Affine control problems arise naturally from controlled mechanical systems. Building on previous results [Agrachev and Biolo, J. Dyn. Control Syst., 23 (2017), pp. 577--595; Caillau Daoud, SIAM Optim., 50 (2012), 3178--3202], we prove that, in the case of time minimization with disk, extremal flow given by Pontrjagin's maximum principle is smooth along strata a well-chosen stratification. We al...