Extra distance for changing lanes

It is 1,000 miles from Point A to Point B. Drivers 1 and 2 drive the trip making exactly the same pitstops. However, Driver 1 changes lanes an average of twice per mile to pass slower cars while Driver 2 stays in one lane the entire trip. How much extra mileage will be recorded on the odometer of Driver 1?

It depends on:
(1) how wide the lanes are, and
(2) how quickly the driver changes lanes.


According to this,
(1) most common lane change distance is 12 feet
(2) most common lane change time was 6 seconds
(nice histograms in the cite)

At 60mph, 6 seconds carry you 528 feet. Assuming a straight-line lane change (not accurate, but approximate), the lane change takes the car an extra 0.136 feet. Passing two cars per mile (4 lane changes total) means an extra 0.545 feet per mile, or 545 feet over 1000 miles: just over 1/10 of a mile.

If Driver 1 changes lanes to get on the inside of curves he might travel a smaller distance.

I was going to say this. Is the 1000 miles in a straight line, or does the road have curves in it?

To put this in perspective, go out and do the following excercise.

Step 1: At the Equator, measure the circumference of the Earth.

Step 2: Then hammer in a series of stakes around the Equator, each extending one foot above the ground. You’ve essentially added one foot to the radius of the Earth.

Step 3: Run a rope around the Earth at the top of these stakes.

Step 4: Measure the length of this rope.

Question, How much longer is the measurement in step 4 than is step 1?

Answer: Just a teeny bit more than six feet, 3 and one quarter inches.

This will be the answer whether the diameter of the Earth is one mile or 8 thousand miles. what this means is that adding curves to a road doesn’t change the length very much, especially if for every right hand curve there is a similar left hand curve which is usually the case.

  1. If someone is changing lanes, then left- and right-hand turns don’t cancel out, they’re additive.
  2. The effect is bigger when you have sharper curves - the curvature of the earth is very small, essentially flat over any distance. The sharper the turn, the great the differential between the inside and outside lanes.
  3. We’re comparing it to 545 feet over 1000 miles, the effect doesn’t have to be very big.


Using your diameter:

c[sub]1[/sub] = pi * r[sup]2[/sup]
c[sub]1[/sub] = pi * 4000[sup]2[/sup]
c[sub]1[/sub] = 16e6 * pi

c[sub]2[/sub] = pi * (4000 + 1/5280)[sup]2[/sup]
c[sub]2[/sub] = 446054442240001/27878400 * pi

c[sub]2[/sub] - c[sub]1[/sub] = 42240001 / 27878400 * pi = 4.760 miles

Also, why would the curves cancel out? As muttrox already noted, upon preview.

The circumference of a circle isn’t πr[sup]2[/sup]. It’s 2πr

Back to “work” for me!

If we take as typical a lane spacing of 12 ft and a curve which causes the road to change direction by 30 degrees (one-twelfth of a circle), then the distance you save by using the inside-the-curve lane as opposed to the outside lane is:
2 * pi * 12 / 12
which works out to 6.28 ft.

After just 840 such curves you will be (OTBE) a mile ahead of the guy who always takes the outside lane.

…if I follow Xema correctly, that would be for a two-lane road (the 12 foot difference being the two lanes). So a curving highway would be more.

On the other hand, we’re comparing to someone who stays in one lane all the time. Assuming there’s equal numbers of left- and right-hand turns, half of the time there is no difference as the two cars are in the same lane.

On a two-lane road (assuming this term is used in the normal sense, to mean one lane in each direction) it’s often impractical or downright suicidal to drive in the lane that’s inside a curve. I’m thinking this scheme is realistic only on a divided highway with two or more lanes in each direction (and only when traffic is light to moderate).

If you have three lanes to work with, you can double your lane spacing at each curve, from 12 to 24 ft. That would of course result in twice the distance saved - though probably still not enough to be of great significance.

I was apparently using it in the abnormal sense, sorry about that. We’re saying the same thing.

I do it all the time, but not to save gas; I can maintain my speed better on the larger radii. I often even drift into the left lane so I can cut across the right lane, and I do it on my motorcycle within the lane as well. It depends on the terrain, but I’d say I do it 80% of the time.

If you mean you’re doing this on a 2-lane road, I hope it also depends on the traffic headed the other direction, and your visibility of it.

As my old grandfather always said, pi ain’t square. Pies are round, cornbread are square.

Sorry - couldn’t restrain myself.

ah, never mind!

If curves are adding distance, then so are hills !

How often does one lane go up a hill but not the other? We’re only looking at incremental distance due to switching lanes vs. constant lane.