A reaction dynamometer measures torque through the force needed to restrain its absorber housing. A load cell acts at a known perpendicular distance from the shaft axis. That measured force gives torque; a separate speed reading converts torque to shaft power.
Dynamometer Interactive Calculator
Enter measured reaction force, perpendicular arm length and shaft speed to calculate torque and power. Keep arm-length sensitivity separate from the nominal readings.
Equation Used
- Reaction force is perpendicular to the entered moment arm.
- Steady reaction balance; relevant tare removed.
- Force and speed held fixed for arm-error sensitivity.
- No absorber capability, dynamic, thermal or complete uncertainty model.
Steady reaction balance with perpendicular force. The error output describes arm length only, not total instrument accuracy.
The shaft turns; the reaction arm stays restrained
The end-view drawing separates the rotating input shaft from the surrounding housing. The torque arm is fixed to the housing, and a vertical link carries its reaction into a load cell anchored to the base.
The support carries the assembly about the shaft axis while the load-cell connection restrains the housing torque. Under the ideal steady balance used here, the measured housing reaction represents the torque transferred by the shaft to the absorber.
The housing bolts and arm stay still as the shaft markings rotate. Housing and load-cell deflection are outside this steady reaction model. The drawing shows the measurement arrangement without claiming to reproduce the absorber internals of a particular dynamometer.
Convert a reaction reading to torque and power
Enter measured reaction force F in newtons, the perpendicular arm L in millimetres, and measured shaft speed N in rpm. The nominal outputs use those readings directly.
The separate arm-error input estimates sensitivity to uncertainty in L. Its band is shown relative to the arm dimension; it does not alter the nominal force or make the mechanism wobble.
All housing, support and lever proportions are schematic. The dimension label represents the entered arm measurement. No torque capacity, speed rating, thermal rating or test-machine selection follows from the picture.
Moment balance and rotational power
Convert arm length to metres: Lm=L/1000. With force perpendicular to the arm, torque is T=F×Lm in N·m. Shaft angular speed is ω=2πN/60 radians per second, so P=Tω/1000 in kW.
Mechanical horsepower is P/0.745699872 when P is in kW. This conversion is mechanical horsepower, not metric horsepower.
For the arm contribution alone, holding F and N fixed, the relative magnitude is 100δL/L percent. The absolute torque change is FδL/1000. At nonzero speed the same relative change applies to power. At zero torque or power, treat the percentage as a geometric sensitivity, not a relative error of a nonzero measured output.
The actual moment is the force times its perpendicular distance to the axis. If L is instead the full lever length and the force is inclined by angle α to it, use FL sin α. This calculator uses perpendicular distance directly.
Default force and arm
A 1000 N reaction at 250 mm gives 250 N·m. At 1800 rpm, the nominal shaft power is about 47.124 kW, or 63.19 mechanical horsepower.
A 1 mm arm error is 0.4% of 250 mm. With the other readings held fixed, that corresponds to ±1 N·m and about ±0.1885 kW around the nominal values. This is only the arm-length contribution.
Setting shaft speed to zero makes power zero while the entered reaction can still imply nonzero static torque. This is an algebraic measurement case, not a claim that every type of dynamometer can produce full torque at zero speed.
Measurement limits
The calculation assumes a steady moment balance with the relevant tare removed. Housing weight balance, support friction, misalignment, acceleration and cable or hose reactions can affect a real measurement.
The arm-only percentage excludes force-sensor calibration, speed measurement, resolution and dynamic effects. It must not be presented as total accuracy or as a guaranteed uncertainty bound for a test.
The page does not calculate the absorber’s braking law, temperature, cooling or control response. Input force and speed are readings to evaluate, not operating points the software proves attainable. Instrument capacity and overall accuracy depend on the actual absorber, sensors and installation.
Reaction dynamometer questions
Why does the torque arm not rotate?
It is restrained by the load-cell link. The shaft rotates relative to the housing while the housing reaction is measured.
Why measure from the shaft axis?
The moment arm is the perpendicular distance from that axis to the force’s line of action. The dimension on the drawing starts at the shaft centre.
Does the arm-error slider change nominal torque?
No. It reports a separate sensitivity to the entered length error. Nominal torque still uses the entered nominal arm.
Can power be zero with a nonzero force?
Yes, at zero angular speed mechanical power Tω is zero. Whether a real absorber can maintain that static load depends on its design.
Is this a drawing of a specific commercial dynamometer?
No. It shows the reaction measurement path, with schematic proportions and a supported housing, torque arm and load-cell link.
Reference and calculation basis
Taylor Dynamometer: Load Control and Transmitter Stand Assembly, page 2, shows commercial torque-arm, load-cell and linkage arrangements. The illustration shows those component roles with schematic dimensions and no assigned capacity rating.
The numerical model is independently defined by static moment balance T=FL, rotational power P=Tω, and the arm-length sensitivity described above.
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