This friction-machine calculator represents a Prony-style absorption dynamometer: a brake loads a rotating shaft, and a restrained torque arm measures the reaction. Enter shaft speed, net reaction force and perpendicular arm length to calculate torque and absorbed power.
Friction Machine Interactive Calculator
Vary shaft speed, brake force, and torque arm length to see torque and brake power for a Prony-style friction dynamometer.
Equation Used
The friction machine reads a brake force W at a known arm length L, giving torque T = WL. Brake power is torque times angular speed, so BP = 2*pi*N*W*L/60 when N is in rpm.
- SI units: force in newtons, arm length in metres, speed in rpm.
- Brake force acts perpendicular to the torque arm.
- Load and speed are steady; the entered force is the net perpendicular arm reaction after tare and other relevant corrections.
Measuring the brake reaction
As the shaft turns, the brake resists it and converts absorbed mechanical power mainly into heat. The brake assembly tends to rotate with the shaft. Restraining that assembly through a measured force at a known perpendicular distance gives its reaction torque.
The force reading needs to account for the arm's own weight, zero offset and other reactions that affect the measurement. With a steady torque balance, multiplying net force by the moment arm gives the absorbed torque. Simultaneous shaft speed then gives power.
Brake material, loading adjustment, support stiffness and heat removal affect a real test. The calculator takes measured force and speed as inputs; it does not predict them from friction coefficient or brake adjustment. Changing contact conditions can change the load, but that does not invalidate the torque relation when the actual reactions are correctly measured.
The animation shows a rotating drum inside stationary split brake shoes. Their yoke carries a horizontal torque arm restrained by a force sensor. The upward reaction balances the tendency of the brake to turn with the drum. The dimension line runs from the shaft axis to that vertical force line. Changing L alters the drawn arm position, but the arm break and drawing scale are illustrative. Drum playback is slowed in proportion to entered RPM. The diagram does not predict sensor deflection, contact pressure or brake temperature.
Understanding shaft-power measurement
A friction dynamometer is useful for demonstrating the relation between force, torque and rotational power. It is an absorption instrument: the tested shaft supplies energy that the brake must dissipate.
A real engine or motor test needs equipment rated for the speed, torque, absorbed energy and duration. This calculator supplies the conversion from readings to power. It does not select the brake, cooling system, guarding or a rated test procedure, and it does not predict engine efficiency.
Force, moment arm and power
For net perpendicular force W in newtons and moment arm L in meters, T = WL in N·m. With shaft speed N in RPM, angular speed is ω = 2πN/60 in rad/s. Absorbed brake power is P = Tω = 2πNWL/60 in watts.
The outputs convert watts to kilowatts by dividing by 1,000, and to mechanical horsepower by dividing by approximately 745.699872. Mechanical horsepower here is not metric horsepower. Enter a force, not a mass reading in kilograms; a mass-equivalent scale must be converted using the appropriate gravity and calibration.
L is the perpendicular distance from the shaft axis to the force's line of action. If a force acts at an angle to a physical arm, its moment is Fr sin θ; entering the entire arm length with the full force would overestimate torque unless they are perpendicular.
A rope brake with two measured tensions is a different measurement arrangement. Its torque is (F_tight − F_slack)r_effective, where the effective radius follows the rope centerline around the drum. Do not combine that tension difference with an unrelated torque-arm length.
Example: a restrained torque arm
The defaults are 1,200 RPM, 250 N and a 0.50 m perpendicular arm. Torque is 125 N·m, angular speed is 125.664 rad/s and absorbed power is 15.708 kW, about 21.065 mechanical hp.
At the same force and arm but 600 RPM, torque remains 125 N·m while power falls to 7.854 kW. Doubling force or arm length instead doubles both torque and power at a fixed speed. These are hypothetical readings, not a prediction of a particular engine's output.
For comparison with a rope-brake calculation, a 400 mm drum and 25 mm rope give an ideal centerline radius of (0.400 + 0.025)/2 = 0.2125 m. A net tension difference of (8.0 − 1.2) × 9.81 = 66.708 N gives 14.18 N·m and about 1.069 kW at 720 RPM. Using 0.812 m instead would describe a different moment arm and a different apparatus.
The controls permit mathematical torques of 1–4,000 N·m and powers of about 0.01047–1,507.96 kW. These bounds are not the capacity of the illustrated brake. A reading displayed as 0.01 kW near the minimum reflects rounding, not a higher-precision measurement.
Measurement limits and other dynamometers
Hydraulic and electromagnetic absorption dynamometers produce the resisting load through different physical processes. Instrument range, calibration, heat rejection and response determine their suitability; there is no universal accuracy or cost ratio among the types.
Because P is proportional to force, arm length and speed, relative errors in each affect the result. A 0.5 N zero error is 10% of a 5 N reading but only 0.2% of a 250 N reading. A 5 mm arm error is 0.5% of a 1 m arm. The calculator does not estimate measurement uncertainty.
Steady absorbed power becomes a heat-removal requirement, but allowable duration depends on the brake's thermal design and rating. The formula supplies neither a cooling-flow prescription nor a safe surface temperature. Use instrument readings and the equipment's procedure; the drawing is not an operating guide.
Frequently asked questions
What force should I enter?
The net reaction force acting perpendicular to the torque arm, with tare and other relevant corrections applied. Use newtons rather than an unconverted kilogram reading.
Where is the arm length measured?
From the shaft axis to the force line of action, using the perpendicular distance.
Why does torque stay the same when RPM changes?
For fixed force and arm, T = WL is unchanged. Power changes because it also depends on angular speed.
Is this a rope-brake calculation?
The illustration is a restrained torque arm. A rope brake uses the difference in tensions times the effective drum-and-rope radius; do not mix the two geometries.
Why is there no friction-coefficient input?
The tool uses the measured reaction directly. A coefficient would be needed to predict contact behavior, which is not calculated here.
Can I infer efficiency from brake power alone?
No. Efficiency needs a relevant input-power measurement or, for engine mechanical efficiency, indicated power on a consistent basis.
Does the hp output use metric horsepower?
No. It uses mechanical horsepower, about 745.7 W per hp.
Can the calculator set test duration or cooling flow?
No. Brake thermal capacity, heat transfer and equipment ratings are not inputs.
Dynamometer references
Building or designing a mechanism like this?
Explore the precision-engineered motion control hardware used by mechanical engineers, makers, and product designers.
