Wheel alignment angles and tyre size numerical

(a) Wheel alignment angles

Wheel balancing (static and dynamic) corrects uneven mass of the wheel and tyre by adding weights, to prevent vibration.

(b) Tyre size

Marking 205/55 R16: width $w = 205$ mm, aspect ratio $55\,\%$, radial, rim diameter 16 in $= 406.4$ mm.

$$\begin{aligned} h &= 0.55 \times 205 = 112.75\ \text{mm} \\ D &= 406.4 + 2(112.75) = 631.9\ \text{mm} \\ C &= \pi D = 1.985\ \text{m} \\ \text{rev/km} &= \frac{1000}{1.985} = 504 \end{aligned}$$

New tyre 215/60 R16:

$$\begin{aligned} h' &= 0.60 \times 215 = 129\ \text{mm} \\ D' &= 406.4 + 2(129) = 664.4\ \text{mm} \quad (5.1\,\%\text{ larger}) \\ \text{rev/km} &= \frac{1000}{\pi \times 0.6644} = 479 \end{aligned}$$

The speedometer counts wheel revolutions, so it reads according to the old diameter:

$$v_{actual} = 100 \times \frac{664.4}{631.9} = 105.1\ \text{km/h}$$

Answer: sidewall $= 112.75$ mm, $D = 631.9$ mm, $504$ rev/km; new $D = 664.4$ mm; actual speed is $105.1$ km/h when the speedometer reads 100 km/h (it under-reads by about 5 %).