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Question #91725 posted on 10/24/2018 11:46 p.m.
Q:

Dear 100 Hour Board,

Runners always move to the inside when going around a curve because it's shorter.

How many miles would you save on a trip across the US (say on I-80 from SF to NYC but if you'd rather take I-10 from LA to Jacksonville, that's fine too) if you always moved to the inside of the curve of the road?

Related to that, how much gas would you save if you always drove the inside of the curve of the road?

-Yuki Kawauchi in a panda suit

A:

Dear Yukikawhat?

What a great question. Fun fact: the outside lane of a standard track is 453 meters, which is 53 meters longer than the inside lane. Calculating that distance is relatively simple, because you just measure the straightaways, and then use the formula arc length=radius*angle. You add those up and you end up with the difference if you're good at math and putting things into calculators. Figuring out how much of a difference it would make driving on the inside is trickier though because we don't know how many curves there are, and how much we save on each curve. How will we find out? We shall guesstimate!

Guesstimate 1: How many curves are there?

So, to estimate how many curves there are, I will count the number of curves on a 10 mile stretch of 1-10 (Jacksonville baby!) and then use that number to estimate the total number of curves. So, this is the stretch of road I chose:

Between Los Angeles and Ontario there were 26 turns over the 39.4 miles. The trip from Los Angeles to Jacksonville is 2,416 miles. So if we take 2,416 miles/ 39.4 miles * 26 turns we end up with an estimated 1594 turns on our trip.

Guesstimate 2: How much do we save on each curve?

How much are we saving on each turn. Well, the majority of the spots on 1-10 I looked were 2 lanes and looked like this:

The average two lane road is 24 feet wide, but the cars will drive in the middle so the the distance between the center of both cars is more like 12 feet. The majority of turns, as you can see actually aren't very big turns. I would say that the majority of the curves you will find are only about 45 degrees, and most of them won't be more than 90 degrees. We'll guess that each curve is somewhere in the middle. We'll go with a generous 57.29 degrees because that gives us a 1 radian per curve and makes our math easier. So, now for our final guesstimate:

1594 turns * 1 radian/turn * 12 ft. radius differential per turn *(1/5280) miles/ft. = 3.622 miles

There you have it folks, it looks like cheating the inside corners will save you about 4 miles on your trip. This only works out to saving you about 0.15% of the distance. Now we could be off, but I honestly don't think we'd be off by much for three reasons:

1. A standard 400 m track is going around curves half the time and the outside lane is only about 13% longer than the inside. So I would but the absolute maximum for any route at 13%, but that would be for driving around on winding roads.
2. Have you ever driven accross Wyoming, Nebraska, or Arizona. Let me tell you, those roads are heckin' straight. The stretch of road I picked for our estimate went through cities, which means we probably overestimated.
3. The downside with switching lanes, is that the inside curve often alternates, so you would have to switch lanes a lot, which would defeat the purpose a little.

So, in the end, how much does our 3.622 miles save us on gas?

3.622 miles / 20 mpg * \$3/gallon = \$0.54

That's right folks, 54 cents. The moral of the story here is that cutting corners doesn't pay, kids.

Peace,

Tipperary

P.S.  Enjoy your well earned cash. Don't spend it all in one place though, eh?