Accuracy of the BC mpg - K-Bikes.com - Excellence in Motion
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post #1 of 11 (permalink) Old Feb 16th, 2009, 4:44 pm Thread Starter
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Accuracy of the BC mpg

Abstract: It actually works reasonably well.

Introduction

Previous research by the author (emzed, 2007, 2008) showed that for purposes of estimating miles to exhaustion, both the Reserve indication and the BCs Miles Remaining feature are about as accurate as darts thrown by a drunken blind hippopotamus. The BCs MPG feature in theory could be used to estimate miles remaining but only if the values it presents are reasonably consistent if not entirely accurate. It seems incredibly unlikely to be the case, but in the interests of science, this paper compares the BCs MPG against actual mpg calculated for each fill-up.

Apparatus

2007 BMW K1200GT, blue.

Method

From 6/13/2007 through 6/11/2008 the following data were recorded with each refueling, except when I forgot:
- F: Fuel to fill tank.
- T: Tripo miles at refueling.
- M: BC reported mpg.

This resulted in data for 82 fuelings. From these data, actual mpg was calculated as T/F.

Results

Figure 1 plots actual versus BC MPG as one blue diamond per refueling. The dashed line represents perfect accuracy. As can be seen, the BC tends to over-estimate the mpg, but fairly consistently so. A least-squares linear regression[1] found that you can predict actual mpg from the BC MPG by using the following equation:

Actual mpg = 0.897 * M + 3.266

The line corresponding to this equation is shown as a thin blue line in Figure 1. The predictions from this equation are accurate to plus-or-minus 1.3 mpg (at 95% confidence). Note that about 0.9 of that 1.3 can be attributed to the granularity of the BC display (e.g., it shows either 46.1 or 47.0 mpg, but never anything in between), suggesting the underlying computation of the BC may be consistent to within less the 0.5 mpg. Not that it helps you any.

Discussion

Astonishingly, it appears that the BC might actually be useful for something. The display of the Reserve indicator can mean you have anywhere from 47 to 73 miles remaining to exhaustion, if you get the mileage I typically get (emzed, 2008). The BC Miles Remaining feature tells you, well, I dont know what the hell its telling you. However, if you reset your BC MPG with each refueling, the BC MPG feature along with the formula above can be used to tell you the total miles you can expect from your tank to an accuracy of plus-or-minus 8 miles (6.3 gallon fuel tank at +/-1.3 mpg; ). The estimate ranges from this formula for each BC MPG reading are provided in Table 1. Using the BC MPG in this way is actually more accurate than using the Reserve indicator.

Alternatively, if playing chicken with your gas tank is not your idea of thrills, the above formula can be used to provide the minimal number of miles remaining when the Reserve indicator appears (i.e., under the assumption that only 1.1 gallons remain). This is provided in Table 2.

When using these tables, remember that they assume your MPG remains steady. If youre getting 50 BC MPG at 100 mi, and then hit a mother of a headwind for the next 150 miles, dropping BC MPG to 39.1, well, youre not going to make it that far. And the usual disclaimers, these results are based on the performance of a single rider on a single bike, YMMV, blah, blah, dont sue me if buzzards have you for breakfast on a lonely desert road.

References

emzed (2008). Irregularities in the Point of Reserve. http://www.k-bikes.com/forums/showthread.php?t=13313
emzed (2007). Demonstrated Usable Fuel Capacity. http://www.k-bikes.com/forums/showthread.php?t=9886

End Notes

1. A quadratic regression resulted in the squared term of the equation being marginally statistically significant, but it only reduced the standard error of regression by 0.02 mpg, to which I say, Who cares? I mean, its not like Im really anal or anything.
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post #2 of 11 (permalink) Old Feb 16th, 2009, 5:11 pm
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Quote:
Originally Posted by emzed
Abstract:

1. A quadratic regression resulted in the squared term of the equation being marginally statistically significant, but it only reduced the standard error of regression by 0.02 mpg, to which I say, Who cares? I mean, its not like Im really anal or anything.
I don't see anyone accusing you of that.

tim-----still on the right side of the frostline

you can't stop the signal
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post #3 of 11 (permalink) Old Feb 16th, 2009, 5:21 pm
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Wow, yeah what he said. I believe you, in fact I would like it if you were handing out Obama's Stimulus money, at least it would all be accounted for. So if you just stop paying your taxes maybe Obama will consider you

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post #4 of 11 (permalink) Old Feb 16th, 2009, 9:19 pm
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Yeah, I did all the calculations too (I'm an engineer myself), including running the tank dry a few times. I came to the conclusion that I consistently average 40 mpg. So that's 250 miles on a tank, or 450 if my aux fuel cell is on.

And if that's not accurate enough, I have two 1-liter MSR fuel bottles tucked in the saddlebag, which is good for an extra 20-25 miles if I really need it.

Other than that, I just ride and don't worry about it.

Ken
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'13 Dark Graphite Metallic K16GTLD, 24K miles and counting...
'09 Magnesium Beige Metallic K13GT, 60K miles miles and counting...
'02 Mauve Metallic K12LTC, 106K miles and sold
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All lower 48 states plus Alaska on the K13GT in two weeks . . .

Some people see the gas tank as half empty. Some see it as half full. All I care is that I know where the next tankful is coming from...

Last edited by Meese; Feb 16th, 2009 at 10:35 pm.
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post #5 of 11 (permalink) Old Feb 17th, 2009, 4:40 am
 
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Are all these calculations based on a US gallon which is smaller than a UK gallon and is this difference programmed into the BC or do BMW just have a one sized gallon for both the US and the UK?
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post #6 of 11 (permalink) Old Feb 17th, 2009, 1:24 pm
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WHAT???????????????????


You get over 40 MPG?????????????????




Wish I could do that. Maybe I need to stop running full throttle....

When in doubt, apply more throttle.
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post #7 of 11 (permalink) Old Feb 17th, 2009, 6:44 pm
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Mine seems to work pretty good, especially compared to my 07 GS. Now THAT thing can leave you walking.
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post #8 of 11 (permalink) Old Feb 20th, 2009, 8:41 am Thread Starter
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Quote:
Originally Posted by wellsy
Are all these calculations based on a US gallon which is smaller than a UK gallon and is this difference programmed into the BC or do BMW just have a one sized gallon for both the US and the UK?
The calculations are based on US gallons. I don't know if BMW adjusts the BC software for the UK, but I think you can check by comparing your calculated mpg with BC MPG. If you BC MPG is about 20% less than your calculated mpg, then the BC is using US gallons.
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post #9 of 11 (permalink) Old Feb 20th, 2009, 9:47 am
 
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My BC mpg is more than my calculated mpg. I guess that makes sense since my speedo reads fast and my odometer goes long.

Calculated seems about 2mpg less than the BC, or approx 5%. Don't know the % difference between the odo and gps. For that I must venture to the garage.
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post #10 of 11 (permalink) Old Aug 4th, 2013, 1:04 pm
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Last year on the motorway trudge up to Scotland for our annual blast around the highlands and glens we sat at 2mph below the legal limit of 70 mph on the cruise control.

Doing so got 65.7mpg (uk gall is 4.54 litres)



Which I figure is an awesome mpg for a large capacity motorcycle
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