We propose new mathematical models to study the variation of lens distortion models when modifying zoom setting in the case of zoom lenses. The new models are based on a polynomial approximation to account for the variation of the radial distortion parameters through the range of zoom lens settings and, on the minimization of a global error energy measuring the distance between sequences of distorted aligned points and straight lines after lens distortion correction. To validate the performance of the method we present experimental results on calibration pattern images and on sport event scenarios using broadcast video cameras. We obtain, experimentally, that using just a second order polynomial approximation of lens distortion parameter zoom variation, the quality of lens distortion correction is as good as the one obtained individually frame by frame using independent lens distortion model for each frame.