In regards to whether it is best to use a lower gear and more RPMs while towing or whether to use a higher gear and fewer RPMs, I am in favor of keeping the RPMs up.
Every time the piston goes up and down there is a little wear. It isn't much but it isn't nothing either. Higher RPMs also mean more inertia loads on the engine. Those increase as the square of the speed so they build up quickly.
On the other hand, lower RPMs mean you need more torque which means higher cylinder pressures and temperatures. More cylinder pressure makes the rings press against the cylinder walls harder which also leads to more wear. This is probably more important than more revolutions. Higher temps make the oil thinner and everything weaker leading to increased wear and increased stress.
On balance it is better to run the engine near it's midrange than near the maximum RPMs and at mid throttle rather than full throttle. Not only is it better for the engine stress-wise but it is better for economy and driveability.
When running empty and
light it is possible to have low RPMs and low throttle at the same time which gets the best economy and wear. When towing though it is often the case that you have to compromise one or the other. By staying near the middle on both you can minimize the adverse effects.
An automatic transmission almost never wears out the gears inside. When a transmission goes it is the clutches that die. Clutches only wear during a shift. Once the shift is done the clutches don't wear at all. Clutches that shift a lot absorb a lot of power and get hot fast. If a transmission is constantly hunting back and forth between gears, the clutches can get hot enough to be damaged even if they aren't worn out.
For this reason it is a good idea to shift an automatic transmission into a gear it can live with and let the engine take a little more wear instead.
I have a car that tries to figure this out for me. It does an okay job but using a tow/haul button works better. By using tow/haul mode you cause the transmission to calculate shifts with a different goal in mind. The computer tries to protect the transmission by staying in lower gears and shifting less.
As far as the transmission is concerned, a really firm, borderline harsh, sift is best because it involves less slipping and so less heat buildup. People don't like to even feel that the transmission is doing anything. We like slow, gradual shifts that we can't feel. These are pretty hard on the clutches.
It isn't easy to make a drive train that will do everything any of us can think of and do it well. Things are pretty well sorted right now but when we have all electric vehicles we will wonder why we ever put up with all of this nonsense.
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