## 382 Setting bottom gear

The maximum payload and gradient the vehicle is expected to haul and climb determines the necessary tractive effort, and hence the required overall gear ratio. The greatest gradient that is likely to be encountered is decided by the terrain the vehicle is to operate over. This normally means a maximum gradient of 5 to 1 and in the extreme 4 to 1. The minimum tractive effort necessary to propel a vehicle up the steepest slope may be assumed to be approximately equivalent to the sum of both the rolling and gradient resistances opposing motion (Fig. 3.31).

The rolling resistance opposing motion may be determined by the formula:

Rr = 10CrW

where Rr = rolling resistance (N)

Cr = coefficient of rolling resistance W = gross vehicle weight (kg)

Average values for the coefficient of rolling resistance for different types of vehicles travelling at very slow speed over various surfaces have been determined and are shown in Table 3.2.

Likewise, the gradient resistance (Fig. 3.33) opposing motion may be determined by the formula:

where Rg = gradient resistance (N)

W = gross vehicle weight (10W kg G = gradient (1 in x) = sin 9

 Vehicle type Coefficient of rolling resistance (Cr) Concrete Medium hard soil Sand Passenger Car 0.015 0.08 0.30 Trucks 0.012 0.06 0.25 Tractors 0.02 0.04 0.20

Note The coefficient of rolling resistance Is the ratio of the rolling resistance to the normal load on the tyre.

Note The coefficient of rolling resistance Is the ratio of the rolling resistance to the normal load on the tyre.

 Cû fie__ W f Vn A f 9 ~ G G - 1 in x

Fig. 3.33 Gradient resistance to motion

Fig. 3.33 Gradient resistance to motion where GF = final drive gear ratio Gb = bottom gear ratio ^m = mechanical efficiency E = tractive effort (N) T = maximum engine torque (Nm) R = effective road wheel radius (m)

Example A vehicle weighing 1500 kg has a coefficient of rolling resistance of 0.015. The transmission has a final drive ratio 4.07:1 and an overall mechanical efficiency of 85%.

If the engine develops a maximum torque of 100 Nm (Fig. 3.34) and the effective road wheel radius is 0.27 m, determine the gearbox bottom gear ratio.

Assume the steepest gradient to be encountered is a one in four.

Rr = 10CrW

10 x 1500

3750N

TGf^m 3975

0.27

Tractive effort = Resisting forces opposing motion

where E = tractive effort (N)

R = resisting forces (N)

Once the minimum tractive effort has been calculated, the bottom gear ratio can be derived in the following way:

Driving torque = Available torque ER = T GbGF^M

TGF^M

Engine speed IN) [rgv/min)

Fig. 3.34 Engine torque to speed characteristics

Engine speed IN) [rgv/min)

Fig. 3.34 Engine torque to speed characteristics

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