Advance ratio and tip speed
J = V / (n D)
V is true airspeed, n is revolutions per second, and D is diameter, in consistent units. J is the standard independent variable on a propeller map (thrust and power coefficients versus J). The rotational tip speed is π n D. The helical tip speed — the resultant of forward speed and rotational tip speed — is
Vtip,helical = √(V² + (π n D)²)
Tip Mach is that speed divided by the local speed of sound, taken from the standard atmosphere at the geometric altitude you enter (U.S. Standard Atmosphere 1976), then scaled by √(T / TISA) if you type a non-standard OAT. At 100 kt, 2,400 rpm, and a 6.5 ft propeller at sea level, J is about 0.65 and helical tip Mach is about 0.75.
Sources
NACA / NASA propeller theory (advance ratio J); FAA PHAK (propeller, tip speed); U.S. Standard Atmosphere 1976 (speed of sound); standard helical tip-speed geometry. For Mach and dynamic pressure of the airplane, see the Mach and dynamic pressure calculator.
Frequently asked questions
Should I use indicated airspeed or true airspeed?
True airspeed. J is a ratio of the actual forward speed through the air to the rotational tip speed. Using IAS would understate J as altitude increases.
Why is helical tip Mach higher than rotational tip Mach?
The blade tip has both a rotational velocity πnD and the airplane’s forward speed. The resultant is longer than either component, so the helical Mach is higher. At zero TAS (static) they are equal.
What J is typical in cruise?
It depends on the propeller and the flight condition, but many light-airplane cruise points fall roughly in the 0.5–0.8 range. Use the propeller map for the blade you have; this page only computes the kinematics.