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

Question

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.

But all helicopters have few blades of significant length. So: What are the advantages of longer blades, or disadvantages of shorter blades, that lead to the rotor designs in common use?

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.

Answer 1

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.

See also: Is there any equation to bind velocity, thrust and power? (via Energizer777's deleted answer).

Answer 2

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.

• As the number of blades increase, the interaction of subsequent blade with the advancing blade's vortex increase (i.e the blade flies into the preceding blade's wake), which affects the lift produced.

• 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.

Answer 3

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.