Slider-Crank Piston Position
The instantaneous piston position at a crank angle, for degreeing a cam, port timing, or piston-to-valve clearance.
Example
You enter
- Stroke (in) 3.48
- Connecting-rod length center-to-center (in) 5.7
- Crank angle after TDC (deg) 90
You get
- Position from tdc (in) 2.0121
- Percent of stroke 57.8
No published worked example is on file for this calculation. It is checked against a hand-worked derivation of its method and an independent reference test.
Details, formula, and sources
Scopex = r + L - (r cos + sqrt(L^2 - r^2 sin^2)), r = stroke/2. Because the rod swings, the piston is PAST mid-stroke at 90 degrees: a 3.48 in stroke, 5.7 in rod at 90 deg puts it 2.012 in below TDC (57.8% of stroke, not 50%), 0.27 in past the pure sinusoid - so degreeing on the simple figure is off by a quarter inch. The shorter the rod, the bigger the shift. Enter a crank speed for the piston velocity and acceleration; wrist-pin offset and rod stretch are separate. A design aid; Machinery Handbook and the engine builder govern.
Formula or tabler = stroke/2; x = r + L - (r cos(theta) + sqrt(L^2 - r^2 sin^2(theta))); simple = r(1 - cos theta); rod/stroke = L/stroke.
Source and editionThe exact slider-crank piston displacement x = r + L - (r cos(theta) + sqrt(L^2 - r^2 sin^2(theta))) (Machinery's Handbook; standard mechanism kinematics), by name.
Free accessThe slider-crank displacement is a standard published kinematics result; the stroke, rod length, and crank angle are the user's inputs.
What governsEstimate. AHJ and licensed professional govern.
API field namesstroke_in, rod_length_in, crank_angle_deg, position_from_tdc_in, percent_of_stroke
- Displacement x = r + L - (r cos + sqrt(L^2 - r^2 sin^2)), centered slider-crankMachinery's Handbook
- Rod angularity piston is past mid-stroke at 90 deg; effect grows as rod/stroke shrinkskinematics
- Scope position only; velocity/acceleration, pin offset, rod stretch, loads are separatescope of this tile