Lawn tennis balls, Rolling friction experiment and Trouton viscosity

We took three lawn tennis balls arbitrarily. One was moderately old, one was old and another was new. Fabricating a conveyor belt set-up we have measured rolling friction coefficients, $\mu_{r}$, of the three balls as a function of their angular velocities, $\omega_{ball}$. In all the three cases, plotting the results and using linear fits, we have obtained relations of the form $\mu_{r}= k_{rol} \omega_{ball}$ and have deduced the proportionality constant $k_{rol}$. Moreover, core of a lawn tennis ball is made of vulcanised India-rubber. Using the known values of Young modulus and shear viscosity of vulcanised India-rubbers in the theoretical formula for $k_{rol}$, we estimate $k_{rol}$s for the cores made of vulcanised India-rubbers, assuming Trouton ratio as three. The experimental results for the balls and the semi-theoretical estimates for the cores, of $k_{rol}$, are of the same order of magnitudes.