher disk loading.

Answer 2

that can not flap or pitch or adjust otherwise?

Yes, you can design one like that, but you won't get many people to fly it.

In the early days of helicopter flying, any number of crashes occurred before the designers began to account for the problem of differing airflow over the retreating and advancing bladed in forward flight. If you don't change the pitch angle, the lift changes constantly with the change in airspeed coming over the airfoil.

Without pitch change (called feathering) you will have continually changing lift values rather than a stable "disc" that makes the helicopter controllable. In the picture above, the blades on the "red" side would have more lift than on the "blue" side, so the helicopter would naturally roll or pitch, with a stronger rolling motion the faster forward you are going. Flapping is a reaction to the lift increase as the blade advances, and is needed to avoid that same kind of imbalance between advancing and retreating blades. (Getting that right is some serious engineering, test, and development work). It also addresses that fact that you don't have a perfect blade track, and thus you will be "flying" each blade into the vortices of the one preceding it.

Answer 3

Yes, controllability can even be accomplished with only one (rigid) rotor.

Degrees of freedom

In a three-dimensional space there's generally six degrees of freedom (DoF):

1. forward/backward
2. left/right
3. up/down
4. roll
5. pitch
6. yaw

Most aircraft allow engine rpm and velocity to be controlled separately (variable pitch propeller/rotor) as a seventh DoF.

7. rpm

Multi-engine aircraft can have even more degrees of freedom. In your proposed helicopter design, the pilot can only use main and tail rotor rpm to control seven DoF.

How to control seven DoF with only two levers?

Turns out you can't. At least not independently. We'll have to sacrifice the independence of some of them.

5 DoF

The most obvious thing to drop is the independence of horizontal movement and attitude. To move horizontally, we can just roll/pitch the whole chopper in the desired direction and apply upward power. Most real world helicopters use this configuration.

4 DoF

When we're not constrained by the rotor's tip speed, its moment of inertia or the engine's useful rpm range, we can drop their independence next. This is the case with most electric RC helicopters. Quadcopters, for example, have four control inputs (the four engines' power settings) and thus allow independent control of the four remaining DoF:

3. up/down
4. roll
5. pitch
6. yaw

Other 4 DoF configurations, like two coaxial rotors plus cyclic pitch and roll, achieve the same level of controllability.

3 DoF

The next thing usually sacrificed is the ability to perform coordinated turns. A lot of fixed wing RC aircraft don't have ailerons and thus allow only skid turns, but are pretty well behaved otherwise and still easy to fly. The same applies to helicopters, so we ditch cyclic roll control.

2 DoF

Things become a bit harder now. We had reduced our helicopter to three control inputs (main rotor rpm, tail rotor rpm, cyclic pitch) and it was still pretty capable and useful. Now we loose something valuable: the ability to contol forward speed. We fix the main rotor at a slightly forward position, so our helicopter moves slowly forward at all times, just like a gyrocopter. We can't hover in place anymore nor fly fast, and we need a runway to take off and land. We still reach our destination though.

1 DoF

Things. Become. Nasty.

When we give up our tail rotor, the helicopter starts turning around itself at high speed. A human pilot will fail to keep it under control, and the passengers won't enjoy it either. It is, however, still possible to move it around in a coordinated manner: every time the helicopter points in the desired direction we momentarily increase power, making it move forward a little faster, and vice versa. Modulating power means the helicopter will violently move up and down, but average power over a full turn still allows us to control its average altitude. As already stated, timing and magnitude of the power variations allow for position corrections.

Such a helicopter has actually been built by the ETH Zürich. Enjoy.

Answer 4

It is indeed possible. One of the first helicopters was the Petróczy-Kármán-Žurovec PKZ 2 Helicopter, fitted with two contrarotating, coaxial rotors that had fixed blades, with no provisions for flapping or pitch change:

https://oldmachinepress.com/2012/09/24/petroczy-karman-zurovec-pkz-2-helicopter/

Answer 5

Theoretically yes, you could build a full-size quadcopter with four fixed pitch rotors, and control it through independent variation of the rpm of each rotor. The power density now achievable in permanent magnet electric motors (eg, 25 hp in a 85mm diameter motor) makes it seem possible to build a small, one man quadcopter with a single motor/generator, but I don't think it would be a very useful machine. The larger and heavier the rotors, the more inertia they have and so the more pronounced the lag in control response that would result in comparison with a conventional helicopter.

Answer 6

Yes and no.

I've never seen such a design for a large helicopter but there are plenty of micro sized RC helicopters which utilize such a scheme using a pair of contra rotating main rotors and a smaller tail rotor to control pitch.

This kind of design works fine, albeit difficult to control for Palm sized toys but does not scale well for larger vehicles.

First off, while the design does offer yaw and pitch control, it does not offer a means of roll control making flight - and in particular hovering - much more difficult. Second, helicopters are designed with rotor blades that can flex, flap and feather to dampen vibrations and yield a smoother ride with less chances of structural damage from turbulence, mishandling, etc. than a fixed rotor design.

There are also the problems in cruise with lift asymmetry over the rotor disc, the is would create unwanted rolling moments which the design could not cope with, as mentioned above.

Answer 7

Please see the Japanese product Gen H-4 which has no pitch control but only speed control - that too differential speeds to take care of yaw. This unique system not only has tail rotor but the tail boom also is absent.

Answer 8

I think it is possible to design such a helicopter with a fixed rotor blade only. Yet it won’t fly very well. And you’ll be facing some difficulties in controlling it. In order to make a more complex helicopter, you’ll need to count a lot of things, the moment of inertia, for instance.

Answer 9

Thinking outside the box:

If you can't effectively brake the rotors could you break the airflow that applies the lift?

Given that the amount of lift is controlled by the air flow I see no reason why it wouldn't be possible to interfere with that using separate structures above and/or below the blades. By raising or lowering this interference you could adjust the amount of lift by increasing/reducing the distance between the interfering structure and the blades themselves. You'd no longer need to tilt the blades themselves, which could improve the structural integrity. The distance of the interfering structures on the right and left could be differentiated to compensate for forward (or reverse) motion.

Unfortunately I have no way to establish whether this could be implemented without risking the blades hitting the interfering structures or whether it could apply enough of a difference to the lift. I'm no engineer, but there would obviously be other risks to at least discount, particularly as I'm unsure whether it would be possible to make the interference continuous, otherwise resulting in stress on the blades as they bend slightly each time they move into/out of the interference, which could also result in vibration build up.