My 328 Fuel Log After One Year of Ownership

Fellow F-Chatters,

Today is the one-year anniversary of my first fill-up in the 328!

I thought I would take a moment and post for the community my fuel log over the the past year.

Most people see me do this and think that I'm ridiculously "detail oriented" (they use a different word), but to each their own, ya know? I like to do it because it is a tremendous way to monitor one health characteristic of the engine and car in general. Of course, there probably is no better way to document the mileage of a car. I've seen my share of shady-mileage 308s/328s. Besides, when I was a kid, I would watch my grandfather do the same for his Buick. Wisdom, I think you call it!

Anyway, here it is.

I've uploaded a spreadsheet, but here's a general analysis.

This data is for 15 "fill ups" over the past calendar year.

Also note that all fill-ups, except for the last three, occured in Albuquerque, NM, at elevation=5,000 feet. The last three occured in Boulder, CO at elevation=5,340 feet. In all cases, the octane gas used was the highest available, 91, which is intentionally "scaled back" due to the altitude. This is premium fuel and is "equivalent" to 93/94 octane (US rating method) at sea level.

The spike in mileage in December corresponds to a 450-mile trip where I drove the 328 from Albuquerque to Boulder (greater Denver area)... Highway miles. Actual highway mileage I would estimate to be more, say 22mpg, because part of each of these tanks was consumed "in city".

Other comments: reduced mileage in winter I attribute in part due to longer warm-up periods, and in general the tendancy for shorter trips (less long exploratory trips in the mountains, etc.).

So... Here we go. In about one year of ownership:

Total Miles Traveled: 3120 miles
Total Fuel Cost: $418.54
Total Fuel Consumed: 202.26 gallons
Total Average Fuel Cost per Mile: 13.4 cents per mile
Average cost per gallon of fuel: $2.08
Total Average Mileage: 15.426 miles per gallon


Now, what I've found is, my tripometer and odometer read approximately 10% high. This means that more miles accumulate on the car according to the odomoter than the car has actually travelled. This also means that our fuel figures above are optimistic in terms of mileage and cost per mile.

Corrected for 10% mileage overread:

(Actual) Total Miles Traveled: 2836 miles
(Actual) Total Average Fuel Cost per Mile: 14.8 cents per mile
(Actual) Total Average Mileage: 14.021 miles per gallon

Microsoft Excel 2003 spreadsheet attached to this post.

Enjoy!

--Mike
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Guys,

I spent a lot of time thinking about this. I know both formulas are missing a row. That is intentional.

If you want to be accurate, you have to be very careful with the formulas.

The idea is calculate the fuel cost based not on "replacement cost". It would be INACCURATE to use to entire fuel cost column--because the first fill-up was replacing fuel that I did NOT have mileage data for.

So, if I filled up tomorrow, then I have a full tank of gas. That fuel costs what it cost TOMORROW. Two weeks later, when I fill up, only then will I know how much I travelled, that is, how much fuel I consumed (assuming I fill up every time). How much fuel of today's fill-up's fuel I consumed, at today's cost, I will know after two weeks from now.

Similarly, the very last time I filled up, while I used the numbers for how much of the previous fill-up's fuel burned (i.e. how many gallons it took to fill up) for mileage and cost calculations, I did NOT use the total cost of the fuel for that fillup towards the total aggregate cost... because I'm still burning that fuel, I and I will to the next fill up!

So this is a more accurate (though more difficult to follow) way of calculating the fuel cost--what I burn today gets counted based on the cost of the fuel when I filled up. The easier (and less accurate) would be to calculate it based on "replacement" cost, but I still would use every fill-up total cost figure.

Following me at all? For something so trivial, yeah, it requires a bit of wrangling to get your mind around it. And I could still be wrong!

 

Thanks for your thoughts! Responses in line--

Glad you're on the same page with me re: the spreadsheet logic. Actually though, I can't delete A7 through F7. The Cost-per-gallon figure (column D) for this entry is used in subsequent calculations--after all, in the weeks that followed this fill-up, I'm burning fuel that cost the amount per gallon as specified by the figure in THIS row. So that data point is important, and hence the other figures around it, so no, I can't delete A7 through F7!

What you say above is one way to do it, but you basically want to take the "unweighted" or straight average. This doesn't take into account how much gas you actually USED. In the extreme, if there were only two fillups, one fillup was 2 gallons and one was 20 gallons, the 2-gallon fillup was at $1.50 per gallon in a highway town, and the 20-gallon fillup was at $2.80 a gallon in L.A., your method would (misleadingly) calculate the "Average cost per gallon of fuel" just by taking the average of $1.50 and $2.80. This is the unweighted average, and gives you $2.15.

That's not the figure we want. The better and more accurate way is to use the actual amount of fuel for each fillup as a weight, and calculate the weighted average. In the above example, this would be like (2gal * $1.50) + (20gal * 2.80) / 22 gal, which gives you the figure $2.61. This latter value is far more representative of the actual "average" fuel cost, right? You used more of the expensive stuff than you did of the cheap stuff. So the weighted average is how you take that into account. The formula I used in the spreadsheet is precisely this weighted average... not the straight average. I admit, though, that unless your looking for it and get your "head" around the whole thing, it can be tricky to understand exactly what it means.

The weighted average formula over the straight average formula has no bearing on rounding errors at this precision (two/three decimal places). You'll note that excel uses IEEE 754 standard for floating point representation, which, as you point out, means therefore it is susceptible to rounding errors like all finite-representation floating point computing machines. It is not an issue here... but point well made and well taken.

No, not inconsistency--that was the precision of the data source I was dealing with. The trip odometer in Ferrari 308s and 328s has a precision of one decimal place, with three total significant figures. The standard odometer has five significant figures, and no decimal places. I was true to the data and put it in exactly and as accurately as it was displayed. I made no attempts to "interpolate" to the hundredths place, for example, by looking at where the trip odometer's decimal point was on its "spin".

I was very careful to round where appropriate and obeyed all significant figures. Nowhere in my results are decimal places beyond three, or total significant figures beyond five. I will remember your above point though.

SO true! Roundoff error is the real deal, and if you work with floating point numbers to any great decision and over some number of operations, you better keep an eye out for it!

(Nerd note: For any who are interested in implications of the finite floating point representation of computing machines, I recommend the early chapters of this text: D. Kincaid and E. W. Cheney. Numerical Analysis: Mathematics of Scientific Computing, Third Edition. Brooks/Cole, Pacific Grove, CA, 2002.)


Thanks for your thoughts, guys!

And just remember, the big idea here was just to give back something to the community, give an idea of fuel operating costs for these cars as well as an accurate number for fuel economy from real-world experience. Hopefully someone out there found this useful .


--Mike

 

When I first got the car and noticed it, I would do checks along a five mile stretch of road with mile markers, and came up with about 10% high. This is obviously a very rough figure.

I also noticed that friends' trip odometers would read higher than mine for the same trip.

And, my speedometer reads high, even with the sending unit replaced! But, it's not a fixed amount--it seems to be a percentage. I.e. when it shows 40, I'm doing 35, when it shows 70, I'm doing 63. (I confirmed the 40/35 figures with a road "speed advisory" radar the other day, but haven't confirmed the 70/63 figure). My subjective feeling is that when the speedo shows 60, I'm actually doing 50--which is more than 10% obviously.

As far as I know, I have stock size tires--will double check later.

That said, I seem to recall that Rob Lay got a ticket in the 328 when he assumed the speedo was reading 10mph over (indicated 85 if I recall).

 

One quick note about my previous response to Air Cooled Nut - the Ferrari 308/328 trip odometer has four digits, three before the decimal, one after, for a total of four significant figures (not three, like I said earlier).

 

LOL! Dude, I'm a total nerd . But chicks dig nerds these days!