Proof that:
"Wall Friction Losses Grow as
the Cube Root of the Number of Cylinders"
by L. Van Warren
© 1998 L. Van Warren • All Rights Reserved


For a "square" engine where bore equals stroke, we seek a relation between contact surface area (friction) and engine displacement (volume) as the number of cylinders increases.

If we make the preliminary assignments that:
 

n
=
the number of cylinders in the engine
Sn
=
contact surface area of cylinder walls
for an engine with n cylinders
V
=
some fixed engine displacement or volume
dn
=
cylinder diameter
for an engine with n cylinders
 

and note that the volume rule is given by:

Then the relationship between frictional losses, volume and cylinder count is given by:
where n is the number of cylinders and c is a constant.

Thus the frictional loss for an engine fixed volume with n cylinders grows as the cube root of the number of cylinders.