Tutorial : propeller blade speed

Whether on a radio-controlled model, on a microlight or a hovercraft, you must be careful that the maximum speed of the blade tips does not exceed 290 meters per second, for two reasons : maintaining optimum performance, and having a safety margin before reaching the speed of sound.

Let's say you want to build a hovercraft having these specifications :

Propeller diameter 0.90 meters (we actually need the radius : 0.45 meters)
Engine with 3600 RPM at full speed (we actually need the number of rotations per second : 3600 / 60 = 60 RPS)
Maximum speed of 50 km/h (13.9 meters per second)

1 - Calculate the maximum speed at the blade tip

Use the foolowing formula :

Maximum speed at the blade tip (m/s) = propeller radius (m) X 2 X PI X maximum engine RPS

With our data, it gives: 0.45 * 2 * PI * 60 = 170 meters / second

As we are well below the limit of 290 meters per second, this configuration is safe.

If you wish to get a more accurate result, you can take into account the maximum speed of the vehicle.

2 - Take into account the maximum speed of the vehicle

When running at maximum speed, the vehicle will make the blade run a bit faster. Let's continue using the following formula :

Actual blade tip speed (m/s) ² = previously calculated blade speed (m/s) ² + maximum vehicle speed (m/s) ²

Actual blade tip speed (m/s) ² = 170 ² + 13.9 ² = 28900 + 194 = 29094

Actual blade tip speed (m/s) = square root of 29094 = 170.6 meters / second

3 - Take into account the use of a reducer

Let's take another example with other specifications which will give an unsafe configuration :

Propeller diameter 1 meter (we actually need the radius : 0.5 meters)
Engine with 6000 RPM at full speed (we actually need the number of rotations per second : 6000 / 60 = 100 RPS)

Use the following formula :

Maximum speed at the blade tip (m/s) = propeller radius (m) X 2 X PI X (maximum engine RPS / reductor ratio)

0.5 * 2 * PI * 100 = 314 meters / second

As we are above the limit of 290 meters / second, this configuration needs a reducer in order to make it safe.

In this calculation, we will include the usage of a 1.1 reducer, meaning the propeller will have a complete rotation when the engine shaft makes a little bit more than one rotation. This gives enough decrease to the propeller speed :

0.5 * 2 * PI * 100 / 1.1 = 285 meters / second

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