I live in a pretty hilly area of my city and while cruising around the curves, I often wonder how much distance I would save if I took the inside lane on every curve on a long-distance trip?
I-80 is the second-longest highway in the US at 2899.54* miles and winds its way through a few mountain ranges…how much mileage would I save by taking the inside lane?
*According to this, I-80 is actually only 2,881.94 miles due to 17.6 miles on I-15 and I-35, but whatever.
Wow. I almost moved this to the Game Room.
Taking an inside curve* takes lots of nerve.
*baseball
There’s an exact formula for this usually the mileage saved is so minuscule that it doesn’t affect cost. In racing, it shaves hundredths of a second off the lap which is the difference between winning and losing especially if multiple laps are involved.
In racing on an oval track, don’t they ALL try to go low into the curve though? I’m not sure, I’m not a car racing fan.
Anyway, I’m not asking about the cost, I’m wondering about the difference in actual miles traveled over long distances between taking the inner- and outermost lanes. If it shaves “100ths of a second off the lap” in something like the Indy 500, surely it has to shave distance off on the SueDuhnym 3K, right?
Sorry for the confusion, I grew up in Detroit. For a brief, shining moment in 1984, I was a baseball fan…but mostly I’m all about the hockey.
I can’t answer the question, but I would assume that taking the inside curve doesn’t help except when a particular lane is more likely to be the inside lane. On a highway, the furthest left and furthest right lanes are equally likely to be the inside lane for any particular curve, so I imagine any the gains you make from taking the curve on the inside are counterbalanced by the losses you suffer from having to switch lanes all the time.
Drive as straight as you can. Helps if no other cars are in the way. Rather dangerous on a two lane road if you can’t see ahead.
Do some math with circles and straight lines vs following all the circumferences…
YMMV <-- pun intended.
Best possible savings:
If the road is a series of circular curves, one after another, of outside-lane-line-radius equal to the road width (such that you could go straight the whole way if you wanted to), then you could theoretically take your distance down to 2/[symbol]p[/symbol] = 64% of normal. However, the Great Circle distance from start to finish for this trip is only 88% of the highway distance, so the best-case savings can’t be better than that (which is to say that the curves are not arranged in the most geometrically favorable way).
Best-case, then: a savings of 12%.
Least possible savings:
Approximatly 0%. Picture a road which went in a perfectly straight, but misdirected, line for a while, and then took a sharp turn in the direction of the destination. The only savings would be the little bit you could get at that one turn, which would be on the order of a few meters.
Realistic savings?
From having driven the entire length of I-80 myself (twice, actually), I can attest to the fact that most of it is painfully straight. Let’s say that CA, NE, IA, IL, IN, OH, half of PA, and NJ are straight and that NV, UT, WY, and half of PA are curvy. That means (according to wiki) that 40% of the highway distance is curvy. If we take an aggressive average radius of curvature in the curvy parts of r=200 meters, then we can fit N=0.4L/(2[symbol]p[/symbol]r) complete curve cycles in the trip, and each cycle can save us 2[symbol]p[/symbol]w in distance (w=road width). Thus, we can save 0.4Lw/r. A mountain road might be 10 m across, so this portion of the trip becomes 0.4L(0.05) shorter.
Putting it all together, then, we would save 5% on 40% of the trip, which is 2% overall. This is about 60 miles.
And here I was telling my kid he might not use that math stuff in real life!
The other option is to drive it “reg’lar”, and then drive all the inside curves, and compare odometer readings.
Now, the tricky part is to find a time when there’ll be NO OTHER CARS on the road. I think many of us here would volunteer to fly out there and stop traffic with little flags for you… if you buy us our own day-glo vests.
Here’s a track and field site that says the outside lane on a 400-meter track is 46.2 meters longer than the inside lane. And the entire width of a standard track equates well to a Interstate-width road lane.
Of course, that extra distance is found on the 200-meters of curved track, not the 200 straight meters. Simple division tells us that 100 meters of that curve will give a 23.1 meter difference = about 75 feet.
So all you have to do is take the 2899.54 miles of I-80 and subtract all the straight parts from it. Take what’s left, divide it into 100 meter chunks, add 23.1 meters/75 feet to each segment and there you go!
Of course, not all curves are created equal, so this should only be used for a rough estimate 
Let’s take a typical example, where the curve is 1/3 of a circle. Let’s also say that the distance from the middle of the innermost lane to the middle of the outermost lane is 30 feet.
If we were comparing full circles, the bigger one (whose diameter is 60 feet longer than the smaller one) would have a circumference of 60*pi (about 188) feet longer than the smaller. But since this is only 1/3 of a full circle, the outside lane is only 63 feet longer than the inside lane.
63 feet is more than 1/100 of a mile. If you encounter a few dozen of these in the course of your trip, it can add up to a significant distance. But keep in mind that the significant savings occur when you’re on a multi-lane road and move all the way from the outermost to the innermost; is the shorter distance really worth the danger and fuel of jockeying those lanes?
Also, the biggest savings are on the sharpest turns, because they’ll be a larger proportion of the circle. But the radius of the circle is not relevant to the calculations.
I think this overstates the case. It’s pretty rare for an interstate highway (or any other road, for that matter, unless you’re running Deals Gap) to turn through 1/3 of a circle, i.e. 120 degrees. I would guess the typical turn is usually about half of that, and probably much less than that if we’re regarding I-80 from coast to coast.
Moreover, standard lane width in the US is approximately 12 feet. Altogether, I would reduce your calculated savings by a factor of 5.
Joe Frickin Friday makes some very good points. I chose the 1/3 size because the OP described himself as living in “a pretty hilly area”. A much smaller fraction would indeed be more reasonable for an interstate highway, but I wasn’t sure how to explain that in dumbed-down terms.
And I admit that I have no idea how wide a standard lane is. My guess was 15 feet, and even with that, 60 is pretty exaggerated.
Thanks for setting it straight. … err… properly curved!
While it is true that a race car driver tries to stay on the inside of the track as much as possible on an oval, if the car is not handling very well, it will tend to loose more speed going around the turn, for that reason, some car run better/faster closer to the outside.
