How to use this calculator
Enter the crank and rod lengths, the slider offset (0 for an in-line engine), the crank angle from the line of travel and the crank’s angular velocity and acceleration (counterclockwise positive).
Formulas
Rod anglesin φ = (r sin θ − e)/L
Positionx = r cos θ + L cos φ
Rod angular velocityωBC = rω cos θ/(L cos φ)
Piston velocityvC = −rω sin θ − LωBC sin φ
Relative motionaC = aB + αBC × rC/B − ωBC²rC/B
Worked example
Beer Sample Problem 15.3/15.8: crank 3 in, rod 8 in, 2000 rpm, θ = 40°
- sin φ = 3 sin 40°/8 = 0.241, φ = 13.95°.
- ωBD = rω cos θ/(L cos φ) = (3)(209.4)(0.766)/(8 × 0.970) = 62.0 rad/s.
- vP = 43.6 ft/s.
- With α = 0: aP = 9290 ft/s² and αBD = 9940 rad/s².
Frequently asked questions
Why is the piston acceleration larger at top dead center than at bottom?
At θ = 0 the rod’s angularity adds to the crank’s centripetal term: a ≈ rω²(1 + r/L). At θ = 180° it subtracts: rω²(1 − r/L).
Can I use the instantaneous center instead?
Yes. For velocities, the rod’s instantaneous center is where the crank line meets the perpendicular to the piston path; this calculator’s loop equations give the same numbers.
What does the offset do?
An offset slider makes the forward and return strokes take different crank angles (quick return) and changes the stroke slightly.