Mountains and Fuel Economy

I've only been driving my Prius for a couple weeks, but I'm finding my best MPG for a trip happens when I do an out-and-back to a trailhead in the hills. It's only 440 feet higher than my house (and 6 miles away), but it seems to make a huge difference:
46 mpg up, 96 mpg down --> 71 mpg average
47 mpg up, 142 mpg down --> 94.5 mpg average
Outside of that, for somewhat flat driving, I've been averaging 48.5 mpg.

This reminds me that I have always had fantastic gas mileage on mountain trips. That was with regular cars (I never had a Prius until recently). Those were mostly day trips, a couple hours each way, going up from 5200 ft. to around 10,000-11,000 ft. My theory was always that the thinner atmosphere was putting less drag on the car. I figured, any gains in mpg on the way down have to be paid for on the way up, so they should cancel out.

But maybe it's something else entirely? With these short trips it can't be thin air! Maybe there's something about how an engine responds to the up vs. downslope so that the effect isn't a simple average?

I realize I don't have a lot of "data" on this yet, still haven't driven up to the Rockies with it... probably shouldn't make a mountain out of a molehill, just yet

 

You are 'averaging' incorrectly. Actual numbers are:
46 mpg up, 96 mpg down --> 62.2 mpg average
47 mpg up, 142 mpg down --> 70.6 mpg average.

The proper way to 'average' these round trips is to compute the fuel used uphill, fuel used downhill, add them together, then divide into the round trip distance.

Otherwise, you'll run into the farce of getting just 20 mpg on some steep uphill, then infinite on the coasting downhill return. The improper 'average' is still infinite (or infinite/2), while the correct average is just 40 mpg.

 

Whups, thanks, I should have known it wouldn't be that simple!

Let's see if I have this right now:

Let's say you travel M miles and get E fuel efficiency (mpg), using G gallons. E = M / G, so gas used G = M / E.
The average mpg is (M1 + M2) / (G1 + G2) = (M1 + M2) / [(M1/E1) + (M2/E2)] = 1 / ([(M1/E1) + (M2/E2)] / (M1 + M2)). If M1 = M2 = M, then (I had to work this out on paper) that's 2 / (1/E1 + 1/E2).

So for 46 up, 96 down --> mpg = 2 / (0.021739 + 0.010417) = 62.2 mpg. Whew!

 

I just found this thread. Interesting stuff. As to the Plugin experience in the mountains, we spent a few days last year cruising around Great Smokey Mountain National Park. We averaged a little over 60 mpg. We would routinely top the pass or Clingman's Dome with a spent EV range and fill the battery again before getting to the bottom. I think the Prime's battery would have swallowed those descents easily.

Next month we'll get to take the Prime to the Colorado Rockies and I can hardly wait to see what that's like.

 

Bingo!

For cold engine starts on both legs, and a relatively short distance per leg, those are still very nice numbers.

 

I was thinking, that formula 2/(1/E1 + 1/E2) is not very much fun to work with in your head. But if you know the ratio between E1 and E2, then it's a lot easier... say E2 = E1 / k. So then the mean is 2/(1/E1 + k/E1) = 2 * E1 / (k+1).
So for the example above (rough approximation), averaging 45 and 90: 90/45 = 2 = k, so
Avg. = 2 * 90 / (2+1) = 60. Pretty close to the calculated value above.
Or for the other trip with 47 and 142, it's roughly 45 and 135, and k = 3, so avg. ~ 2 * 135 / (3 + 1) = 67.5, not that far off from 70.6.
Anyway, just something to think about while driving...

 

OK, just one more mental arithmetic example, from yesterday. This time, going downhill, then back up the same route:
63.5 mpg out
40 mpg back
It's roughly 60 and 40, for a 3 to 2 ratio... so k = 1.5.
I think the lower number, in general, weighs more heavily in the formula.
But, can use 61 since the real value was 63.5.
So, that gives avg. mpg with the formula above at 2 * 61 / (1 + 1.5) = 2 * 61 / (5/2) = 244/5 = 488/10 = about 49.
The real value from calculator is 49.1, very close!
(Yes, I cheated... first effort used 63, which gave 50.4)

Sorry, I'm still on my first tank of gas (down to about 1/4 full), so I guess I'm a LITTLE obsessed with this.
When I first started noticing the tank-average mpg it was 47.5, rather disappointing (but I had been using cruise control etc.), so ever since then have been trying to increase it - currently at 50.5.

 

If you do the trips in one day, you can just look at the daily average in the dashboard display. Press up on the steering wheel to move from the energy display to your daily average.

When I drive to Utah from my home, it's about 800 miles. I go from California, over Donner Pass, across Nevada, into SLC and then north to where my family lives. Heavy freeway traffic through California at 55 to 60 MPH. 75 or more through most of Nevada and 85 through the salt flats. Round trip I get a little over 55 MPG.

 

We did our first "mountains" trip with the Prius, about 96 mi. each way to Breckenridge, elevation from about 5,200' to 9,600'. On the outbound it was about 45.3 mpg (likely a little higher, as I missed a short segment in Boulder), mostly uphill (but with substantial downhill segments). On the return, 80.5 mpg, which averages about 58 mpg. It's good, but I'll admit I was a little disappointed, since I often get better averages toodling around in Boulder. So, possibly the Prius won't give me quite the boost to MPG in the mountains that I saw with a regular Toyota.

From Breckenridge, we also had a short steep drive (11 mi.) to Hoosier Pass (11,500'). That gave me 25.8 mpg uphill and "199" downhill. I'll assume that "199" means "infinity" in which case the average is 2 x 25.8 = 51.6 mpg. That was a little disappointing too, although it was first drive of the day so possibly engine warm-up was a factor.

I can really see why freeways depress MPG on the Prius. On uphill segments, If I try to keep the Hybrid System Indicator at the "sweet spot" (just below PWR zone), the car slouches along at 45 mph or so, passing trucks but with most vehicles swerving recklessly around me, so I soon learned there was little choice but to burn extra gas just to keep up with the Joneses.

 

I'm not sure, but think going up a hill and then back down, you're not going to achieve the mpg of flatland driving of the same distance. I appreciate you do recoup some on the way back down. Maybe an engineer can weigh in?

 

The biggest reason for improved MPG on mountain roads is the reduced speed. (and yes the system burns leaner at altitude)
So the MPG numbers are really only relevant if you also look at the average speed for the trip.
The winner in any MPG contest is the one who spends the most time (miles) in EV mode. Even on uphill stretches if you can pulse and glide just a little you can add several MPG to the trip.

 

We only have a Gen3 but on our road trips we always tend to get the best overall MPG when driving in the mountains. This is probably true because we take back roads, and speed limits within the national parks and such are much slower than usual.

In fact, our all time best of 65MPG was in our 2010 liftback driving around Yellowstone for a few days and then coming out of the south entrance of Yellowstone, and then going south thru Grand Tetons on Hwy 191, and then SE on Hwy 26 and on from there. Granted, it was some of the best conditions we could have hoped for ( slower speeds, a lot of downhill, etc... ) but still...65MPG was a sight to behold for our Gen3. With that said...I have not come close to that on any other trip since then...but we have seen mid 50s a couple times.

 

Sounds about like what I'd expect. Those mountains can fill a regular Prius battery pretty quickly and then you're engine braking. When we went through CO a few weeks ago in the Prime, we got 57.7 from southeast AZ to Farmington, NM. Then 62.8 from Farmington to Delta, CO (slower speeds here, especially toodling around Mesa Verde NP). Then 58.7 from Delta to Broomfield. The last stretch was almost all I-70. The big battery makes a bigger energy buffer, but there's no avoiding the physics of gravity.

 

199, or 99 on an earlier generation, usually means infinity, but can mean something in between. E.g. engine warmup fuel burn rates of 0.2 gal/hr while sort of gliding downhill at 60-70 mph would really be 300-350 mpg, which the display cannot show.

Even after warmup, some shallow downslopes actually need a slight bit of power to maintain speed, thus could be producing this mpg. But infinity on steeper slopes is more common.

Your up-and-down mpg disappointment comes from extended steep downslopes wasting energy in engine braking. Better results come from shallow downslopes with little or no engine braking.



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People around here drive between 55 and 65 mph. If I don't have anyone behind me, I'll increase my speed as I'm going down hills in small increments to 60 mph. The battery is charging usually and I take advantage of that momentum. I don't want a ticket and I feel I'm safe there. Going up hills, I'll back off one tick on the cruise control as the engine/motor indicator hits that first bar (in what I call the hocky stick indicator). I may sometimes get down to 40 mph uphill as long as I have no one behind me. I did a hundred mile trip yesterday with a total difference of 1800 vertical feet and was able to achieve 63.7 MPG according to my odometer.

When people are behind me, I'll drive a standard 58 mph and I get two or three mpg less.

 

What's the posted speed limit, just curious.

 

Speed limit is 55 MPH

 

This is a bit embarrassing but I thought I'd mention. A couple weeks ago it finally occurred to me to just use the trip meter! I did a trip to the mountains, ~30 mi. each way. Doing my best to pulse & glide, I got 31.7 mpg going up (5-6,000 feet vertical gain, but with some flattish miles at the start). On the way down, I got "199.9" mpg. If that were really "infinity", the overall mpg for the trip would have been 31.7 x 2 = 63.4 which would be great. But the trip meter eliminated the guesswork, and unfortunately reported 55.0 for the round trip. So the downhill leg must have been not far above 200 mpg.

 

Did you get into much engine compression braking on the downhill run? Did the traction battery completely fill up? If so, you would have lost some of your hoped-for round-trip fuel economy there, simply because the slopes are too steep for best round-trip efficiency.

The average downhill slope would have been in the 3.2% ( for 5k vertical) to 3.8% (6k) range, which is steeper than ideal for efficient downhill gliding and gravitational energy recovery-use, thus leading to 'disappointing' MPG. This slope is not all that bad at full highway speed, but if some portions were steeper than average, they would have added to the problem. I suspect anything steeper than (very roughly, and speed-dependent) 2% will cause some loss.

I don't believe that Pulse&Glide is all that useful in Gen3-4 Prii on significant uphill slopes. The ICE is already operating at damn near its top possible efficiency at steady cruise speed, as revealed by the engine BSFC charts posted here long ago, so there is little or no room for the pulse phase to be more efficient. Uphill P&G has a bit more potential in a Gen2 (less broad efficiency peak on BSFC chart) , but not much. This is why I generally say that the downhill segment is more important to round-trip efficiency. Numerous folks get excited with 80+ mpg on the downhill side and see no point in further optimizing that side, when in reality, their downhill shortfall from infinity is what is really determining their round trip results.

 

Well, this trip is basically a few miles of flat followed by 20ish miles of continuous steep climb, so I can see why there is very little ability for the battery to be useful as a buffer - it fills up very quickly on the return (downhill) leg. Yes, pulse-glide seemed pretty pathetic as i was climbing steeply, but I decided to just try it out of curiosity. One thing I always do now, including with this trip, is aim to accelerate in the "sweet spot" (just below the PWR zone in the HSI). I assume that still helps, because that is supposed to be where the engine is most efficient. But one of these days I will try the same trip with "regular" driving technique (with no thought at all to hypermiling) and compare the results... I have a feeling it will not be all that different and will allow me to enjoy the scenery more