# What is the realistic accuracy & precision of typical consumer MPG calculations (tripmeter miles/pump gallons)

On Thu, 20 Jul 2017 17:32:39 +0100, Mike Coon wrote:

Every reading a mom and pop does has inaccuracies that, I posit, are tremendously higher than most people seem to think they are (at least most people who quote mpg figures with decimal places in them).
Most people have a tripmeter reading and a gas pumpmeter reading. Where they fill the tank and reset the tripmeter before driving away.
I can't find any reliable source that says what the accuracy or repeatability of that mom-and-pop tripmeter/pumpmeter calculation, but basic logic dictates that the errors compound such that there is likely (IMHO) no way to get anywhere near decimal-point accuracy, and worse, probably plus or minus 1 mpg is the closest anyone can get in terms of repeatability and precision.
Even the EPA's \$360,000 machine only claims plus or minus 2% of the indicared reading. I can't find where I got the notion that a mom and pop can't possibly get closer than about 4% with a tripmeter/pumpmeter mpg calculation - but I'm still seeking those numbers as we speak.
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On 07/21/2017 11:51 AM, Mad Roger wrote: ...

...
Why do errors compound in your view?
And, it depends on what you mean in terms of accuracy -- in terms of absolute one needs to know the calibration error of the odometer; most folks are satisfied to just assume it's close enough for the purpose.
If you look at simply a single fillup, it's not unreasonable to expect a few tenths of a gallon difference between the first fillup level and the subsequent; if you try it on shorter distances than a full tank then the fractional error goes up.
OTOH, if one keeps track over longer periods of multiple fillups and take some care to use the same filling pattern and only fills up after using near the full tank capacity, then over time plus/minus targets _will_ tend to cancel out and I have no qualms in believing a relative performance number in the 0.1 mpg can be determined.
As noted, I've done this on long trips a number of times (generally on first trip or so with a new vehicle, either actually new (rare) or (most often) new to me) just to see how it compared with previous and have had quite good comparisons on recent ones with the computer-computed results. These would be over total distances of 1500 to 2000 miles, not just 20 miles test runs.
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On Fri, 21 Jul 2017 12:42:08 -0500, dpb wrote:

It's like a chain is no stronger than the weakest link.
No calculated result can be better than the worse inaccuracy.

Accuracy, precision, and sigfigs are standard terms: http://www.chem.tamu.edu/class/fyp/mathrev/mr-sigfg.html Accuracy: how closely a measured value agrees with the correct value. Precision: how closely individual measurements agree with each other. Sigfigs: accuracy is no better than the least accurate measurement.
By way of off-the-cuff example, if the accuracy of the odometer is to the billionth of a mile and the accuracy of the pump gallons is to the billionth of a gallon, but the accuracy of the fillup is plus or minus one gallon, then the resulting mathematical (division or multiplication) accuracy can be no better than plus or minus one gallon.

A single fillup will never suffice.
We're trying to compare a MPG *change* between two situations, so, by definition, there _must_ be (at the very least!) /two/ separate calculations. + Calculation before the change (say, smaller tire/wheel diameter) + Calculation after the change (say, larger time/wheel diameter)

That's not necessarily true, because it depends on the understimations balancing out the overestimations, but I'm not going to quibble that more calculations done over time are likely going to randomize the precision and accuracy fluctuations over time.
While I will not quibble with your statement (because I essentially agree with you), I can point out that your speedometer can be consistently wrong in the same direction in either precision or accuracy, in which case it's *not* going to balance out over time. It will be consistently wrong, over time.
But, let's not quibble about that because we both can assume that, for our purposes, the randomization of measurement results will be half the time underestimating and the other half the time overestimating - such that they could balance out.

Nobody yet, and even not me, has supported a claim for any better accuracy than my presumed plus or minus one mile per gallon using the standard mom-and-pop test of dividing the number of miles driven based on the tripmeter reading by the pump indication of gallons used to fill back up to a presumed similar previous starting point of amount of fuel consumed.
Remember, the resulting accuracy can't possibly be better than the least accurate measurement.
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On 07/21/2017 2:05 PM, Mad Roger wrote: ...

On a _point_ estimate, yes.
The point I'm making is that it is the _total_ fuel consumed over the total distance; the changes in hitting the target level on a tank-by-tank basis goes away for all excepting the last tank as it doesn't matter in the total. So, if you miss by 0.1 gal on the one tank, yeah, that roughly will translate to 0.1 on the mpg number. But, over the 9 tanks prior to the tenth and last, it doesn't matter; it was all used and so the 0.1 gal error on the last is only a tenth of the size on the overall as it was on the first.
So, over a time, you can get quite precise estimates this way.
As noted, the bias in odometer calibration is a bias, yes, but presuming there's not a reason it is getting worse with time it's not compounding, it just makes a percentage difference in the computed result.
--

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On Fri, 21 Jul 2017 14:20:43 -0500, dpb wrote:

Your multiple-runs argument only holds water for both random accuracy and random precision, but not if one is random and the other is not.
For example, I think it's well known that most speedometers read high *most* of the time (at least that's my understanding - but I could look that up if you question that assertion).
Assuming that assertion is close to correct, let's say they read high by about 5% accuracy most the time (just to make a point), where the precision is about plus or minus 1%.
Notice the accuracy is *always* high while the precision is random around a set point.
http://www.chem.tamu.edu/class/fyp/mathrev/mr-sigfg.html Accuracy: how closely a measured value agrees with the correct value. Precision: how closely individual measurements agree with each other.
If the speedo reads high by 5% all the time, whether you measure your speed once or if you measure your speed a billion times, you'll never any closer to the right speed than 5% plus or minus 1%.
In repeatability, the gauge may give you different figures within + or - 1% of that 5%, which is only to say that the speed will be consistently reading from 4% to 6% higher than the actual speed.
But a billion test runs won't get you any better than that, all of which are at least 4% off from the "correct" measurement (in the example).
My point is that a billion test runs only randomizes that which is random.
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On 07/21/2017 5:05 PM, Mad Roger wrote: ...

We'd already thrown the mileage calibration bias out as being simply that. It can be compensated for by comparison over set measured course and recording the offset. Red herring for the discussion.
The point I'm making is that it doesn't matter at all about whether there's any random error in the fillup on individual tanks at all on the intermediary answers--yes, they may have some fluctuation owing to inconsistent fillup, but one can assume the pump is accurate since they're checked by the State weights and measures folks on a regular basis. So, all the fuel that went in went out in accumulating the miles and it didn't matter how much went in on each individual measurement at all in the end--it's the total. Only that random error on the final fillup when you make the calculation at the end does that error enter in -- and it becomes quite small by then in comparison to the total.
And, if one computes the mean of the billion trials, the error in the mean is quite small even if the random error in each trial is sizable.
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On Fri, 21 Jul 2017 18:05:52 -0500, dpb wrote:

I agree with you that the tripmeter calculation is inaccurate to some degree, for which there are ways of "calibrating" the equipment.

The answer to the question depends on only 3 factors, I think.
Given these three factors are critical to answer the question, I think everyone is talking out of their ass (including me) if they can't answer these three questions to validate their own thought process:
+ How accurate & precise is a reading of 300 miles on a your tripmeter? + How accurate & precise is a reading of 20.25 gallons on the gas pump? + How accurate & precise is the matching of the prior fuel level?
I posit both the tripmeter and the previous-fill-level measurements suck. How much to they suck?
I don't know.
I would not be surprised if they suck so badly that the end result is a calculation which is plus or minus 1 mile per gallon in either accuracy or repeatability.

While it will be useful to know what the accuracy and precision (repeatability) of the pump is, I think we can all assume that the pump is within something like (at least) plus or minus a few percent of what it reads.
But that number can be accurate to a billionth of a gallon, and it still would be meaningless if the fill level was off by plus or minus a gallon because the accuracy of any one measurement is only as good as the worst measurement and the accuracy of the final calculation (when multiplication adn division are involved) compounds inaccuracies.
Anyway, all the words are moot if we don't know the answer to 3 questions: + How accurate & precise is a reading of 300 miles on a your tripmeter? + How accurate & precise is a reading of 20.25 gallons on the gas pump? + How accurate & precise is the matching of the prior fuel level?

Am I correct to understand that you are saying if you go only 300 miles on one tank, then the fill-level inaccuracy is (say) plus or minus 1 gallon per tank; but if you go 3,000 miles (obviously on multiple tanks), that the fill-level inaccuracy is one tenth of that plus or minus one gallon per tank?

As long as the error is random (i.e., in both directions of the true answer).
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On 07/21/2017 6:30 PM, Mad Roger wrote: ...

What do you not understand about "random"?
And the mean is still the mean, whether it is zero or not.
--

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On Fri, 21 Jul 2017 22:05:13 -0000 (UTC), Mad Roger

True of the speedometer, but NOT of the odometer. The odometer repeatabilty is as close to 100% as you will get even with a cable driven odometer. (it is a directly geared measuring device with ZERO vatiability - X number of cable turns per mile from the day it's made till the day it is scrapped ( generally 1000 turns per mile, but some older cars were 600 turns per mile, some motorcylses 1450, etc - but they never change) With electronic speedos and odos (virtually all cars today less than 15 years old) repeatability is almost 100%. Accuracy CAN be very close to 100% too, as on most cars under 10 years old today, the speedometer can be accurately reprogrammed to the tire diameter so repeatability is only affected by tire wear (mabee 3/8 inch in 24 over the life of the tire)

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On Fri, 21 Jul 2017 19:05:32 -0000 (UTC), Mad Roger

Actually it is - because you only make ONE calculation. The measurement accuracies do not change. The precision gets better, because you are not using numerous mileage measurements that can only be accurate to the closest 10th of a mile or KM (more accurate in the metric system becuase a KM is smaller than a mile) The precision is now 1/10km over 5000 km instead of 1/10 kn over 500, ten times.
Your accuracy on the fuel used is to the 10th of a liter (or gallon if you are a Yank)- again more accurate with the metric system because liters are smaller than gallons. So your accuracy is to the closest 10th of a liter 5 times - and the accuracy of the fillup is only the closest you can get it ONCE instead of 5 times.
Accuracy of fuel used will be, at the very most, 5X 1/10th liter more - that's plus half a liter over to -0 liter under over 365 liters at 20 miles per US Gallon that's within better than 1.5% (1.369) at the outside.(assuming the calibration of the pumps is accurate - pumps are calibration tested on a more or less regular basis - when I was "in the business" we were still running imperial gallons for the most part - the pumps were inspected and certified accurate to within 1/10 gallon in 5 gallons ( the closest the meter could read) IIRC when the switch to metric was made, it was 1/10 of a liter in 20 liters (the size of the test container remained virtually the same) so accuracy improved by roughly a factor of 4.
If I kept track of the fuel mileage on my vehicle over a period of 50,000 km, the accumulated average fuel economy could be easily calculated to within that percentage of error. ( I used to do that when I ran a vehicle log for business purposes)

Or consistently right. If you KNOW the accuracy of the speedo, it is a simple mathematical correction to achieve accuracy. The speedo may vary in accuracy because it is an inductive coupling device on a mechanical speedo, while the ODO will not vary as it is a direct geared connection to the driven wheels. With electronic speedos and odos, their calibration does NOT change. The only vatiance is tire wear ( aproxematelt 3/8 inch difference in diameter of a , say, 24 inch diameter tire, over it's lifetime - and that wear is pretty linear - so it is not rocket science to work in a correction for that too if you want to be a very anal engineer.

Or they could not - better to eliminate the randomization, or account for it in calculating accuracy.

I've averaged it over 240,000 miles - - -

I'm sure I could claim accuracy to closer than 1 MPG, but what good would it do over 240,000 miles??????? (and how could you prove me wrong?)
For COMPARISON testing, accuracy is not important - only precision and repeatability. On my electric conversion I could compare one type of tire to another by driving a given distance and route on one set, measure the watt hours of charge used, and compare to a different set of tires over the same route under the same conditions and KNOW how much better "mileage" I would get with one tire over the other.
Modifying the tune on my '63 Valiant, or a customer's Celica, or whatever - I could do a "before and after" run of 5 miles with my calibration can and know, to the ounce, how much more or less fuel was consumed over the same route, Using the "official" fuel mile tester I could measure to the cc over a half liter - that's an accuravy of 1 part in 500, or 0.2 percent. If I had a "rolling road" I could repeat the drive cycle accurately too - but I only had access to that at trade school (a chassis dynamometer) Not as easy to do today with fuel injected cars - but dynos are a LOT more common today than they were 40 to 45 years ago . . . and more programmable. If you know the cd of a vehicle today, a computer simulation can run a vehicle over a virtual course, correcting for ambient wind, changes in elevation, accelleration (knowing mass of the car) -every conceivable condition - to make direct case to case comparisons EXREMELY accurate. (and fuel measurement technology has advanced so it's very simple to very accurately neasure the amount of fuel consumed as well - and also get very accurate measurements of instantaneous consumption - and with strain guages even know EXACTLY how much horsepower is being delivered to the road to figure out specific fuel consumption -
All stuff you "engineers" should understand.

Which can vary from no better than a SWAG to pretty darn close, even for the "mom and pop" or "hobyist" to EXTREMELY accurate for the engineer.
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With my scanguage on my Ranger the calculated MPG and the MPG figured out by me using a calculator and fuel volume vs mileage is generally pretty darn close. If the ScanGuage says they injectors have passed 13.7 gallons, my fillup is generally somewhere within .1 to .2 gallons. The speedo and GPS are within less than 1 kph on speed at 100kph (62Mph), and the odo within about the same. This is after making corrections over many tanks for the fuel volume adjustments. Neither of my ancient machines has a built in "trip computer"
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On 07/21/2017 8:41 PM, snipped-for-privacy@snyder.on.ca wrote: ...

I find all that perfectly believable...the speedo on the Buick I noticed on the last trip to NM was deadnuts on the wife's GPS. I presume if that's the case the odo would be, too, altho I never actually checked on it specifically.
Instrumentation is pretty good and pretty cheap to get pretty good for ordinary measurements any more...electronics is a wunnerful help in many ways. :)
As I've turned into old fogey, I've come to rely on the 'puter for such info more than would've cared at 20. There's just only so many times one really wants to get down on the ground and measure tire pressure after 70... :( There's getting to be a lot of fluff besides the useful, but the basic stuff is helpful.
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On 07/21/2017 07:55 PM, dpb wrote:

When you consider how the old speedometers worked it's amazing they came anywhere close to reality. I had a '60 Plymouth where the speedometer looked like a red bar progressing across a horizontal display rather than the usual needle. The guts were a tube about a foot long and an inch and a half in diameter suspended in bearings and loaded with a spiral spring. The mechanical cable from the tailshaft of the transmission tweaked the tube with each revolution via a magnetic link. It was an analog integrator with the spring controlling the tube's rotation.
The standard dial type was the same principal but the Chrysler engineers went out of their way to be weird. That was also the era of the pushbutton Torqueflite tranny and left handed lugnuts on one side.
A lot of modern speedometers are just as bizarre converting a perfectly good digital pulse train to an analog voltage to drive a dial rather than going straight digital.
But now
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The EPA doesn't have the time to do accurate MPG numbers Plus/Minus 2% is good enough for the EPA. I'm sure my "mom and pop" MPG number are more accurate than that. But so what? The MPG I get depend on the driving circumstances. For instance, I've measured my MPG on a number of cars on 3000 mile round trips to Florida. I can tell you the EXACT total MPG I got on those 3000 mile trips because I carefully noted the exact metered amount of gas I used, and I verified the odometer accuracy using mile markers. The only real useful thing that gives me is my MPG for the entire trip. That includes local traffic when getting off the highway, and my travels at my destination. But I know my approximate MPG at steady highway speed because I sometimes do tank to tank calculations by filling to the filler tube. That too is an EXACT calculation, but is still only approximate MPG because maybe the terrain and weather may vary. So before you ask about "accurate MPG" you have to define what that is.
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On Friday, July 21, 2017 at 8:31:07 AM UTC-10, Vic Smith wrote:
wrote:

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My guess is that the EPA gets very accurate mileage numbers. They use the s ame startup/warming procedures and routes for the cars they test. They prob ably compensate for temperature and weather and other factors. They know ex act distance traveled and the exact amount of gas used. These guys are whit e coat scientists and technicians. Why would you think your mom would do be tter? I'm sure she's a nice lady though.
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Then why are they claiming plus/minus 2%? I can do much better than that - for my MPG only. I'm sure the EPA doesn't take my weather, my terrain, my foot and my factors into their calculations, because they haven't asked me for input.
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On Friday, July 21, 2017 at 9:00:46 AM UTC-10, Vic Smith wrote:

om> wrote:

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.
e same startup/warming procedures and routes for the cars they test. They p robably compensate for temperature and weather and other factors. They know exact distance traveled and the exact amount of gas used. These guys are w hite coat scientists and technicians. Why would you think your mom would do better? I'm sure she's a nice lady though.

- for my MPG

my factors into

They claim 2% because that's the nature of science. One of the basic tenets of science is that one cannot be absolutely sure of anything. There's only percentages of occurrences. Only bozos and religious fanatics are absolute ly sure about things in this world.
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On Fri, 21 Jul 2017 13:31:01 -0500, Vic Smith wrote:

We're trying to compare a MPG *change* between two situations: + Calculation before the change (say, smaller tire/wheel diameter) + Calculation after the change (say, larger time/wheel diameter)
If the change itself causes, say, a 1 mpg difference, but if our measurement accuracy is, say, plus or minus 1 mpg, then we'll never see a measurable difference between the two test runs.
Even if we run ten thousand test runs, we'll still never see a statistically valid difference, even though the 1 mpg difference is actually there.
We can't measure any better than our accuracy and repeatability allows.
The factors, I think, are accuracy, precision, repeatability, and, since multiplication/division is involved, each offset worsens the results.
Without answering these questions, nobody, yes, not even you, can say you have an "exact" number, and, I posit, that you can't even get remotely close to exact, using the standard mom-and-pop tripmeter/pumpmeter method.
+ Tripmeter accuracy is what in the average car over a 300-mile tank? + Owners ability to "match" the previous level of fuel is what? + Gas station pump reading accuracy is what?
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Putting different size wheels on the rear will affect the mileage measurement apart from the mpg, so you will have to correct the miles measurement before computing mpg. Smaller wheels => higher miles for the same real distance. You will have to take into account how you drive with the wheel change. If you maintain the same real speed for smaller wheels your engine will be turning over faster than before. Driving at the same speedometer speed with smaller wheels reduces the load on the engine.
As a somewhat off-topic point, manifold vacuum is directly related to instantaneous mpg. It is relatively easy to install a vacuum gauge in the driver's compartment.
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wrote:

Directly related? but not necessarily 100% linearly related High manifold pressure (low vacuum) means heavy load which means poor mileage. The reverse is also true - but calibrating vacuum to MPG is virtually impossible with any level of accuracy. It WILL give you a good, better, worse indication though. Keep the vacuum up and you will get better mileage.
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