Advances in the Modelling of Motorcycle Dynamics - ResearchGate

262 R.S. SHARP ET AL.Figure 8. Tyre lateral force results for 180/55 tyre from [20] (thick lines) with best-fit reconstructions(thin lines). Camber angles 0, 10, 20, 30, 40, 45 ◦ .4.3. ALIGNING MOMENTS IN LATERAL SLIP AND CAMBERAligning moment results are included in [23] for the 160/70 tyre and in [20] for120/70 and 180/55 tyres. Three loads are covered in the former but only two inthe latter, which makes the model very heavy in parameters for the amount ofexperimental data available. In setting the parameters for the 160/70 tyre of [23]assuming the full quadratic dependency of B t on load, the fitting is good within theload range used for the measurements but the extrapolation is poor, with constraintviolations at low and high loads. With linear dependency, the fitting is almost as goodand the extrapolation problem can be eliminated. Consequently, B t is consideredlinear with load. Even so, there are many parameter combinations which givealmost equally good fits to the limited data. It is advantageous to use some physicalreasoning to guide the choice between the alternatives. The product of B t , C t andD t is the aligning moment stiffness of the tyre. According to the “Brush Model”[23], the aligning moment stiffness is proportional to load to the power 1.5, so thatfeature is used to aid the choice of the secondary parameters q Bz1 and q Bz2 , see (18).It turns out to be quite feasible to match that characteristic closely. Also, as before,