Bore and stroke calculator

What the ratio means

Bore is the cylinder's diameter. Stroke is how far the piston travels between top and bottom dead centre, and it is exactly twice the crank throw. Divide bore by stroke and you get a single number that describes the cylinder's proportions without reference to its size, so a 250 cc single and a 6-litre V12 can sit in the same column.

• Oversquare, above 1.02. The bore is wider than the stroke. A wide bore is a wide combustion chamber roof, and valve area scales with the square of the bore, so this is where the breathing comes from. The short stroke keeps piston speed down, which is what lets the engine rev.
• Square, 0.98 to 1.02. Bore and stroke within a couple of per cent. A compromise nobody arrives at by accident: it is what you get when you want decent breathing and decent mid-range from the same block.
• Undersquare, below 0.98. The stroke is longer than the bore. Gas pressure gets a longer lever on the crank and the chamber is compact, which suits a high compression ratio and a slow, complete burn. It also puts a hard ceiling on rpm, which is why diesels and industrial engines live here.

None of the three is better. Each is what you get after you have decided which of valve area, piston speed and chamber shape you are prepared to give up.

Piston speed is the real rpm limit

An engine does not come apart because the tachometer reads a big number. It comes apart because the piston is being stopped and reversed twice per revolution, and the load that does that scales with how fast the piston is moving. The standard measure is mean piston speed, the average velocity over one stroke:

mean piston speed (m/s) = 2 × stroke (m) × rpm ÷ 60

Bore, cylinder count and displacement are all absent. Stroke and rpm, and that is the whole equation. Production road engines mostly land between 18 and 22 m/s at their redline; racing engines accept 24 to 26. Above roughly 25 m/s you have left the catalogue behind and are buying racing rods, racing pistons and racing service intervals.

Two engines in the simulator make the point better than the band does. The F1 V8 2.4L runs a 39.75 mm stroke and reads 25.5 m/s at its 19,250 rpm power peak. The V8 7.0L Pushrod runs 101.6 mm and is already at 23.7 m/s at 7,000 rpm. The revs differ by a factor of 2.75. The piston speeds differ by 8 %. The F1 engine is not asking more of its pistons than a big pushrod V8 already asks of its own; it just collects that many more power strokes per minute for the same trouble.

The simulator takes this seriously enough that it charges friction on mean piston speed rather than on engine speed. Before that change the F1 preset made negative torque at its rated rpm, because a model that bills by revolutions thinks a 39.75 mm stroke costs the same as a 101.6 mm one. The whole story is in why F1 engines could rev to 20,000 rpm.

Solving for a bore or a stroke

One cylinder's swept volume is π/4 · bore² · stroke, so fixing any two of volume, bore and stroke gives the third by rearrangement. Fixing the volume and the ratio instead needs a cube root, because the ratio ties bore to stroke and the volume then depends on the stroke cubed:

stroke = ∛( 4·V_cyl / (π · ratio²) ) , bore = ratio × stroke

The arithmetic will hand you any answer you ask for. The engine will not. Bore is capped by bore spacing — the distance between cylinder centres, which is fixed by the block casting and cannot be changed without a new block — and by how much iron is left in the wall once you have bored it. Go too far and the cylinder distorts under clamping load, the rings stop sealing, and the engine you gained 40 cc on drinks oil.

Stroke is capped at both ends of its travel. A longer stroke swings the counterweights and the rod's big end wider, so they start to hit the block skirt, the camshaft or the bottom of the piston, and a stroker kit that clears none of those is a stroker kit that needs the block grinding. Then piston speed caps it again: every extra millimetre of stroke costs rpm at the top. Solve for the number, then check the number against both.

The roster by ratio

Every crank engine in the simulator, sorted by bore/stroke ratio. Bore, stroke and redline come from the preset's own configuration; the horsepower column is measured on the simulator's dyno, not quoted.

The ends are computed, not chosen. Top of the list: F1 V10 3.0L and F1 V8 2.4L, at 2.47 — 98 mm of bore against 39.75 mm of stroke, 300 cc a cylinder, which is what a mandated 98 mm bore cap leaves you. The U-16 3.8L Blown sits at the bottom on 0.71, 60 × 84 mm: 3.80 L split 16 ways is 238 cc a cylinder, and a 60 mm bore is what fits that. Read the piston-speed column beside the redline column and the pattern falls out: the ratio is not the constraint, piston speed is, and the ratio is how a designer buys their way around it.

Worked example: 2.4 litres, eight cylinders, 20,000 rpm

Start from the rpm, because that is the thing being bought. Holding 25 m/s — the top of the racing band — at 20,000 rpm needs a stroke of 37.5 mm and nothing else will do: rearranged, stroke = speed × 60 × 1000 ÷ (2 × rpm). Feed 37.5 mm and 2,400 cc across 8 cylinders back through the volume equation and the bore comes out at 100.9 mm.

That is where the real engine ran into the rulebook. The 2006 Formula One regulations capped the bore at 98 mm, so 100.9 was not available. Take the maximum bore instead and the stroke is forced: 2,400 cc across 8 cylinders at 98 mm leaves 39.77 mm, and Cosworth built the CA2006 at 98 × 39.75 mm. There were no choices left to make.

That stroke reads 25.5 m/s at the 19,250 rpm Cosworth rated the engine at, hits the 25 m/s line at 18,868 rpm, and reaches 26.5 m/s at 20,000, where the engine ran on track. The rated speed was a rating point, not a mechanical ceiling. Our preset, built on that published geometry, measures 743 hp at 19,250 rpm.

Questions people ask

Sources

• John B. Heywood, Internal Combustion Engine Fundamentals, chapter 2. The geometric relations — bore, stroke, crank radius, swept volume — and mean piston speed as the parameter that engine designs are actually constrained by.
• Charles Fayette Taylor, The Internal-Combustion Engine in Theory and Practice, volume 2. Where the piston-speed limit comes from: inertia loading, ring and bore wear, and why the practical ceiling has moved so little in eighty years.
• grandprixengines.co.uk, Note 108 Ian Bamsey's technical note on the Cosworth CA2006, marking which figures are Cosworth's and which are the author's arithmetic. Bore, stroke, compression ratio and the rated power pair are published; displacement and mean piston speed are computed.
• 2006 Formula One Technical Regulations FIA, 15 December 2005. Article 5.1.2 (2,400 cc), 5.1.4 (eight cylinders) and 5.4.1 (98 mm maximum bore) — the three lines that wrote the worked example above.

Related reading

• Why F1 engines could rev to 20,000 rpm The same arithmetic against a nine-point published power curve.
• Cross-plane vs flat-plane V8 What the crank does with the stroke once you have chosen it.
• Inline-6 vs V6, measured at matched displacement Two layouts, one displacement, and where the difference actually shows up.
• Every engine in the simulator Filterable by layout, induction and cycle, with each preset's real geometry.

Other calculators

• Compression ratio calculator Static, dynamic and boosted CR from bore, stroke, chamber, gasket and piston.
• Engine displacement calculator Bore × stroke × cylinders to cc, litres and cubic inches, with overbore.
• Horsepower calculator Torque and rpm to hp, kW and PS, or a measured estimate from displacement.
• Dyno correction calculator SAE, STD, DIN and EC corrected power from one reading.

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