# Fuel efficiency when decelerating on a hill

Another efficiency question from me out of curiosity.

Let's say that I am driving at a decent efficiency rate (say 40 MPG) and am coming up on a hill, with no cars immediately behind me or traffic lights ahead of me. I know that once I crest the hill I will start to accelerate rapidly, building up enough speed going down that I'll eventually need to brake to avoid going above the speed limit.

It makes sense that taking my foot off the gas before I fully crest the hill could help. Decelerate a little as I go up the last tiny bit of the hill, then regain that speed on the way down, avoid having to break soon.

However, this only works to a point. Worst case scenario I allow my car to decelerate going up the hill until I'm going at nearly idling speed, with 70% of the energy output from my idling car going to counteracting gravity on the hill and my overall efficiency being horrible.

So my question is where is the sweet point? How much can one allow a car to decelerate going up a hill before they start to lose more efficiency letting their engine idle to push the car the rest of the way, compared to using gas to overtake the hill sooner despite knowing your have to brake on the way down?

• I think you mean 40MPH? Commented Nov 4, 2015 at 7:35
• I don't get your question. What does this sentence with 70% of the energy output from my idling car going to counteracting gravity on the hill and my overall efficiency being horrible mean? Where does 70% come from? I also guess that here and in your next sentence "efficiency" does not mean fuel efficiency, but something like 'how fast you get to your destination'. Please edit your question, use strict definitions, and do not put guesses or estimates in (that's for answering, not for asking).
– user2451
Commented Nov 4, 2015 at 7:44
• @HighlyIrregular lol. I wrote this after being side tracked while comparing cars for fuel efficiency. Call it a Freudian slip, 40 MPG was an important price point in my calculation of more fuel efficient vehicles (a basis for my way-to-complicated-because-I'm-a-geek-and-like-game-theory math to get a rough average savings per extra MPG a vehicle had. My fingers forgot I was discussing something different here :) Commented Nov 4, 2015 at 14:15
• Why not get an electric car? Then you get most of the energy back when you brake. It is FAR cleaner and a much better vehicle. It is also very cost effective.
– user2433
Commented Nov 16, 2015 at 18:08
• @zagadka314 because I can do more then 6 hours of driving a night on occasions, more then 300 miles total with as little as 15 minute pit stop in the middle, and I don't think that an electric can handle that long a drive without stranding me. Commented Nov 16, 2015 at 21:36

Generally a driver doesn't know the exact angle of the hill at any point in time, nor do they generally know the exact combination of gear and gas-pedal that will be the most efficient.

Maybe some day those things become standard features, and maybe the car could even calculate where the top of the hill is and work out how to optimise fuel consumption too.

In the meantime, I tend to assume that if I can relax my foot on the gas-pedal as much as possible without losing too much speed, and remain in the highest possible gear while doing it (without making the engine do a "pinking" sound!), then I'm getting a sensible combination of speed and efficiency. As Simon W mentions in his answer, it's also important to be courteous to drivers behind you.

An experienced driver should, with a little practice, easily get a feel for when to ease their foot off the pedal as they approach the crest.

The reverse of the situation applies too; just before the start of the hill, adding a little extra speed can reduce the time spent having to fight gravity while going up the hill, and thus improve efficiency.

Keep in mind that as per the formula for drag, air resistance increases exponentially as speed increases.

• Do you have a reference for adding a little extra speed can reduce the time spent having to fight gravity while going up the hill, and thus improve efficiency? Especially in light of your comment about drag - by adding speed, you're fighting something that increases with the square of your speed. Certainly it stands to reason the if you want to maintain your speed this intuitively makes sense, but if you don't care about speed any only care about efficiency, is it really better to speed up before you go up the hill? Commented Nov 4, 2015 at 21:19
• Highly irregular isn't exactly correct, but he could be depending on circumstances, an engine is designed to produce the most horse power at an optimal rpm, when going uphill you want to maintain that optimal RPM, if you can do that in 5th gear, then great, if not then you need to drop to 4th or whatever is appropriate for that slope. If you lug your way up a hill you may save gasoline, but you are damaging your engine. Commented Nov 5, 2015 at 17:22

Counteracting gravity on the hill will require roughly the same amount of energy regardless of the speed you are travelling at (with some small variation according to the engine's efficiency at different rpm).

The sweet spot is probably not a technical one about efficiencies, but a practical one about how slowly you are willing to crest the hill, and (if there is other traffic or poor sightlines) how slowly it is safe and considerate to other road users to be travelling.

• While it's true that the same amount of potential energy is needed to get to the crest of the hill, a car traveling faster over the crest will have more kinetic energy that needs to be scrubbed off (and lost unless the car has some energy recovery mechanism like a hybrid). So the driver that maintains a steady 40mph speed until the crest of the hill then rides the brakes on the downhill will be using more fuel than the driver that takes his foot off the gas 500 ft before the crest and lets his car slow almost to a stop at the crest before picking up speed on the downhill. Commented Nov 4, 2015 at 21:12
• @Johnny yes, that was the point of the question. I hadn't missed that. Commented Nov 4, 2015 at 21:21
• Shouldn't an answer to the question have an actual answer to the question? Commented Nov 4, 2015 at 21:25
• @Johnny I had intended it to, but on re-reading it wasn't obvious. I've clarified. Commented Nov 4, 2015 at 21:27
• Although it's true that energy needed to climb 100 ft is the same regardless of speed, maintaining the correct RPM is the most efficient conversion of fuel to energy. Commented Nov 5, 2015 at 17:25

All engines have an optimum operating range, most cars this is somewhere between 3000 and 5000 rpm depending on the engine and gearing.

To use the least fuel without damaging your engine while climbing a hill, you want the car to maintain the proper rpm. Efficiency is all about rpm.

Trying to climb a hill in 5th gear going 20 mph is very bad for the engine. It's called lugging. It causes pits and additional wear on your pistons, cylinders and head and by the time you save \$500 worth of fuel consumption you may have set yourself up for a \$500 or more engine overhaul.

Acceleration is easier and more efficient on a horizontal plane, so for efficiency, you want to accelerate to your peak speed before you begin to slope upward. Then again as you reach the crest, you can allow your self to naturally decelerate as the slope approaches horizontal again and allow your car to accelerate naturally while going down hill.

For hyper-miling this will burn the least amount of fuel.

Remember this non-intuitive fact, it's braking that burns more fuel, not acceleration. You need to accelerate a car to make it go, but if you are hitting the brakes, it means you wasted perfectly good fuel

• I think the asker understood most of that, but was intending to ask how much they should allow themselves to naturally decelerate when reaching the crest. Commented Nov 5, 2015 at 17:39
• As much as possible without having to hit the gas or be a nuisance to others. Commented Nov 5, 2015 at 17:42
• I think that bits of this that aren't irrelevant are wrong.
– Móż
Commented Nov 6, 2015 at 1:44