Kinetics, coasting, and you

[sbergman27]

The topic of coasting to save fuel comes up fairly frequently here, and there are a few comments that I've been meaning to make about it. After all, if we're going to coast, we'd do best to have a realistic feel for how much good, relatively speaking, the coasting is doing. And that is *not* intuitive.

Question: If you are exiting a freeway at 60mph, how much would you have to let the car coast down for the car to retain half the energy it had when you were doing 60mph? If you think the answer is 30mph, you're probably in the majority... and incorrect.

The equation for kinetic energy is:

E = 1/2 mv^2

Where m is the mass of the car, v is the velocity, and "^2" means "squared". Energy increases with the square of the velocity and not directly with the velocity, as most people (including me) would consider intuitive. This has some significant consequences. For example, the correct answer to the question above is that you'd only have to coast down to 42.4 mph (a 17.6 mph decrease) to halve the kinetic energy of the car. Here is a table which describes relative amounts of kinetic energy at given speeds. For simplicity, I'm not using real units like Joules, but only relative numbers that can be compared to get meaningful answers:

75mph: 562
70mph: 490
65mph: 422
60mph: 360
55mph: 302
50mph: 250
45mph: 202
40mph: 160
35mph: 122
30mph: 90
25mph: 62
20mph: 40
15mph: 22
10mph: 10
05mph: 2
00mph: 0

So, what does this mean? Well, let's take a hypothetical example to help illustrate. Say your daily commute involves your exiting an Interstate highway starting from 75 mph. Normally, to avoid dissipating all that energy as heat by using the brakes, you've been letting your foot off the accelerator early enough to allow for coasting down to 10mph before applying the brakes. This has gotten you noticeably improved results on your Scangauge or Eco-meter. The only problem is that sometimes the driver of the car behind you flashes his lights, speeds past you on the shoulder, and gives you the finger on the way by. You're wondering how much of that improvement you might be sacrificing if you time things to coast only down to 20 mph before hitting the brakes.

Well, let's use the table to calculate this:

Relative energy at 75mph is 562.
Relative energy at 20mph is 40.
Relative energy at 10mph is 10.

Energy salvaged by coasting to 10mph is 562 - 10 = 552.
Energy salvaged by coasting to 20mph is 562 - 40 = 522.

522/552 = 0.942 = 94.2%

So, by coasting to 20mph, you are still salvaging over 94% of the energy as you would coasting down to 10. Is the extra 10mph of coasting worth it? Well, you can be the judge of that.

But this at least provides a way to get the information to help make an informed decision.

-Steve