Development of a Vertical Stiffness Relationship for Belted Radial Tires

Vertical stiffness is a fundamentally important property of tires. This property is often expressed by some empirical formula not directly tied to the physics of the tire. It would be useful to have a physics-based formula that could reliably predict vertical stiffness from a minimum set of pertinent, easily obtained parameters. This paper extends the ring model used by Koutny in his thermodynamic studies of tire stiffness and applies it directly to the question of vertical stiffness without regard to thermodynamics. A master curve of tire vertical stiffness is obtained that includes all tires that meet the assumptions of the model, regardless of size. A simple formula for tire vertical stiffness is developed from the master curve. The formula is correlated to a wide variety of tire stiffness measurements. One use of such a formula could be to develop more reliable tire load capacity standards. In the course of the analysis, it is found that the vertical stiffness depends significantly on the structural shear stiffness of the tire sidewalls.