In a car with automatic transmission, what's the best way to accelerate so as to minimize fuel consumption? Assume I'm not going to change the gears manually.
Note that I'm also considering non-flat scenarios, such as going over a hill.
For example, should I keep speed constant, or minimize the braking time, or keep the RPM at a constant value, or minimize the RPM, or accelerate as quickly as possible...? Is there a general rule?
Each car is a bit different but the highest efficiency for automatic transmission acceleration is usually at the point before the the transmission decides to automatically downshift.
The data you should look for is called "brake specific fuel consumption".
This may be a broad generalization, but your highest efficiency for normal gasoline cars with throttle plates would be at the highest throttle opening in the highest gear possible, and in some cars with fuel enrichment, below the engine load that would require fuel enrichment to prevent engine detonation.
For Hypermilers they do something called "pulse and glide" to take advantage of this engine attribute.
In other words... "Maximize Throttle!!" ... but dont let the automatic transmission shift to a lower gear. You are basically borderline lugging the engine. And if you feel adventurous turn off the engine when acceleration is no longer needed.
This is a good article on brake specific fuel consumption
Wikipedia entry on Pulse and Glide
The more throttle you apply the worse your gas mileage is going to be. If you want to absolutely maximize your gas mileage, use the minimum throttle possible. So accelerate only enough to just barely creep the speed upwards. On a hill, you would want a constant velocity and use terrain to your advantage. Basically put the car in neutral when going down a hill and gain all the speed you can. This will help you coast over whatever terrain comes after the downhill. On uphills, don't accelerate. Run a high gear and keep the RPM as low as possible to climb the hill.
Since you can't do these things and stay within the law, safety, and other factors, it's not clear the savings on gas is worth the hassle of driving this way.
Doing these things might change your miles per gallon by 2 or 3. Call it 2 MPG, and assume your tank has a 15 gallon capacity. You would increase your trip tank by 30 miles, and that's only for highway miles. For the city you would probably not see a 2 MPG difference. If gas costs $2.50 US per gallon, and your mileage is roughly 25 MPG, your savings is about $2.25 US per tank. Given the pain of driving like this, might not be worth it.
Hope that helps!
I don't know if they still have them, but back in the '60's they'd hold "economy contests" where the contestants would try to maximize economy on an oval track. The preferred method was to get a manual transmission car and lug it in high gear from 10 mph or so up to 25, then they'd push in the clutch and shut off the engine and coast back down to 10 mph, turn on the ignition and dump the clutch to start the car again. The gas pedal was held to the floor the entire time. The economy savings came from lack of engine vacuum fighting the pistons on the intake stroke, and since the gas pedal was held steady, no accelerator pump action to squirt extra gas in.
I tend to accelerate normally up to just before the point where the transmission shifts, then let up on the gas a bit to "help" the transmission shift, then resume acceleration. Accelerating too slowly obviously keeps you in the lower gears longer than necessary.
