A rope-brake dynamometer measures a tension difference around a rotating drum. Multiply that difference by the effective rope-centre radius to obtain torque, then multiply torque by angular speed to obtain shaft power.
Rope Brake Dynamometer Interactive Calculator
Enter both rope-end force readings, drum and rope dimensions, and measured speed. Watch the drum turn beneath a restrained rope while the torque and power outputs update.
Equation Used
- End tensions entered as forces, not masses.
- Uncompressed round-rope centreline at drum radius plus half diameter.
- Entered speed is prescribed, not predicted from load.
- No bearing-loss, cooling, friction-capacity or rope-strength model.
Force readings are in newtons. The illustrated clockwise absorption requires W≥S; friction capacity and heat are not solved.
A stationary rope resists a rotating drum
The animation is an end view with a load hanger on the left and a spring balance anchored below on the right. Both ends of the rope stay in place. The drum rotates clockwise under the rope: the contact slides rather than carrying the rope around with the drum.
For this orientation, the downward left-end force W contributes a counterclockwise moment while the downward right-end force S contributes a clockwise moment. When W exceeds S, the net rope moment opposes the imposed drum rotation.
The drawing exposes a half-wrap and its two vertical tangents. Real instruments can use other wrap arrangements. Wrap and friction affect which tensions are possible, but they do not change the torque balance once the actual end tensions and effective radius are known.
Calculate from measured tensions and speed
Enter the hanging load and spring-balance reading as forces in newtons, including the applicable hanger weight. Enter drum surface radius and rope diameter in millimetres. The speed input is the measured clockwise shaft speed in revolutions per minute.
This is a measurement calculation: it does not predict engine speed from load. The animation therefore retains the entered speed when the tensions change. Its display speed is slowed for readability.
If a balance reads mass-equivalent kilograms, convert that reading to force before using these inputs. For example, under standard gravity, 1 kg corresponds to about 9.80665 N. Do not multiply by gravity again when readings are already in newtons.
Opposing rope-end moments
For an uncompressed round rope, the effective radius in metres is r=(R+d/2)/1000. The signed resisting torque is T=(W−S)r in N·m, with positive T opposing the clockwise rotation shown.
Angular speed is ω=2πN/60 radians per second. Signed shaft power is P=Tω/1000=2πNT/60000 in kW. This is positive absorbed power only when the readings and rotation represent a resisting brake.
The bare-radius comparison is 100(r−R/1000)/r percent. It is the relative underestimate in a nonzero torque magnitude caused by neglecting half the rope diameter. At equal tensions, torque is zero with either radius; the displayed percentage remains a geometric comparison.
These relations do not calculate friction capacity, temperature or rope compression. The entered tensions must come from a mechanically possible operating condition.
Work through the default readings
With W=200 N, S=50 N, R=300 mm and d=12 mm, the effective radius is 306 mm. The opposing torque is 150×0.306=45.9 N·m. At 1500 rpm, that gives about 7.210 kW of absorbed shaft power, assuming the readings describe a steady resisting brake.
Using the bare 300 mm radius would give 45 N·m, about 1.96% below the corrected torque. Increasing speed changes power but leaves the measured torque unchanged. At zero speed, shaft power is zero even if the force difference is not.
Changing W to 50 N and S to 200 N reverses the signed torque. The page identifies this as incompatible with the illustrated clockwise absorption direction. The signed result distinguishes resisting torque from torque acting with the illustrated rotation.
Limits of the illustration
The rope is shown stationary and taut to explain the moment balance. The calculator does not prove that the selected tension ratio can be sustained by a particular rope, wrap angle or surface. Zero-tension cases are algebraic limits rather than a prediction of a stable taut-rope brake.
Rope thickness and drum radius share one drawing scale. The pedestal, scale case and load hanger are schematic. Scale-case length is not a computed spring extension, and the load block height simply distinguishes larger entered loads.
Absorbed power becomes heat at the slipping contact. No cooling, temperature, wear, guarding or component rating is designed here. Measurement accuracy and permissible operating conditions depend on the actual apparatus and its calibration.
Rope-brake calculator questions
Why does the rope stay still?
The brake dissipates power through sliding contact between a rotating drum and a restrained rope. A rope moving with the surface without slip would describe a different operating condition.
Why include rope diameter?
The moment arm is measured to the rope centreline, approximated as one rope radius outside the drum surface.
Why can power be negative?
The arithmetic retains the sign of W−S. A negative result means the selected readings do not resist the illustrated clockwise rotation. It is not a prediction of negative heat production.
Does more load automatically slow the animation?
No. Speed is a separate measured input. The engine torque-speed response and rotating inertia are not supplied.
Does the tool calculate a safe rope size?
No. It calculates torque and power from entered readings, not rope strength or thermal capacity.
Reference and calculation basis
Projectech: Rope Brake Dynamometer for Engine Power Measurement describes its apparatus using a drum, rope, dead-weight loading, a spring balance and a speed measurement. It supports the component arrangement and measurement principle, not a rating for this schematic.
The equations and sign convention on this page follow the moment balance of the two drawn rope ends and P=Tω. Dimensions, display timing and examples are independently specified here.
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