I tried the acceleration downhill techniquie and what I've found out is this...
You use gas going down the hill/risk getting caught by cops/and if you don't judge the next hill right - you have to shift it back into drive and continue up the hill.
I've found it's better to just coast down the hill and TRY to get to a fast speed and coast up until I HAVE to shift in drive and maintain a speed above the point of downshifting. I've noticed gains that way and it's so much more common sense and easier on the stress level when you're unsure if you'll make it from the cops or shifting in drive again...
There have been some good comments here, but I wanted to make a comment regarding the "gravity multiplier" idea:
The laws of physics disagree with this idea. Regardless of whether you are coasting in neutral or accelerating in gear, gravity will pull on your car with the exact same amount of force. You do not get any kind of "multiplier" effect by accelerating downhill--you just get the same extra acceleration you would have gotten by coasting. Likewise, you are going to have to fight the same amount of drag for going up the hill whether you do it with leftover momentum from coasting or with the accelerator pedal.
I'll try to summarize that effectively:
It will take a certain amount of power to travel up a hill and down the other side (or down into a valley and back out), and, in terms of physics, it makes no difference when you apply that power (i.e. accelerate to 100MPH at the beginning and coast, or coast the beginning until you must press the gas pedal, or anything in between).
Here's the only possible difference that I know of (and I do not have perfect knowledge, so there could be something I'm missing): If you coast down a hill in gear, then you are effectively "engine braking", and you would be better off in neutral (in terms of FE -- safety and local laws may differ on this).
Oh, and whatever you do, don't use your brake pedal on a hill unless you absolutely must. It's a pet peeve of mine that I run into on my commute on a regular basis--people brake to keep from going 5MPH over the speed limit, and then have to hammer the gas to get up the other side. There's one spot where, if no one is in front of me, I can coast for almost a mile (up to a stop sign), but that only happens about once a month.
Anyone here gone over the continental divide? 6393 ft, start at about 5300. That's one of 4 passes I cross to get to Coeur De' Alene. With 5 passengers in my GP I managed 34mpg. I held it in 4th (no lock) as long as possible going up, maintaining about 50-55mph. Going down, I put in N and coasted, no braking. That isn't safe, nor do I advocate doing 97mph down a pass. But I did manage 34mpg with 800 extra lbs in the car than I normally have crossing those passes.
I usually can hold the throttle at about 2/3-3/4 without it hopping outa lockup. With that I can eek up to 80-85 before the pass, and just slowly ease off the throttle till I want to backshift (tapping the brakes with the left foot while maintaining throttle) has worked quite well for me.
I know this works because my friend drove back and didn't do any of the things I do, he just drove. 29.4mpg. Yeah. He won't be driving my car again.
I know what you mean about people braking down a hill only to accelerate to get back up it. They have effectivly wasted the gas in their car as well as everyone that is behind them. I usually will try to figure out how fast the car in front of me is going and back off .5 to 1 mph, let anyone who wants to pass me, and most of the time I'm free of other drivers costing me fuel/money because of their poor driving habits.
I can't remember whether it was on this site or somewhere else on the Internet, but what I was reading was suggesting coasting down the grade and then on the uphill grade rather than maintaining your previous speed let it drop a few mph to save fuel. I think they were talking about decreasing speed by 5 mph or less, although it is something that I rarely do.
Remember aero drag is by far the greatest source of energy losses at high speeds, close to 2/3 at 65 MPH.
I thankfully was able to follow an unloaded dumptruck up the grade this week and was able to keep the car in OD without downshifting for the entire grade at 60 mph! Shows me the drag loss is much higher than I thought.
I usually just keep my right foot steady and let the car pick up speed down the hill then let it slow slightly on the up hill side.The speeds are kept within reason though and there aren't that many big hills around here anyway.I try to keep it less than 10 m.p.h over the limit and 5 m.p.h. under.