Predicting Tyre Diameter
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1 Predicting Tyre Diameter by Ian D. Greenwood INTRODUCTION The HDM-4 rolling resistance model uses tyre diameter as an independent variable. Since this is a difficult item to estimate, an analysis was conducted to develop a method for predicting the tyre diameter from the tyre size. This memo presents the results of this analysis. DATA The conventional tyre sizing typology is as follows: aaa/bbrcc where aaa bb cc is the nominal width of the tyre in mm is the aspect ratio is the rim size in inches. For standard tyre sizes the aspect ratio of 82 is usually omitted so it is specified as 175/R13 instead of 175/82R13. Data were obtained from two manufacturers on tyre diameters versus tyre sizes. This is given in Annex A. Several different diameters were reported (or could be inferred): the "maximum overall diameter ; the "static laden radius"; the "calculated rolling circumference".
2 The overall diameter was used in the calculations. The second and third values give diameters typically within 5 per cent of the first. Figures 1 to 3 shows the relationship between the overall tyre diameter and the tyre measurements. ANALYSIS An analysis was conducted to develop a relationship for predicting the rolling diameter. The resulting equation was: DIAM = 25.4 * cc + 2 * aaa * bb /100 where DIAM is the tyre diameter in mm Figure 4 is a plot of the observed vs predicted diameters using this equation. This shows a good correlation between the observed and predicted diameters Rolling Diameter in mm Nominal Width in mm Figure 1: Nominal Width vs Rolling Diameter
3 Rolling Diameter in mm Aspect Ratio Figure 2: Aspect Ratio vs Rolling Diameter Rolling Diameter in mm Rim Size in iinches1 Figure 3: Rim Size vs Rolling Diameter
4 Predicted Tyre Diameter in mm Tyre Diameter in mm Figure 4: Observed vs Predicted Tyre Diameters IMPLEMENTATION INTO HDM-4 The user should be able to select the tyre size from the VFM input screen. The data should then be parsed to establish the nominal width, the aspect ratio and the rim size. Substituting these data in the above equation will give the tyre diameter.
5 Annex A Tyre Data Make Size Rolling Overall Nominal Aspect Wheel Loaded Static Predicted Circum. Diam. Diam. Width Ratio Diam. Radius Diam. Diam. (mm) (mm) (mm) (mm) (in) (mm) (mm) (mm) Dunlop 10.00R20 16PR Dunlop 10R Dunlop 11.00R20 16PR Dunlop 11R Dunlop 12.00R20 18PR Michelin 125R Michelin 125R Dunlop 12R Michelin 135/70R Michelin 135/80R Michelin 135R Michelin 135R Michelin 135R Michelin 145/70R Michelin 145/70R Michelin 145/80R Michelin 145R Michelin 145R Michelin 145R Michelin 145R Michelin 145R Michelin 155/65R Michelin 155/65R Michelin 155/70R Michelin 155/70R
6 Michelin 155/80R Michelin 155/80R Michelin 155R Michelin 155R Michelin 155R Michelin 155R Michelin 165/60R Michelin 165/65R Michelin 165/65R Michelin 165/70R Michelin 165/70R Michelin 165/80R Michelin 165R Michelin 165R Michelin 165R Michelin 175/60R Michelin 175/60R Michelin 175/65R Michelin 175/65R Michelin 175/70R Michelin 175/70R Michelin 175/70R Michelin 175R Michelin 175R Michelin 175R Michelin 185/55R Michelin 185/55R Michelin 185/60R Michelin 185/60R Michelin 185/65R Michelin 185/65R
7 Michelin 185/70R Michelin 185/70R Michelin 185/80R Michelin 185/80R Michelin 185R Michelin 185R Michelin 195/45R Michelin 195/45R Michelin 195/50R Michelin 195/55R Michelin 195/55R Michelin 195/60R Michelin 195/60R Michelin 195/65R Michelin 195/65R Michelin 195/70R Michelin 195/70R Michelin 195/70R Michelin 195/80R Dunlop 195R Michelin 195R Michelin 205/40R Michelin 205/45R Michelin 205/50R Michelin 205/50R Michelin 205/50R Michelin 205/55R Michelin 205/55R Michelin 205/55R Michelin 205/60R Michelin 205/60R
8 Michelin 205/60R Michelin 205/65R Michelin 205/70R Michelin 205/70R Dunlop 205/75R Dunlop 205R14 C 6PR Michelin 215/40R Michelin 215/40R Michelin 215/45R Michelin 215/45R Michelin 215/50R Michelin 215/60R Michelin 215/65R Michelin 215/75R Dunlop 215/75R Michelin 215/80R Michelin 225/40R Michelin 225/40R Michelin 225/45R Michelin 225/45R Michelin 225/50R Michelin 225/50R Michelin 225/55R Michelin 225/55R Michelin 225/55R Michelin 225/60R Michelin 225/60R Michelin 225/65R Michelin 225/70R Michelin 225/75R Dunlop 225/75R
9 Michelin 235/40R Michelin 235/40R Michelin 235/45R Michelin 235/50R Michelin 235/60R Michelin 235/70R Michelin 235/70R Michelin 235/75R Dunlop 235/75R Michelin 245/35R Michelin 245/40R Michelin 245/40R Michelin 245/45R Michelin 245/45R Dunlop 245/70R Michelin 255/40R Michelin 255/45R Michelin 255/60R Michelin 255/70R Dunlop 255/70R Michelin 255/75R Michelin 265/35R Michelin 265/40R Michelin 265/40R Michelin 265/70R Dunlop 265/70R Michelin 265/75R Michelin 275/40R Dunlop 275/70R Dunlop 275/80R Michelin 285/35R
10 Michelin 285/40R Dunlop 285/70R Michelin 295/35R Dunlop 295/80R Dunlop 295/80R Dunlop 305/70R Dunlop 305/70R Dunlop 315/70R Dunlop 315/80R Michelin 325/30R Dunlop 365/80R Dunlop 385/65R
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