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As the title suggests, how does an automatic gearbox know when to change gear?

For example, how does the autobox know to shift down when you hit a gradient? How does it know to shift up at 2000 rpm when driving gently? When driving 'enthusiastically' how does it know to hold the shift until redline?

On a modern vehicle this will be computer controlled. In addition to the above, how did older analogue transmissions accomplish this before computer controls?

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To put it bluntly, they had to implement a fuzzy logic analog computer based on hydraulics rather than a digital computer based on binary states:

The hydraulic paths as illustrated by How Stuff Works.

As usual, How Stuff Works has a reasonable introduction to the basic concepts with enough vocabulary to kick off more detailed research if you're really interested. That link will take you directly to the breakdown of the hydraulic paths and the speed governor. Those are the core parts required to provide input to that analog computer.

A high level summary of the shift circuit as illustrated by How Stuff Works.

If you look at the shift circuit at the very highest level, you can see how the analog computer is going to work. Vacuum states are generally interpereted as low load, off-throttle or generally as situations suited for higher gears. As the throttle opens, the transmission will tend to gear down. As the governor speeds up, the lower gears cease to be an option.

Slightly off-topic: If you have ever worked in any sort of device control situation, these sorts of pictures give you the creeping heebie jeebies. In any work that I've ever done, I need to know for certain what state the machine is in and what's going to happen next when I provide my input. An analog control computer made out of metal and oil? Ick.

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    Lol, yeah mechanical state machines are really bizarre, thus the move away from carburetors ;-) – Matt Jun 2 '15 at 16:20
  • Hydraulic systems work well without digital - all the platform lifts, a huge amount of agricultural equipment with proprtional control valves : ok definitely needing a delicate touch – Solar Mike Jun 12 '17 at 10:15

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