An inclined paddle-wheel engine connects a reciprocating cylinder to the wheel shaft through a connecting rod, often called a pitman. Hiscox’s entry 222 also identifies an upright crank-connected beam for an air pump. Use the calculator to compare three illustrative rise-and-run geometries and watch the connected piston, wheel crank and air-pump beam. These proportions do not determine engine power.
Inclined Paddle-wheel Engine Interactive Calculator
Compare inclination from an entered rise and three assumed horizontal runs proportional to wheel diameter. These are illustrative geometry cases, not measured vessel dimensions.
Equation Used
Inclination requires both rise h and horizontal run L. This tool assumes three ratios L/D rather than accepting a measured run. Those ratios give 14°, 15° and 16° at D = 22 ft and h = 8 ft; they are illustrative reference cases, not typical sternwheeler proportions.
- Each case treats rise and run as the legs of a right triangle between a cylinder-axis reference point and shaft center.
- Horizontal run is assumed proportional to wheel diameter; no historical or manufacturer proportion is asserted.
- The three angle results compare chosen geometric assumptions, not uncertainty bounds or recommended mounting angles.
Cylinder, crosshead and wheel shaft
A piston rod moves along the cylinder axis. A crosshead guides that straight-line motion, and the pitman connects it to a crank on the wheel shaft. Inclining the cylinder changes the installation layout; a complete mechanism still requires consistent crank, rod and guide geometry.
A second rod connects the wheel crank pin to the upper end of an upright beam, as shown in Hiscox’s entry 222. The beam rocks about a fixed pivot, and its lower end drives an air pump. The animation keeps both connecting rods and the beam rigid. The air pump itself and steam valve timing are omitted. Apart from the middle-case rise-and-run relationship, the dimensions and playback speed are illustrative.
Use the calculator for a geometry comparison
Change the rise to see how inclination changes when the assumed run is held in proportion to wheel diameter. The middle case also reports its assumed horizontal run.
Wheel diameter and cylinder height alone do not determine an installation angle. A real layout needs the measured horizontal separation and the actual cylinder, guide, crank and connecting-rod geometry.
Inclination from rise and run
For vertical rise h and horizontal run L, θ = atan(h/L). The calculator defines L = kD, where D is entered wheel diameter and k is a fixed illustrative ratio.
| Case | Assumed L/D | Angle at D = 22 ft, h = 8 ft |
|---|---|---|
| Long run | 1.458466 | 14° |
| Middle run | 1.357109 | 15° |
| Short run | 1.268151 | 16° |
These ratios are defined by k = (8/22)/tan(θreference). They are chosen examples, not dimensions inferred from Hiscox’s drawing. No pressure, bore, stroke, wheel speed, horsepower or thrust calculation is included.
Worked geometry example
Set wheel diameter D = 22 ft and rise h = 8 ft. In the middle case, k = (8/22)/tan15° ≈ 1.357109, giving L ≈ 29.8564 ft. Then atan(8/29.8564) = 15°.
The long-run case uses L ≈ 32.0862 ft and gives 14°. The short-run case uses L ≈ 27.8993 ft and gives 16°. These values describe three hypothetical triangles; they are not records from a vessel restoration or a recommended operating range.
What the geometry does and does not establish
For a fixed rise, increasing horizontal run reduces inclination. For a fixed run, increasing rise increases inclination. The calculator follows these geometric relationships.
Installation inclination by itself does not impose a cosine loss on indicated engine power. Indicated work comes from cylinder pressure acting through piston displacement; shaft output also depends on the actual mechanism and its losses. This tool contains none of the pressure, displacement, speed or load data needed to evaluate that performance.
The illustration is not a basis for component clearances, repair limits, steam-system changes or operating instructions.
Frequently asked questions
Can wheel diameter and cylinder height determine the angle?
Not without the horizontal run. This calculator supplies three illustrative run-to-diameter ratios. A real installation needs measured geometry.
Are the long-run and short-run angles a tolerance range?
No. They are three separate geometric assumptions, not manufacturing tolerances or recommended angles.
Does inclination alone reduce power by cosθ?
No. Indicated work is based on cylinder pressure and piston displacement. Tilting an otherwise equivalent mechanism does not create a universal cosine power penalty.
Does the illustration reproduce Hiscox’s engine?
It follows the cylinder, crosshead, wheel crank and air-pump beam arrangement in Hiscox’s entry 222. The moving rods keep their lengths, but the proportions are illustrative rather than measured engine dimensions. The air pump’s internal mechanism is omitted.
Can these results guide restoration or operation?
No. They are triangle geometry only. Component dimensions, condition, pressure systems, loads and operating limits are not evaluated.
Historical reference and calculation basis
Gardner Dexter Hiscox, Mechanical Movements, Powers, Devices and Appliances, entry 222, identifies an inclined paddle-wheel engine with an upright crank-connected beam for an air pump.
The calculator separately uses θ = atan(h/L) with three stated illustrative L/D ratios. No vessel-specific dimensions, operating limits or maintenance recommendations are inferred from the historical entry.
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