For a fixed radius more blades can provide more lift but more blades also increase the cost. To get more lift you need a stronger engine. Another option to ger more life is it incre
A Sea Stallion is a large heavy-lift helicopter with an empty weight of 10.7 tonnes and a max takeoff weight of 19 tonnes. It has a rotor with a diameter of 22 meter with 6 blades
A Huey is a medium helicopter with an empty weight of 2.3 tonnes and a max takeoff weight if 4.3 tonnes. It has a rotor diameter of 14.6 meters with two blades.
So to the Sea Stallion rotor need to lift 4.4x the weight of a Huey rotor. It manages to do that with 3x the number of blades and longer rotor blades.
Short answer; weight, more blades mean more thrust, but more expense to build and maintain and more weight that needs to be moved around, costing fuel.
Long answer; fewer blades are desirable as they generate less drag and have less weight. Ideally a helicopter would use only one blade, but imaging a single blade spinning at high speed and you can probably see the issues that would create
As the weight of a helicopter goes up, the speed at which a set of rotors must be spun goes up. Wind resistance goes up with the square of the speed with which something is going through the air, so higher rotation speed mean exponentially more energy spent to spin them. This becomes far worse as the tips of the blades approach the speed of sound.
After some speed, as determined by the engineer, it becomes more practical to add more blades and reduce the rotation speed accordingly
More blades means that you generate more thrust (move more air) but this comes at a loss of efficiency, more blades means more drag so you need more power. Ideally you want less blades because then they don’t interfere with each other aerodynamically.
The problem then becomes the speed of sound. As you add more power you need a bigger propeller, but eventually it gets too big and fast and the tips break the sound barrier. This stops the blades from working.
The best solution to this problem is to add more blades, because then you get more overall surface area without having to increase the overall size of the props or make them spin faster. So it becomes a trade off.
More blades is more expensive though, and the more complex the shape the higher the cost. Such rotor blades are made out of composite materials, while the original Huey’s 2 blades are made mostly of aluminum, very cheap and easy to maintain by comparison.
Another advantage is that more blades makes it quieter, and that is good for both passengers and people on the ground.
Normally its converting the power of the engine into thrust for the craft. Smaller helicopters dont have a use for 4 or 6 blades where as large lifting helicopters wouldnt be able to transfer the power from their engines efficiently with only 2 blades.
Truthfully there is no magic number and is has to do a whole lot with engineering for power, sound, feeling, vibration, etc. Something like a UH-1 isnt going to have the same mission as a sea stallion, thus different blade designs, length, profiles, etc.
As for adding more blades to a helicopter, i am unsure if you would gain anything as another blade would in theory be another lifting surface, but weight and drag to overcome as well. The same holds true for planes. A 2 blade prop vs 3 have very little difference in most applications other than noise in the cabin.
More blades is more lift but less control. Less blades is more control and less lift.
The non-ELI5 answer is more complicated, but it comes down to the generic engineering problem. How to design something that meets certain requirements. There’s a lot of constraints and factors that go into it and ultimately it’s a design choice.
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