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Theoretical Relationships The closure stress σ_{b} is a measure of the stress present in the ring when installed in the cylinder. For a ring of rectangular cross section σ_{b} is stated in terms of the total free gap m by
and in terms of the tangential force by
For a slotted oil control ring σ_{b} is expressed in terms of the total free gap m by
and in terms of the tangential force by
l_{u} = moment of inertia of the unslotted cross section l_{s} = moment of inertia of the slotted cross section x_{1} = twice the distance between centre of gravity and outside diameter k = piston ring parameter 



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