Chain pull from power and speed

What does this quantity describe?

Chain pull (circumferential force) Ft at the sprocket follows from the power relation P = Ft·v, so Ft = P/v. Equivalently, Ft can be found from drive torque T1 and the driving sprocket's pitch radius r1: Ft = T1/r1.

This works like a bicycle: at the same pedaling power, a lower gear with lower chain speed at the sprocket produces a higher chain pull than a higher gear at greater speed.

Formula and variables

Ft = P / v

• Ft = P / v
• P = Ft · v
• v = P / Ft

Choose the inputs correctly

Transmitted power P and mean chain speed v set the pull. Chain speed can first be found with the chain speed calculator from pitch, tooth count and rotational speed if needed.

How to use the calculator

Enter the power to be transmitted and the mean chain speed to compute chain pull. For a sizing question — such as what speed is needed to stay under an allowable maximum pull — choose v as the target.

Worked example

5.5 kW at a chain speed of 5.3975 m/s (19.05 mm pitch, 17 teeth, 1,000 rpm) gives a chain pull of Ft = 5,500 W / 5.3975 m/s ≈ 1,019 N.

Understand the result and units

A chain pull of about 1,019 N is the useful circumferential force that transmits torque. It is markedly smaller than the actual operating tension in the loaded chain span, which additionally includes centrifugal tension, catenary tension and a service factor for shock loading.

Power is given in kW, speed in m/s and the resulting force in N.

Useful pull versus actual operating tension

The chain pull Ft computed here is only the share that actually transmits torque. The real operating tension in the loaded chain span additionally consists of the centrifugal tension Fz = q·v² (significant at higher speeds), the catenary tension Fs of the sagging slack span, and a service factor KA for shock and starting loads: Fges ≈ Ft·KA + Fz + Fs. Ft alone is often enough for a first-pass estimate; a complete verification needs these additional force contributions from manufacturer literature.

Typical applications

The relationship is used for first-pass chain drive sizing, for estimating shaft load together with the other force contributions, and to sanity-check whether a chosen chain size can transmit the required force at all.

Assumptions, limits and common mistakes

This is the pure useful force derived from power and speed, not a complete chain design. For the actual operating tension in the loaded span, centrifugal tension at higher speeds, catenary tension in the slack span, and a service factor for shock loading must additionally be considered — see the linked service-factor calculator.

Common mistake: A common mistake is treating this useful force as the chain's complete design tension without adding centrifugal tension, catenary tension and a service factor. It is also easy to substitute an instantaneous speed instead of the speed averaged over one revolution.