Slider-Crank Calculator (Piston Position, Velocity and Acceleration)

What this tool does

A piston does not move like a simple sine wave: the connecting rod leans over, so the piston covers more than half its stroke in the first 90° of crank rotation: it moves faster near the top than a sine would give and lingers longer near the bottom — the chart sets the exact velocity beside the sinusoid. The shorter the rod relative to the crank, the bigger the difference, and the larger the acceleration at top dead centre, ω²r(1 + r/l), which sets the inertia load on the rod and bearings. Mean piston speed 2·stroke·rpm/60 is the number engine builders keep under control for wear.

Formula

x = r cos θ + √(l² − r² sin² θ) · v = ω r (sin θ + r sin θ cos θ ÷ √(l² − r² sin² θ)) · a at TDC = ω² r (1 + r ÷ l)

Variables

Worked example

Limitations

• The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
• Mixing units is the most common source of error. Convert every input to the units shown next to each field before calculating.