Why would I use them? Does the minus make me slow, and the plus fast?
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Gasoline engines work by turning something around in a circle quickly. This circular motion of the engine is transferred to the wheels to make the car go. Gasoline engines work best when they’re turning at a certain rate. If they turn too slow, the engine stalls out and dies. If they turn too fast, the engine becomes less efficient and can overheat. The speed that an engine is running is measured in revolutions per minute (rpm).
A typical engine works best around 500-5000 rpm, roughly. If you just hooked up the wheels directly to the engine and revved it up to 5000 rpm, you wouldn’t go very fast, maybe 15mph max. In order to get around this limitation of gasoline engines, we use gears. Gears allow the wheels to turn at a different rate than the engine. In other words, you can insert a gear so that the wheels turn around 5 times every time the engine turns around once. This means that the engine can still remain in the 500-5000 rpm range while the wheels can be taking the car down the road at 70mph.
A transmission is the part of the car that switches gears. Older cars had manual transmissions, which the driver has to constantly manage which gear is being used and manually switch from one to another. These cars have a third pedal called a clutch, and a gear stick to change gears. Later, automatic transmissions were developed to manage the gears automatically so that the driver doesn’t need to worry about it. However, an automatic transmission makes some assumptions about how you want to drive. It generally tries to manage the gears so that you’re driving efficiently and minimizing fuel usage. A manual transmission gives you more control because you get to choose when to shift gears. There might be a situation where you keep the car in a lower gear because you want to accelerate more quickly and you don’t care that it takes more fuel to do that.
So, there are now cars that have automatic transmissions but still allow the driver to manually choose when to shift gears. One popular way that these cars are designed uses paddle shifters, where two paddles behind the steering wheel allow the driver to shift gears without taking their hands off the wheel. This is mostly used for racing and other high performance driving, and is rarely used just for normal trips to the grocery store or commuting.
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