Those who have acquired an engineering degree or diploma, may recall the standard analysis of the inertia forces which result from the reciprocating motion of the piston. Briefly, the position of the piston along the line of stroke is described mathematically (using trigonometric ratios), and this is then differentiated twice to obtain expressions, first for the velocity, and finally the acceleration. The last when multiplied by the mass of the reciprocating parts gives the inertia force, acting along the line of stroke, and all these values may be calculated for any angular position of the crank. The exact mathematics is unmanageably cumbersome, so certain simplifying assumptions are made, which reduce the final form of the equations to just two terms, described as the primary and the secondary, respectively. Those assumptions are themselves based on the average values of certain engine dimensions, which are usual in the greatest number of cases (which means mostly automotive engines, numerically the overwhelming majority).

Using this expression for the inertia forces acting on one piston, the resultant for any number of cylinders, and for any configuration (in-line, V etc) can be calculated, and the best arrangement of the cranks (from the viewpoint of balance of forces) decided. This has been done for a century or more, and I believe still continues to be done.

But to the best of my knowledge, no analysis has been done for the force that acts transversely, or at right angles to the line of stroke. This force is of course the result of the angle which the connecting rod makes with the line of stroke, (which is zero only at TDC and BDC), and known as the side thrust of the piston. It is possible that when the analysis was first carried out, the rather long connecting rods that were then common, meant that the side thrust was too small to be of concern, at least in comparison with those described above.

However, it seems possible, or even probable, that the extremely short connecting rods that are used in modern racing engines make this assumption invalid, in which case there must now be a method to calculate it over the entire cycle. Anyone know of a text or a technical paper that addresses this subject? (I’m sure there must be software that does this, but “black box” solutions are not what I am looking for).