Tip speed is ΩR; advance ratio is V / ΩR
With rotor speed n in revolutions per second, Ω = 2π n and the tip speed is ΩR. The advance ratio is μ = V / (ΩR). Tip Mach is ΩR / a, and a simple helical (advancing) tip Mach is √((ΩR)² + V²) / a — it does not add cyclic flapping or a local blade angle. A 400 rpm rotor of 5.5 m radius has ΩR ≈ 230 m/s, or about Mach 0.68 in 15 °C air; at 120 knots, μ is about 0.27. Typical cruise advance ratios are often in the 0.3–0.4 range, and advancing-tip Mach is a compressibility limit.
For a propeller in forward flight the usual parameter is the advance ratio J = V / (n D) = π μ. That form, plus rotational and helical tip Mach for a prop, lives on the propeller advance ratio page. Hover power and disk loading are on hover power.
Sources
- Leishman, Principles of Helicopter Aerodynamics (tip speed, advance ratio μ, advancing-tip Mach).
- FAA Helicopter Flying Handbook (rotor-system limits, retreating-blade stall, and advancing-tip Mach — conceptual).
- U.S. Standard Atmosphere, 1976, speed of sound a = √(γ R T), with the same constants as this site’s atmosphere pages.
Frequently asked questions
Is helical tip Mach the advancing-blade Mach number?
It is √((ΩR)² + V²)/a, the speed of the tip if the blade is simply moving forward at V. Real advancing-blade Mach also depends on azimuth and flapping; this is the usual first-order figure.
How does this relate to propeller J?
J = V/(nD) = π μ for the same rotor. Use the propeller-advance-ratio page if you think in J rather than μ.
Does this tell me when the rotor will stall?
No. Retreating-blade stall depends on blade section, load, and μ, and is a flight-manual limit, not a single Mach or μ number.