A new constant in physics

Question

For the cylinder $(t,\theta)$ as time in the space, we have:

$$v^2 =||\frac{\partial q}{\partial t}||^2 +\frac{r^2}{R^2} ||\frac{\partial q}{\partial \theta}||^2$$

with $r$ the radius of the cylinder and $R$ the new constant in physics.

Can we mesurate the constant $R$?