What is the theoretical limit to a helicopters speed?

Submitted by RufusSwink t3_zfetcx in askscience

I have been wondering lately what the theoretical top speed of a helicopter would be. I have a basic understanding of retreating blade stalls and keep seeing it listed as one of the main limitations to a helicopters top speed, along with the advancing blade eventually breaking the speed of sound creating shockwaves and the more obvious ones like drag.

In theory if we imagine we have a helicopter with an infinitely powerful engine and made of materials that would never be damaged from heat or the forces caused by flying at high speeds, would these limits still apply? If it is a coaxial helicopter then the retreating blade stall shouldn't be a problem as it would be stalling on opposite sides at the same time and if the rotors are made of this theoretical material the shockwaves wouldn't damage them. Would this theoretical helicopter still have some hard limit to the maximum speed it could achieve?

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GenericUsername2056 t1_izeifbn wrote

Regular, subsonic propellers or rotors going supersonic are incredibly inefficient, with efficiencies close to zero, or the propellers/rotors even producing a net drag. It's not a question of material strength. The book 'Introduction to Flight' by Anderson has a nice exercise (6.24 for edition 5) in which it is shown that claims by WWII fighter pilots of breaking the sound barrier in vertical, power-on dives are theoretically impossible. Rotors naturally suffer from the same problems as propellers.

The only propeller aircraft I know of which broke the speed of sound is the modified McDonnell XF-88B fitted with a turboshaft engine. It did not use the propeller as a primary source of thrust, but it did achieve a supersonic dive using only the propeller. I assume this was using basically flat, angled plates as propellers, which would be better suited for generating lift (which in this case would be thrust) in a supersonic airflow than regular, subsonic propellers.

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RufusSwink OP t1_izf1mfx wrote

Why does the efficiency drop so low with a rotor but not with wings on a supersonic airplane?

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GenericUsername2056 t1_izf3xsr wrote

It does, which is why fighter jets for instance have very flat airfoils which are not very efficient for generating lift in subsonic flight. The cross-section of the wings of the famous SR-72 Blackbird reveals a simple ellipse. They require a tremendous amount of thrust to generate enough lift when flying at supersonic speeds, hence why their jet engines have afterburners. When flying at supersonic speeds, airfoil shape is of lesser importance to generating lift.

Aircraft designers are very keen to prevent (local) shockwaves forming on their wings. If you look at a passenger jet, you will notice it has swept wings. These swept wings delay the formation of shockwaves on the wing when flying at transonic speeds, thus increasing efficiency whilst still enabling the aircraft to fly at these speeds.

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RufusSwink OP t1_izgmau4 wrote

That is very interesting, thank you so much for the detailed answer.

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[deleted] t1_izp21g4 wrote

[removed]

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GenericUsername2056 t1_izse72j wrote

u/philosopherssage:

>The vast majority of lift comes from near the tips of the blades. The transition from subsonic to supersonic is where the pressure from the moving object is greater than the fluid pressure (air). When this happens vacuum bubbles form and contact with the fluid is lost preventing the transfer of force. This is why lift is lost when the portion of the prop/rotor goes supersonic. The little bubbles also cause many shockwaves and can damage the surface, underwater this is called cavitation. The bubbles also disturb the flow of air and causes turbulence which even further reduces lift.

Cavitation flow is distinctly different from compressible flow in gases, as it involves a local phase change from the bulk liquid into its gaseous state. No 'vacuum bubbles' are formed in either case. In the case of wings, normal shocks on top of the wing cause flow separation, this is called wave drag which leads to loss of lift or in case of rotors or propellers, loss of thrust.

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