A nutating disk engine uses a circular piston whose plane rocks around a fixed center. In the Davies form illustrated here, the disk is fixed to an inclined shaft supported at the apex of conical cylinder heads. The shaft end follows a circular crankpin orbit, connecting disk nutation to output-shaft rotation. Hiscox identifies a spherical outer shell and alternating steam admission to the disk’s sides.
Disk Engine Interactive Calculator
Inspect a Davies-type nutating disk and estimate mean shaft power from entered cycle measurements. The geometry controls the illustrated motion, while the entered mean effective pressure and cycle displacement determine the torque and power estimate.
Equation Used
- Rigid fixed-center nutating disk and inclined shaft.
- Illustrated pivot-to-crankpin distance is 0.9D.
- Measured cycle displacement entered independently of the schematic geometry.
- Mechanical efficiency applies after indicated cycle work.
Mean effective pressure and displacement must use the same output-revolution convention. Changing the illustrated geometry leaves the entered measured displacement unchanged.
A fixed center, a moving disk plane and a rotating crank
The blue disk stays centered on the gold spherical pivot. Its normal follows the inclined shaft as that shaft sweeps a cone. The shaft end is connected to an offset crankpin on the gold output disk. The output axis remains fixed while the pin circles around it.
The transparent case exposes the motion. Its conical heads meet at the central bearing, and the disk rim lies on the spherical outer boundary. The historical illustration is turned upright for this view. The shaft length from pivot to crankpin is an explicit illustrative proportion, 0.9 times disk diameter.
This shows the Davies construction identified in Hiscox figure 352. Steam-port timing, seals and any anti-rotation details are outside this geometric view, so no simulated pressure pulses or claimed torque waveform are shown.
Keep geometric motion and measured performance distinct
Disk diameter and cone angle change the illustrated nutation geometry. Mean effective pressure, measured displacement per output revolution, mechanical efficiency and speed determine the performance estimate. The measured displacement must correspond to the actual engine and the same cycle convention used for mean effective pressure.
The case drawing alone does not establish swept volume or valve timing, so displacement is entered independently of disk diameter and crank radius. Geometry changes do not automatically alter the entered measured displacement. Update that value when comparing a different actual engine.
Work per revolution gives average torque
Let pm be net mean effective pressure and V the total displacement per output revolution under the same cycle convention. Indicated work per revolution is W=pm V. With pressure in kPa and displacement in cm³/rev, W in joules is 0.001 pm V.
Mean indicated torque is Ti=W/(2π). Estimated mean shaft torque is T=η Ti, where η is mechanical efficiency expressed as a fraction. Shaft power in watts is P=T·2πn/60, or equivalently η W n/60. Divide by 1,000 for kW.
Mean effective pressure is a work-equivalent cycle quantity, not simply boiler or inlet gauge pressure. It already accounts for the pressure-volume cycle used to define it. Mechanical efficiency here represents the conversion from indicated work to shaft work; it is not an additional estimate of admission or expansion losses.
For disk diameter D, cone half-angle θ and illustrated pivot-to-pin length L=0.9D, opposite-tilt rim-height range is D sin θ. Crankpin orbit diameter is 2L sin θ and axial distance from the pivot to the crank plane is L cos θ. These are geometric outputs, independent of the entered performance measurements.
Example using measured displacement
At 350 kPa mean effective pressure and 95 cm³ per output revolution, indicated work is 33.25 J/rev. Mean indicated torque is 5.29 N·m. At 70% mechanical efficiency, mean shaft torque is 3.70 N·m.
At 300 rpm, estimated shaft power is 116.38 W, or 0.116 kW. Doubling speed while holding the same mean effective pressure, displacement and efficiency doubles this estimate; that arithmetic does not show whether a real engine can maintain those conditions.
For the illustrated 150 mm disk and 18° cone half-angle, the rim-height range is 46.35 mm and the crank orbit diameter is 83.43 mm. These dimensions explain the visible motion and do not determine the separately entered 95 cm³ displacement.
Limits of the illustration and calculation
The disk, shaft and crank are rigid. The center remains fixed, the disk is perpendicular to the inclined shaft and the rim stays on a sphere. The case is transparent to reveal these constraints. Shaft cone angle and radius do not represent a detailed seal or valve design.
The power estimate needs measured or otherwise justified mean effective pressure, cycle displacement and mechanical efficiency. It does not infer a safe pressure, allowable speed, starting torque, leakage rate, wear life or load rating. Actual operating limits and tolerances depend on the engine construction and test data.
Animation is slowed for inspection while the displayed rpm and cycle frequency retain their entered physical values. Setting speed to zero stops the motion and makes power zero; the work-per-revolution and mean-torque figures remain the stated cycle estimates, not a guarantee of static starting torque.
Disk-engine questions
Is the disk spinning flat like a flywheel?
No. Its plane nutates about a fixed center. The offset shaft end follows the output crankpin around a circular orbit.
Why is boiler pressure not enough to calculate power?
Power depends on net work over the pressure-volume cycle. Mean effective pressure and the matching cycle displacement express that work; inlet pressure alone does not.
Why does changing disk diameter leave the power estimate unchanged?
Diameter changes the displayed geometry. Performance uses the separately entered measured displacement. The source does not supply enough chamber and port geometry to derive that displacement automatically.
What does efficiency mean here?
It is mechanical efficiency from indicated cycle work to shaft work. It is not thermal efficiency or a second correction for the steam-admission cycle.
Which disk-engine arrangement is illustrated?
The animation illustrates the Davies nutating disk construction, with an inclined shaft, crank, conical heads and spherical shell.
Historical construction reference
Gardner D. Hiscox, Mechanical Movements, Powers and Devices, printed page 96, figure 352, describes the Davies disk engine’s inclined shaft, crank, conical heads and spherical shell. The power equations follow work per revolution; they are not a performance rating supplied by that historical drawing.
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