Piston Speed Calculator

How piston speed is calculated

The piston covers the stroke twice in every revolution, once down and once up, so its average speed, the mean piston speed, is simply twice the stroke times the rpm. It is the usual way to compare how hard engines of different sizes are working: a long-stroke engine at moderate rpm can have the same piston speed as a short-stroke engine revving much higher.

The average hides how uneven the motion is. The piston stops dead at top and bottom dead center and is fastest somewhere in between, where the crank and the rod are close to a right angle. How fast it gets, and where, depends on the rod ratio, so the calculator works it out from the crank and rod geometry, degree by degree, and plots one full revolution.

In US units the speed is given in feet per minute, the figure engine builders quote; switch to metric for meters per second, the unit used in engineering books.

What to enter and where to find it

• Stroke. From the crankshaft specification, or twice the crank throw.
• Rod length. The center-to-center length of the connecting rod, from the big-end bore to the wrist pin bore, as the rod maker lists it. It doesn’t change the mean piston speed, only the shape of the motion and the peak.
• Engine speed. Any rpm you want to check, usually the redline or the rpm of peak power.
• Mean piston speed to match (second tab). A piston speed you want to compare against, in ft/min, or m/s in metric.

Mean piston speed: what the number tells you

Heywood’s Internal Combustion Engine Fundamentals points out that mean piston speed is often a better yardstick than rpm when comparing engines, because the speed of the gas through the ports and the loads on the parts scale with it. Heywood gives 8 to 15 m/s, about 1,575 to 2,953 ft/min, as the usual band at maximum rated power, with large diesels at the bottom and car engines at the top. That figure dates from the late 1980s: many current performance car engines reach their rated power above it.

Purpose-built racing engines go further still, with parts designed for it. The calculator reports the figure; it does not tell you how much your engine can take, which depends on its parts, the balance of the rotating assembly and how it was built.

Because mean piston speed is proportional to the stroke, a stroker crank raises it at every rpm by the same percentage the stroke grows. The second tab answers the reverse question: the rpm at which a new stroke reaches the piston speed of the old one.

Rod ratio calculator: what a longer or shorter rod changes

Rod ratio is the rod length divided by the stroke. Heywood gives 3 to 4 as the usual ratio of rod length to crank radius in small and medium-size engines, which is 1.5 to 2.0 as rod length divided by stroke, the way US builders quote it.

A shorter rod leans further over as the crank turns, so the piston gets away from top dead center faster: with a rod ratio of 1.5 it has covered 58.6% of its stroke after a quarter turn of the crank, against 56.4% with 2.0. Its peak speed is higher and comes earlier, at about 73° after top dead center against 77°.

A longer rod does the opposite and also leans less, which lowers the side load of the piston on the cylinder wall. Across the usual range the peak speed only changes by a few percent, from 1.62 to 1.66 times the mean, so rod length is largely a packaging choice: a longer rod needs a piston with a shorter compression height to fit the same block, which you can check on the deck height tab of the compression ratio calculator.

Piston speed formulas

Mean piston speed is plain arithmetic; the peak speed and its crank angle come from the geometry of the crank and rod, as set out in Heywood’s section on the geometry of reciprocating engines. Neither is an estimate.

1. Mean piston speed (ft/min) = 2 × stroke (in) × rpm ÷ 12
2. Rod ratio = rod length ÷ stroke
3. Piston speed at crank angle θ ÷ mean piston speed = π/2 × sin θ × [1 + cos θ ÷ √(R² − sin² θ)], with R = rod length ÷ crank radius
4. Largest rod angle = asin(crank radius ÷ rod length), at a quarter turn from top dead center
5. RPM for a piston speed = piston speed (ft/min) × 12 ÷ (2 × stroke in inches)

The π/2 is there because the crankpin travels π times the stroke in one revolution while the piston averages twice the stroke. The peak is where the third formula reaches its maximum; it has no simple closed form, so the calculator finds it numerically to a small fraction of a degree. In metric, mean piston speed in m/s is twice the stroke in meters times the rpm, divided by 60 seconds.

Worked example

Three questions about one engine, worked out with the same functions that run the calculator.

Typical mean piston speeds

Mean piston speed for a range of common strokes across the rev range, in ft/min, worked out with the formula above. For reference, Heywood puts the mean piston speed of production engines at maximum rated power at 8 to 15 m/s, or 1,575 to 2,953 ft/min, a figure from the late 1980s; current performance engines run higher.

Read across a row and piston speed rises in a straight line with rpm; read down a column to see the effect of the stroke. A short-stroke engine can rev a long way further before it reaches the mean piston speed of a long-stroke one.

Common mistakes

• Forgetting the factor of two. The piston travels the stroke twice per revolution. Stroke times rpm alone gives half the mean piston speed.
• Mixing inches and feet. With the stroke in inches, divide by 12 to get feet per minute; otherwise the result is twelve times too high.
• Comparing a mean with a peak. Figures quoted for engines are almost always mean piston speeds. The peak is roughly 1.6 to 1.7 times the mean, so compare like with like.
• Treating rod length as the rod ratio. Rod ratio is the rod length divided by the stroke, a number around 1.5 to 2.0, not the length itself.
• Expecting the rod to change the mean speed. Rod length changes the shape of the motion and the peak, never the average: only the stroke and the rpm set that.