Converting Crank Rotation to Piston Drop

Andy Marks
Mar 12
2 min read

Some manuals show how to time an engine using degrees of rotation at the crankshaft, some show how to do it measuring piston drop down the bore. Few, if any, give figures for both.

If your manual gives a number of degrees from top dead centre (TDC) but you would prefer to use piston drop as a distance before TCD - this page will show you how to convert. If you don’t fancy doing the maths yourself just skip to the bottom and download our spreadsheet that will work it all out for you.

Measuring a distance down the bore can be less accurate than putting a degree disc on the crankshaft but is often far more convenient, especially if the engine is fully assembled and in the frame as this usually results in no easy access to either end of the crankshaft.

Required Information for Calculation

Silver, metallic mechanical component with two circular ends. Blue inner ring on larger end. Isolated on white background.

The method shown on this page uses trigonometry to do the conversion and all you need to know before starting is:

The length of your conrod (between centres of the big end and small end)
Stroke of the engine

Notation and Symbols

a = third side of the imaginary triangle made up with the conrod (c) and line between the big end and main shafts (b) in mm

b = half stroke in mm (Stroke/2)

c = conrod length in mm

C = angle of engine rotation from top dead centre in degrees

d = piston drop in mm

S = engine stroke in mm

Draw the imaginary triangle

Scalene triangle with labeled sides a, b, c and angles A, B, C. Angles shown in the diagram along with a right angle highlight.

It always helps to start by drawing an imaginary triangle made up by the half stroke (b), conrod (c) and a vertical line from the main shaft to the small end (a).

Calculate missing angles using the sine rule

Mathematical equations on a black background. Shows the sine rule: sin(C)/c = sin(B)/b, leading to B = sin⁻¹(b*sin(C)/c). Text: "therefore".

The first thing to do is calculate the two missing angles. Angle B can be calculated using the Sine rule shown here.

Calculate angle A

Angle A can then simply be calculated by subtracting angles B and C from 180.

White mathematical equation "A = 180 - B - C" on a black background.

Calculate the length of side a

Equation on black background: a/sin A = b/sin B and a = b sin A/sin B. The word "therefore" appears on the left.

Now that you have all three angles and two sides the length of the remaining side (a) can be calculated by further rearranging the Sine rule as shown here.

Calculate piston drop (d)

Right triangle with sides labeled a, b, c, and a height d. Angles are marked A, B, and C. White lines on a black background.

If the piston was at TDC (C=0) half the stroke (b) plus the conrod length (c) would make a straight line equal to a. With that in mind it is simple to calculate the piston drop by adding half the stroke to the conrod length and subtracting a.

White formula "d = c + b - a" on a black background, in italic font. Minimalist and mathematical theme.

Feeling baffled?

If you have read all of the above and are left feeling confused, or would rather be out on your bike than sitting indoors with a pen and paper, we’ve created a spreadsheet do all the hard work. Simply input the information from your bike and get the answers calculated for you.

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