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Model
If one considers the car to have an ideal lateral dynamics then the vehicle can be represented as in Figure car.png, where w is the wheelbase and delta is the steer angle. Actually the dynamics is affected by some slip angles that I am going to assume negligible for the purpose of this model. I am interested in the curvature radius of the center of the car (i.e. R) because that is the position tracked by the CPS. I assume also that the steer angle delta is proportional to the steer input or, in other words, that delta = c * u, where c is the steer factor and u is the steer input which belongs to the interval (-100, 100).
With some simple trigonometry one can obtain
Rr = w / tan(c * u)
which means that
R = sqrt(Rr^2 + w^2/4)
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