## Bushie Gearing

The following tables and charts show the overall gear ratios, and road speed with LT315/75 R16 tyres, for a range of engine speeds in each gear combination. Note: these results are calculated for a final drive ratio of 4.875:1 Low Fourth and High First are practically identical, Low Fifth and Sixth split High First and Second.     What Gear To Use For Best Acceleration

For linear motion:

1. $\mbox{force} = \mbox{mass} \times \mbox{acceleration}$
2. $\mbox{power} = \mbox{force} \times \mbox{velocity}$
3. $\mbox{power} = \mbox{mass} \times \mbox{acceleration} \times \mbox{velocity}$ (combine eq 1. and eq 2.)
4. $\mbox{acceleration} = \frac {\mbox{power}} {\mbox{mass} \times \mbox{velocity}}$ (rearrange eq 3.)

From eq 4. if mass is fixed, acceleration increases with power, and reduces with velocity. This tells us that for maximum acceleration, at any particular road speed, select the gear that provides the most power, at that road speed.

Notes: eq 1. could be used to calculate acceleration, but then it would be necessary to calculate the torque at the wheels for every combination of gear ratio and road speed, then divide wheel torque by the dynamic radius of the tyre to find the value for ‘Force’ (AKA ‘motive force’, and ‘tractive effort’). Using power gives the same results, but simplifies the calculations. It is a common myth that maximum acceleration, at any particular road speed, will be obtained by using a gear that puts the engine speed corresponding with maximum engine torque. This is incorrect because it doesn’t factor in the torque multiplication at the wheels that results from the overall gear ratio. If we look at the curves for fourth, and fifth gear at 100 km/h on the chart below, the engine will be producing maximum torque in fifth gear, but fourth gear will produce more torque at the wheels, hence better acceleration.

The following table lists the engine power and torque for a range of engine speeds (taken from Isuzu data for a 1989 year model 4BD1T.  The engine power (kW) that corresponds with the engine speed in each gear for a range of road speed (km/h) is plotted on the following chart. Note tyre size is 315/75R16, and final drive ratio is 4.875:1. Engine torque peaks at the speed corresponding with engine power of 72 kW (2200 rpm).

The chart shows that maximum performance (acceleration) will be achieved when the engine is taken up to to its maximum rpm before changing to the next higher (numerical) gear. Because of the narrow power band of the engine and the wide spacing between gear ratios, the power drops considerably when changing up to the next gear.

Actual acceleration was not determined here, simply how the gearing options affect performance. Four different final drive ratios, 4.111:1 (37×8 teeth), 4.375:1 (35×8 teeth),  4.625:1 (37×8 teeth), and 4.875:1 (39×8 teeth), were evaluated before deciding that 4.875:1 ratio was the better choice for LT315/75R16 tyres. Note: 4.875:1 is only available aftermarket, while the other three ratios are genuine factory Nissan for the Y61 axles and have a better reputation.

With LT315/75R16 tyres, the final drive ratio of 4.875:1 will make the lower three gears useful on 4×4 tracks. Fourth gear is the best gear for maximum acceleration from 80 km/h and the engine is operating within the usable power band from 60 to 110 km/h. Sixth gear will be suitable for cruising at 90 to 100 km/h, giving good fuel economy.  Calculated available Tractive Force from 1989 Isuzu 4BD1T with MXA-6R gearbox for each gear in high range and total (rolling + gradient + aerodynamic) resistance force for various grades, vs speed. Maximum gradient in first gear is shown as approximately 80%. Note: these results are calculated for LT315/75R16 tyres and a final drive ratio of 4.875:1 Open or Save Bushie Ute Tyres and Gearing.ods spreadsheet  (open document format).