Miles per Gallon

http://www.solipsys.co.uk/new/MilesPerGallon.html?HN_20150507

by ColinWright • 11 years ago

87 94 11 years ago

solipsys.co.uk

markild2• 11 years ago

The illustration at the bottom of this[0] xkcd "what if?" illustrates this pretty well.

[0] http://what-if.xkcd.com/11/

ColinWright3• 11 years ago

Yes, I've been meaning to add that link at the bottom of the page with a short piece of text for context - I'll do that soon.

Thanks.

Edit: Done that now. Not sure why this comment got a downvote, though.

Extra Edit: Hmm, now been re-upvoted. Bizarre, but thanks for the votes! I know that they're not actually worth anything, but they do indicate that what I've done is appreciated, and considered to be of value.

markild2• 11 years ago

With or without illustration, really enjoyed the write up.

Also fun to think about what would happen if you plot the value that is represented by the "mm^2" over time, and do an integration of the plotted graph. You somehow end up with a volume, or total fuel consumption over the period you integrate over.

Unit cancellation is cool stuff.

ibmthrowaway2712• 11 years ago

Vote cancellation is weird.

I wonder if posts that have no genuine reason to be downvoted (like yours) get more votes if they add a comment to the effect "Not sure why this comment got a downvote" since multiple people will try and correct the erroneous downvote with no idea whether anyone else already has.

Edit: Ha! Thanks for the downvote.

ZeroGravitas• 11 years ago

It's very easy to downvote comments by mistake when trying to upvote them on mobile. Shortly after posting just one mistake can make people feel they've done something wrong but it usually sorts itself out over time.

Khao• 11 years ago

Thanks for that! Not being a native English speaker I couldn't really grasp what the author was trying to describe when he started talking about a "trough with a cross-sectional area of 0.1 mm2" and the following paragraph. This image made everything clear!

unwind• 11 years ago

This is probably the kind of trough that's meant: http://en.wikipedia.org/wiki/Watering_trough, detailed image: http://en.wikipedia.org/wiki/Watering_trough#/media/File:Cat....

If you "think away" the actual trough and keep only the liquid, you get the cuboid that the text is referring to.

mdellabitta• 11 years ago

Of course, you'd probably do a little better than that, because at no point would your car be carrying all of that gas. But the trough would have to get wider when you went uphill or had to get going at a light.

DougBTX• 11 years ago

Instead of scooping up the fuel, you could think of it as laying out the fuel in a line behind the car. All the fuel starts off in the fuel tank, and slowly drains out of the car. Fuel efficiency is how large the hole is that the fuel drains out of. In reality, it gets turned into a gas and blows away, but the effect is much the same.

maxerickson6• 11 years ago

The environmental concerns with having fuel evaporating everywhere would be the first practical problem you would want to solve.

(a small working reservoir handily solves the problem of needing more fuel at some moments.)

brudgers5• 11 years ago

Not really, fuel consumption as an input takes carrying or not carrying fuel into account...same as wind resistance of the pickup or the friction of it moving through a trough of liquid or the force of the liquid moving into the void behind the pickup, etc.

Serow225• 11 years ago

As a car nut, this actually seems pretty reasonable; if you take that diameter and divide it by (fuel injector duty cycle at cruise rpm, times number of injectors), the resulting diameter should be pretty close to the car's injector outlet effective diameter!

valarauca1• 11 years ago

Hi, I actually work in fuel system analysis.

The one issue with the blog post that nobody seems to realize or point out. Is that fuel consumption is measured, and calculated internally as kilograms per kilometer. The change to volumetric units is done for the benefit of the population.

This comes into play because namely, thermal expansion. Normally even in return less engines fuel is used to cool injector heads, as well as some body block parts (depending on engine design), as hotter fuel more readily reacts, and is already being routed to the warmed parts of the engine.

raldi• 11 years ago

That seems like a coincidence, that the relative velocity between the car and the fuel shooting through its injector should be approximately the same as the relative velocity between the car and the road.

One could conceivably build a car with half-size injector nozzles that squirt in the same volume of fuel per unit time.

mark-r• 11 years ago

You could do even better if the tube were carrying electricity instead of gas. Maybe it would have enough power to carry a whole bunch of people at once? Hey, I think I'm on to something!

pcarolan• 11 years ago

Agreed, the south shore chicago trains have feelers to harvest electricity as they go. Maybe a Tesla with a whisker on top could go indefinitely on long stretches of highway.

ableal3• 11 years ago

;-) http://commons.wikimedia.org/wiki/File:Wheeler_Dealer_Bumper...

ableal3• 11 years ago

(0.1 mm^2 is half the cross-section of AWG 24, getting close to hair thin.)

I don't think you're correct here. For round numbers, let's take a 100 kW engine (134 hp), and suppose we feed 100 V. At full power, we'd be running 1000 Amps down that wire. Even at 1 kV it would take 100 A.

Better get a superconductor. Or a much thicker power cable.

pdx• 11 years ago

He was using the wire AWG as a way to visualize the size for those of us that are familiar with human hair, but unfamiliar with visualizing things that are fractions of a mm thick.

He was not saying anything about replacing the amazing energy density of gasoline with electricity over a copper wire.

kitd• 11 years ago

How about a pressure differential?

https://en.wikipedia.org/wiki/Atmospheric_railway

Cross-section of pipe = available power

ableal3• 11 years ago

Using liters/100 km, it's a tad easier, we just have to get the orders of magnitude right

- liter = (100 mm)^3 = 1e6 mm^3

- 100 km = 1e8 mm

So, 10L/100 km is 0.1 mm^2.

(Note that we want low values, and this is on the high side for European cars - the usual advertised numbers for sedans are half of that, with reality somewhere in between.)

rm999• 11 years ago

For comparison, what would be the radius of a continuous cylindrical battery that powers the Tesla Model S? Assume, perhaps, that the battery has the same energy density as a typical AA battery.

TheLoneWolfling• 11 years ago

The Model S has an EPA rating of ~237.5 Wh/km. I also see that the Model S has a volumetric energy density of ~700Wh/l.

Cancelling, I get ~0.34 mm^2.

Another question would be the mass per unit length. At 250 Wh/kg, that works out to ~0.95g/m. For comparison, the 30mpg car works out to ~0.057g/m.

samolang2• 11 years ago

How big of a solar panel would you have to stick on top of an electric car to keep it going forever (ignoring the extra weight/wind resistance)?

QuercusMax2• 11 years ago

I suppose it depends on your definition of "car", but they've been doing this for many years in the World Solar Challenge. GM's Sunraycer drove across Australia in 1987 on solar power alone: http://en.wikipedia.org/wiki/Sunraycer.

samolang2• 11 years ago

Yeah, I meant more like a Tesla or Chevy Volt.

maxerickson6• 11 years ago

It becomes important to decide how much it weighs and how fast you want to go (and if it has to work at night in Alaska...).

Meredith023• 11 years ago

I think 2*4 will do the job just fine but you may want to check with the folks at http://www.onlysolars.com/ for this.

userbinator2• 11 years ago

Incidentally, the volume of air required to ideally burn a litre of gasoline is also quite large.

http://en.wikipedia.org/wiki/Gasoline#Energy_content

1 kg of fuel reacts with 3.51 kg of oxygen to produce 3.09 kg of carbon dioxide and 1.42 kg of water

Scaling that to the standard density of 0.755kg/L, that means 2.65kg of oxygen for 1L of gasoline. Assuming the typical 20% oxygen content of air at standard temperature and pressure, that is over 9000L of air.

So the air consumption of a car with fuel consumption of 0.1mm^2 is 0.0009m^2 or 900mm^2.

Edit: 900mm^2, not 900000.

lmilcin• 11 years ago

If one needs 9000L of air to burn 1L of fuel, that would be 9000(0.1mm^2) not (90000.1mm)^2. 900mm^2 is much saner don't you think. I doubt the car would be able to scoop 900000mm^2 as it is 0,9m2. Can you imagine that amount of air fed into engine? Me neither.

userbinator2• 11 years ago

Yes, you're right - I somehow thought 1L was 1m^3, when it should be 1L = 0.001m^3.

perakojotgenije3• 11 years ago

I will never understand why Americans keep using miles per gallon instead of liters per 100 km. Miles per gallon is only good if you want to advertise your car ("look, with this car you can travel 50 miles with one gallon whereas with that one you can only travel 40 miles").

But you never do that in real life, you never fill your car with say, two gallons and say "now I'll travel 80 miles".

Instead you always know the distance between two points and you want to know how much will that travel cost you. So you think like this: "distance from point A to point B is 250km, my car uses 6 liters per 100 km so I'll use 15 liters, 1 liter price is 2€ so it'll cost me 30€". Easy as pie and you can't do that with miles per gallon.

sdrothrock• 11 years ago

So you think like this: "distance from point A to point B is 250 miles, my car gets 25 miles to the gallon, so I'll use 10 gallons, 1 gallon price is $3.00 so it'll cost me $30.00". Easy as pie.

That's why. It's exactly the same thing you're talking about.

obsurveyor2• 11 years ago

Yeah, it's the same mental arithmetic. These arguments just don't make sense for making some kind of change.

sukilot3• 11 years ago

Nice cherrypick for that pie.

And if your car gets 18 or 27 mpg, on a 230 mile trip?

Multiplication is generally easier than division.

perakojotgenije3• 11 years ago

Because it's easier for an average person to multiply than to divide.

benihana• 11 years ago

I'll never understand why different [organizational unit] does things differently than me. My way is superior because I've formed a mental model of it.

sukilot3• 11 years ago

In actual real life human decision making, one of the models generates more accurate answer. Humans are estimators.

superuser2• 11 years ago

If people start thinking of individual car trips as spending money (rather than the generalized cost of having a car), I wouldn't be surprised if people drastically reduced their travel and, correspondingly, consumption (by not leaving their houses). People seem to highly resistant to impulse purchases for dollar amounts smaller than they are willing to spend on road travel without thinking. This would be a Very Bad Thing for the American economy, so I'm not surprised that we are encouraged to reason about gas milage in language that makes this more difficult.

ghaff• 11 years ago

Who is doing this encouraging "to reason about gas milage in language that makes this more difficult"? MPG as a fuel efficiency metric goes back many decades.

I don't actually disagree that that if there were a big ticking dollar gauge that tallied up the cost of each trip in a car, some people might drive less. But it's not the reason we use the MPG metric.

ugexe• 11 years ago

It's just as simple doing the same conversion for mpg. If I'm going 250 miles and get 25mph I instantly know that's 10 gallons multiplied by whatever the cost of fuel is

maxerickson6• 11 years ago

The thing about mpg that is problematic is that it obfuscates the savings in going from a 10-20 mpg vehicle to a 20-30 mpg vehicle (and exaggerates the benefits of a 50 mpg vehicle).

15 mpg -> 25 mpg is a much bigger step than 25 mpg -> 35 mpg (a savings of 2.6 gallons per 100 miles vs a savings of 1.15 gallons per 100 miles). The jump from 35 mpg to 50 mpg only saves 0.85 gallons per 100 miles.

For everything else it just introduces some trivial difference in the arithmetic.

mc32• 11 years ago

This is a great point, but except for policy makers, where this information matters, to say, incentivize mfgs, or consumers with rebates, this context is not practical in day to day dealings of most drivers.

Perhaps publish the information in both formats.

astolarz• 11 years ago

To me, this is the best argument for l/100km (or gal/100mi). I don't know of anyone who really thinks about how far they can go before they have to refuel. They just check the gas gauge and fill up when it's low. There's very few places, even in the US, without a nearby gas station so it's not really much of an issue. The arguments about multiplication vs. division also seem silly, especially since your math teacher lied about not always having a calculator.

That said, as an American I grew up with MPG so that's what's intuitive to me and I'm happy with it. Something like l/100km seems like it would be mostly useful when shopping for a car than actually getting around.

dragonwriter4• 11 years ago

The thing about mpg that is problematic is that it obfuscates the savings in going from a 10-20 mpg vehicle to a 20-30 mpg vehicle (and exaggerates the benefits of a 50 mpg vehicle).

I think the EPA's estimated-fuel-cost-per-year (based on standardized assumption), which I believe is part of the standard rating disclosure for new vehicles just like MPG is, addresses for most consumers that better than MPG or gal/100mi, and for the subset of consumers for whom it isn't better -- i.e., the ones that have good numbers on their own usage patterns that they are going to calculate out from to get a personalized estimate -- MPG and gal/100mi are exactly equal in utility.

abruzzi• 11 years ago

MPG is useful when you are thinking in terms of vehicle range. This isn't most people's default, but it does have its usefulness.

As for why US doesn't use l/100km. the simplest answer is all our vehicle odometers are calibrated in miles, and we buy gasoline in gallons, so l/100km is a number with no grounding. To get most people in the US looking at it it would have to be gal/100miles or similar.

ascorbic• 11 years ago

Confusingly, the UK also uses mpg despite the fact we buy fuel in litres.

alwaysdoit• 11 years ago

I mean, if your question is Can I go 300 miles?

1/25 GPM * 300 Miles = 12 gallons

Which is either larger or smaller than your gas tank, so I think fuel volume over distance traveled is still easy enough to use for the range calculation, and better for almost everything else.

bitwize• 11 years ago

The USA is BIG. Foreigners who come here often have little idea what an unfathomably huge place the USA is. And unlike say, Russia or Canada which are even bigger geographically, virtually all of that territory is navigable by car throughout much of the year.

In the USA, therefore, it was historically pretty likely that grandma and grandpa lived far away, say, back at the farm while mom and dad moved into the big city or the suburbs to get jobs and raise a family. So in America there was a much bigger market for grand tourers -- cars designed to go long distances and be fun to drive. Early consumer automobiles were promoted as such -- "See the USA in your Chevrolet" and the like. Now you know why American cars are reputedly so big and ugly: in Europe GTs are rich boy toys whereas in America they had to appeal to middle-class sensibilities which meant things like big engines and rocket fins on the rear and such.

So in this environment, it made much more sense to market a fuel-economical car not with statements like "you can use less fuel and save money over your trips to the market and to work" -- oil was cheap at least until the 1970s -- but with statements like "you can go this much further on a single tank of gas". Hence the metric of miles per gallon, rather than litres per 100km or gallons per 100 miles -- which is still in use today.

maxerickson6• 11 years ago

Gas is still cheap:

http://inflationdata.com/inflation/images/charts/oil/gasolin...

(Inflation happens to be a well used purchasing power adjustment, I think comparisons of the cost of gasoline will survive others.)

galago• 11 years ago

I've never been to Europe, and I'm actually curious if the Eurozone has changed driving behavior much. Would it be unusual for someone in Berlin to drive to Rome or Athens on vacation? For similar distances in the USA my experience is that it would be common, partly because Americans like to have their car when they arrive. Even when gas prices were quite a bit higher Americans still drove. Who gets in a car and only burns one gallon of gas? An F150 only gets about 20mpg, and I know people who go farther than that for groceries.

Kluny• 11 years ago

I'm Canadian and buy litres of gas, but I still check the mileage in mpg. It's just because I have an instinctive idea of how many mpg I should get, whereas I have no instinct for l/100km. I know 35mpg is decent and 50mpg is exceptional, and 10mpg is unacceptable. What does 10L per 100km mean? I have no idea.

_lce0• 11 years ago

I can understand that it's not intuitive for you, but for me it's all the way round, so it's just everybody's bias according to different cultures

btw, moving between unit is simple math:

    35 MPG:
    -------
      35 miles ... 1 gallon
     100 miles ... x gallon = 100 * 1 / 35 [gallon]
                           -> ~2.86 gallons/100 miles

.. and, look mom, no math!

   10 L per 100 KM: 
   ----------------
      10 l ... 100 Km
       1 l ...   x Km -> 10 Kms per liter

.. which now that you think.. made sense for "10L per 100Km", isn't? that's the power of MKS

petercooper• 11 years ago

I'm British and prefer mpg. Why? Because for starters kilometres are alien to me, but also because it's just familiar and relatable. But with that said, the numbers manufacturers give are never even vaguely useful IMHO (my car is technically 40mpg but I get low 20s) so it's more for comparison of efficiency between journeys than anything else.

dragonwriter4• 11 years ago

I will never understand why Americans keep using miles per gallon instead of liters per 100 km.

Because:

(1) neither liters nor km or meaningful measures to Americans in general; were Americans going to use a measure of fuel:distance, it might be gallons per 100 miles, but not liters per 100 km, and

(2) Even then, I think there's a pretty strong preference for more-is-better measures rather than less-is-better.

Miles per gallon is only good if you want to advertise your car

That's pretty much the only thing MPG ratings are used for, manufacturers selling cars. So, its not really surprising that that is what is used.

But you never do that in real life, you never fill your car with say, two gallons and say "now I'll travel 80 miles".

No one I know ever do the reverse, either; you don't decide "I'm going to go eighty miles, and this car consumes 2 gallons per 100 miles, so I need to make sure the taken has at least 2×80/100 = 1.6 gallons".

Instead you always know the distance between two points and you want to know how much will that travel cost you.

For people who care about that, there is a reason that auto magazines doing reviews often publish things like total per-mile fuel + maintenance costs for reviewed vehicles. If you just care about fuel costs, it takes about as much work (same number of multiplications and divisions, just changes which figures are being multiplied and which divided) to calculate that from MPG and gas price as it does from gal/mi (or gal/100mi) and gas price, so there's no real advantage to using one over the other for that purpose.

(And, IME in practice, fuel costs are usually a concern with trips where the consumption consideration isn't "how many gallons will I get based on the cars stated ratings" but "how many tanks will it take based on my driving experience", in which case the people using it often are using something like the miles per unit of fuel ratings, but the rating is determined by experience with the vehicle, and the unit is whole fuel tanks.)

rebootthesystem2• 11 years ago

Sorry, this is a non-argument because you are trying to solve a non-existing problem.

The calculation used to determine range or cost when you have miles-per-gallon or km-per-liter is trivial and just as familiar as the liters-per-distance calculation when viewed in context.

My point is that if you actually LIVE in an environment where miles-per-gallon is the norm you develop familiarity with the numbers. You develop a sense of proportion. The calculations are not difficult because they are normal to you. To anyone transitioning back and forth between the two systems, well, there will have to be an adaptation period during which things will be uncomfortable until they are not.

Besides, people very rarely have to make these calculations today. My car tells me how many miles I have left in the tank based on the average historical fuel consumption since I've owned it. No math required. When I fill up, it updates that number.

Still, you very quickly learn that you get X number of miles with a full tank of gas. You just know that. You also learn you need to refill your tank N number of times in the course of a month on average due to your normal driving patterns. None of this requires much thought. And, if you are going on a long trip you generally know how far you can go on a single tank of gas and hopefully you've verified that there are gas stations along the route to top-off as you go (which in the US is generally the case).

As far as calculating the cost of a trip, again, if you live in miles-per-gallon land it is easy. Nobody goes into a crying frenzy screaming "Why, oh why don't we use liters per 100 km. This is so hard!". No, instead people have an estimate of their average miles-per-gallon or an accurate historical average from their car's information display system. They get the distance to their destination and divide. And, no, there's no need to divide 483.5 miles by 21.3 miles-per-gallon. That's insane. Nobody does that. Your goal is to get a sense of proportion of how much fuel you'll need. So, you divide 500 by 20 and you'll get a decent number. It won't be twice that many gallons nor half. There are plenty of gas stations along the route. No worries. And, if you need an accurate number for reimbursement purposes, well, keep the receipts.

So, again, I think you are trying to solve a non-existing problem.

Now, on the question of metric vs. imperial. Well, I detest the imperial system of units. I hate it. I use metric for engineering purposes. The world is metric. It is ridiculous that we haven't made the switch.

That said, I fully understand why. Unless you've traveled through the US it is hard to get a sense of proportion. This place is huge. The infrastructure is of unimaginable proportions. Going metric could very well take 100 years due to the sheer amount of work and cost involved. So, yeah, I get it.

There are other seemingly minor examples of this. We sell internationally so I am very aware of cultural and systemic differences. For example, most of the world would write one thousand dollars like this: $1.000,00. In the US it is written like this: $1,000.00. In the US 1/2/2015 means January 2nd, 2015. In the rest of the world it means February 1st, 2015. In the US we use AM and PM. In a good deal of the world it is a 24 hour clock (which makes far more sense).

There are a lot more examples of this. If we can't fix something as simple as what the comma and period mean when speaking about money or the order of the day and month on a date we are doomed to fail in shifting the US to the metric system.

perakojotgenije3• 11 years ago

Sorry, but I never never said it was metric vs imperial. The emphasis was on mpg vs gallons per 100miles if you prefer it this way. The first one is good for advertisers the other one for truly understanding how much your travel costs you. (Yes, you can do a division instead of multiplication as pointed out but ask an average Joe how much a trip costs him)

drzaiusapelord2• 11 years ago

Only on HN would a stupid "herp derp you guys are using the wrong metrics" post be voted this highly. I get it, snotty Eurpeans get snotty upvotes from each other with their snotty, "We dont like your imperial units" whining on the internet. Umm, congrats? The rest of your argument is bunk as its trivial to find out what your gas capacity is and know your max range is. Most people don't worry about how much it will cost to drive to grandma's cost.

Also, gas is cheap and Americans are wealthy. We don't buy one or two gallons and walk away hoping to get through the weekend. We typically fill our tanks and off we go. Long drives are the norm here as you may have friends/relatives in the suburbs or out of state.

On top of it, our geography is HUGE and unlike "big" countries like Russia or China or Canada its almost all drivable/livable/usable. Knowing your range is more important to most people than knowing how much it costs to get to grandma's house. Its in your countries where gas is super-expensive that you have to worry about those things. Not here, at least for most people.

MPG is a perfectly rational way to talk about car efficiency, even in everyday use. Considering the typical IT automation in cars nowadays, this argument is academic as you can trivially bring up up all sorts of info on the console.

Sorry, but the usual "the Euro way is the only and the best way" whining is wrong again. Turns out there are lots of good ways to do things and "good" is relative to the needs and expectations of the user.

lkbm• 11 years ago

When buying a car, the difference between 10mpg and 20mpg looks the same as the difference between 20mpg and 30mpg. This is the usual complaint.

pontifier• 11 years ago

For a while, I avoided using gallons at all. I'd drive a hundred miles, then fill up. Then dollars to fill up = cents per mile.

Now I just put 5 bucks in when I can afford it.

logfromblammo• 11 years ago

If you start with mass per distance (kg/km), and you divide by fuel density (mass per volume, kg/L or g/mL), you get area (ca or m^2).

If you start with distance per volume (km/L) and cancel the matching units, you get inverse area (ca^-1 or m^-2).

This doesn't make sense until you realize it is the conversion factor between volumetric flow rate and volumetric flux, and is the number you need to associate volumetric fuel consumption rate (volume per time) with speed (distance per time), which is exactly what you're doing when you think of the fuel supply as a continuous trough.

This is a simplification. Different vehicle speeds will be more or less efficient. Volumetric flow rate is an integral of the volumetric flux over an area. So the area is the average aperture size. If your vehicle had a mass-ignoring, initially-empty reserve tank of infinite size, scooping up fuel from an infinitely long trough with the specified cross sectional area, it could go an infinite distance. You need the tank because different speeds may require more or less fuel flux. You need to travel at a more efficient speed before you can go to a less efficient speed.

bariumbitmap3• 11 years ago

This kind of calculation is trivial with GNU units:

    You have: 30 mpg
    You want: 1/(mm^2)
            * 12.754311
            / 0.078404861

It does reciprocal conversion automatically (12.75 mm^-2 corresponds to 0.0784 mm^2).

Note also that there are approximately 3.785 liters in a gallon, not 4.5461 as stated in the original article.

ColinWright3• 11 years ago

    ... there are approximately 3.785 liters
    in a gallon, not 4.5461 as stated in the
    original article.

Not if you're in Europe. Which I am.

bariumbitmap3• 11 years ago

Apologies for my US-centric calculations!

dragonwriter4• 11 years ago

Note also that there are approximately 3.785 liters in a gallon, not 4.5461 as stated in the original article.

"gallon" is a unit of volume in several systems of measures, most notably the US Customary system and the Imperial system (these systems are often incorrectly conflated because many of the units are the same, and where the units are different many of the names are still the same.) The size of the gallon is not the same in those systems:

  3.785 l/gal(US)
  4.5461 l/gal(Imperial)

bariumbitmap3• 11 years ago

Thanks, that makes a lot more sense.

  You have: 30 miles/imperialgallon
  You want: 1/(mm^2)
  	* 10.620186
  	/ 0.094160312

Miles per Gallon

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