Previous work in the open-loop behavior of magnetically driven screws in soft tissue has focused on the impact of magnetic field rotation speed and pitch angle, measured between the field's rotation axis and the screw's principle axis, on the average magnetic torque, both in-plane and out-of-plane. However, prior work did not rigorously consider the role of screw geometry and tissue material properties on the resulting trajectory. This study seeks to develop a plausible empirical model from experimental measurements in an agar gel tissue phantom for use in further research and feasibility studies of magnetic screws for in vivo applications. Non-dimensional parameters representing rotation speed, pitch angle, screw size, magnetic strength, and tissue stiffness are varied orthogonally. Circular trajectories are fitted to the resulting recorded trajectories. Using physical insight and observation of the trends of the non-dimensional turning radius/curvature, simple models for each parameter group are proposed. A final empirical model is then proposed to unify the individual models.