Originally Posted by DaveJackson
However, the possibility of using single-speed, low-rpm rotors with wide chord blades (large solidity ratio) for tomorrow's high speed rotorcraft appears to have significant advantages.
Can anyone suggest one of more potentially viable reasons for using multiple-speed main rotors?
Dave, your arguements hold water. I will adapt my response from the linked thread:
RW Prouty "Helicopter Performance Stability and Control" page 26 shows that for ideal twist:
Figure_of_Merit = 1 / (1 + ( 1.5*SQRT(3) / (SQRT(Solidarity_Ratio)*(Cl^1.5/Cd)) ))
This equation can be rewritten for hover tip speed:
Figure_of_Merit =
1 / (1 + ( 1.5*Tip_Speed / (Cl/Cd)*SQRT(2*Disk_Loading/Air_Density) ))
The results are plotted for ideal twist on page 28 (fig 1.13), and indeed show that the higher the solidity ratio the higher the hover figure of merit. For each solidity ratio curve max FM is achieved at Ct/Sigma = 0.125 (or Cl = 0.75).
My interpretation is that a helicopter runs at peak efficiency when the blades are operating just below stall, for maximum Cl/Cd. Using wide chord blades allows a nice low tip speed, by chosing a low Nr for hover. For conventional heli forward flight, Nr ideally increases due to the need to avoid retreating blade stall. For counterrotators forward flight, Nr ideally reduces to keep advancing blade airspeed constant - this depends entirely on unloading the retreating blades.
The counterotator ideal is a control system which beeps down N1 with airspeed, and up with rotor load factor. A pusher prop is better running at constant speed, or beeping down with airspeed. Rotor dynamics generally favour approximately constant Nr, or at least Nr regions to avoid. My guess is that the Sikorsky engineers puzzled over the problem and decided on a 2 speed stategy as opposed to continuously variable speed. At 250kts rotors should be regarded as a wing that happens to be rotating - regardless of whether engine or pusher system causes that rotation.
Mart