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Crank & Piston Geometry

Engine Room · Demo

How a circle becomes a straight line — and what the rod ratio does to it.

Live values

Crank angle0°
Rod angle φ0.0°
Piston velocity0.00 m/s
Piston acceleration883 m/s²
Side-thrust factor0.000×

This geometry

Rod ratio L/r3.33
Bore / stroke1.00
Mean piston speed3.4 m/s
Peak velocity5.6 m/s
Accel @ TDC883 m/s²
Accel @ BDC-475 m/s²
Max side thrust0.315×

TDC acceleration is the biggest inertia load on the rod and bearings; it grows as ω²·r·(1 + r/L), so it rises with the square of RPM. Side-thrust factor is the lateral force the piston presses on the wall per unit of axial force.

The crank-slider geometry

The crank turns a circle; the rod makes it a line. With a very long rod the piston would glide up and down as smoothly as a pendulum swings. A real rod is short — so the piston rushes through the top of its travel and lingers at the bottom, and the shorter the rod, the stronger the lopsidedness. That one geometric fact decides how violently an engine shakes and how hard its pistons scrape the walls.

More detail

With crank radius r=12 stroker = \tfrac{1}{2}\,\text{stroke} and rod length LL, the piston’s distance below TDC is the exact slider equation d(θ)=r(1−cos⁡θ)+L−L2−r2sin⁡2θd(\theta) = r(1-\cos\theta) + L - \sqrt{L^2 - r^2\sin^2\theta}. An infinite rod would give pure simple harmonic motion, d≈r(1−cos⁡θ)d \approx r(1-\cos\theta) — the dashed reference in the charts.

The finite rod makes acceleration asymmetric: aTDC=ω2r(1+rL)a_{\text{TDC}} = \omega^2 r\left(1 + \tfrac{r}{L}\right) versus aBDC=− ω2r(1−rL)a_{\text{BDC}} = -\,\omega^2 r\left(1 - \tfrac{r}{L}\right). And the rod’s lean angle φ=arcsin⁡ ⁣(rLsin⁡θ)\varphi = \arcsin\!\left(\tfrac{r}{L}\sin\theta\right) presses the piston sideways with force Faxialtan⁡φF_{\text{axial}}\tan\varphi — why engines favour rod ratios of 1.5–2.

Pure kinematics. Geometry and inertia only — no gas pressure or combustion. Velocity and acceleration scale with rpm; the curve shapes depend only on the rod ratio.