Gear ratio Totally Explained

Everything about Gear Ratio totally explained

The gear ratio is the relationship between the number of teeth on two gears that are meshed or two sprockets connected with a common roller chain, or the circumferences of two pulleys connected with a drive belt.

General description

In the picture to the right, the smaller gear (known as the pinion) has 13 teeth, while the second, larger gear(known as the gear) has 21 teeth. The gear ratio is therefore 13/21 or 1/1.62 (also written as 1:1.62).
   This means that for every one revolution of the pinion, the gear has made 1/1.62, or 0.62, revolutions. In practical terms, the gear turns more slowly.
   Suppose the largest gear in the picture has 42 teeth, the gear ratio between the second and third gear then is; 21/42 = 1/2 and for every revolution of the smallest gear the largest gear has only turned 0.62/2 = 0.31 revolution, a total reduction of around 1:3.
   Since the number of teeth is also proportional to the circumference of the gear wheel (the bigger the wheel the more teeth it has) the gear ratio can also be expressed as the relationship between the circumferences of both wheels (where d is the diameter of the smaller wheel and D is the diameter of the larger wheel):
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gr = frac

Gear	nches per engine revolution	peed per 1000 RPM
1st gear	8.1 inches	7.7 mph
2nd gear	11.6 inches	11.0 mph
3rd gear	16.8 inches	15.9 mph
4th gear	24.0 inches	22.7 mph
5th gear	28.6 inches	27.1 mph
6th gear	42.9 inches	40.6 mph

Wide-ratio vs. Close-ratio Transmission

A close-ratio transmission is a transmission in which there's a relatively little difference between the gear ratios of the gears. For example, a transmission with an engine shaft to drive shaft ratio of 4:1 in first gear and 2:1 in second gear would be considered wide-ratio when compared to another transmission with a ratio of 4:1 in first and 3:1 in second. This is because, for the wide-ratio first gear = 4/1 = 4, second gear = 2/1 = 2, so the transmission gear ratio = 4/2 = 2 (or 200%). For the close-ratio first gear = 4/1 = 4, second gear = 3/1 = 3 so the transmission gear ratio = 4/3 = 1.33 (or 133%), because 133% is less than 200%, the transmission with the 133% ratio between gears is considered close-ratio. However, not all transmissions start out with the same ratio in 1st gear or end with the same ratio in 5th gear, which makes comparing wide vs. close transmission more difficult.
Close-ratio transmissions are generally offered in sports cars, in which the engine is tuned for maximum power in a narrow range of operating speeds and the driver can be expected to enjoy shifting often to keep the engine in its power band.

Idler Gears

Note that in a sequence of gears chained together, the ratio depends only on the number of teeth on the first and last gear. The intermediate gears, regardless of their size, don't alter the overall gear ratio of the chain. But, of course, the addition of each intermediate gear reverses the direction of rotation of the final gear.
An intermediate gear which doesn't drive a shaft to perform any work is called an idler gear. Sometimes, a single idler gear is used to reverse the direction, in which case it may be referred to as a reverse idler. For instance, the typical automobile manual transmission engages reverse gear by means of inserting a reverse idler between two gears.
Idler gears can also transmit rotation among distant shafts in situations where it would be impractical to simply make the distant gears larger to bring them together. Not only do larger gears occupy more space, but the mass and rotational inertia (moment of inertia) of a gear is quadratic in the length of its radius. Instead of idler gears, of course, a toothed belt or chain can be used to transmit torque over distance.

Further Information

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