The Holly rotary engine uses two intermeshing pistons on parallel shafts. Large working cogs pass into matching recesses in the opposite piston, while smaller teeth coordinate their rotation. The animation shows this paired-piston arrangement in an open casing. The calculator separately compares an assumed mean effective pressure, entered displacement and speed.
Holly Rotary Engine Interactive Calculator
Compare an assumed mean effective pressure with entered volume per revolution and speed. The pressure factor is a chosen scenario assumption, not a solved steam-expansion or cutoff model. The paired pistons turn at one fifteenth of the entered speed so their engagement is easier to follow.
Equation Used
Mean pressure is the entered reference gauge pressure multiplied by the chosen factor. That product is only an assumed net mean effective pressure, not a result derived from port timing, steam properties or an indicator diagram. Power and mean torque follow pressure-volume work identities. Swept flow is geometric volume per minute, not steam mass consumption. Entered displacement is total effective working volume per shaft revolution and is independent of the illustrative piston dimensions. Friction, leakage, condensation and exhaust back pressure are not calculated.
Long cogs, recesses and smaller teeth
Two shafts carry the rotary pistons inside the casing. Each piston has large peripheral cogs and corresponding recesses. A long cog enters the opposing recess as the pistons counter-rotate, while the smaller teeth between these features maintain their relationship. The long cogs sweep close to the casing wall, separating the working spaces around the outside of the pair.
The illustration uses two large cogs on each piston, following the arrangement in Holly’s 1855 patent. The front cover is removed. The blue and gold pistons are rigid, their shaft centres stay fixed, and the upper and lower passages indicate admission and exhaust. It is an explanatory profile with small visual clearance, not a dimensioned replica or a model of sealing.
Hiscox’s engine illustration explains the pressure-driven action through the difference between the longer working radius near the casing and the shorter radii at the intermesh. Pressure-volume history is still needed to determine actual work. The animation does not assign pressure to every moving chamber or calculate displacement from the colored spaces.
Holly’s engine and pump connection
Holly’s 1855 patent describes a rotary pump with large cogs, matching recesses and smaller teeth. It also discusses using the arrangement as an engine, with different packing for steam or other gases. His 1856 patent shows an engine and pump based on that earlier design, with engine exhaust routed into the pump suction water for condensation.
These sources establish the historical arrangement and pumping connection. They do not provide the operating condition of a surviving machine. The interactive calculation is a hypothetical work comparison; it does not select operating pressure, certify a restoration or predict regulation under changing load.
Pressure-volume work and mean torque
Let Pm be assumed net mean effective pressure in psi, V the entered effective displacement in cubic inches per revolution, and n revolutions per minute. The assumed work per revolution is PmV in pound-force inches.
Indicated power is PmVn/396,000 horsepower. The divisor is 12 inches per foot multiplied by 33,000 foot-pounds per minute per horsepower. Mean indicated torque is PmV/(2π) in pound-force inches, and geometric swept flow is Vn/1,728 in cubic feet per minute.
Here Pm=Pin×f, where Pin is a reference gauge pressure and f is the chosen factor. Gauge inlet pressure alone does not determine net mean effective pressure. An appropriate pressure-volume model or measured indicator diagram is needed to establish Pm for an actual engine.
These are indicated-work quantities. Mechanical efficiency and auxiliary loads are needed to relate them to delivered shaft power. No steam density is entered, so the calculator does not determine mass flow or steam economy.
Hypothetical worked example
The presets are 80 psig reference pressure, factor 0.75, displacement 1,980 in³/rev and 150 rpm. They give assumed Pm=60 psi, indicated power=45 hp, mean indicated torque approximately 18,908 lb-in and swept volume rate approximately 171.9 ft³/min.
Doubling speed doubles indicated power and swept volume rate in this model, while mean torque remains unchanged. That arithmetic does not establish an allowable speed or predict how actual mean pressure changes with speed. The presets are not dimensions, test results or operating settings for a historical engine.
What the drawing and calculation leave open
The animated profiles illustrate the large-cog/recess engagement and the intervening small teeth. Their scale, tooth details and clearance are chosen for explanation. They do not determine sealing, chamber displacement, the admission schedule or steam expansion. The physical piston thickness and end clearances are not shown.
The pressure-volume calculation also omits bearing friction, thermal behavior, steam quality, leakage and load dynamics. A favorable numerical result does not establish strength, efficiency or suitability for steam operation.
Frequently asked questions
Does the picture show two Holly-type pistons?
Yes. It shows two counter-rotating pistons with large cogs, mating recesses and intervening small teeth, following the topology of Holly’s 1855 patent. The profiles and dimensions are explanatory.
Is the pressure factor the fraction of a revolution before cutoff?
No. It is a chosen multiplier for an assumed mean effective pressure. A cutoff model must account for chamber volume and pressure throughout the cycle.
Why does speed change power but not mean torque?
At fixed assumed pressure and displacement, work per revolution stays fixed. More revolutions per minute increase work per minute; dividing work per revolution by 2π gives the same mean torque.
Is swept flow the steam consumption?
No. It is entered displacement multiplied by speed. Steam mass consumption also needs admission timing, density and losses.
Can displacement be read from the drawing?
No. The profile illustration is independent of the entered effective working volume. Use a displacement consistent with the actual chamber cycle and the chosen mean-pressure definition.
Why does the animation turn more slowly than the speed input?
Playback is slowed by a factor of fifteen so the cog and recess engagement is visible. The power and flow calculations use the full entered speed.
Mechanism references
- Birdsill Holly, US Patent 12,350 (1855), Elliptical or Rotary Pump: paired pistons, large cogs, recesses and smaller teeth.
- Birdsill Holly, US Patent 14,239 (1856), Condensing Steam-Engines Which Are Used for Pumping: engine/pump arrangement and exhaust routing.
- Gardner D. Hiscox, Mechanical Movements, Powers, Devices and Appliances, printed page 94, entry 342: Holly Rotary Engine.
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