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:
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?
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.
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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.
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.
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,
A tripmeter of 300 miles is neither accurate nor precise
A pumpmeter of 20.25 gallons is likely relatively accurate & precise
Matching fuel level in the tank isn't even close to accurate nor precise
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:
How accurate & precise is a reading of 300 miles on a typical tripmeter?
How accurate & precise is a reading of 20.25 gallons on a gas pump?
How accurate & precise is the matching of the prior fuel level done?
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.
How accurate & precise is a reading of 300 miles on a typical tripmeter?
How accurate & precise is a reading of 20.25 gallons on a gas pump?
How accurate & precise is the matching of the prior fuel level?
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,
A tripmeter of 300 miles is neither accurate nor precise
A pumpmeter of 20.25 gallons is likely relatively accurate & precise
Matching fuel level in the tank isn't even close to accurate nor precise
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:
How accurate & precise is a reading of 300 miles on a typical tripmeter?
How accurate & precise is a reading of 20.25 gallons on a gas pump?
How accurate & precise is the matching of the prior fuel level done?
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.
How accurate & precise is a reading of 300 miles on a typical tripmeter?
How accurate & precise is a reading of 20.25 gallons on a gas pump?
How accurate & precise is the matching of the prior fuel level?
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:
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).
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.
How accurate & precise is the combined reading of 3000 miles on your tripmeter?
How accurate & precise is the combined reading of 202.50 gallons on the 10 gas pumps?
How accurate & precise is the matching of the 1st & last fuel levels?
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.
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.
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"
Occaisionally on a longish trip I'll see how well I can drive for economy - to see if I can better the last time I did that trip. This is generally over pretty close to a full tank - and small differences in driving technique can make a HUGE difference. So can a small change in route.Or a difference in the wind. I've registered a good 25% difference in mileage between 2 trips, both trying to squeeze the last foot out of a liter of fuel. Round trip averages out the difference in altitude.
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.
We'll never get that - he admits he's an "engineer"
1) Someone who gets excited obout things most other people don't care about
2) Someone who solves a problem you didn't know you had, in a way you don't understand.
3) The optimist sees the glass as half full. The pessimist sees the glass as half empty. The engineer sees the glass as twice as big as it needs to be
Q: What is the definition of an engineer? A: Someone who solves a problem you didn't know you had in a way you don't understand.
Q: When does a person decide to become an engineer? A: When he realizes he doesn't have the charisma to be an undertaker.
Q: How can you tell an extroverted engineer? A: When he talks to you, he looks at your shoes instead of his own.
Q: Why did the engineers cross the road? A: Because they looked in the file and that's what they did last year.
Q: How do you drive an engineer completely insane? A: Tie him to a chair, stand in front of him, and fold up a road map the wrong way.
Real Engineers consider themselves well dressed if their socks match Real Engineers buy their spouses a set of matched screw- drivers for their birthday. Real Engineers wear moustaches or beards for "efficiency". Not because they're lazy. Real engineers have a non-technical vocabulary of 800 words. Real Engineers think a "biting wit" is their fox terrier. Real Engineers know the second law of thermodynamics - but not their own shirt size. Real Engineers say "It's 70 degrees Fahrenheit, 25 degrees Celcius, and 298 degrees Kelvin" and all you say is "Isn't it a nice day" Real Engineers don't find the above at all funny.
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.
Whatever it is off, repeatability will be very close to 100%.
300 miles, repeatabilty to within less than 1/10 mile, or .2%
If he's as smart as the average fifth grader, within less than a cup at the same station, in the same spot, Lets nake it within a pint - that is 1/8 gallon in 15 - call it .8% on 15 gallons - - - so at LEAST within 1%
Again, repeatability within well under 1/10 gallon per fill (15 gallons) - about .6%?? Accuracy doesn't mean anything if the refill is at the same pump as the initial fill. Again, if you are in the "metric world" instead of the USA, accuracy improves by a factor of almost 4 on the fuel measurements, and 1.6 on the distance.
All of this accuracy can be accomplishes with NO special equipment.
Where the REAL fun comes in is duplicating the "drive cycle" - for the average driver, on the average road, "virtually impossible". If you have a closed course, and you are a VERY good and consistent driver, - perhaps you can get within a REASONABLE approxemation (repeatability over 5 runs, perhaps within less than 5%) - in open traffic, you'l be doing VERY good to get repeatability better than within 10% on a short run - over 300 miles, averaged over 5 runs (total 1500 miles) mabee within 1% on open road, or 5% running with traffic. Repeatability gets a LOT better over a short distance where fewer variables are involved. (Start from the gas station, accellerate to
30MPH in 2 blocks, enter the "expressway" and accellerate to 60mph by the first exit, maintain 60MPH to the 5th exit, slow down and exit the highway, stop. pull away from stop and re-enter the highway going the opposite direction, accellerate to 60 mph as you merge with traffic, decellerate from the 4th exit to the third exit, return to the gas station Repeat. Repeat Repeat.
That kind of driving can be very repeatable.
Fill with gas, Drive 3 blocks to the highway, drive 100 miles to "the city" Drive 5 miles across the city to restaurant, sports arena, or place of work, then return
Repeat Not much chance the 2 trips will be anywhere close. (I have had variances of more than 25% between 2 trips between Waterloo and Barrie Ontario over the same route, at the same time of day, and day of the week (and even the same month) - (even when the overall travel time was very close to the same for the round trip). generally WITHIN 10% IS PRETTY DOABLE - AND AT 20mpg THAT'S +/- 1 mpg at best
If you are in open country with very little traffic, repeatability gets MUCH better. Driving back and forth from Flagstaff to Jeddito Arizona you could likely repeat within well less than 1/4 MPG in the middle of the week
- or from Enid to Chickasha Oklahoma - or from Saskatoon to Regina.(very little traffic variability)
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