The Cochrane arrangement illustrated here has one wing rotating about the outer casing axis and passing through a hollow inner drum on a separate, fixed eccentric axis. The inner drum is tangent to the casing at one point. The exposed part of the wing changes length as it sweeps the crescent-shaped working space.
Cochrane Rotary Engine Interactive Calculator
Explore the single-wing Cochrane arrangement illustrated in Hiscox figure 325. Set casing size, axial width and axis offset, then an assumed constant effective pressure difference and speed. The calculator shows crescent volume and ideal work; it does not estimate leakage from clearance.
Equation Used
- One wing and tangent circular boundaries with separate fixed axes.
- Offset remains smaller than the inner drum radius.
- Constant effective pressure difference through the ideal sweep.
- No steam-cycle, seal or leakage prediction.
Hiscox figure 325 geometry. Ideal tangent contact; no finite seals or clearance-loss curve. Constant effective pressure difference over a complete sweep gives ideal work only, with no cutoff, expansion, leakage or mechanical-loss model.
One wing and two fixed axes
Hiscox’s figure 325 shows a central wing shaft, a hollow inner cylinder and a separate eccentric pivot. That single-wing arrangement is the basis of the illustration below.
O is the wing axis at the center of the casing. E is the fixed drum axis, offset downward by e. The drum radius r and casing radius R satisfy r + e = R, giving a fixed tangent at the bottom. The wing passes through the drum opening. That opening follows the intersection between the radial wing and the inner circle.
The diagram is a geometry cutaway. Colors distinguish the two sides of the crescent. Supply and exhaust timing, seals, end passages and steam expansion are not reconstructed. The rotating wing and drum opening remain connected throughout the cycle.
Historical mechanism, explicit idealization
This tool illustrates the historical rotary-engine geometry and its ideal swept-work relationship. It is not a specification for a restored engine or evidence of a particular commercial installation, speed rating or efficiency.
The calculator determines crescent volume and ideal work from the entered geometry and pressure assumption. It does not calculate steam leakage or power loss from clearance: those effects also depend on leakage-path shape, pressure, temperature, fluid properties and timing.
Crescent volume and ideal work
With casing radius R, inner drum radius r = R − e and axial width L, the crescent volume is V = π(R² − r²)L. Dimensions in millimetres give cubic millimetres; divide by 1,000,000 for litres.
Under a constant effective pressure difference Δp throughout one complete sweep, ideal work per revolution is ΔpV. Conveniently, kPa × litres equals joules. Ideal mean torque is ΔpV/(2π) N·m and ideal indicated power is ΔpVn/60,000 kW for n rpm.
For wing angle θ measured in the drawing plane from the rightward axis, the distance from O to the inner-circle intersection is ρ = e sin θ + √(r² − e² cos² θ). The exposed wing length is R − ρ and varies from zero to 2e. The allowed offset range keeps O inside the hollow drum, so that intersection remains defined for the whole cycle.
Worked geometry example
For a 200 mm casing diameter, 100 mm axial width and offset equal to 20% of the casing radius, R = 100 mm, e = 20 mm and r = 80 mm. The crescent volume is 1.131 L/rev and the maximum exposed wing length is 40 mm.
At an assumed constant effective pressure difference of 100 kPa, ideal work is 113.10 J/rev and mean torque is 18.00 N·m. At 600 rpm, ideal indicated power is 1.131 kW. These are ideal-work results, without leakage, cutoff, expansion, friction or exhaust losses.
What changes with each input
Casing diameter, offset and axial width determine volume. A wider drum increases volume without changing this end-section outline. Pressure changes ideal torque and power, while rpm changes power and animation speed without changing ideal mean torque.
The model does not predict thermal efficiency, actual shaft output, running clearances or service life. The effective pressure is a stated idealization rather than boiler inlet pressure automatically treated as available across the wing. Mechanical construction and steam-cycle analysis require more information than this geometric illustration.
Cochrane rotary-engine questions
Is this a multi-vane motor?
No. The pictured version follows Hiscox figure 325: one central rotating wing and a hollow drum on a fixed eccentric axis.
Does the calculator estimate leakage from seal clearance?
No. It calculates crescent volume and ideal work. A leakage estimate would need seal and passage geometry, fluid conditions and timing beyond the inputs provided here.
Does boiler pressure equal the effective pressure input?
Not generally. The input is an assumed pressure difference acting through the ideal sweep. Admission, exhaust and expansion determine the real cycle.
Why does speed change power but not mean torque?
At fixed geometry and assumed pressure, work per revolution stays fixed. More revolutions per second increase power.
Does the drawing specify a running seal clearance?
No. It uses ideal geometric contact and omits finite seal details, heat distortion and leakage paths.
References & further reading
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