The Napier rotary engine places an eccentric rotor on a shaft centered in a circular shell. Two wings slide in fixed shell slots and follow the rotor surface. Explore this cross-section and calculate the limiting gaps and the space between the two circles.
Napier Eccentric-Rotor Geometry Calculator
Enter declared shell radius, rotor radius, eccentricity and axial width. The worksheet reports limiting radial gaps and rotor-subtracted annular area/volume. It does not predict steam displacement, pressure, torque, power, sealing or safe operation.
Equation Used
- The shell and rotor cross-sections are ideal circles with the declared radii.
- The rotor remains fully inside the shell: e is clamped below Rs-Rr.
- Two opposed wings slide radially in stationary shell slots and maintain ideal point/line contact with the rotor.
- Ports, wing width and loading, springs, cam wheels, end clearance, leakage, thermodynamics, materials, force, torque, speed, wear and safety are excluded.
The eccentric rotor changes the gaps around the shell as it turns. The area between the two circles stays constant while the rotor remains inside the shell; it is a geometric area, not steam displacement.
An eccentric rotor meets two wings in stationary shell slots
Hiscox item 331 places the shaft on the shell centreline and mounts the working cylinder eccentrically on that shaft. Two sliding wings occupy slots in the stationary shell and are held against the rotor by springs or external cam wheels.
The viewer solves the two ideal wing/rotor intersections throughout one turn. Port dimensions, spring forces and cam-wheel geometry are outside this model.
A nineteenth-century rotary-engine design
Hiscox documents the cross-section, and historical research records David Napier's unsuccessful rotary-engine trial in the vessel Rotary in 1852. The calculator explores the circular geometry rather than the performance or operating requirements of a particular engine.
Declared eccentric-circle geometry
The area and volume are geometric differences, not steam swept volume or indicated displacement.
Declared geometry example
For a 300 mm shell radius, 220 mm rotor radius, 25 mm eccentricity and 150 mm axial width, the limiting radial gaps are 55 mm and 105 mm. The rotor-subtracted section area is 130,690 mm² and area times width is 19.60 L.
Geometric volume and steam displacement
The difference between shell and rotor areas, multiplied by axial width, gives a geometric volume. Steam displacement also depends on the working chambers and port timing. Power and torque require pressure and thermodynamic information that this geometry calculation does not provide.
Napier rotary-engine questions
Is the rotor concentric with the shell?
No. The shaft is concentric with the shell; the rotor is eccentric on that shaft.
Are the two wings carried by the rotor?
No. Hiscox places them in slots in the shell.
Does the displayed annular volume equal steam displacement?
No. Port timing and the detailed working chambers are not established.
Napier rotary-engine references
- Hiscox, Mechanical Movements, Steam Power item 331: public-domain plate and caption identifying the eccentric rotor, concentric shaft and two sliding shell wings.
- University of Glasgow thesis on Clyde engineering history: records David Napier's rotary engine in the experimental vessel Rotary in 1852 and reports that the design was unsuccessful.
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