Is my hill climb theory sound?

[redpoint5]

I just read the 108 hypermiling tips and questioned the logic behind DWL. It suggests that the most efficient way to travel an incline is to let speed drop off, and to build it back up on the decline.

When I started pondering the question of how to maximize fuel economy on hills, I used the most extreme example I could think of; vertical travel. Obviously, it is least efficient for a rocket to gain altitude as slowly as possible. It takes an enormous amount of energy just for the rocket to sit in place at it's current altitude (1G of thrust). So if the rocket is producing 1.01G of thrust, it is expending 99% of the energy just to maintain the current altitude, and a measly 1% on gaining. Ignoring friction such as wind resistance for a moment, it follows that the more thrust (throttle) that is produced, the greater percentage that is used to gain altitude. At 100G of thrust, 99% is being spent on acceleration and altitude gain, and 1% is "wasted" on overcoming gravity.

If we consider that it takes energy to simply hold position on a hill (brakes off and in gear obviously), it follows that getting to the top of the hill quickly is most efficient.

Interestingly, I have observed the greatest MPG on trips involving very steep mountain climbs. In my old Subaru AWD, I consistently averaged 27mpg with about 75% freeway and 25% city driving. However my trips into the mountains and hills returned 30-32MPG. I applied my theory of getting to the top of the hill quickly, and coasted down either idling or engine off.

So it seems to me that it is most efficient to climb a hill as quickly as possible, even if that means opening the throttle further and watching the MPGs momentarily plummet. By doing this, you are minimizing the amount of time that gravity is working against you. Of course, there would be a speed at which aero drag negates any benefit of cresting the hill quickly.

Comments, criticisms?

[alvaro84]

There must be something wrong about it, but I can't put a finger on it.

• With a land based vehicle to stay at one place you don't need any engine power, just hold the brake, which means zero energy
• You can't stay at one place with engine power. It would need zero rpm with any gear ratio, so the engine would not turn at all, and would not use any fuel. But it also wouldn't work because gravity would be able to turn the engine backwards so the vehicle would roll down.
• IRL there's a way to stay at one place with engine power: to rev it and let the clutch slip exactly that much that the remaining torque is enough to balance the force of gravity. But in that case the engine would do no useful work (every single bit of its movement would be converted to heat in the engine and the clutch) thus its efficiency would be zero.

So what's wrong here?
Anyway, I usually accelerate uphills to get longer glides on the other side (given that I don't know of a sharp turn or stop sign at the bottom) - I ride a motorcycle and those are light and have bad aerodynamics so on slight downhills they can't even hold a decent speed let alone accelerating from there.

[brucey]

I too seem to get better MPG in the mountains. The car is essentially FORCED to do pulse and glide. I also am not leaving it out of the question that weight could actually be a major help in these conditions. But only in those conditions. I plan to test this out soon.

[tumnasgt]

After 15min of thinking, I think I have found the flaw. It takes exactly the same amount of work to go a given distance (Work = force x distance), so it's more about getting the most work from the engine on the least amount of fuel. That's where DWL comes in, if you drive over a 2 mile distance up hill at 60mph getting 15mpg, you're going to be worse off than driving at 30mph at 25mpg.

As I'm poor and can't afford a scangauge (or even use it in the car I normally drive), I DWL based on throttle position. I find that on a moderately steep incline, my car moves with the least amount of throttle at 2000-3000rpm, anything much over that and you are pressing really hard, anything under that you are flooring it only to slow down. I say "much over" because 2nd to 3rd in my car is a big jump, and changing up before about 3200rpm puts me in slowing down with my foot to the floor mode.

alvaro84, to hold a brake is zero energy, but not zero force. I think the best example is an electric motor, as you can get them to apply enough force that you don't roll back, while not so much that you go forwards.

[basjoos]

You also have to account for the thinner, air in the higher elevations of the mountains, which has a huge effect on improving mileage. I once calculated the density-altitude to see how hot it would have to get here at 500 ft elevation to give me the same air density as I would if I was driving at 10,000 ft elevation at a normal air temperature. The air temperature here at 500 ft elevation would have to reach 170 degrees F to give me the same air density as driving around at 10,000 ft at 70 degrees F. You know how much your coasting distances improve when going from 10 degrees F to 80 degrees F. Imagine doubling that improvement which is what you would see when going from 500 feet elevation to 10,000 feet elevation.

In general, I get my best mileage when I climb the hills as slow as I can while still keeping the rpm over 1200, usually at around 70% to 80% throttle. That translates into a speed of 40 to 45mph.

[alvaro84]

Originally Posted by basjoos

In general, I get my best mileage when I climb the hills as slow as I can while still keeping the rpm over 1200, usually at around 70% to 80% throttle. That translates into a speed of 40 to 45mph.

Hm, it's similar to my other strategy I use when I don't Pulse&Glide, just the rpms are different. My opportunities to DWL are very limited, Teresa has a 5th gear which is usable from ~70km/h(44mph, 2800rpm) on level road and needs a bit more to climb depending on the incline - so if I ride at a constant speed I don't really have any extra speed to lose (actually sometimes I have to go faster uphills).
If other circumstances make me go slower, I try to do the same in 4th (and so on). Lower gears work at a bit lower rpms.

But I can't support this practice with scientific data, I can't connect that ScanGauge to anywhere

[evilskillit]

On the hilly road that goes east from my house and connects me to the city where my parents live and where I used to work the speed limit is 55. I'll usually just use 6th gear the whole way when I get to the top of the first hill I'll get up to 65 or 70 going down it and bleed off back down to 50-55 by the top of the next hill and repeat. You could probably do a bit better gas mileage wise by keeping the speed a bit lower but those speeds seem to be perfect for keeping from bogging the engine and be able to go up the back side of each hill without having to add any throttle or down shift. Obviously you have to speed a bit, which I'm aware isn't condoned but on a road with a lot of hills thats how I do it.

What do you do if you hit a stop sign at the bottom of a hill or have to go up a mountain? Use your Scangauge I suppose, if you have one. Like most people say best results would probably be yielded by getting the highest gear you can and then keep the engine just above the point where it is dying just to keep moving.

[bikin' Ed]

I use my bike to gauge most efficient approach. Since the HP of the vehicle is so greatly limited, the effects are easily seen. To use the least energy going from the flat to a climb I use a short burst at the bottom followed by sustained power output to just over the top of the climb.

Somehow the short burst at the bottom seems to give you a bit of momentum to carry into the climb. The sustained output lets the engine maximize efficiency. The continued effort just over the top brings you back to speed with minimal effort.

[alvaro84]

Originally Posted by evilskillit

What do you do if you hit a stop sign at the bottom of a hill

I swear...?
I can't do much more than to coast or force DFCO to the stop sign if I behold it when I crossed the crest
Of course if I know that it's there I won't pulse before the decline

or have to go up a mountain?

If it's steep enough I just climb up at a speed that matches the bends, in the highest possible gear, just as I described above.And then may take a pulse at the top. If the decline is steep enough, it's not necessary.
If the incline isn't steep I may P&G upwards too, then coast down after the final pulse at the crest.

Use your Scangauge I suppose, if you have one. Like most people say best results would probably be yielded by getting the highest gear you can and then keep the engine just above the point where it is dying just to keep moving.

I don't have a SG as I can't connect it to anywhere

Anyway, I just don't dare to let the single cylinder engine rev too low, it's prone to pinging under the revs I mentioned above (~2000-3000, depending on the gear, the incline and the extra weight (e.g. passenger)).
I know that, for example, on level road it can accelerate from under 2000rpm in 4th (with firm throttle, does not need WOT), but I never do it deliberately, it sounds suspicious to me under ~2500 (like a little jackhammer or so).

[redpoint5]

Originally Posted by tumnasgt

After 15min of thinking, I think I have found the flaw. It takes exactly the same amount of work to go a given distance (Work = force x distance), so it's more about getting the most work from the engine on the least amount of fuel.

We have to factor in the fact that vertical distance takes more force to get work done, and the longer you spend doing that work, the longer one must sustain that force. The force is generated by expending energy (burning gas).

That's where DWL comes in, if you drive over a 2 mile distance up hill at 60mph getting 15mpg, you're going to be worse off than driving at 30mph at 25mpg.

Of course, your efficiency numbers were conjured, and not based on any real world figures.

As I'm poor and can't afford a scangauge (or even use it in the car I normally drive), I DWL based on throttle position.

I am without a scangauge because my ODBII port is already being used by Progressive's Snapshot device.

Originally Posted by basjoos

You also have to account for the thinner, air in the higher elevations of the mountains, which has a huge effect on improving mileage... You know how much your coasting distances improve when going from 10 degrees F to 80 degrees F. Imagine doubling that improvement which is what you would see when going from 500 feet elevation to 10,000 feet elevation.

I think that is a significant factor, although I have never noticed a difference between coasting in 30 degree weather and 100. Perhaps the effect will be more pronounced now that I know to pay attention.

In general, I get my best mileage when I climb the hills as slow as I can while still keeping the rpm over 1200, usually at around 70% to 80% throttle. That translates into a speed of 40 to 45mph.

It follows that if the most efficient way to climb a hill is as slow as possible while over 1200 rpm, then doing it in 1st gear would be most efficient. I find this difficult to believe.

As Brucey has pointed out, dashing up a hill is comparable to a pulse and glide. I still have not heard compelling evidence as to why my practice is inferior to DWL. It must be explainable in a scientific way, or described using a simple scenario such as I have done with my rocket concept.