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Impact of temperature on fuel efficiency (math nerds unite!)

Discussion in 'Gen 4 Prius Main Forum' started by wgary, Jul 11, 2018.

  1. wgary

    wgary Member

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    (Warning: There is a little math ahead, but math is our friend! Plus there is a possibly interesting punchline.)

    I bought a 2017 Prius 4 in spring 2017. This winter I became concerned when my MPG dropped off, wondering if there was something wrong... but then started wondering if perhaps the temperature was perhaps impacting battery efficiency more than I expected -- even though it is parked in a garage.

    Fortunately, I have an Automatic Pro that collects minute data on fuel consumption, among other things, through the OBDII port. I compiled the data, and it appeared that there was a fairly good linear fit mapping average weekly low temperature to average weekly MPG, but something seemed off... For kicks, I tried a quadratic fit, which was even better -- y=-0.0035x^2+0.422x+38.69 with r^2=0.27! Using my advanced mathematical knowledge (ok, actually wolframalpha.com), I rewrote this as: y=51.4103 - 0.0035(x-60.2857)^2

    So, it's true: my MPG was worse at lower temperatures. But it reached peak efficiency at 60˚F. (average low) after which it started to fall again. Lightbulb moment -- air conditioning (which I definitely use in Alabama) is very likely cutting into the fuel efficiency at the higher temperatures.

    So maybe this isn't earth-shaking, but I thought it was interesting to have this data-based revelation about fuel efficiency, proving once again that math is so very awesome! (Yes, I am a mathematics educator.) Bonus for math nerds: You can also tell what my peak weekly average MPG is; yes, my foot can be a little heavy!

    Here is the scatterplot for your enjoyment! (x=temp, y=MPG)

    chart2.png
     
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  2. krmcg

    krmcg Lowered Blizzard Pearl Beauty

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    fascinating...
     
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  3. alanclarkeau

    alanclarkeau Senior Member

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    Yes precisely - can you interpret it please?

    Seriously - I loved maths - the concepts etc - but I wasn't really very good at it.

    Now retired, I don't tend to dabble in it like I did while working, where I was involved in budgeting and estimates (loved that) and accounting (hated that) at a very large High School where I was Business Manager.
     
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  4. The Professor

    The Professor Senior Member

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    I love this... Real science at work! Confirming other people's results with independent data and independent methodology.

    So yes... Lower temperatures means things like greater rolling resistance of the tyres, greater viscosity of lubricants, lower battery efficiency, and so on... Greater temperature means the Aircon kicks in... Lots of other variables at play too.

    Wind, air pressure, and humidity, also have a effect on wind resistance and combustion engines...

    Fascinating indeed!

    Pixel 2 ?
     
  5. alanclarkeau

    alanclarkeau Senior Member

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    Thinking it through since I first read it - I'm a bit more awake now:
    • Colder air is denser - in the olden days of carburettors that meant an improvement in both power and economy - is that still the case with fuel injection.
    As The Professor mentioned - what about these 2 - is it significant?
    • question - higher air pressure at lower altitudes should improve economy? - does it? I seem to remember a car race where the vehicles struggled at high altitudes?
    • question - how does humidity affect things - surely "wet" air wouldn't be as good? - is it?
     
  6. GadgetVirtuoso

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    I have noticed that my fuel efficiency is impacted by the temperature I select for the AC. Being in TX, there are few months of the year when the AC isn't on. The key is to not keep the AC temp any lower than necessary. Even with the 100+ temperature days lately, in DFW I haven't been comfortable with eco 74 with the fan on 2-3 bars. The car knows when there are other people in the car and activates the rest of the vents when needed but like most people, I'm alone in the car most of the time.
     
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  7. bbald123

    bbald123 Thermodynamics Law Enforcement

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    With modern cars, variance of air density due to temperature is much less of an effect. And that effect can largely be eliminated by measuring the amount of air entering the engine with a Mass Air Flow sensor.

    Cold temperatures or wet conditions that cool the catalytic converter have very large effects because maintaining tailpipe emission levels is a primary design consideration.

    I know humidity has an effect on engine efficiency (just look at NHRA races to see how important that can be). But, I don't know if the car can correct for it or even if it is an appreciable effect for a Prius in normal operating conditions.
     
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  8. wjtracy

    wjtracy Senior Member

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    Many reasons why MPG is lower in cold weather as per Professor above...another reason is USA winter gasoline blend has butanes which contains less energy, so the fuel itself is about -1 to -2% MPG..
     
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  9. bbald123

    bbald123 Thermodynamics Law Enforcement

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    This is very true too. And, I should have mentioned it.
     
  10. Since2002

    Since2002 Senior Lurker

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    I have found that I need much less AC if I point the vent at my face, of course at a lower fan setting. I realize some people just can't stand that which I understand, and I don't do it all the time, no need to be uncomfortable to save a little gas. But especially starting off I try and remember to do that, and then after awhile if I get tired of it then I point the vent in another direction and crank up the AC a little more.
     
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  11. Starship16

    Starship16 Senior Member

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    AC set at 65, every day, 12 months a year. MY HYBRID BATTERY THANKS ME. :LOL:
    No cold weather here. 85 on Christmas! :eek:
    MPG stays at 54-57 all year. Depending on who you ask. :ROFLMAO:
    I stunk (and STILL stink) at Math. Never liked it. God bless all the hard-working teachers.
     
    #11 Starship16, Jul 12, 2018
    Last edited: Jul 12, 2018
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  12. bisco

    bisco cookie crumbler

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    my battery efficiency has really been peaking in the warmer weather. kinda surprised, thought it was mor in the 60's and 70's.
     
  13. pilotgrrl

    pilotgrrl Senior Member

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    I'm fine with eco 76-80 depending on the outside temperature. I feel like I work in a walk-in cooler, so it always feels good when I get out and warm up.

    I put the air conditioner on for the battery's sake.

    Posted via the PriusChat mobile app.
     
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  14. TinyTim

    TinyTim Active Member

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    Here is a homework assignment for you. Get two or three 5 gallon gas cans. Fill them in the next month or two. Wait until December or January and run your car down to fumes. Fill your gas tank with those 5 gallon cans and report back. My guess is that ethanol is the reason why your fuel efficiency decreases. There is a summer blend and a winter blend of ethanol. In the winter time states that add ethanol reduce fuel consumption roughly 10%.
     
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  15. Starship16

    Starship16 Senior Member

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    "The car knows when there are other people in the car and activates the rest of the vents when needed..."

    HUH??? How can that be?

    Is she also watching me eat my chili-dog and getting angry at me?! Maybe she will roll the windows down... and toss it out. :)
     
    #15 Starship16, Jul 12, 2018
    Last edited: Jul 12, 2018
  16. TinyTim

    TinyTim Active Member

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    If you have or had a gen 4 prius. I am certain there is Knight Rider like capabilities built in. I have yet to have a conversation with Devon Miles or any members of the Foundation For Law And Government.
     
  17. wgary

    wgary Member

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    Yes, lots of variables. Interestingly, trip length is also a mild predictor... I have thought about putting in humidity as well. (Done in Numbers on my MacBook.)
     
  18. wgary

    wgary Member

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    OK, may need to add in humidity -- I think I can pull that data from NOAA.
     
  19. wjtracy

    wjtracy Senior Member

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    But there is no winter/summer difference in ethanol anymore....in my RFG area we are 10% ethanol all the time, every grade. You might be thinking back about the late 1990's when the "oxygenate" mandate first started, there was a winter/summer oxygenate content differential.
     
  20. bbald123

    bbald123 Thermodynamics Law Enforcement

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    I've posted this before. But, here it is again. Winter is the corner case to the graph presented. So what is presented here applies to one degree or another to any temperature differences noted. Fuel economy in cold weather.

    As for oxygenation, it is still required dependent on locale: Gasoline Winter Oxygenates