Mountains and Fuel Economy

Discussion in 'Gen 4 Prius Fuel Economy' started by axle2152, Aug 28, 2016.

  1. Awap

    Awap New Member

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    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 :)
     
  2. fuzzy1

    fuzzy1 Senior Member

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    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.
     
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  3. Awap

    Awap New Member

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    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!
     
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  4. jerrymildred

    jerrymildred Senior Member

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    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.
     
  5. fuzzy1

    fuzzy1 Senior Member

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    Bingo! (y)

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

    Awap New Member

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    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...
     
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