Calculate blade tip speed from diameter and RPM in m/s, ft/s, ft/min, km/h or mph, solve RPM or diameter from tip speed, and add wind speed for tip speed ratio.
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Calculator Functions
| Function | What it does | What it requires |
|---|---|---|
| Tip speed from diameter and RPM | Finds the speed of the tip of a blade, impeller, propeller or wheel | Requires the full diameter and the rotational speed in RPM |
| RPM from diameter and tip speed | Finds the rotational speed that gives a set tip speed | Requires the full diameter and the tip speed |
| Diameter from RPM and tip speed | Finds the diameter that reaches a set tip speed at a set RPM | Requires the rotational speed in RPM and the tip speed |
Diameter can be in millimeters, centimeters, meters, inches or feet, and tip speed in m/s, ft/s, ft/min, km/h or mph. The first function also lists the tip speed in the other four units and the distance the tip travels per revolution. Optional settings add a wind or flow speed, which gives the tip speed ratio, and set 1 to 4 decimal places.
Tip Speed Formula
| v | Tip speed, in meters per second when D is in meters |
| D | Full diameter across the tips, not the radius |
| N | Rotational speed in revolutions per minute (RPM) |
Every point on a spinning part turns at the same angular velocity, and its speed along the circle is that angular velocity times its radius [1], so the tip moves fastest. One RPM is 2π ÷ 60 = 0.1047 radians per second [2], and the radius is half the diameter, which gives the formula above. Put another way, the tip covers one circumference, π × D, in each revolution.
Tip speed from diameter and RPM
The formula applies directly. A 0.5 m impeller at 3,000 RPM has a tip speed of π × 0.5 × 3,000 ÷ 60 = 78.54 m/s, and a 1.25 ft impeller at 100 RPM has a tip speed of 6.54 ft/s. The result is converted to the chosen speed unit with 1 ft = 0.3048 m and 1 mile = 1,609.344 m [2].
With a wind or flow speed entered, the calculator also shows the tip speed ratio, which is the tip speed divided by that speed. A tip speed of 78.54 m/s in a 10 m/s wind is a ratio of 7.85.
RPM from diameter and tip speed
A 2 m rotor reaches a tip speed of 100 m/s at 60 × 100 ÷ (π × 2) = 954.93 RPM. The larger the diameter, the lower the RPM for the same tip speed.
Diameter from RPM and tip speed
A tip speed of 20 m/s at 1,500 RPM needs a diameter of 60 × 20 ÷ (π × 1,500) = 0.25 m. A positive tip speed at zero RPM is rejected, because a part that is not turning has no tip speed.
Limits of This Estimate
- The result is geometry only. It is not a safe operating speed, and the limit for a fan, grinding wheel, mixer or propeller comes from its manufacturer.
- Tip speed is the speed of the tip around its circle. It is not the speed of the air or liquid being moved, and it does not include the forward speed of an aircraft or boat.
- Changing a unit relabels the number already typed in and does not convert it. Results marked ≈ are rounded to the chosen decimal places.
Sources
- NASA Glenn Research Center, Angular Displacement, Velocity, Acceleration: tangential velocity as angular velocity times radius, with all points sharing one angular velocity
- NIST, Guide for the Use of the International System of Units (SP 811), Appendix B.8: RPM to radians per second, and the foot and mile in meters
