There's something strange going on here...
Discussion
Miles per gallon.
We measure fuel economy in miles/gallon — which could just as easily be written as gallons/mile.
But regardless of which units you use, there’s something strange going on here. Miles are units of length, and gallons are volume — which is length^3. So gallons/mile is length^3/length. That’s just length^2.
Mileage is measured in square meters.
If you took all the fuel you burned on a trip and stretched it out into a thin tube along your route, 0.1 square millimeters would be the cross-sectional area of that tube.
Shamelessly stolen from xkcd; I thought it was very interesting - never really considered it before. 'Gassing' seemed an appropriate place, apologies if it's wrong.
We measure fuel economy in miles/gallon — which could just as easily be written as gallons/mile.
But regardless of which units you use, there’s something strange going on here. Miles are units of length, and gallons are volume — which is length^3. So gallons/mile is length^3/length. That’s just length^2.
Mileage is measured in square meters.
If you took all the fuel you burned on a trip and stretched it out into a thin tube along your route, 0.1 square millimeters would be the cross-sectional area of that tube.
Shamelessly stolen from xkcd; I thought it was very interesting - never really considered it before. 'Gassing' seemed an appropriate place, apologies if it's wrong.
jkb89 said:
If you took all the fuel you burned on a trip and stretched it out into a thin tube along your route, 0.1 square millimeters would be the cross-sectional area of that tube.
Is that 0.1 mm^2 figure not just for one particular fuel economy though... I don't have time to work out what fuel economy!A car that did half as many miles per gallon would use twice as much fuel, and so have double the area of tube.
AJB said:
Is that 0.1 mm^2 figure not just for one particular fuel economy though... I don't have time to work out what fuel economy!
A car that did half as many miles per gallon would use twice as much fuel, and so have double the area of tube.
I'm not very good at maths, but wouldnt the distance you covered just be shorter for the same amount of fuel?A car that did half as many miles per gallon would use twice as much fuel, and so have double the area of tube.
ETA: The 1mm^2 would be same, but you'd have a relatively shorter "fuel line" for the same number of gallons of fuel.
The "weirdness" is because we use the volume of the fuel as a convenient substitute for the energy contained in it. We could measure fuel efficiency in miles per joule, but as we know that petrol/diesel has fairly uniform energy density (i.e. joules per gallon) we can substitute in the volume of fuel.
The fact the units end up as m^2 (or the reciprocal) doesn't really matter.
The fact the units end up as m^2 (or the reciprocal) doesn't really matter.
jkb89 said:
Miles per gallon.
We measure fuel economy in miles/gallon — which could just as easily be written as gallons/mile.
But regardless of which units you use, there’s something strange going on here. Miles are units of length, and gallons are volume — which is length^3. So gallons/mile is length^3/length. That’s just length^2.
Mileage is measured in square meters.
If you took all the fuel you burned on a trip and stretched it out into a thin tube along your route, 0.1 square millimeters would be the cross-sectional area of that tube.
Shamelessly stolen from xkcd; I thought it was very interesting - never really considered it before. 'Gassing' seemed an appropriate place, apologies if it's wrong.
Friday afternoon, I'm bored.We measure fuel economy in miles/gallon — which could just as easily be written as gallons/mile.
But regardless of which units you use, there’s something strange going on here. Miles are units of length, and gallons are volume — which is length^3. So gallons/mile is length^3/length. That’s just length^2.
Mileage is measured in square meters.
If you took all the fuel you burned on a trip and stretched it out into a thin tube along your route, 0.1 square millimeters would be the cross-sectional area of that tube.
Shamelessly stolen from xkcd; I thought it was very interesting - never really considered it before. 'Gassing' seemed an appropriate place, apologies if it's wrong.
Sorry, but the above explanation is really unclear and misleading.
"Mileage is measured in square meters.
If you took all the fuel you burned on a trip and stretched it out into a thin tube along your route, 0.1 square millimeters would be the cross-sectional area of that tube."
I don't see how the 2nd statement is a consequence of the previous statement. Why 0.1 square mm ? Surely, this would depend on the actual MPG of the vehicle considered.
Let's do some maths: let's say a car does 40MPG. The volume of the fuel contained within the tube over a lenght of 40 miles would be: V=L*S=L*0.1mm^2=40*1609 (meters in a mile)*0.1/1000^2 (to convert from mm^2 to m^2)=0.006436m^3, which is 6.436dm^3 or liters. In gallons that is 1.42 gallons. So your 40MPG car should really have used 1 gallon. Hence the 0,1mm cross section is wrong.
HTH
david
I'll just leave this here. It's on topic, I promise. http://what-if.xkcd.com/11/
CraigyMc said:
I'll just leave this here. It's on topic, I promise. http://what-if.xkcd.com/11/
First post: "Shamelessly stolen from xkcd; I thought it was very interesting - never really considered it before"jkb89 said:
CraigyMc said:
I'll just leave this here. It's on topic, I promise. http://what-if.xkcd.com/11/
First post: "Shamelessly stolen from xkcd; I thought it was very interesting - never really considered it before"
jkb89 said:
Just checked the source, the 0.1mm^2 figure is from Wolfram|Alpha for a car doing 20mpg, apologies.
Indeed, it should be clear that the x-section has to change by MPG of the car.In the EU a lot of places measure fuel economy using liters per kilometer. If your car used 1 liter per kilometer, imagine a tube a kilometer long, what x-section does it need to fit 1 liter of fuel in it? What if your car uses 2 liters per kilomter? It's half as efficient as the first car, so the xsection will be twice the size so that the 1km tube can fit 2 liters in it.
All of this should be intuitive. All you need to do is think about a tube the lenght of your journey, which is the correct width to hold the fuel you used on that journey. The xsection is a measure of fuel efficiency.
(Also, if your fuel pipe from your tank to engine is that same diameter, then I think the average rate of fuel flow will be equal to your average speed.)
mrmr96 said:
Indeed, it should be clear that the x-section has to change by MPG of the car.
In the EU a lot of places measure fuel economy using liters per kilometer. If your car used 1 liter per kilometer, imagine a tube a kilometer long, what x-section does it need to fit 1 liter of fuel in it? What if your car uses 2 liters per kilomter? It's half as efficient as the first car, so the xsection will be twice the size so that the 1km tube can fit 2 liters in it.
All of this should be intuitive. All you need to do is think about a tube the lenght of your journey, which is the correct width to hold the fuel you used on that journey. The xsection is a measure of fuel efficiency.
(Also, if your fuel pipe from your tank to engine is that same diameter, then I think the average rate of fuel flow will be equal to your average speed.)
This makes perfect sense now, I'd just never thought about rearranging the units like this before - intrigued me a little. In the EU a lot of places measure fuel economy using liters per kilometer. If your car used 1 liter per kilometer, imagine a tube a kilometer long, what x-section does it need to fit 1 liter of fuel in it? What if your car uses 2 liters per kilomter? It's half as efficient as the first car, so the xsection will be twice the size so that the 1km tube can fit 2 liters in it.
All of this should be intuitive. All you need to do is think about a tube the lenght of your journey, which is the correct width to hold the fuel you used on that journey. The xsection is a measure of fuel efficiency.
(Also, if your fuel pipe from your tank to engine is that same diameter, then I think the average rate of fuel flow will be equal to your average speed.)
Also, assuming those conditions would fuel flow/s be equal to average speed? Wouldn't it relate more to average acceleration? (taking drag and fuel flow at rest (idle) in to account?)
This is getting over my head now!
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