Non-circular piston rings

DETAILED DESCRIPTION What is claimed is: 1.
A piston ring for a non-circular engine cylinder, which cylinder has a wall contacted by the ring, the cylinder being in an engine which is in a cold state before being placed into operation, said ring having a plurality of first circumferential regions spaced apart around the circumference of said ring and each having a defined radius of curvature which differs from one first region to the next around the circumference of said ring, and a plurality of second circumferential regions each interposed between two succeeding first regions and each formed to effect a transition between the radii of curvature of the two succeeding first regions, wherein said second regions are configured for exerting on the cylinder wall a radial contact pressure which is less than that exerted by said first regions when said ring is installed in the cylinder and the engine is in its cold state.
2.
A piston ring as defined in claim 1, wherein the change in curvature of the circumference of said ring between a non-installed and an installed mode is determined by a differential equation as follows: ##EQU2## where .
DELTA.
k.
sub.
.
DELTA.
is the change in curvature between the installed state and the non-installed state; u, v.
sub.
.
DELTA.
are the cartesian coordinates of the non-installed state after solving the differential equation; x, y.
sub.
.
DELTA.
are the cartesian coordinates of the installed state after solving the differential equation; M.
sub.
.
DELTA.
is the moment generated by the contact pressure; E.
sub.
.
DELTA.
is the modulus of elasticity; I.
sub.
.
DELTA.
is the moment of surface inertial; v'=.
sub.
.
DELTA.
dv/du is the first derivative of v with respect to u; v"=.
sub.
.
DELTA.
d.
sup.
2 v/du.
sup.
2 is the second derivative of v with respect to u; y'=.
sub.
.
DELTA.
dy/dx is the first derivative of y with respect to x; and y"=.
sub.
.
DELTA.
d.
sup.
2 y/dx.
sup.
2 is the second derivative of y with respect to x.
3.
A piston ring as defined in claim 1 wherein each said second region has a circumferential extent of 5