The Question
Shaun McQuaid, who is never afraid, don’t be delayed or I’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? I’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