Original post by PTMalewskiGears should be changed depending on five factors:
1. Engine characteristics
2. Current RPMs
3. How quick acceleration or deceleration do you need
4. Are you going on flat ground, hillclimbing or descending
5. Is the car heavily loaded or not.
How to interpret that:
1. Every engine reaches maximum torque and maximum power at different RPMs. Generally speaking, when accelerating gently or going uphill you should use RPMs up to those of maximum torque. When you're going stable speed, it's better to stay a little lower. In gasoline engines you should usually maintain rpms between 2-3k when driving gently.
2. From what has been said above, you can conclude you actually need to monitor RPMs to know if you need to shift-up or kick-down.
3. If you don't need to accelerate quickly you should maintain low-rpms, as has been said above. But if you need rapid acceleration, eg. when accelerating on a slip-road, you should kick-down to get engine rpms between those of maximum torque and maximum power. To get maximum acceleration you should be going full throttle up to rpms of maximum power, and only then shift up. That way your engine produces much more power, but also, because you're using the lower gear, that has shorter ratio, engine rpms are converted to produce even more torque at the wheels. That combined gives you much better acceleration.
On the other hand, the engine also serves as a brake. The higher the rpms, the more rapidly engine will decelerate your car when you get your foot off the throttle. This is usefull especially in the mountains, when using brakes only can cause brakes to overheat and result in brakes failure.
4. Generally when you hillclimb, you might need slightly higher rpms, closer to those of maximum torque of your engine.
When you're going downhill, everything depends on how fast do you want to go. If you want to acceleate, you can shift up to a very high gear, like even 5 or 6 and then your call will accelerate downhill without using the throttle. As a result you will accelerate using no fuel, as ECU will detect negative load and cut fuel injectors off.
If you wish to decelate, you shuld stay on a lower gear, or you might even wish to kick down, to get higher engine rpms, and then get stronger braking effect from the engine. You will still save fuel, as ECU will detect negative load, and cut off the fuel.
5. Well, as above. I think it's obvious now.