+1
I measure my gas mileage on every fillup. I get 19 to 20 MPG every fill unless I do a lot of around town driving. Very consistent. I watch it to see if it drops off which would mean something is wrong.
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.
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:
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.
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.
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.
We're trying to compare a MPG *change* between two situations:
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.
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.
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.
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.
You obviously don't check your mileage very often. I do and seldom see even
1 MPG difference. I get high 19 or low 20 MPG on 19 out of 20 tanks. I think the idea of uneven filling of the tank is a red herring. I can't remember the last time I saw a gas station on a slope.Bottom line is try it and see. I expect the major factor in MPG variation is actual MPG variation from driving a different mix of town and highway driving.
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.
I don't think I've ever seen a gas station on a slope. However ... The errors in the calculation stem from errors that nobody seems to know what they are, which means nobody knows what they're talking about.
Assuming the tripmeter/pumpmeter calcultion is the method used,
Any one measurement (either miles or gallons alone) can only be as accurate and precise as the worst measurement, while the miles/gallons calculation compounds those inaccuracies and imprecisions (in loss of sig figs).
I think most of us would probably assume the pumpmeter is the most accurate and the most precise, but the other two measurements aren't even close to accurate or precise.
What matters is how accurate & precise is a 300 mile tripmeter reading? And how accurate and precise is the match to the previous fuel level?
I posit that the best you can do, overall, after running the calculation, is something like plus or minus about 1 mile per gallon such that 20 mpg is actually anywhere from 19 to 21 miles per gallon actual.
What I'm seeking is data that tells us the three main questions that must be answered for anyone to say that my hypothesis is even close to being right or wrong:
No calculation can do better than the worst measurement, and worse, errors compound when you multiply or divide.
But that's the kind of things we're looking for, which is why the minimum number of calculations possible is two, since you have to have a "before" situation and an "after" situation.
For example, if the change that you are testing causes about 1 mile per gallon decrease in fuel economy overall (but which isn't linear), but if your calculations are no better than plus or minus 1 mile per gallon in accuracy or precision, then you'll never even see the very real difference because it will be unmeasurable given the plus or minus 1 mile per gallon typical accuracy and precision that I posit the typical mom-and-pop tripmeter/pumpmeter calculation provides.
But there's no sense in talking about *any* of that, if we don't know the answer to these three questions.
I don't think I've ever seen a gas station on a slope. However ... The errors in the calculation stem from errors that nobody seems to know what they are, which means nobody knows what they're talking about.
Assuming the tripmeter/pumpmeter calcultion is the method used,
Any one measurement (either miles or gallons alone) can only be as accurate and precise as the worst measurement, while the miles/gallons calculation compounds those inaccuracies and imprecisions (in loss of sig figs).
I think most of us would probably assume the pumpmeter is the most accurate and the most precise, but the other two measurements aren't even close to accurate or precise.
What matters is how accurate & precise is a 300 mile tripmeter reading? And how accurate and precise is the match to the previous fuel level?
I posit that the best you can do, overall, after running the calculation, is something like plus or minus about 1 mile per gallon such that 20 mpg is actually anywhere from 19 to 21 miles per gallon actual.
What I'm seeking is data that tells us the three main questions that must be answered for anyone to say that my hypothesis is even close to being right or wrong:
No calculation can do better than the worst measurement, and worse, errors compound when you multiply or divide.
But that's the kind of things we're looking for, which is why the minimum number of calculations possible is two, since you have to have a "before" situation and an "after" situation.
For example, if the change that you are testing causes about 1 mile per gallon decrease in fuel economy overall (but which isn't linear), but if your calculations are no better than plus or minus 1 mile per gallon in accuracy or precision, then you'll never even see the very real difference because it will be unmeasurable given the plus or minus 1 mile per gallon typical accuracy and precision that I posit the typical mom-and-pop tripmeter/pumpmeter calculation provides.
But there's no sense in talking about *any* of that, if we don't know the answer to these three questions.
Under just moderately controlled conditions, 1 MPG is actually a significant amount, and would be easily detectable using your mom and pop method, assuming the mom and pop competently applied the method.
I never used the tripmeter for MPG, because I never bothered testing them with mile markers. Matching gas level is trivial - and it only has to done at the beginning and end of the trip. Gas station pumps - I assume they are accurate, and can't control that anyway. I'm confident that my measurements are accurate to within .1 MPG. Because I don't care about .135867 on the total. I round it down to .1 That's pretty "exact." Repeatability is meaningless when measuring MPG, unless you're driving on a covered track, with a temperature controlled environment. On every trip the MPG can vary. BTW, I don't disagree that perfect measurement of MPG in unattainable. Perfection is impossible even under lab conditions. But you too easily discount "mom and pop" MPG calculations.
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:
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:
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).
Assuming one tank is about 300 miles and about 20.25 gallons read on any one pump, on a long trip of ten times that, you still can't be confident of that 1/10th of a mpg unless you know the answer to these questions.
Remember the exammple of the speedometer, where it's *always* going to be a few percent wrong, even if you drove a billion miles to try to "randomize" out the errors.
No, he's been saying the same thing for many posts now. If you fill up the tank 10 times, any inaccuracy from not exactly filling the tank to the same level at the first time and last time is reduced by an order of magnitude, because it only matters on the last fill. All the other 9 fills, you have the gas pump reading.
On 07/21/2017 6:13 PM, Mad Roger wrote: ...
For a specific vehicle, it really doesn't matter to determine _changes_ in mpg for a given test condition (unless, of course, you're futzing with the tire size in which case that would have to be compensated for but is doable to pretty precise number by knowing the tire profiles or simply doing the "measured mile" computation.
NIST tolerance is 6 in^3 in a 5 gal measure. AFAIK that's what all state W&M departments use for their tolerance. A NIST document of
20,000 tested meters showed 0-mean normally distributed discrepancies at about 90% bounds on the +/-6 number. The 6/5gal --> ~0.5%That's entirely dependent upon the tester -- in older vehicles without the emissions control folderol on the gas tank filler spout it was pretty easy to be quite precise if one were trying. Now it would take some doing, but I suspect if really cared, one could manage to get pretty close to the same height.
...
But properly designed 'spearmints can cause cancellation of many sources often and besides the simple "combination of error" the math of the numbers also enters into the relative magnitude of the error on the final result.
In this case, for example, the second can be effectively eliminated or reduced significantly by simply taking multiple runs...then the actual level on each intermediary measurement is immaterial because whether it was high or low on any given case, the total amount of fuel is the denominator and so the fractional error in it is much smaller owing to the same presumed error in the last measurement.
On 07/21/2017 7:02 PM, dpb wrote: ...
And remember that is the "shut 'er down" tolerance, not the average...as noted, the most probable based on the NIST sample was in the +/-0 bin (
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.
On 07/21/2017 6:48 PM, trader_4 wrote: ...
I'm glad I "only" had to explain reactor power trip setpoint uncertainty analysis/error propogation to the NRC staff statisticians and then sit through the ACRS (Advisory Committee on Reactor Safeguards) hearings, not usenet. :)
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"HomeOwnersHub website is not affiliated with any of the manufacturers or service providers discussed here. All logos and trade names are the property of their respective owners.