Determining glide eMPG

Discussion in 'Gen 3 Prius Fuel Economy' started by WPWoodJr, Jul 15, 2009.

  1. WPWoodJr

    WPWoodJr New Member

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    Apologies for the length of this post!

    In the myth of pulse and glide thread, many have objected to the inclusion of an mpg figure for the glide phase of P&G (for hybrid cars) since the Prius and Ford Fusion Hybrid get "infinite" mpg when gliding. However, due to battery losses during the glide (due to A/C, electric motor current draw, and other factors) the glide uses battery charge which must be recharged later by the engine. To account for this we can assign an "equivalent MPG" (eMPG) amount to the glide. This is the amount of MPG used by the internal combustion engine (ICE) to recharge the battery due to the battery discharge during the glide.

    The question becomes, what is the actual glide equivalent MPG for a hybrid? I've worked out an experimental protocol for determining the glide eMPG.

    We need to establish values for all variables except glide eMPG. Then we can calculate glide eMPG from the other variables. The variables that we need measured values for are:

    • Ratio of Glide distance to Pulse distance (eg 4 to 1)
    • Total Distance
    • Pulse MPG
    • Total MPG
    Once we have measured those values experimentally we can determine the glide eMPG for the experiment as:
    Pulse Distance = Total Distance/(Ratio + 1)
    Glide Distance = Total Distance - Pulse Distance
    Pulse Gal = Pulse Distance/Pulse MPG
    Glide Gal = Total Distance/Total MPG - Pulse Gal
    Glide eMPG = Glide Distance/Glide Gal
    So, how do we determine these values experimentally? I propose setting up an experiment on a long stretch of level roadway (as long as 5 miles if possible).

    Phase 1: Establish baseline Glide to Pulse Ratio
    Initially we run a pulse and glide test with a target range of, say, 30 - 45 MPH. The battery should have a high initial state of charge (SOC) so that the ICE does not need to run to recharge the battery. All electrical equipment should be off (A/C, lights, etc) so as not to drain the battery and force the ICE on. Its important to do a true glide, not a glide assisted by EV mode or reduced by regen, so we put the car in neutral during the glide. We measure the average length of the pulse and glide phases. We may determine that the pulse lasts 20 seconds and the glide lasts 80 seconds (4 to 1 ratio of glide to pulse).

    Phase 2: P&G test with low battery SOC and electric equipment on
    Next, we run the experiment. The battery SOC should be low, very near the point where the engine will turn on to recharge it. The reason is, we want the engine to turn on during the experiment to recharge the battery as necessary. If we started with a full battery, the test would not determine the glide eMPG because we would be running the battery down for a portion of the test.

    Turn on any electrical equipment such as lights and A/C used in normal driving. These will be a primary cause of lower pulse eMPG, as will electrical draw from the drivetrain.

    We start the experiment by accelerating to 30 MPH, then resetting the trip distance and trip MPG computers. Then we start the pulse and glide routine:

    1. Pulse at 20 MPG to 45 MPH for however long it takes
    2. Glide down to 30 MPH in neutral for however long it takes
    3. If the engine stays on or turns on during the glide, ignore it. Keep the car in the glide until it gets to 30 MPH.
    4. Repeat for the length of the course until the last glide is complete, then note Total MPG and Total Distance
    Phase 3: Calculate glide eMPG
    Once the experiment has been run, we can calculate the glide eMPG. We know Total MPG and Total Distance from the car's computer. We know the Pulse MPG because we will held that steady at 20 MPG during the experiment. We know the Ratio from the initial test. We can plug these values into the formula above and calculate glide eMPG.

    Here's a sample calculation:
    Total Distance = 10 miles
    Total MPG = 50 MPG
    Ratio = 4 to 1
    Pulse Distance = 10 / (4 + 1) = 2 miles
    Glide Distance = 10 - 2 = 8 miles
    Pulse MPG = 20 mpg
    Pulse Gal = 2 miles / 20 mpg = 0.1 gal
    Glide Gal = 10 miles / 50 mpg - 0.1 gal = 0.1 gal
    Glide eMPG = 8 miles / 0.1 gal = 80 mpg
    Phase 4: Use pulse eMPG to predict Total MPG in other situations
    Armed with glide eMPG for the given experimental conditions (eg A/C on or off, lights on or off, etc) we can predict Total MPG for varying pulse MPGs and glide to pulse ratios as follows:
    Glide Gal = Ratio/Glide eMPG
    Pulse Gal = 1/Pulse MPG
    Total MPG = (Ratio + 1)/(Glide Gal + Pulse Gal)
    For example, if your pulse MPG is 25 and glide to pulse ratio is 5:
    Glide Gal = 5/80 (80 is eMPG from above example)
    Pulse Gal = 1/25
    Total MPG = (5 + 1)/(5/80 + 1/25) = 58.5 MPG
    Be gentle! These are initial thoughts.
     
  2. donee

    donee New Member

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    Hey Bill,

    MPG stands for MILES PER GALLON, and ALL Electricity in a stock Prius or Fusion Hybrid is generated ONLY when the engine is runing. REPEAT AFTER ME - THERE IS NO FUEL CONSUMPTION WHEN THE ENGINE IS NOT TURNING ....

    I refuse to read more the than the first paragraph of your comments until you live by reality. And the reality here is REPEAT AFTER ME - THERE IS NO FUEL CONSUMPTION WHEN THE ENGINE IS NOT TURNING....

    Now, if you want to figure the impact of varying electric loads, factor them AFTER you figure the P+G Mileage. Any computation that includes fuel consumption when the engine is off is WRONG.
     
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  3. ksstathead

    ksstathead Active Member

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    ... because you can force SOC to a no change result in testing the P&G benefit.

    Measure fuel consumed with P&G and no delta soc.
    Calculate average speed under that P&G.
    Measure steady state fuel consumed at that average speed over the same course/conditions.
    Difference is the savings, if any.
     
  4. WPWoodJr

    WPWoodJr New Member

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    Hi donee, eMPG is a pretty well-established concept, see [ame="http://en.wikipedia.org/wiki/Miles_per_gallon_gasoline_equivalent"]Wikipedia entry[/ame]. For instance, the electric [ame="http://en.wikipedia.org/wiki/Tesla_Roadster"]Tesla roadster[/ame] is said to get 120 eMPG.

    If you're open to a new way of looking at things, putting a new tool into your arsenal, take a look at the other paragraphs! :)
     
  5. WPWoodJr

    WPWoodJr New Member

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    Yes, this would measure the advantage of P&G over cruise control, which is not in question and its not the subject of my post. :focus:
     
  6. ken1784

    ken1784 SuperMID designer

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    Following picture was taken at a famous Prius Marathon Run in 2005.

    They used the SuperMID M-1 mileage meter.
    The 3rd and the 4th line of the picture tells us following data.

    Total MPG: 49.51km/L
    Total driving time: 4 hours 21 minutes
    Total distance: 200.95km
    Pulse MPG: 12.83km/L
    Pulse ratio: 26% (more preciously 12.83/49.51=25.91%)
    Total(=Pulse) fuel usage: 4.058L
    Then...
    Pulse Distance = Total Distance/(Ratio + 1) = 200.95 * 0.2591 = 52.07km
    Glide Distance = Total Distance - Pulse Distance = 200.95 - 52.07 = 148.88km
    Pulse liter = Pulse Distance/Pulse MPG = 52.07 / 12.83 = 4.058L
    Glide liter = Total Distance/Total MPG - Pulse liter = 200.95/49.51 - 4.058 = 0.000 L
    Glide eMPG = Glide Distance/Glide liter = 148.88/0.000 = infinity
    [email protected]

    [​IMG]
     
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  7. WPWoodJr

    WPWoodJr New Member

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    Hi Ken, can you explain how you got pulse ratio? It doesn't look correct to me. Ratio should be the length of glide divided by the length of pulse under high SOC conditions.
     
  8. ken1784

    ken1784 SuperMID designer

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    The pulse ratio is ( (pulse distance) / (total distance) ) X 100%.

    [email protected]
     
  9. WPWoodJr

    WPWoodJr New Member

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    You seem to be trying to show that glide eMPG is infinite using some existing data with my formula - but your ratio is not calculated according to the experimental protocol. You can't calculate ratio as proportion of MPG contributed by the engine as you did here:
    Your approach will always show infinite glide mpg because it has no way to differentiate what proportion of the pulse fuel usage is due to recharging the battery and what proportion is due to getting to the P&G top speed.

    Ratio should be experimentally determined as follows:
     
  10. HTMLSpinnr

    HTMLSpinnr Moderator
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    I'm not sure I agree w/ the benefit of measuring battery "eMPG" in a Prius unless you're using a Plug-In Hybrid. All energy consumed in the Prius for motive power ultimately comes from gasoline, for which the consumption is fairly easily measured in real time, and average consumption measurable when refilling into a known volume of space.

    Running in EV only mode is only using previously stored energy, which will then be replenished through regeneration or charging from the ICE. Until you introduce a second source of power that isn't derived from gasoline, eMPG will remain inappropriate for measuring *overall* Prius efficiency, which is what most of us ultimately care about.
     
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  11. DaveinOlyWA

    DaveinOlyWA 3rd Time was Solariffic!!

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    other than participating in a mileage contest, P&G is not a valid real world option for anything. there are other ways to increase your mileage. now i understand the desire to want to know the mechanics, but the #'s involved all boil down to the driving conditions experienced at the time, so #'s to shoot for is all fine and dandy but i think the emphasis needs to be technique and results.
     
  12. ksstathead

    ksstathead Active Member

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    So you stay at constant throttle all the way until you emergency stop at every stop sign and light? If not, then you are P&Ging, yes?
     
  13. WPWoodJr

    WPWoodJr New Member

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    Knowing eMPG gives us a predictive tool for determining Total MPG:
     
  14. WPWoodJr

    WPWoodJr New Member

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    No argument from me :) but the predictive modeling is fun too.
     
  15. WPWoodJr

    WPWoodJr New Member

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    For the experiment, which must only be run once to determine eMPG for given battery use conditions (eg lights on/off, AC on/off, etc), you need an open road.
     
  16. DaveinOlyWA

    DaveinOlyWA 3rd Time was Solariffic!!

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    yep thats exactly what i am doing... bummer is, that sometimes when following my "guidelines" i end up rear ending someone at the stop sign because i hadnt calculated him being there.
     
  17. DaveinOlyWA

    DaveinOlyWA 3rd Time was Solariffic!!

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    i agree with that and also, you never know what can be achieved until you try it. after all, someone was playing with their driving technique one day years ago and not only invented a new method of driving, but also created a few new dictionary terms.

    i do it as well because every once in a while, i am in a position where it can work for me. so knowing how to do it is the key. but the parameters are going to change constantly
     
  18. wfolta

    wfolta New Member

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    I think the distinction, at least in my mind, is how you respond to other traffic and how consistently you allow your speed to vary.

    Any smart Prius driver will obviously look to glide or coast as much as possible. I look at P&G (the technique) as basically ignoring other traffic and sticking to a pulse-to-max-target-then-glide-to-min-target regimen as much as terrain allows.

    The former certainly involves pulsing at times and gliding at times, but not in a near-continuous cycle, and will basically maintain speed most of the time. Gliding to a stop sign is different from gliding down to a min-target speed on a flat road with no stops in sight.
     
  19. DaveinOlyWA

    DaveinOlyWA 3rd Time was Solariffic!!

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    BINGO!! now we on the same page...

    FYI... i dont glide to a stop sign and why should i?? am i thinking its going to fall down and i dont have to stop??

    i might coast...but not glide.
     
  20. ksstathead

    ksstathead Active Member

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    I have never heard anyone espouse P&G while ignoring other traffic. To the contrary, one is hyper-sensitive to surrounding traffic so as to plan a VARYING pulse & VARYING glide taking traffic into account.

    Isn't your choice to coast versus glide merely a tradeoff to save you time at the expense of more regen (conversion losses)? Perfectly rational, but I don't glide forever, and the brakes are there when I need them.
     
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