The Hodges compound blower described by Hiscox uses successive fan stages and stationary return passages, with air entering from both sides and discharging through a central annular chamber. The calculator below is a separate comparison of two ideal reciprocating cylinders; it does not model that staged fan blower.
Ideal Double-Acting Cylinder Phase Calculator
Add two ideal piston-speed magnitudes, normalize by their cycle mean and compare the resulting delivery range as phase changes.
Equation Used
- Two equal double-acting cylinders with sinusoidal piston motion and identical phase-independent scale factors.
- Instantaneous incompressible delivery is proportional to piston-speed magnitude on both strokes.
- Ideal check valves select delivery without delay, leakage or reverse flow.
- No bore, stroke, rod-ratio, clearance volume, pressure, compressibility, manifold, valve, friction, volumetric-efficiency, torque or operator model.
The calculation adds the speed magnitudes of two equal ideal sinusoidal pistons. It describes normalized geometric delivery only, with no compressible-flow or fan-stage calculation.
The Hodges blower and the separate piston comparison
Hiscox describes a triple-effect fan arrangement. Air enters on each side, passes successively through rotating fans and stationary return passages, and leaves through a central annular chamber.
The interactive illustration instead shows two ideal double-acting cylinders. For sinusoidal piston motion, speed magnitude is proportional to |sin θ|; shifting the second piston by α adds |sin(θ+α)|. This is useful for exploring phase relationships, but it is not a drawing or performance model of the Hodges fan arrangement.
Playback is slowed and clamped for viewing. The rods are schematic connections; their lengths and valve timing are not solved.
Use as a phase-waveform teaching model
The comparison shows how phase changes an ideal normalized sum. It cannot predict volume flow, pressure, handle effort, temperature, valve behavior or suitability for a forge, burner or pneumatic device.
Derived ideal relative-flow waveform
Let q(θ)=|sin θ|+|sin(θ+α)|. Its cycle mean is 4/π. For 0≤α≤π, its minimum is sin α and its maximum is 2 max[cos(α/2), sin(α/2)]. Dividing by 4/π expresses the range as percent of mean.
The displayed maximum deviation is max(100−qmin%, qmax%−100). It expresses the larger departure from the cycle mean, not a measured pressure ripple.
Worked 90-degree example
At α=90°, ideal relative flow is |sin θ|+|cos θ|. Normalized by its mean, the range is about 78.5% to 111.1% of mean, so the larger deviation is about 21.5%. At 60 rpm the two double-acting cylinders have four ideal delivery strokes per revolution, or four events per second.
Scope and limitations
Real delivery requires bore, stroke, connecting-rod geometry, clearances, valve lift/area/dynamics, leakage, inlet and discharge pressure, gas compressibility and temperature, manifold volumes and losses, volumetric efficiency versus speed and pressure, mechanical friction, torque and measured condition.
Frequently asked questions
Does the calculator model the Hodges compound blower?
No. Hiscox describes a staged fan blower. The calculator is a separate ideal double-acting piston waveform comparison.
Does it predict litres per minute?
No. It has no bore, stroke or volumetric-efficiency inputs.
Is 90 degrees ripple-free?
No. The ideal velocity sum ranges from about 78.5% to 111.1% of its mean, so the larger deviation is about 21.5%.
Are four events per second at 60 rpm four pressure pulses?
Not necessarily. Four is the delivery-stroke count for two ideal double-acting cylinders. Coincident events and real pressure variation require a separate analysis.
Why does speed not change the percentage range?
Both piston-speed magnitudes scale with speed, and the same factor cancels when the sum is divided by its cycle mean. The delivery-event count still changes with speed.
Historical reference and calculation basis
Internet Archive scan of Hiscox, Mechanical Movements, Powers and Devices, book image page 179 contains the Hodges compound-blower description. It identifies successive fan stages and stationary passages.
The separate piston model follows q(θ) = |sin θ| + |sin(θ+α)|. Its mean is 4/π; its extrema give the displayed normalized range. It does not supply historical machine dimensions, pressure or output ratings.
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