A single horizontal cylinder drives an internal centre crank in the narrow-gauge locomotive shown by Hiscox. For a selected constant line-of-stroke force and ideal crank, normalized torque magnitude is |sin θ|. This page compares two selected crank angles and reports angle A's distance from either dead center. Its 30° proximity indicator is a disclosed heuristic, not a starting probability.
Single-Cylinder Crank · Selected Leverage Reference
Compare ideal normalized crank leverage at two selected angles and inspect angle A's proximity to dead center.
Equation Used
- Applied force magnitude is constant and parallel to the horizontal line of stroke.
- Only normalized torque magnitude is compared.
- Dead centers occur at 0° and 180° modulo 360°.
- Pressure history, valve events, adhesion, resistance, inertia and starting reliability are excluded.
The A proximity indicator is a selected linear heuristic: 100% at dead center and 0% at or beyond 30°.
Two selected crank positions
The main animation shows a horizontal piston driving the centre crank through a guided crosshead and a constant-length connecting rod. The near wheel is shown as a cutaway so the internal crank is visible. Smaller carrying wheels turn faster than the driving wheels at the same rolling speed. Below it, two separate crank diagrams show the selected angles A and B and a horizontal force direction. Those comparisons use the ideal moment-arm formula and omit connecting-rod angularity.
What the calculator determines
Select crank angles A and B. The calculator reports normalized ideal torque magnitude for each, A's nearest angular distance from dead center, and a selected linear proximity indicator that reaches zero at 30°.
Ideal crank leverage and disclosed indicator
Torque fraction = |sin θ|; off-dead angle = min(θ mod 180°, 180° − θ mod 180°); A proximity indicator = clamp[100(1 − off-dead/30°), 0, 100].
Selected-input arithmetic
At 0°, ideal torque magnitude is zero and A is on dead center. At 90°, normalized ideal torque magnitude is 100%.
Leverage only
The model excludes cylinder pressure history, valve timing, finite connecting-rod angularity, wheel adhesion, train resistance, inertia, reversal, multiple cylinders, controls and actual starting reliability.
Questions
Is the proximity indicator a probability?
No.
Why use absolute torque?
The page compares magnitude only; direction and power stroke state are not modeled.
Mechanical reference
Gardner D. Hiscox, Mechanical Movements, Powers, Devices and Appliances (1901), page 387, figures 1608 and 1608a: single-cylinder, centre-crank locomotive for narrow-gauge roads.
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