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Poll: Indicated vs Actual MPG vs Date

Discussion in 'Gen 3 Prius Fuel Economy' started by bwilson4web, Nov 24, 2009.

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  1. Made 02-03/2009 - 0% or less error

    0 vote(s)
    0.0%
  2. Made 02-03/2009 - 3% error

    0 vote(s)
    0.0%
  3. Made 02-03/2009 - 5% error

    0 vote(s)
    0.0%
  4. Made 02-03/2009 - 7% error

    0 vote(s)
    0.0%
  5. Made 02-03/2009 - 10% or higher error

    0 vote(s)
    0.0%
  6. Made 04-05/2009 - 0% or less error

    0 vote(s)
    0.0%
  7. Made 04-05/2009 - 3% error

    10.0%
  8. Made 04-05/2009 - 5% error

    40.0%
  9. Made 04-05/2009 - 7% error

    10.0%
  10. Made 04-05/2009 - 10% or higher error

    10.0%
  11. Made 06-07/2009 - 0% or less error

    0 vote(s)
    0.0%
  12. Made 06-07/2009 - 3% error

    0 vote(s)
    0.0%
  13. Made 06-07/2009 - 5% error

    10.0%
  14. Made 06-07/2009 - 7% error

    20.0%
  15. Made 06-07/2009 - 10% or higher error

    0 vote(s)
    0.0%
  16. Made 08-09/2009 - 0% or less error

    0 vote(s)
    0.0%
  17. Made 08-09/2009 - 3% error

    0 vote(s)
    0.0%
  18. Made 08-09/2009 - 5% error

    0 vote(s)
    0.0%
  19. Made 08-09/2009 - 7% error

    0 vote(s)
    0.0%
  20. Made 08-09/2009 - 10% or higher error

    0 vote(s)
    0.0%
  21. Made 10-11/2009 - 0% or less error

    0 vote(s)
    0.0%
  22. Made 10-11/2009 - 3% error

    0 vote(s)
    0.0%
  23. Made 10-11/2009 - 5% error

    0 vote(s)
    0.0%
  24. Made 10-11/2009 - 7% error

    0 vote(s)
    0.0%
  25. Made 10-11/2009 - 10% or higher error

    0 vote(s)
    0.0%
  1. bwilson4web

    bwilson4web BMW i3 and Model 3

    Joined:
    Nov 25, 2005
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    Location:
    Huntsville AL
    Vehicle:
    2017 Prius Prime
    Model:
    Prime Plus
    I'm preparing a poll to look at date of manufacture versus the indicated and actual MPG error. You may see this note as I get it ready.

    INSTRUCTIONS

    We need two pieces of information:

    • manufacture date - found on the door jam label
    • % error of indicated vs actual MPG - another calculation
    The best way to calculate your indicates versus actual MPG error is:

    1. SUM_INDICATED - add "n" tanks, one or more, that you have indicated MPG values.
    2. SUM_ACTUAL - add "n" tanks, one or more matching the "SUM_INDICATED" records to give a sum of actual MPG.
    3. DIFF_MPG = SUM_INDICATED - SUM_ACTUAL
    4. %ERROR = DIFF_MPG / SUM_INDICATED
    The poll will run for 30 days so there is plenty of time to get a fresh tank if you've not been recording the data. It is perfectly OK to post your work before answering the poll and ask questions. This is not a 'race.' <grins> However, you only get one answer and we can't erase it.

    F8L and I collaborated on what the poll needs to ask.

    Thanks,
    Bob Wilson
     
  2. bwilson4web

    bwilson4web BMW i3 and Model 3

    Joined:
    Nov 25, 2005
    27,068
    15,372
    0
    Location:
    Huntsville AL
    Vehicle:
    2017 Prius Prime
    Model:
    Prime Plus
    Example:

    indicated - actual MPG
    57.7 - 51.7
    60.6 - 53.6
    58.1 - 52.0
    59.4 - 53.1
    74.5 - 67.2
    76.4 - 64.0
    56.4 - 49.9
    ---- ----
    443.1 - 391.0 = 52.1

    52.1 / 443.1 = 11.75%

    Now to go read the door jam value. I have to admit I'm surprised at this error.

    Bob Wilson
     
  3. F8L

    F8L Protecting Habitat & AG Lands

    Joined:
    Aug 14, 2006
    19,011
    4,080
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    Location:
    Grass Valley, CA.
    Vehicle:
    Other Non-Hybrid
    Model:
    N/A
    Thanks doing this Bob. It looks great. :)
     
  4. bwilson4web

    bwilson4web BMW i3 and Model 3

    Joined:
    Nov 25, 2005
    27,068
    15,372
    0
    Location:
    Huntsville AL
    Vehicle:
    2017 Prius Prime
    Model:
    Prime Plus
    Early morning algerbra, I need to double-check how ACTUAL_MPG and INDICATED_ MPG are used to determine the error. Sometimes I work fast and don't checked my work. I should have done this first:

    1. ACTUAL_MPG = A_MPG; INDICATED_MPG = I_MPG; PERCENT_ERROR = N :: variables
    2. A_MPG = N*I_MPG + I_MPG :: Calibration formula
    3. A_MPG = (N+1) * I_MPG :: separate terms
    4. A_MPG / I_MPG = N+1 :: put known on one side
    5. (A_MPG / I_MPG) - 1 = N :: good enough to stop here
    6. (A_MPG / I_MPG) - ( I_MPG / I_MPG) = N :: convert "1" to ratio
    7. (A_MPG - I_MPG) / I_MPG = N :: the formula I should have posted
    Looking at my earlier posting, I posted two steps:
    but I failed to explain all of the parts involved. Now I did the formal proof using a different set of variables to make sure my earlier posting is not confused with the formal analysis. We can make a one-for-one conversion table:
    N = %ERROR :: the calibration constant
    I_MPG = SUM_INDICATED :: the indicated MPGs
    A_MPG = SUM_ACTUAL :: the actual MPGs
    Using the same formula terms, we get:

    1. (I_MPG - A_MPG) / I_MPG = N :: inverts the sign of the error
    2. (A_MPG - I_MPG) / I_MPG = N :: correct sign, ~ "-5%"
    We speak of the error being the indicated MPG is high so the actual MPG is lower. Although negative numbers are perfectly OK, I wrote the poll to reflect the error as positive error percentages when in fact they are actually negatives. It is an English language trick to avoid using negatives even in numbers since too many negatives can make a sentence confusing. Not really needed here, I was being a little lazy.

    I also wrote the methodology to 'average the averages' rather can calculate a true average. A true average would weight each MPG by the number of miles (or fuel consumed) to achieve that indicated MPG. For example, if one drove 500 miles (800 km) and got an error of 5% and then drove 50 miles (80 km) and got an error of 10%, the true average error would be:

    1. ((10/11) * 5%) + ((1/11) * 10%) :: weighted sum
    There are several other ways to calculate a true error including summing the distances, summing the fuel, and calculating the actual MPG. Then using the indicated MPG and distance, calculate the indicated fuel burn and sum them. But you can see this quickly becomes a lot of operations ... trivial with a spreadsheet but not so easy if like me, the indicated and actual MPG are what is readily available.

    In engineering I sometimes to use 'good enough,' back of the envelope, to save time and reduce workload. However, the clever engineer also does a 'sanity check' to make sure the simplification did not induce an error. In my case, I did individual error calculations for each pair and quickly noted the errors were nicely grouped regardless of the miles covered. The unweighted error is likely to be pretty close ("close enough") to the true value. Furthermore, I knew the poll would require interpolation to the closest value ... exact accuracy and would not be of great use as long the accuracy was "close enough." Unfortunately, I didn't go far enough to explain the 'average of averages' short-cut and its implications.

    Sad to say, I had a limited amount of time when I first posted the approach but today is a USA holiday, Thanksgiving Day. The spritual core of Thanksgiving Day is to give thanks for our blessings and life itself and share what we have with others. Happy Thanksgiving my friends. Often the best Thanksgiving meals are when everyone brings a dish. Perhaps someone else would like to bring one of of at least two methods to calculate a more accurate error? <GRINS>

    Bob Wilson