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With no belt slip, belt speed equals the pulley pitch-line speed.
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Formula
v in m/s; D in m; n in min−1
| Symbol | Meaning | Unit |
|---|---|---|
| Belt and pitch-line speed | m/s | |
| Effective pulley diameter | m | |
| Rotational speed | min−1 |
v=\frac{\pi D n}{60}Distance per revolution is πD; rpm must be converted to revolutions per second. Slip, elastic creep and differing effective diameters cause deviations in real drives. Catalog outside diameter is not always the effective pitch diameter.
Distance per revolution is πD; rpm must be converted to revolutions per second. Slip, elastic creep and differing effective diameters cause deviations in real drives. Catalog outside diameter is not always the effective pitch diameter.
With no belt slip, belt speed equals the pulley pitch-line speed.
Base equation for the target quantity
Preserve signs, boundary conditions and units when rearranging.
Work through the numerical example for “Belt-drive peripheral speed” and check its unit and magnitude.
For D=0.20 m and n=1,500 rpm, v≈15.7 m/s.
Substituting a related quantity that shares the same symbol.
Use variable definitions and check: v in m/s; D in m; n in min−1.
Formula cluster
With no belt slip, belt speed equals the pulley pitch-line speed.
For D=0.20 m and n=1,500 rpm, v≈15.7 m/s.
Relate belt speed and pulley speed in drive design.
Here is how to work through a typical Belt-drive peripheral speed (v = πDn/60) task step by step:
Task
Work through the numerical example for “Belt-drive peripheral speed” and check its unit and magnitude.
Solution path
For D=0.20 m and n=1,500 rpm, v≈15.7 m/s.
Speed n is given in revolutions per minute. Divide by 60 seconds per minute to get metres per second. If n is already in s−1, omit this factor. Use effective pitch diameter and convert rpm to revolutions per second. Application: Relate belt speed and pulley speed in drive design. The numerical example For D=0.20 m and n=1,500 rpm, v≈15.7 m/s anchors the idea in a concrete measurement case. The corresponding units are v in m/s; D in m; n in min−1. For D=0.20 m and n=1,500 rpm, v≈15.7 m/s. This checks that the reference quantities are compatible.
Use the effective pitch diameter at the belt centreline. Outside dimensions may differ by belt profile. Take the reference dimension from the manufacturer or design definition rather than assuming outside diameter. Use effective pitch diameter and convert rpm to revolutions per second. The corresponding units are v in m/s; D in m; n in min−1. For D=0.20 m and n=1,500 rpm, v≈15.7 m/s. This checks that the reference quantities are compatible. Scope: Distance per revolution is πD; rpm must be converted to revolutions per second. Slip, elastic creep and differing effective diameters cause deviations in real drives. Catalog outside diameter is not always the effective pitch diameter. A practical application is Relate belt speed and pulley speed in drive design.
Slip lowers actual output speed from the ideal peripheral-speed model. Elastic creep can create a smaller difference between tight and slack spans even without gross sliding. Include these effects in accurate speed or power predictions. Use effective pitch diameter and convert rpm to revolutions per second. Scope: Distance per revolution is πD; rpm must be converted to revolutions per second. Slip, elastic creep and differing effective diameters cause deviations in real drives. Catalog outside diameter is not always the effective pitch diameter. A practical application is Relate belt speed and pulley speed in drive design.
Write the quantity and unit from the variable list next to every value: v in m/s; D in m; n in min−1. Substitute only after converting to a consistent unit system, and state sign or reference direction explicitly. The example For D=0.20 m and n=1,500 rpm, v≈15.7 m/s. is a calculation check: result, unit and order of magnitude must fit the described situation. Round after intermediate calculations so small contributions are not lost prematurely. Use effective pitch diameter and convert rpm to revolutions per second.
The background states this starting condition: Distance per revolution is πD; rpm must be converted to revolutions per second. Slip, elastic creep and differing. That limits when the result is a valid model prediction. Compare the problem’s boundary conditions with this assumption before substituting values; real components, material properties or loads can introduce additional effects. The cited reference supports the relation used here but does not remove the need to check whether the specific case fits the model. Use effective pitch diameter and convert rpm to revolutions per second.
Quanta exam set
Curated exam set for "Belt-drive peripheral speed":
Question (front)
Which formula describes Belt-drive peripheral speed?
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Question (front)
How do you rearrange Belt-drive peripheral speed for Base equation for the target quantity?
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Question (front)
Which common mistake happens with Belt-drive peripheral speed?
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Create a curated FSRS exam set for v = πDn/60: formula recall, variables, derivation, rearrangement, worked example, common mistakes and exam context.
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