What is the relation between a helicopter's length and rotor diameter?

Question

I was looking at a couple of helicopters on Wikipedia (specifically the Boeing A160, the Robinson R22, and the Sikorsky S-46) and I noticed the main rotor diameters seem to be pretty similar to the helicopter length (see below).

Is there a reason for this, or is it just coincidence? I thought it might be that helicopters are just long enough for the tail rotor to not interfere with the main rotor, but that doesn't seem to work out, because the rotors aren't quite centered over the helicopter.

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Helicopters' length and main rotor diameter legend:

                Length     Rotor Diameter
Boeing A160      35'0"        36'0"
Robinson R22     28'8"        25'2"
Sikorsky S-64    70'3"        72'0"

Answer 1

Important. I am a helicopter pilot, with no expertise or experience in design so I can give you reasons for this, but not design detail.

Most design decisions are compromises. Helicopter rotors are definitely compromises.

What is the aim of the rotor design? To have the smallest possible rotor to achieve the performance requirements of the craft.

What limits the smallest size? Let's assume that the blades are as efficient at generating lift as you can make them. There are only 2 ways to increase lift for any given blade at any given angle of attack. That is to increase the length of the blade or to move it faster through the air, i.e. to make the rotor spin faster.

What limits the speed at which the rotor can rotate? As the blade tip speed gets faster, drag increases with the square of the speed. Increased drag means increased power required which means heavier engine and heavier gearbox. As speed moves to a high percentage of supersonic, turbulence and therefore drag increases enormously. The longer the blade, the lower the possible rotor RPM since the tip approaches supersonic speed more quickly.

Why not just increase the length? Because the blade becomes increasingly difficult (and expensive) to manufacture to handle the loads on the blade and the heavier they become requiring more robust and heavier rotors hub assemblies.

The inner part of the rotor also produces little lift since it is moving relatively slowly and since lift decreases with the square of the speed, the lift generated falls away rapidly as you move to the inside portion of the disc. As you increase the length of the blade, without being able to increase the speed of the disc as above, the area of the disc which is "useless", increases as a proportion of the overall disc size. Therefore, more power is needed to rotate the increasingly large useless area of the disc.

The lower the disc loading, the more efficient the helicopter is in the hover. The disc loading is the ratio of the weight of the helicopter and the area the rotor disc describes as it rotates. The disc loading should be as low as possible to reduce the required strength, and thus weight, of the blades especially as the weight of the helicopter increases under positive G which in turn increases the disc loading.

Non-performance considerations. Parking; hangar space required; ability to operate in confined areas.

Given these (and other design parameters), the rotor sizes you quote will have been arrived at by factoring each of the variables to find the best compromise, according to the designer, between them to achieve the desired performance goals.

Therefore, I don't believe that there is a relationship between the fuselage length and rotor size, possibly with some influence from the need to park and hangar the resulting craft.

[EDIT] I've been hoping that some better informed answers would be added. As there are none, I'll continue with my simple pilot guesswork.

What is the aim of the fuselage design? To have the smallest possible fuselage to achieve the performance requirements of the craft.

What limits the smallest size? How many crew? How many PAX? Level of comfort (utilitarian - R22, or comfortable - Long Ranger). Fuel load. Engine and gearbox size. Cargo and other payload. Baggage stowage?

What limits the maximum size? Weight. Profile drag. Cost to manufacture.

Non-performance considerations. Parking; hangar space required.

Answer 2

Disclaimer: I am a copter pilot, but not a designer

The rotor generates a certain amount of torque that would swing the body in the opposite direction of the turning rotor (Newton III).

The pedals are called anti-torque pedals, which counteract this behavior, and allow the body of the copter to be yawed independently of the rotor. In a copter which has either a tail rotor or a ducted fan (rather than two main rotors), the amount of force generated by the tail must be sufficient to allow a 360 degrees of yaw in nearly any regime of flight. Increasing the distance between the main rotor and the tail rotor increases the effectiveness of the anti-torque pedals. A longer tailboom would allow a smaller tail rotor, and require less engine power to be diverted by the transmission, and vice-versa.

Answer 3

If the helicopter has a main rotor and a tail rotor:

• The main rotor is attached very near the centre of gravity.

• The tail rotor needs as long a moment arm (tail boom) as you can give it, but needs to be balanced weight-wise with the business end of the helicopter, where the pilots sit.

• The tail rotor axis is preferably mounted at the same height in the helicopter as the main rotor - outside the main rotor radius of course. This is done to prevent a rolling moment to occur when lateral stick compensates for tail rotor side force is the hover.

So yeah, for that configuration that's what you end up with, roughly similar dimensions for fuselage length and rotor diameter.

Not for this one though: it has two rotors, each one with a diameter 40% wider than the fuselage length. They do have a stubby tail boom to provide directional stability via the vertical tails, otherwise this helo could just be shaped as a laundry tub, really.

Answer 4

Just to add to some prior comments.

1. Larger main rotors are actually desirable aerodynamically. They burn less fuel per unit weight lifted. Main rotors create thrust by throwing air downward, and throwing a larger volume downward at a lower speed (i.e. large rotor diameter) is more efficient than throwing a smaller volume down at a higher speed (smaller rotor).

2. A smaller main rotor can also carry more weight by increasing the chord length of the blades (in addition to other things mentioned).

3. Increasing helicopter length gets the tail rotor further aft which makes it more efficient at countering main rotor torque. A tail rotor twice as far aft can counter twice as much torque with the same tail rotor thrust. Of course, making the helicopter longer adds weight and hence increases main rotor thrust & torque requirements, so there's a balancing act here.

4. Regarding the rotor speed comments. Noise and advancing blade compressability are normally limit the rotor speed. Blade tips need to stay below Mach 1 for reasonable aerodynamic loads.