# Why don't helicopters prefer shorter rotors with more blades? [duplicate]

My understanding of helicopters is that, despite theoretically increasing efficiency, longer blades are worse in practice than short ones in every respect (except, perhaps, cost):

1. Longer blades are more prone to vibration and resonance dynamics, if for no reason other than that their rigidity is reduced by length, holding all else constant.

2. Longer blades provide less operating clearance.

3. Longer blades not only stall before shorter blades (retreating), but also hit the Critical Mach number at lower air speeds (advancing).

4. Fewer blades require higher rotational speeds for a given "rotor disk" area, which is inefficient from not only an aerodynamics perspective but also, presumably, a transmission-and-control perspective.

I would imagine that in the limit it would be optimal to run something more like a ducted turbine segment, where the swept area is virtually covered in blade surface (i.e., maximizing the number of blades over the swept disc).

Noting that in practice blade size seems somewhat proportional to the body size of the aircraft, I'll deduce that in practice the bulk of the downforce needs to be generated some minimal distance away from the aircraft's body, though with some attention to the body's vertical aerodynamic aspect it seems like that could be reduced. I guess tilt-rotors could support this hypothesis since their rotors are positioned at a distance from the body and they use smaller rotors, although it seems like they still use blades as large as possible given the wing size and body configuration.

• @fooot - The best answer to that question is inspiration for this question; it does not answer it (as far as I can tell). – feetwet Oct 27 '15 at 0:18
• @feetwet, that answer, among other things, states that “…improve efficiency, which you could do by making the blades longer”. – Jan Hudec Oct 27 '15 at 6:01
• voting to leave this question open. The question is more precise, and it attracted better answers that the other inspirational question – user23573 Oct 27 '15 at 6:51
• – fooot Oct 27 '15 at 14:34
• @feetwet, A smaller diameter rotor with a lot of blades rotating slowly can stall like the wings of a plane. So you can not increase the number of blades reducing the RPM and the propeller diameter (to keep the power and thrust constant) because you propeller will reach the stall point. – Robert Werner Oct 27 '15 at 20:27

The rotor works by accelerating air downwards, therefore creating an upward reaction force on the blades that lifts the craft.

The lift force is equal to

$$L = \dot{m}\Delta v$$

where $\dot{m}$ is mass flow rate through the rotor and $\Delta v$ is the change of speed of the air. To accelerate the air to that speed, it has to give it kinetic energy. This requires power

$$D = \frac12\dot{m}\Delta v^2$$

(the induced drag).

Now a rotor with smaller diameter will be able to affect less air, so the $\dot{m}$ will be lower. To produce the same lift, it will need larger $\Delta v$ and therefore it will need more powerful engine (up to a point, because longer blades will have higher form drag that will eventually outweigh the reduction in induced drag) and, more importantly, burn more fuel.

The blades, like wings, affect air to a significant distance above and below them, so you don't need many blades to use all air within the rotor area. But no matter how many blades you add, they will still only affect the air within the rotor area, so the efficiency won't change much.

As far as tiltrotors go, they have relatively small rotors and that makes them awfully inefficient in hover. But they don't spend most of their time hovering, they spend most time flying somewhere and in the fixed-wing mode they are faster and more efficient, which outweighs the worse efficiency during take-off and landing.

• So the efficiency of a rotor blade is proportional to its length? Meaning the only reason powered rotary wing aircraft ever use more than two main blades is because they have reached some structural limit on their blade length? – feetwet Oct 27 '15 at 12:24
• @feetwet, the blade length is (in addition to structural strength) limited by tip speed and then only so much lift can be generated by single blade, so more blades are needed for higher lift (and thus capacity). But efficiency is proportional to the rotor diameter, so larger rotor is preferred, because it provides lower fuel consumption and thus longer range and lower operating cost. – Jan Hudec Oct 27 '15 at 12:41

The number of (main rotor) blades in a helicopter are dependent on a number of parameters; Usually there are some major issues with having a large number of blades in a helicopter though:

• One main reason is efficiency- In general, lesser the blades, more efficient the system- as it changes the momentum of more air mass i.e. accelerates more air by a lesser amount (akin to the bypass of turbofan engines).

• In general, the performance of the helicopter rotor system is affected by solidity (i.e the ratio of blade area to total disc area) rather than the number of blades.

• More blades means more complex rotor hub (more parts usually translate into more problems- maintenance and otherwise) and more interference in the inboard region of the blades. Also, the rotor hub drag is increased.

• One thing you're missing is that the blade velocity $V$ (in $L \ = \ \frac{1}{2} \ \rho \ V^{2} \ S$ ) is in itself dependent on the blade length (and rotational speed, through $V \ = \ R\omega$). This means that as the blade length reduces, they have to rotate proportionally faster to produce the same lift- thus in reality, the tip speeds of smaller blades will be more. Usually, the inner third length of a rotor blade contributes very little to lift.

• As far as vibration is concerned, (though it is better to have more blades) the whole rotor system has to be taken as a unit rather than as individual blades and the most important consideration is the rotor speed and its harmonics rather than the blade length.

• Holding all else constant, my assumption is that a reduction in disc area (due to shortening blades) can be compensated by the addition of blades instead of by an increase in rotational speed. I assume, based on the density of blades in efficient turbine fans, that wake interference is a solvable problem, even if it requires a stator or something like that? – feetwet Oct 27 '15 at 0:25
• Regarding the rotor hub drag and complexity: Is this entirely an artifact of aircraft motion translational to the rotor plane, and the need to change each blade's angle of attack throughout a single rotation during translational flight? If not, then what? Because even variable-pitch propellers don't require extraordinarily complicated or large hubs. – feetwet Oct 27 '15 at 0:30
• @feetwet - The fifth point above explains why that assumption won't hold. The tips of the blades travel faster than the portion closer to the hub. The difference in velocity is linear based upon rotor diameter, however the amount of energy (and hence, the amount of lift/thrust) grows with the square of velocity. So to cut your rotor diameter in half without adding rotational speed, you need 4x the number of blades. That's if you can keep the mass of your craft exactly the same. Realistically your mass would increase, meaning either even more blades, or more rotational speed. – aroth Oct 27 '15 at 1:43

The blades of a helicopter are long, narrow airfoils with a high aspect ratio, a shape that minimizes drag from tip vortices (see the wings of a glider for comparison). They generally contain a degree of washout that reduces the lift generated at the tips, where the airflow is fastest and vortex generation would be a significant problem.

source: Wikipedia.

• Hence a larger number of blades moving more slowly would be attractive, right? This seems like an elaboration of point #4 in the original question. – feetwet Oct 27 '15 at 12:17
• @feetwet, no, they wouldn't, because the thing that minimizes the “drag from tip vortices” (the vortices are effect, not cause of the drag) is the span. – Jan Hudec Oct 27 '15 at 12:21
• @JanHudec - maybe this warrants a separate question, but isn't unmitigated tip vortex an artifact of long blades? With sufficiently short, rigid blades presumably one could add wingtip devices to counteract tip vortex? Or, in the limit, use a ducted rotor (as suggested in the original question)? – feetwet Oct 27 '15 at 12:34
• @feetwet, no, the vortex is simply result of the fact that the air within the rotor diameter is accelerated downwards and the air outside of it is not. And, as I explained in the other answer, smaller rotor needs to accelerate the air to higher speed, causing stronger vortices (Site note: ducting does not change the picture much; there are still two air masses of different velocity). – Jan Hudec Oct 27 '15 at 12:47
• @JanHudec - Are you sure? My understanding is that wingtip vortices which reduce wingtip lift and waste power creating "washout vortices" are a function of air being allowed to slide centripetally over the end of the airfoil, and that those losses can be significantly mitigated using wingtip barriers. Of course downwash vortices are a separate phenomenon that are primarily a function of the rotor speed. But as suggested elsewhere here: to first order, for a given rotor disc area and blade speed one can increase downforce without increasing rotor speed by adding blades, right? – feetwet Oct 27 '15 at 13:04