§ How it works

The final drive is the last reduction between gearbox and wheels. The small pinion on the propshaft turns the large ring gear bolted to the differential. The ratio is simply the tooth count of one divided by the other.

i_f = \frac{N_{\text{ring}}}{N_{\text{pinion}}}

A 41-tooth ring with a 10-tooth pinion gives $41/10 = 4.10$ : the pinion turns 4.10 times for one turn of the wheels. A numerically higher ratio ("shorter" gearing) multiplies torque more for harder acceleration, at the cost of more rpm at any road speed.

Tire size changes the effective ratio

A taller tire covers more ground per turn, which acts like a numerically lower axle ratio:

i_{\text{eff}} = i_f \times \frac{D_{\text{old}}}{D_{\text{new}}} \qquad\qquad i_{\text{needed}} = i_f \times \frac{D_{\text{new}}}{D_{\text{old}}}

The second formula gives the ratio to fit if you want the engine to sit at the same rpm it did before the tire change.

Hunting teeth

When the two tooth counts share no common factor, each pinion tooth eventually meets every ring tooth, which spreads wear evenly. That is why ratios such as 41:10 or 37:9 are so common, and why sets like 40:10 are avoided.

§ How it works

i_f = \frac{N_{\text{ring}}}{N_{\text{pinion}}}

Tire size changes the effective ratio

A taller tire covers more ground per turn, which acts like a numerically lower axle ratio:

i_{\text{eff}} = i_f \times \frac{D_{\text{old}}}{D_{\text{new}}} \qquad\qquad i_{\text{needed}} = i_f \times \frac{D_{\text{new}}}{D_{\text{old}}}

The second formula gives the ratio to fit if you want the engine to sit at the same rpm it did before the tire change.

Ring & Pinion

Inputsdrag · tap · type

Fig. 08Gear mesh with real tooth counts

§ How it works

Tire size changes the effective ratio

Hunting teeth

Ring & Pinion

Inputsdrag · tap · type

Fig. 08Gear mesh with real tooth counts

§ How it works

Tire size changes the effective ratio

Hunting teeth