- --- In toyota-prius@yahoogroups.com, shrubnews@... wrote:
>

consumed.

> In a message dated 2/1/2006 9:01:27 PM Eastern Standard Time,

> dldorrance@... writes:

> This sort of observation makes me a bit leary about calculating mpg by

> assuming tank replacement volume reliably equals amount of fuel

> ======================

fillups and

>

> You can't do it on a tank by tank basis, but if you sum several

> divide into the total mileage you will get a more accurate measurement,

For example, if

> because the difference will only be the error in the last fillup.

> there is a +- 0.5 gallon error per tankful this can be an error of

up to 10%

> (assuming a 10 gallon fill) on one tank, but is only 2.5% on 4

tanks or 1% on

> 10 tanks.

I believe the calculation of measurement error is not quite so simple.

>

The way to evaluate measurement error is a subject of some length

in Statistics 101. While admittedly I took the course some 40 years

ago, my son took it last semester, so I received a refresher of sorts.

Measurement errors are evaluated by Standard Deviation, which is the

sum of all the errors divided by the number of measurements. It's an

average, but there is a catch. Errors never cancel out, they simply

accumulate. So that, for example, a 2% overestimation on one

measurement does not cancel out a 2% undermeasurement in another

measurement as has been asserted in previous posts on this subject.

*All errors are additive*. While this might not seem reasonable, I

suspect it is based upon probability theory. Perhaps someone here

might elaborate on this?

Now I do not know what all the potential measurement errors are in the

way many people calculate mileage, by assuming that the amount of gas

added is equal to the amount previously consumed. Here is my list:

First there is the error of differential pump shutoff. Then in the

Prius there is the error of the volume of the tank, which is a moving

target, as it is not a tank with a known volume but a

bladder which distends and contracts with its temperature. A

corollary to the bladder issue, I suspect, is the observation

recently discussed on another Prius reflector of how many miles it

takes the first bar's worth of gasoline to be consumed. This varies

from about 50 to about 200 miles as I recall.

I suspect that relying on the Prius MFD calculation probably gives a

more consistent number when comparing one Prius against another, given

some of the aggregious replacement measurement anomolies reported on

this and other Prius reflectors.

Dave '01 Prius - Pot. Kettle. Black.

Actually, you guys are talking apples and oranges. You are tlling him

that the errors don't average out, which they don't if you do it the way

you are talking about, but that isn't the way he's doing it. He's not

taking each individual tank and mpg average and running standard

deviation etc against it. He's taken total driven and total gas in.

The errors cancel out, at least the error of is it really full or not.

There is no error in the total amount of gas that has entered the tank,

or any error in the amount of miles driven.

> -----Original Message-----

> From: toyota-prius@yahoogroups.com

> [mailto:toyota-prius@yahoogroups.com] On Behalf Of JerryW

> Sent: Friday, February 03, 2006 4:42 PM

> To: dldorrance

> Cc: toyota-prius@yahoogroups.com

> Subject: Re: [toyota-prius] Re: gas gauge and mileage

>

>

> On 03/02/06, dldorrance <dldorrance@...> wrote:

> >

> > The error occurs with every fillup and those errors do not

> average out

> > as you are assuming. The net result is that your final

> answer is some

> > figure plus or minus some amount due to accumulated errors involved

> > with each fillup. The plus or minus part is the "slop" I was

> > referring to in the post above.

>

>

> No, that is just wrong...if I made a separate calculation

> every time I filled up you might have a point, but the

> calculation in my post, total miles/total galllons, is exact

> because errors in filling any one tank (except the first and

> the last) are simply not included in the calculation and

> cannot impinge on its accuracy...if one tank was only half

> filled, it would make no difference... I'm impressed you

> can't see this.

>

> Regards

>

> Jerry

>

>

> Are you a Prius owner?

> Put yourself on the MAP!

> http://www.frappr.com/priusowners

>

>

> [Non-text portions of this message have been removed]

>

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