A registering dynamometer records how torque changes during a test. In a mechanical recorder, movement of a torque-sensing element positions a stylus against a moving chart. Use this calculator to compare two repeating torque levels at constant shaft speed and find mean torque, work per cycle and mean power.
Registering Dynamometer Interactive Calculator
Enter shaft RPM, the two torque levels and how long each lasts. One cycle contains both intervals. The drawing illustrates a spring-and-stylus recorder; its deflection and playback speed are for viewing, not instrument calibration.
Equation Used
- Shaft speed is constant throughout each active/idle schedule cycle.
- Torque is piecewise constant at the two entered levels.
- The recorder is schematic; its movement does not determine the entered torque or calculated power.
- Spring movement and chart height are scaled to the larger entered torque; they do not predict spring deflection or measurement accuracy.
How a mechanical torque recorder works
A torque-sensing element deflects under load. A lever or linkage transfers that movement to a stylus, and a moving chart records it against time or shaft motion. The instrument must be calibrated to relate stylus position to torque.
This schematic illustrates the reaction-arm principle: torque acts on a restrained member, an elastic element resists its movement and a stylus indicates the change. Its chart represents the entered active and idle torques on a time axis.
The drawing is a general illustration of recording principles. Its spring, arm and linkage dimensions do not define a buildable instrument, and the calculation uses your entered torque values rather than deriving torque from the pictured spring.
Comparing a repeating load
Use the calculator to compare work and average shaft power when a machine alternates between two loads at one speed. Longer time at either torque gives that level more weight in the mean.
Keeping the same proportions while doubling both interval durations doubles work per cycle but leaves mean torque and mean power unchanged. These averages do not establish the peak torque capacity, temperature limits or cooling needs of a real test rig.
Constant-speed torque integration
For constant angular speed omega = 2 pi n/60 and a schedule with torques Ta, Ti lasting ta, ti, mean torque is (Tata + Titi)/(ta+ti). Cycle work is omega(Tata + Titi), and mean power is omega times mean torque.
If speed changes with time, work instead requires the integral of T(t)omega(t); this calculator does not solve that case.
Worked example
At 300 rpm, with 500 N·m for 2 s and 100 N·m for 1 s, the complete load cycle lasts 3 s. Mean torque is 366.7 N·m, work per cycle is 34.6 kJ and mean power is 11.5 kW, or about 15.4 mechanical horsepower. The shaft completes 15 revolutions during this load cycle.
Reading the animation and results
The chart and spring movement are scaled to the larger torque input. This makes the two levels easy to compare, but it means the drawing is not a fixed calibration scale. Read the result cards for torque, work and power.
Playback uses an eight-second display cycle and an illustrative shaft rotation rate. It preserves the relative duration of the active and idle intervals, not their actual elapsed seconds. At zero RPM the shaft marker stops, while the chart can still illustrate a changing static torque.
For a physical dynamometer, check rated torque and speed, structural loads, absorption and cooling limits, inertia, calibration and measurement uncertainty. The calculator does not determine those instrument requirements.
Recording torque and power: questions
Why are active and idle times used as weights?
Each torque contributes according to how long it lasts. Increasing the time at the higher torque moves the mean toward that value. The names active and idle identify the two intervals; either entered torque can be larger.
What does one cycle mean here?
One cycle is the active interval followed by the idle interval. It is not one shaft revolution. The shaft runs at the same entered RPM during both intervals.
Can there be torque at zero RPM?
Yes. A stationary shaft can carry torque. At zero RPM the calculated mean torque can be nonzero, but work and power are zero because there is no rotation.
Why can the chart look similar after increasing both torques?
The chart and spring movement are scaled relative to the larger entered torque. Increasing both torques by the same proportion can leave the picture unchanged while the numeric torque, work and power results increase.
Does the spring drawing establish measurement accuracy?
No. Its movement illustrates the torque levels; no spring stiffness, arm dimensions, calibration or measurement uncertainty is calculated.
Does playback reproduce the entered timing?
No. Playback takes eight seconds per displayed active/idle cycle and uses an illustrative shaft rotation rate. The relative interval lengths follow the inputs, but use the entered seconds and RPM for the physical timing.
Can I use this for a changing-speed test?
Not directly. When speed varies, work requires integrating torque multiplied by angular speed over time. This calculator assumes one constant speed for both torque intervals.
Technical references
- NIST, Correlating mechanical abrasion with power input — rotational power P = omega T and recorded torque/speed/power data.
- US667920A, Bicycle-dynamometer — torque recording on moving tape and known-weight/lever calibration.
- US2659233A, Dynamometer apparatus — elastic sensing ring, stylus arms and recording chart drum.
- US2306845A, Dynamometer — restrained reaction member and torque indication.
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