Rotating masses such as crankpins and the lower half of a connecting rod may be counterbalanced by weights attached to the crankshaft. The vibration which would result from the reciprocating forces in one cylinder are neutralized by those in another. Where these forces are in different planes, a corresponding pair of cylinders is required to counteract the rocking couple.

If piston motion were truly harmonic (i.e. the connecting rod were of infinite length, the reciprocating inertia force, that has to be balanced, at each end of the stroke would be as follows:

F = 0.000456 * W * N^2 * S

F is force (in pounds), W is the reciprocating mass in one cylinder (in pounds*), N is the RPM, and S is the stroke (in inches)

But the piston motion is not truly harmonic because the connecting rod is not of infinite length. The "fudge factor" (angularity) for this effect is as follows:

A = (R / L) or A = (S / 2L)

A is angularity, R is the crank radius, S is the stroke, and L is the connecting rod length, all in inches.

###### * - I know pounds don't really measure mass, but this is engineering - mass and weight are the same :-)