A torsion dynamometer infers torque from relative twist measured between two shaft stations; paired pickups or optical targets can observe that phase difference. Relating twist to torque requires a calibrated shaft model and instrumentation.
Torsion Dynamometer Interactive Calculator
Enter shaft power, rotational speed, solid circular diameter and gauge length. Results are ideal mechanics quantities, not a sensor calibration, shaft rating or dynamometer specification.
Equation Used
- Entered power and speed describe the same steady rotating shaft state.
- The shaft segment is uniform, straight, solid and circular over the entered gauge length.
- Torque is constant over the ideal gauge segment and bending/axial loads are omitted.
- Maximum torsional shear is the elastic solid-shaft expression; no allowable is inferred.
- G times twist is reported without assigning a material shear modulus.
- Keyways, hollows, tapers, stress concentrations, dynamics, calibration, uncertainty, temperature, fatigue, strength, ratings and safety are omitted.
Measuring Relative Shaft Twist
NACA described an optical torsion dynamometer with rings fixed at two shaft stations: applied torque twists the shaft between them and produces a measurable angular displacement. Modern phase-shift torque systems likewise use two pickups on a torsion shaft.
Converting measured twist to torque requires the shaft's calibrated torque-twist relation. The calculator below instead starts from entered power and speed and reports ideal solid-shaft mechanics quantities.
What This Calculator Does
The tool converts entered power and speed to torque and angular speed. For an ideal uniform solid circular shaft it also reports maximum torsional shear stress and the product G theta over the entered gauge length.
It does not predict a sensor reading, resolution, calibration factor, uncertainty, allowable load or service life.
Power, Speed and Ideal Solid-Shaft Torsion
T = P/omega
J = pi d4/32
taumax = 16T/(pi d3)
G theta = TL/J
For an actual elastic twist prediction, theta=TL/(GJ) requires the applicable shear modulus and validation that the ideal shaft assumptions hold.
Worked Ideal Example
At 5000 kW and 100 RPM, torque magnitude is about 477.5 kN·m and angular speed is 10.472 rad/s. For an ideal 200 mm solid circular shaft, maximum torsional shear is about 304.0 MPa. Over 3 m, G theta is about 9118.9 MPa.
These can be far beyond elastic or allowable values for a real shaft; the calculator does not approve the entered case.
Model Boundary
- Measurement principle: relative twist between separated shaft stations can be observed optically or with paired pickups and related to torque through calibration.
- Calculated: power-speed torque, angular speed and ideal uniform solid-circular-shaft torsion quantities.
- Not calculated: actual material modulus, elastic limit, hollow or keyed geometry, taper, fillets, couplings, bending, axial load, stress concentration, nonuniform torque, torsional vibration, temperature, plasticity, fatigue, buckling, sensor type, tooth count, phase processing, calibration, uncertainty, bandwidth, strength, rating, compliance or safe use.
Frequently Asked Questions
Is torque determined by power and speed?
Yes for the same steady shaft state, through P=T omega. Transients and measurement uncertainty are omitted.
Is angular speed a twist angle?
No. It is shaft rotation rate in rad/s.
Why report G times twist?
The material shear modulus is not an input. Dividing the reported product by the applicable modulus gives the ideal twist TL/(GJ).
Does maximum shear apply to a hollow or keyed shaft?
No. The displayed expression is for a uniform solid circular section.
Does this calibrate a torsion meter?
No. Calibration requires the actual shaft and complete measurement chain.
Can the stress output be compared directly with an allowable?
Not without a complete engineering assessment of material, geometry, loads, dynamics and required factors.
References
- NACA TN 2118, optical torsion dynamometer: shaft-mounted rings, applied-torque twist and optical angular displacement.
- U.S. Naval Air Systems Command, Engine Test Cell Upgrade: paired pickups measuring torsion-shaft twist for torque measurement.
- NASA design report appendix, Angle of Twist: tau=Tr/J and theta integral T/(JG), including the constant circular-shaft case.
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