Touchscreens are increasingly being integrated into modern aircraft cockpits due to their space-efficiency and adaptability. However, operating touchscreens in turbulent conditions reduces input accuracy and alters the applied force. These issues are caused by involuntary limb movements induced by external accelerations such as turbulence, called biodynamic feedthrough. Understanding and mitigating this phenomenon is crucial to be able to provide consistent haptic feedback on touchscreens. This study investigates the dynamics of biodynamic feedthrough into the applied normal force on the screen, by conducting a human-in-the-loop experiment with fifteen participants. In the experiment, participants performed both stationary and dynamic position tracking tasks on a touchscreen, while being exposed to turbulence in all three linear motion directions. It was observed that on average 63% higher normal forces were applied during stationary tasks than during dynamic tasks, likely resulting in increased arm co-contraction. Additionally, a second-order mass-spring-damper model was fitted to the obtained force data. It was found that biodynamic feedthrough into the applied normal force has the highest feedthrough levels when the direction of turbulence aligns with the direction of the applied force, and that up to 90% of the disturbance-induced normal force can be described by the proposed individualized models. The results also show the variability of dynamics between participants and therefore the importance of individualized models. These findings provide insights for future developments in adaptive haptic feedback for touchscreens, aiming to enhance the reliability and safety of touchscreen interactions in turbulent environments.