Carter Aviation Technologies, An Aerospace Research & Development Company


Significance of μ-1

Mu (μ) is the ratio of the forward speed of the aircraft to the rotor tip speed relative to the aircraft (more info). As the rotor rpm (i.e. tip speed) is reduced, mu increases and the drag on the rotor decreases dramatically.


One of the primary benefits of slowing the rotor is remarkable drag reduction, which translates directly to reduced horsepower. These benefits have been understood for over half a century. In fact, a technical paper written in 1957, A Rapid Performance Prediction Method for Compound Type Rotorcraft by Robert D. Foster, predicts rotor profile horsepower as follows:

HP_o=(ρ_o/8 σC_D A(ΩR)^3 (1+4.6μ^2 )  ρ/ρ_o )/550

This can be separated into a drag due to rotation and a drag due to forward speed, with the rotational component being calculated by setting µ=0. With the rotational component being a function of RPM³, slowing the rotor has a very large effect on rotational drag. For example, if rotor supported flight requires 300 rpm, and the rotor can be slowed to 100 rpm in cruise (these are the rpm values seen in flight testing the PAV), this 3-fold reduction in rotor rpm corresponds to a 27-fold reduction in rotational drag, and a 5.5-fold reduction in total rotor profile drag, as seen in the graph above.


Because the rotor provides the lift for VTOL and slow speed flight, the wing can be sized for high speed, reducing the wing area by a factor of 2 to 4 under what would be needed if it had to support the full weight of the aircraft at those slow speeds. This combination of a small, low drag wing with a slowly turning rotor is known as a Slowed Rotor Compound (SR/C™) aircraft, and combines the efficiency and speed of conventional fixed wing aircraft with the VTOL and slow speed flight of helicopters.


Aerodynamicists have known since the 1930's about the benefits of SR/C™. In the mid 50's and early 60's, both the U.S. and British governments funded SR/C™ research (with the McDonnell XV-1 and Fairey Rotodyne, respectively). Both did remarkably well for first prototypes as they both achieved forward speeds of around 200 mph (the Rotodyne even set the official world speed record for rotorcraft), however there were a number of problems that many thought were unsolvable, or at best impractical to resolve. It was this thinking that lead to the focus on tilt rotor development (V-22 Osprey). In hindsight, it can be said that those early SR/C™ projects were abandoned too soon.