A new version of the Spalart-Allmaras model is presented to improve adverse pressure gradient flow predictions. High fidelity numerical simulations confirmed the sensitivity of the log-law region to the pressure gradient, for both its slope and its intercept. The study is limited to the correction of the slope by tuning the von Kármán constant according to the local dimensionless pressure gradient p+ and is a first step towards better approach to account for pressure gradients. A new model is calibrated on a NACA 4412 wing at Rec = 1M section and then applied to 3D cases, including a simplified aircraft configuration. The new model displays encouraging results regarding the inner layer but exhibits limitations in the outer layer and the need for another kind of correction.