# Calculating gearing

## Juggling numbers is now easy!

### by Julian Edgar

Click on pics to view larger images

Gearing – the speed relationship between the driven wheels and engine revs – used to be really hard to get your head around. Not so much in the concept but in the practical reality of working out what gearing changes would result from making changes to – say – the tyre diameter. But these days, with the availability of online calculators, it’s all much easier.

Let’s take a look.

### High or low overall gearing?

Long ago, cars were geared in the following way. In the highest gear, maximum speed of the car was reached at maximum revs for power.

So if the car did 200 km/h in 4th gear (most cars then didn’t have more than four gears), then at 200 km/h the engine might be doing 6000 rpm. Therefore, still in 4th gear, at 100 km/h the engine would be turning at 3000 rpm.

To put that another way, that’s (100 / 3 =) 33.3 km/h per 1000 rpm.

(Incidentally, if you’ve not driven a manual transmission car geared in this way, you might be rather surprised at the throttle response that such a car has at highway speeds. It’s excellent!)

Gearing for maximum-speed-at-peak-power-revs in top gear started to disappear when manufacturers began chasing better fuel economy, lower emissions and lower NVH (noise, vibration, harshness).

Instead of being geared for maximum speed, cars started being geared as high as possible, while still giving adequate hill climbing at normal country road speeds. Therefore, if you could drive along at (say) 100 km/h in top gear (which might now be 6th), and climb normal hills without down-changing, then that was OK.

So rather than the engine turning at 3000 rpm at 100 km/h (33.3 km/h per 1000 rpm), it might now be turning at only 2000 rpm – 50 km/h per 1000 rpm. (And so at 200 km/h, this car’s engine would be turning at only 4000 rpm.)

Throw an auto trans into the mix, and so one where the gearbox can drop a gear of its own accord, or an infinitely variable trans, where it can slide backwards in ratio, and the overall gearing can in current cars be even higher. (And diesels, higher again.)

So if you’re chasing better throttle response and more acceleration at a given engine speed, it’s likely that you will want to lower gearing rather than raise it.

But how do you change gearing – and how do you calculate what you’ve got, first?

### Calculating gearing

In between the engine’s flywheel and the road is a series of gears. Firstly, the gearing provided by the gearbox. Then the gearing provided by the final drive (eg differential). Then the gearing provided by the diameter of the tyres.

Other than the tyres, each of these is expressed as a ratio. These ratios are in the specs for the car. Let’s take a look at an example.

1st gear ratio: 3.461

2nd gear ratio: 1.750

3rd gear ratio: 1.096

4th gear ratio: 0.857

5th gear ratio: 0.710

These are the ratios of each gear in a 5-speed manual gearbox. The lower the number, the higher the gearing – that is, the slower the engine is turning for a given road speed. Note that in this car both 4th and 5th ratios are less than 1:1 – so both 4th and 5th are what is called ‘overdrive’ ratios.

In this car, the final drive ratio is 3.208.

Now there’s also that other ‘gear’ – the diameter of the tyre. The car that we’re using as the example is a very small car, and it has a standard tyre size of 165/65 on 14 inch rims. To work out its influence in the gearing, we need to find out what the rolling diameter of a 165/65 14 tyre is.

An online search for ‘tyre size calculator’ quickly finds a calculator that we can use – see http://www.inawise.com/tyre-calculator/tyre-size-calculator.html.

Plugging the tyre size into the calculator gives us a rolling diameter of 570.1mm – this is the way that the gearing of the tyres is indicated.

What we need next is a gear ratio calculator, like the one at http://www.osella.com.au/gear-ratios.htm.

We type in all the numbers and decide on an engine rpm - let’s say 2150 rpm. That gives the following road speeds:

1st gear ratio: 21 km/h

2nd gear ratio: 41 km/h

3rd gear ratio: 65 km/h

4th gear ratio: 83 km/h

5th gear ratio: 100 km/h

So at 100 km/h in fifth gear, the engine is turning at 2135 rpm – that’s gearing in 5th of 46.5 km/h per 1000 rpm.

(To show how high-geared this is, what speed would the car theoretically do in 5th gear at 6000 rpm? The answer is 281 km/h – but the top speed of this car is actually only 180, achievable in 3rd gear!)

### Changes

So the standard car at 100 km/h in 5th gear is turning the engine at 2150 rpm. But on the road at 100 km/h, it’s actually much nicer to drive around in 4th gear – about 2600 rpm. That’s about 20 per cent faster in revs, which (as you’d expect) matches the percentage change in gear ratio from 0.710 (5th) to 0.857 to (4th).

So what could we do if we wanted to drop gearing by 20 per cent – to be running the current 4th gear revs in 5th gear? We could change the final drive (hard in this front-wheel drive car) or we could change tyre diameter.

But would we get sufficient gearing change by altering tyre diameter?

Let’s go from 165/65 14 tyres to smaller diameter wheels and lower profile tyres – say 165/55 on 13 inch wheels. The tyre size calculator shows that this has decreased rolling diameter from 570.1mm to 511.7mm. Plug that into the gearing calculator and revs in 5th gear at 100 km/h are now just under 2400 rpm.

So the engine revs at 100 km/h were 2150, we wanted 2600 rpm - and by changing tyre and wheel size, we got 2400 rpm. Going to smaller wheels and even lower profile tyres is, in this case, not desirable (or perhaps even possible), so the maximum gearing reduction we’re going to get easily is about 10 per cent.

Of course, in rear-wheel drive cars, the diff can be much more easily changed, so you could then work out the combination of revising the wheel/tyre diameter and changing the diff ratio – or even changing the gearbox completely.

### Conclusion

The availability of online calculators for tyre rolling diameter and gearing means that it now takes only moments to trial different combinations of gearing and see what results. Playing around with the numbers has never been easier!

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