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Quiz: I improved my trip FE by 5 MPG for 100 miles; how much gas did I save?

Discussion in 'Gen 3 Prius Fuel Economy' started by Philosophe, May 19, 2010.

?

I improved my trip FE by 5 MPG for 100 miles; how much gas did I save?

  1. About 0.2 gal

    5 vote(s)
    38.5%

  2. About 1 gal

    0 vote(s)
    0.0%

  3. I don't know, I'm satisfied by the fact I get 5 MPG better FE

    2 vote(s)
    15.4%

  4. How the heck am I supposed to calculate this? Please help me!

    6 vote(s)
    46.2%
  1. Philosophe

    Philosophe 2010 Prius owner

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    I improved my average FE by 5 MPG during my 100 miles trip; how much gas did I save?

    Grab your calculators and have a try! :D

    PS: ;)
     
    #1 Philosophe, May 19, 2010
  2. vday

    vday Member

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    I believe something is missing or do you mean according to your last tank?
     
    #2 vday, May 19, 2010
  3. PaulHS

    PaulHS Member

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    Not enough info
     
    #3 PaulHS, May 19, 2010
  4. EZW1

    EZW1 Active Member

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    not enough info. You're trying to compare a ration (5mi/gal) to a fixed number (100mi). We need to know your mileage before the improvement.
     
    #4 EZW1, May 19, 2010
  5. San_Carlos_Jeff

    San_Carlos_Jeff Active Member

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    On a Hummer that gets 10MPG normally and then went to 15MPG you would save 3.33gallons. Is that what you were looking for?
     
    #5 San_Carlos_Jeff, May 19, 2010
  6. Much More Better

    Much More Better Active Member

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    not enough info. Need to know the MPG first. The 5 MPG saving is a percentage of the MPG. If you had a 100mpg car, 105mpg makes very little difference.
     
    #6 Much More Better, May 19, 2010
  7. bwilson4web

    bwilson4web BMW i3 and Model 3

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    G1 = 100 / MPG
    G2 = 100 / (MPG + 5)
    - - -
    MPG = 100 / G1
    (MPG + 5) = 100 / G2
    - - -
    MPG = 100 / G1
    MPG = (100 / G2) - 5
    - - -
    100 / G1 = (100 / G2) - 5
    - - -
    100 = ((100 / G2 ) - 5 ) * G1
    - - -
    100 = (100 * G1 / G2 ) - ( 5 * G1)
    - - -
    100 * G2 = 100 * G1 - ( 5 * G1 * G2)

    We have one equation with two unknowns. The best we can do is establish one, either G1 or G2 as a function of the other.

    We have to know the fuel consumed using one or the other methods to calculate the other. But you were asking for:

    ? = G1 - G2 or ? = G2 - G1

    So let's see if we can go any further:

    100G2 = 100G1 - 5G1G2
    100 = 100G1/G2 - 5G1
    20 = 20G1/G2 - G1
    1 = G1/G2 - G1/20
    G2 = G1 - G1G2/20
    G2 - G1 = - G1G2/20
    G1 - G2 = G1G2/20
    . . .
    (G1-G2) / G1G2 = 1/20

    We have one equation with two unknows. This becomes a parametric equation which means we can sweep either G1 or G2 and derive the other.

    Do you need to see the graph?

    Unfortunately the question lacks the correct answer:

    (*) There are an infinite number of answers.

    Column 1 Column 2 Column 3
    0 MPG1 MPG2 dG @ 100 miles
    1 10 15 3.333
    2 20 25 1.000
    3 50 55 0.181
    4 100 105 0.047
    5 200 205 0.012
    6 500 505 0.0019
    7 1000 1005 0.0005
    8 2000 2005 0.0001
    Questions?

    Bob Wilson
     
    #7 bwilson4web, May 19, 2010
    1 person likes this.
  8. Philosophe

    Philosophe 2010 Prius owner

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    Bob, thanks for the graph offering but I will pass... :rolleyes:

    The poll didn’t grab the interest I thought it would or smart people contributed to it too soon…;)

    After seeing many comments over time in the forums about someone saying he “gained x or y MPGâ€, I expected to grab interest toward the fact that a difference in MPG mean nothing by itself, or mean a completely different thing depending on the reference value, by the very nature of the MPG beast (1 / fuel consumption).

    Also, as most of us have some interest in ecology, we probably spend too much time looking at fuel consumption / distance instead of looking at our total fuel consumption (ie what is better than a Prius: a parked Prius, or no car at all).

    Thanks to all who took few minutes to post or to make some draft calculations to answer something.
     
    #8 Philosophe, May 20, 2010
  9. mhmercer

    mhmercer New Member

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    If one wishes to solve for two unknowns, substitute a null (0) value for one variable, then solve for the other. Switch variables, then insert the null value for the remaining variable; solve again. Assuming that this is a linear function, one may then plot a line.

    As bwilson4web pointed out, there are no bounds using this method. As we live in a world where there are no negative solutions to this problem, an X-Y boundry of 0,0 can be assumed on one end, and anything-you-like is the limit on the other.

    I was going to propose that the solution could be: X*(-0.05) gallons, where X is the base fuel consumption and -0.05 is 1/20th less of that fuel usage.

    Marshal
     
    #9 mhmercer, May 20, 2010
  10. bwilson4web

    bwilson4web BMW i3 and Model 3

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    I'm embarrassed to admit I had not considered the 0 MPG case. We are in the presence of genius.

    In the 0 MPG case, the fuel cost for 100 miles at 5 MPG would be 20 gallons compared to all gas that will ever be and has ever been in the universe minus 20 gallons if it is burned first. Depending upon whether we live in a finite or infinite universe, these can be big numbers.

    Bob Wilson
     
    #10 bwilson4web, May 20, 2010
  11. GBC_Texas_Prius

    GBC_Texas_Prius Member

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    Since this is a Prius forum, I assumed we were talking about a Prius and not an Escolade. To get an approximation, convert to percentage improvement and back that percentage out of the gallons you normally pump.
     
    #11 GBC_Texas_Prius, May 22, 2010
  12. mhmercer

    mhmercer New Member

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    My take on this is that Philosophe was having some fun with math. I don't think that the "real world" had much to do with it.

    However, I did see an average fuel use of 0 mpg yesterday. True, this was after refueling, resetting the trip meter, and idling. Worst fuel economy ever! :D

    Marshal
     
    #12 mhmercer, May 23, 2010
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