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   Paul Cantrell (inthehands@hachyderm.io)'s status on Tuesday, 01-Oct-2024 09:59:23 JST Paul Cantrell

   Distance per volume (mpg or km/L) is kind of a lousy way to reason about fuel economy; a better system is to take the reciprocal: gallons per mile, or liters per km.

   (Here's an accessible argument for why: https://www.popsci.com/technology/gallons-per-100-miles-best-fuel-economy-metric/)

   But volume / distance = length³ / length = length² = area. That means we can measure fuel economy using area.

   For example, my car gets about 0.08mm². That’s not a rate. It’s just an area (in the rough vicinity of the period at the end of this sentence).

   Huh?

   1/2

   • Embed this notice
     Paul Cantrell (inthehands@hachyderm.io)'s status on Tuesday, 01-Oct-2024 10:04:07 JST Paul Cantrell

     in reply to

     Is this just one of their Weird Unit Things where you can’t really picture it? Or is there actually some reasonable physical interpretation?

     Turns out: yes, the latter! Imagine that area mounted to the front of the vehicle. The volume it sweeps out as the vehicle moves is on average the volume of fuel it uses.

     Is this an even more useful way of thinking about fuel economy? No!

     But it’s fun.

     2/2

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     Paul Cantrell (inthehands@hachyderm.io)'s status on Tuesday, 01-Oct-2024 10:08:06 JST Paul Cantrell

     in reply to

     • Kevin McCoy

     @kmccoy
     I have not, but I hope I am about to!

   • Embed this notice
     Kevin McCoy (kmccoy@spacey.space)'s status on Tuesday, 01-Oct-2024 10:08:08 JST Kevin McCoy

     in reply to

     @inthehands have you seen the cursed units videos?

   • Embed this notice
     Oliver Jensen (ojensen@hachyderm.io)'s status on Tuesday, 01-Oct-2024 10:09:08 JST Oliver Jensen

     in reply to

     @inthehands this was the subject of one of the earliest XKCD what-ifs!
     https://what-if.xkcd.com/11/

   • Embed this notice
     Paul Cantrell (inthehands@hachyderm.io)'s status on Tuesday, 01-Oct-2024 10:16:23 JST Paul Cantrell

     in reply to

     • reviewer 2 :Schwerified:

     @thedansimonson
     You’re the second reply to mention that video!

     I hear your argument about lengths coming from different places, but…dimensional analysis doesn’t care. And per my 2nd post (and the video), there is in fact a perfectly reasonable physical interpretation that units the lengths.

   • Embed this notice
     reviewer 2 :Schwerified: (thedansimonson@lingo.lol)'s status on Tuesday, 01-Oct-2024 10:16:25 JST reviewer 2 :Schwerified:

     in reply to

     @inthehands

     I'd make the case that it's not really the same "distance" being cancelled out. even though they're both the same kind of unit, one is a distance related to the galaxy's motion and the other is a distance *to* the galaxy.

     I think the same reasoning would apply for the lengths composing fuel volume and the distance of a car traveled.

   • Embed this notice
     reviewer 2 :Schwerified: (thedansimonson@lingo.lol)'s status on Tuesday, 01-Oct-2024 10:16:27 JST reviewer 2 :Schwerified:

     in reply to

     @inthehands

     There are a lot of very weird units, when you stare to hard at them. For example, the Hubble Constant is (70 km/s)/Mpc -- that is, a speed per Megaparsec, which checks out. but the distances technically cancel out, so the result is a *frequency.*

     https://www.youtube.com/watch?v=kkfIXUjkYqE

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     Paul Cantrell (inthehands@hachyderm.io)'s status on Tuesday, 01-Oct-2024 10:25:37 JST Paul Cantrell

     in reply to

     • Kevin McCoy

     @kmccoy
     Good stuff!

   • Embed this notice
     Kevin McCoy (kmccoy@spacey.space)'s status on Tuesday, 01-Oct-2024 10:25:38 JST Kevin McCoy

     in reply to

     @inthehands yes! https://youtu.be/kkfIXUjkYqE?si=i8fTHL5JVUJOnKl0

   • Embed this notice
     Sean Murthy (smurthys@hachyderm.io)'s status on Tuesday, 01-Oct-2024 17:18:38 JST Sean Murthy

     in reply to

     @inthehands You probably already know that in Germany and neighbouring countries (perhaps elsewhere in Europe too), it is common to measure "liters per 100 kms".