This also neatly shows how you can do the calculation and miss the middle gear ratios - ultimately you need the ratio of input to output. In this example, the final output is 30 and the original input is 10. 30/10 = 3/1 = 3:1.
Collections of helical gears in a gearbox are what give the gearing down of the speed of the engine crank to the final speed of the output shaft from the gearbox. The table below shows some example gear ratios for a 5-speed manual gearbox (in this case a Subaru Impreza).
| Gear | Ratio | RPM of gearbox output shaft when the engine is at 3000rpm |
|---|---|---|
| 1st | 3.166:1 | 947 |
| 2nd | 1.882:1 | 1594 |
| 3rd | 1.296:1 | 2314 |
| 4th | 0.972:1 | 3086 |
| 5th | 0.738:1 | 4065 |
Final drive - calculating speed from gearbox ratios. It's important to note that in almost all vehicles there is also a final reduction gear. This is also called a final drive or a rear- or front-axle gear reduction and it's done in the differential with a small pinion gear and a large ring gear (see the section on differentials lower down the page). In the Subaru example above, it is 4.444:1. This is the final reduction from the output shaft of the gearbox to the driveshafts coming out of the differential to the wheels. So using the example above, in 5th gear, at 3000rpm, the gearbox output shaft spins at 4065rpm. This goes through a 4.444:1 reduction in the differential to give a wheel driveshaft rotation of 914rpm. For a Subaru, assume a wheel and tyre combo of 205/55R16 giving a circumference of 1.985m or 6.512ft (see The Wheel & Tyre Bible). Each minute, the wheel spins 914 times meaning it moves the car (914 x 6.512ft) = 5951ft along the ground, or 1.127 miles. In an hour, that's (60minutes x 1.127miles) = 67.62. In other words, knowing the gearbox ratios and tyre sizes, you can figure out that at 3000rpm, this car will be doing 67mph in 5th gear.
If you look at the image here you'll see a the internals of a generic gearbox. You can see the helical gears meshing with each other. The lower shaft in this image is called the layshaft - it's the one connected to the clutch - the one driven directly by the engine. The output shaft is the upper shaft in this image. To the uneducated eye, this looks like a mechanical nightmare. Once you get done with this section, you'll be able to look at this image and say with some authority, "Ah yes, that's a 5-speed gearbox".
So how can you tell? Well look at the output shaft. You can see 5 helical gears and 3 sets of selector forks. At the most basic level, that tells you this is a 5-speed box (note that my example has no reverse gear) But how does it work? It's actually a lot simpler than most people think although after reading the following explanation you might be in need of a brain massage.
With the clutch engaged (see the section on clutches below), the layshaft is always turning. All the helical gears on the layshaft are permanently attached to it so they all turn at the same rate. They mesh with a series of gears on the output shaft that are mounted on sliprings so they actually spin around the output shaft without turning it. Look closely at the selector forks; you'll see they are slipped around a series of collars with teeth on the inside. Those are the dog gears and the teeth are the dog teeth. The dog gears are mounted to the output shaft on a splined section which allows them to slide back and forth. When you move the gear stick, a series of mechanical pushrod connections move the various selector forks, sliding the dog gears back and forth.
With the clutch engaged (see the section on clutches below), the layshaft is always turning. All the helical gears on the layshaft are permanently attached to it so they all turn at the same rate. They mesh with a series of gears on the output shaft that are mounted on sliprings so they actually spin around the output shaft without turning it. Look closely at the selector forks; you'll see they are slipped around a series of collars with teeth on the inside. Those are the dog gears and the teeth are the dog teeth. The dog gears are mounted to the output shaft on a splined section which allows them to slide back and forth. When you move the gear stick, a series of mechanical pushrod connections move the various selector forks, sliding the dog gears back and forth.
In the image to the left, I've rendered a close-up of the area between third and fourth gear. When the gearstick is moved to select fourth gear, the selector fork slides backwards. This slides the dog gear backwards on the splined shaft and the dog teeth engage with the teeth on the front of the helical fourth gear. This locks it to the dog gear which itself is locked to the output shaft with the splines. When the clutch is let out and the engine drives the layhshaft, all the gears turn as before but now the second helical gear is locked to the output shaft and voila - fourth gear.
Grinding gears. In the above example, to engage fourth gear, the dog gear is disengaged from the third helical gear and slides backwards to engage with the fourth helical gear. This is why you need a clutch and it's also the cause of the grinding noise from a gearbox when someone is cocking up their gearchange. The common misconception is that this grinding noise is the teeth of the gears grinding together. It isn't. Rather it's the sound of the teeth on the dog gears skipping across the dog teeth of the helical output gears and not managing to engage properly. This typically happens when the clutch is let out too soon and the gearbox is attempting to engage at the same time as it's trying to drive. Doesn't work. In older cars, it's the reason you needed to do something called double-clutching.
Double-clutching, or double-de-clutching (I've heard it called both) was a process that needed to happen on older gearboxes to avoid grinding the gears. First, you'd press the clutch to take the pressure off the dog teeth and allow the gear selector forks and dog gears to slide into neutral, away from the engaged helical gear. With the clutch pedal released, you'd 'blip' the engine to bring the revs up to the speed needed to engage the next gear, clutch-in and move the gear stick to slide the selector forks and dog gear to engage with the next helical gear.
Double-clutching, or double-de-clutching (I've heard it called both) was a process that needed to happen on older gearboxes to avoid grinding the gears. First, you'd press the clutch to take the pressure off the dog teeth and allow the gear selector forks and dog gears to slide into neutral, away from the engaged helical gear. With the clutch pedal released, you'd 'blip' the engine to bring the revs up to the speed needed to engage the next gear, clutch-in and move the gear stick to slide the selector forks and dog gear to engage with the next helical gear.
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