Simplified Turn Slip Modeling by a Parallel Magic Formula Model

When steering at very low forward velocities or standstill the lateral force and self-aligning moment developed by the tire are influenced by turn slip. Steering angle sweep measurements executed on a drum show the impact of forward velocity on these tire characteristics. Although extensions to the base Magic Formula exist to model these effects, it requires additional tests and increases the complexity of the model. An alternative formulation is explored whereby multiple Magic Formula models are used in parallel across the width of the tire. Using this approach the low speed characteristics can be modeled with fair accuracy, in particular the self-aligning moment is improved, whereas at high speeds the results are identical to the base Magic Formula. A disadvantage is the increase in computing time. The parallel formulation may also be suitable to simplify the modeling of the self-aligning moment resulting from camber.