The tire size calculation involves determining the sidewall height, tire diameter, circumference, and number of revolutions per mile based on the tire's width, aspect ratio, and wheel diameter.
Sidewall Height:
\[ \text{sidewall height} = \frac{\text{profile ratio} \times \text{width}}{100} \]
Tire Diameter:
\[ \text{tire diameter} = \text{wheel diameter} + (2 \times \text{sidewall height}) \]
Circumference:
\[ \text{circumference} = \pi \times \text{diameter} \]
Revolutions per Mile:
\[ \text{revolutions number} = \frac{63360}{\text{circumference}} \]
For a tire with code P215/65R15:
Width: 215 mm, Aspect Ratio: 65%, Wheel Diameter: 15 inches
Sidewall Height:
\[ \text{sidewall height} = \frac{65 \times 215}{100} = 139.75 \, \text{mm} \]
Converted to inches:
\[ \frac{139.75}{25.4} \approx 5.5 \, \text{inches} \]
Tire Diameter:
\[ \text{tire diameter} = 15 + (2 \times 5.5) = 26 \, \text{inches} \]
Circumference:
\[ \text{circumference} = \pi \times 26 \approx 81.7 \, \text{inches} \]
Revolutions per Mile:
\[ \frac{63360}{81.7} \approx 776 \]
