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Mileage Climbing and Descending

I’m convinced that mileage per gallon is better if one drives up a mountain and down the other side than if one travels the same distance on a flat road. That is to say, if one drives 100 miles ascending 5000 feet and down 5000 feet, the mileage is better over the whole trip than if one drives 100 miles on a flat road. It would appear to follow that the energy demands of an ascent are less than the energy savings of a descent. Intuitively, I find that puzzling. I would have thought that the average miles per gallon should be the same. Anyone have an insight as to why my observation might hold true, and why the intuitive answer is wrong? Best wishes, Christopher Mueller

I have no technical expertise, but I would imagine that going up hill, the effort, just like walking, is exponentially more difficult then traveling on level ground do to gravity. Going down hill doesn’t decrease the work as substantially do to air resistance remaining constant. So as a math major, I intuitively find a net increase in energy required going up and down compared to traveling on level ground. This all assumes you try to keep the speed constant. I assume also there are other factors I am not considering and could easily be swayed either way. ;=)

Nope, a flat road will yield the best mileage, all else being equal. Nope, I ain’t got the math to back this up.

I suspect you are comparing mileage on a trip with that accent and decent to a flat drive. Over all a flat drive is most likely going to give better mileage than the same distance on a upgrade and down grade, all else being equal. The city drive will almost always be lower than highway drive be it level or hilly.

I could imagine a hill such that going up it required the engine to operate at peak efficiency going up and going down allowed the engine to shut off the fuel injectors but didn’t require using the brakes. That might beat flat surface driving and resembles the hypermiling pulse and glide technique.

Real life hills will tend to be too steep, requiring downshifts, higher rpms, braking, etc.

I often get better gas mileage on hilly roads than flat roads, provided the grades are not so extreme as to require braking downhill to keep the speeds in check.
The problem with flat roads is that the horsepower demand is so low that the engine is way out of its effeciency sweet spot, even in overdrive.
If a car had two engines, a large accerlerating, passing, and hill climb engine that only starts when its power is needed, and a small cruising engine, perhaps with only one cylinder and sized to make about 20 horsepower, then a flat road would get the better gas mileage.
The bigger the engine, the more the hilly road benefits the gas mileage. A small subcompact with a one liter engine would probably do best on a flat road.

Any bicycle riders out there ? My experience has been that hilly terrain (Maine) uses more energy (food and water) than flat (Florida) over the same distance. Bikes aren’t cars I know, but they can’t be that different.

If cars were driven wide open at close to their top speeds all the time, then the bicycle analogy might be relevent.
Gasoline engines have a large efficiency drop off at light loads. That’s why slowing down to a steady 30 mph does not result in 100 mpg fuel economy.

Basically, if all friction/drag/etc were eliminated and the car (and engine) had the same efficiency at all speeds it wouldn’t matter what path the car takes. To simplify things, in this case the only difference between going 100 miles up and then down a mountain (and returning to the same elevation) or going 100 miles over level roadway is gravity. When going up the mountain the car has to work harder because not only is the car working to accelerate itself forward it’s also working against gravity. Work is the dot product of force and distance and when you’re going against gravity (you’re driving uphill) less of the force that your car is exerting is going to making it go forward. However, when the car goes down the mountain gravity now works with the car. Because gravity is working against and working for the car the same amount of work then the difference between going up and down a mountain should cancel out, making it the same as driving over a level roadway.

Then there is the fact that one would probably have to down shift and/or brake going down hill in order to reduce speed. So initially that would tell me that going up and down a hill would require more energy than going level because a lot of energy would be wasted through downshifting/braking when going down hill (rather than just coasting down the mountain like a rollercoaster). Even without any downshifting/braking there’s probably going to be some degree of engine braking as long as the car is in gear.

However, a couple of posters brought up a couple of pretty good points that I hadn’t thought of before in that an engine may operate at a higher efficiency when working harder than just going over a level surface. So it’s very possible a hilly path might get better mileage than a level one. I’m sure there are many other factors that come into play and it could depend on the car.

This sounds similar to the ‘pulse and glide’ technique used by hypermilers - operate the engine a short time at wider throttle (less pumping losses) then coast and let the injectors shut off, resulting in better mpgs that constant light throttle.

There are too many variables to make universal statements.

Different engines, weight of the car, load (cargo etc.) engine, transmission ratios, auto vs. manual transmission, driver’s driving style, wind, hills temperature, tyres, traffic and many others all add up.

Going up hill then coasting back down does not balance out. Otherwise, airliners would fly that that way too. They do vary their altitude to avoid wind resistance when possible, but find avoiding frequent climbing to be more efficient. Falling as a balance to climbing only approaches equality when air resistance is discounted. On many vehicles are higher speeds you need to still apply throttle when going down hill. How much energy loss net, is determined by vehicle type, load and terrain. It’s obvious that heavier vehicles, require more energy going up hill. Because everything falls at a constant velocity, they gain little over a lighter vehicle going down, given similar aerodynamics.

I’m sticking to level ground and cross country skiing on deserted rail road beds. Done too much biking, skiing and mountain climbing to feel otherwise and essentially every car would be a perpetual motion machine if it were otherwise.

Some motor-gliders actually do get their best cruising economy when used as airplanes by “flying a sawtooth”. That’s because the engine power and propeller pitch are both optimized for climbing to altitude, not for level cruise. So in order to get the best fuel mileage, you climb to a high altitude, then shut off and retract the engine/propeller and fly it as a glider until you run out of safe altitude and then repeat.
Of course, if you happen to see a bunch of buzzards circling, it never hurts to join them and let a thermal give you some free altitude.

And, if a car were optimized for climbing and could shut off it’s motor and change it’s shape and could glide and use lift and could use updrafts and carried no additional weight other than fuel and passengers, it possibly might benefit from climbing. For a car, it does not benefit from aerodynamics. It is instead a hinderance and any lift makes it less safe with loss of traction.

Our cars ARE optimized for climbing and aceleration. Do you really believe it takes triple digit horsepower to cruise 70 mph on a flat road?
A car getting 35 mpg at 70 mph is only burning 2 gallons of fuel per hour. An airplane with a 100 horsepower engine will burn about 8 gallons per hour at full power and about 5 gallons per hour at 70 percent power. That should show you just how underloaded a typical car engine is when cruising on a flat road.

For what it’s worth, the best gas mileage we ever got with my wife’s Honda Element was during a week of driving the roads of The Enchanted Circle in the mountains of Taos, New Mexico. On those roads, we were either climbing or coasting. We got over 30 mpg on one tank of gas there. In flatland driving, that car only gets 22-24 mpg.

One possible hybrid scheme would be to have a small gas engine that cycles between two states:
running at optimum speed & power
shut off

The battery could be sized for power, not range. Smaller than the plug-in hybrids.

Cruising on the highway the gas motor might come on for 30 seconds every 2 minutes.
That would require only about a 2 mile range from the battery (or super-capacitor bank) at 75mph.
The gas motor can open its throttle more to climb long hills etc. after the battery is down.

A power-split system like in the Prius could be adapted to work in this mode.

This is one of those physics or math problems you’re given in college.

On paper driving 10 miles on a flat road as opposed to traveling 5 miles up hill then 5 miles down hill SHOULD be the same amount of P (work performed).

But in practical terms there are other things to consider like wind resistance. So those variables have to be applied (which isn’t easy)…and then the answer becomes a less clear.

BLE I believe you are compare apples and oranges. I’ll bet you were going significantly faster on flat land then on the hills. That’s where your difference in mileage occurs, over coming air resistance. With an Element at speed and it’s boxy shape, higher speeds take a terrific toll on mileage. Just being able to drive at higher average speeds on level ground tells you it’s more efficient for the average car allowing you to reduce time traveled over the same distance.

Now check your mileage trying to go up hill at 70’ if you can, or at least the same speed you travel on flats. Level travel then wins every time. Air resistance is culprit, not level ground.

Make sure your average speed is the same for both trips while traveling the same distance, one with hills, one without. If over a ten mile stretch you average 70 mph on level and want to compare that to driving hills for ten miles, remember this. If at any time your speed is reduced to 50 mph going up hill, you MUST attain speeds going down at some point of 90 mph so that the average speed over all is the same, or spend greater distance going down or on the level at higher speeds then 70 mph, theoretically impossible to achieve in the same total distance. Impossible unless you want to change the elevation of the trip, which then again makes the comparison invalid. Then you can say hill climbing is more efficient…not. At least not in the traditional cars that we now drive.

MikeinNH has it right as proponents are omitting average speed and distance remaining constant to get an accurate comparison are necessary. And no, cars do not not get better mileage going up hill…

Circuitsmith, Volt is designed similarly that way. The engine is sized only large enough to meet the average requirements of a trip and can be smaller then the regular engine. As CR points out in their tests, when traveling, even with regenerative braking, the Volt with the engine running averages only 29 mpg both city and highway, much less then a Corolla.
The advantage is only realized keeping keep daily mileage between charges less then 70 miles where EV mode is used most of the time. Hilly travel, by the way, shortens the range of an EV. Everything you do shortens the range it seems.

dagosa , going up a hill at 50 mph and going down the hill at 90 does not average 70 mph. It only averages 64.28 mph. You can’t average speed by splitting the difference. You also can’t average gas mileage by splitting the difference.
I was able to go the road’s speed limits nearly all the time and in fact I was using cruise control a lot to obey the forest road speed limits. I was probably getting about 15 mpg up the hills and infinite mpg going down the hills which averaged to 30 mpg.
The roads in New Mexico’s “enchanted circle” are all posted at 55 or slower and they aren’t all that steep. Most of those roads were built alongside rivers because running water has a way of finding the least up and down path around mountains.