**The Question**

Shaun McQuaid, who is never afraid, donâ€™t be delayed or Iâ€™ll be dismayed. ..

How much money could one save in gas by always staying to the inside of a curve by shifting lanes while driving on the highway? Iâ€™m not looking for an exact value, just a relative comparison between always on the outside of a curve, the middle, and always on the inside. You can ignore traffic and assume that all lanes are equal speed.

Yer Pal,

Jesse

**The Answer**

Let’s make a lovely little “perfect” world. In our perfect world, Boston is at the exact center of a half circle inscribed by Rte. 495 in Massachusetts. In real life, we’ll use I-495 from the intersection of I-93 in Andover, MA to the north, and I-495’s intersection with Rte. 24 in the south. This allows for an almost (meaning not really at all) perfect half-circle around Boston. Using I-90 as the diameter line, we discover that the radius of our circle is 27.5 miles, or 145200 feet.

The plan is simple – we will inscribe 2 circles, one on the “inner” lane of this simplified route, and one on the outer lane. According to my research, the most common lane width is 12 feet. Let’s assume a 3-lane highway – so, the “inner” lane has a radius of 145200 feet and the outer lane adds 24 feet to that total – 145224.

Calculating the perimeter of the circle will give us the distance traveled in each lane. Perimeter of a circle is calculated via 2 * (pi) * r, so a half circle is simple: (pi) * r. (For our estimation, pi is estimated at 3.14159).

Inner lane distance: 86.39 miles

Outer lane distance: 86.41 miles

Assuming 30 miles per gallon in your vehicle, this means:

Inner lane gas used: 2.879 gallons

Outer lane gas used: 2.880 gallons

So, in essence, by travelling only in the inner lane, you would save 0.001 gallons of gas. (Because of the tiny amount here, I ignored the “middle” lane and stuck with the right and left only).

Not quite as exciting as expected, is it?

I commend the ingenuiety used to tackle Jesse’s question, however I content that most turns encountered on a highway are of a much smaller radius than 27.5 miles. Though your conclusion is probably still valid.

maybe assume a two lane road (with the previously determined lane widths), and an average corner angle of 45 degrees (i’m pulling that out of the air, i bet a real average would be more like 20 degrees, but I have no data so 45 is as good a number as any) so outer to inner ratio is given by:

pi/2*(r+12)/mpg

————————–

pi/2*(r)/mpg

ahhh, we see that the angle swept and the actual mpg do not matter, only the relative radi. A graph