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

[yaris-me]

Shouldn't you factor in air resistance, mechanical friction, rolling resistance and road conditions?

[sbergman27]

Originally Posted by yaris-me

Shouldn't you factor in air resistance, mechanical friction, rolling resistance and road conditions?

No. Those things affect the rate of deceleration (kinetic energy loss) at various speeds. (The coast from 20 to 10 takes a *lot* longer than the coast from 70 to 60, even though the energy differential is *much* smaller.) But the kinetic energy at a given speed is totally independent of those.

One thing that I intentionally left out, for simplicity, is that when you do hit the brakes you don't stop instantly. So there is actually some "coasting" left to do even after you hit the brakes. This has the effect of narrowing the gap between, say, coasting to 20 and coasting to 10, even further, since the brakes are not dissipating *all* of the remaining energy. But the difference is likely small, and I wanted to keep this as simple and straightforward as practicable.

-Steve

[Hershey]

LET IT ROLL !!! On down the highway . . Name that tune . .

[Loren]

Damn you, Hershey! Had to Google it just to stop the ear worm.

[YarisOwnersDad]

I got it right without looking it up.

(But then I am an OLD FART.)

[cnw126]

I really like this thread!

Thanks Steve!

[Loren]

Okay, I've been resisting, but you're overlooking something here.

You've examined how much kinetic energy you save or don't save on coasting down to 20 mph vs 10 mph or a full stop, and that's great. But, what about the other side of the coin? When you coast down to 20 mph and DON'T stop, you don't have to accelerate from a stop. So, a properly timed coast-down that allows you to MAINTAIN that 20 mph speed instead of slowing to 10 mph or stopping is more efficient.

What I often (very often) do is when I see something happen in front of me (say, a light just turned yellow 2 blocks ahead) is to hit the brakes immediately and scrub off some speed EARLY. This allows me to coast for a longer period of time. Coasting in DFCO, this costs me less than sitting at the light and idling would. (and I'm not one of those who wants to shut the ignition off at every light) My goal is to maintain as much momentum as I can rather than coming to a stop, thus avoiding the acceleration from zero mph.

I'll let you do the math, but accelerating from a full stop is about the least efficient thing you can do in a car, even with a light foot.

[sbergman27]

Originally Posted by Loren

Okay, I've been resisting, but you're overlooking something here. You've examined how much kinetic energy you save or don't save on coasting down to 20 mph vs 10 mph or a full stop, and that's great. But, what about the other side of the coin? When you coast down to 20 mph and DON'T stop, you don't have to accelerate from a stop. So, a properly timed coast-down that allows you to MAINTAIN that 20 mph speed instead of slowing to 10 mph or stopping is more efficient.

No. I'm not overlooking all the many possibilities. I'm just trying to start out simple. The intent is to present the table in an understandable way and then let people do creative things with it.

Of course my initial example with the profane and rude SUV driver (I always imagine him driving an SUV) was fanciful. But if people stop thinking linearly and start thinking in terms of the velocity squared relationship, it helps their intuition come to better seat of the pants FE decisions.

Avoiding braking from 40 to 30 might be significant. But 30 to 20? 20 to 10? Probably not. 10 to 0? No way. And the corresponding accelerations from 0 to 10, 10 to 20, and 20 to 30 are on the same, relatively minor scale.

-Steve

[Hershey]

noticed that when the YARIS is coasting down a hill in neutral the ECO-METER's overall mileage rises , while when in neutral ( idling ) at a stand still it loses it slowly . So , why is it while the wheels ( axles ) are moving in neutral it reads in a positive way ( the same when in over drive ) ?

[Yaris Hilton]

Because you're covering ground when you're coasting! When you're standing still, you're getting 0 miles per gallon.

[Hershey]

uh huh .

[sbergman27]

I wonder why people have so much difficulty (or disinterest) in translating their qualitative arguments into quantitative ones?

Getting "0 mpg at idle" sounds dramatic enough. But what is the actual significance of getting 0 MPG when you are idling at 0.16 GPH?

Say you drive for an hour at 75 mph and get 37.5 MPG. And then, say, you drive another hour at 75 MPH and then let the car idle at 0.16 GPH for another 15 minutes while you stand around and whistle "Oh! Susanna". What's the difference in MPG?

It works out to 0.73 mpg. About a 2% difference.

Qualitative arguments, even when correct, are basically a "Go / No Go" affair. Quantitative arguments tell you if what you are obsessing over actually matters in any real sense.

-Steve

[Loren]

You can't quantify how much mpg difference it will make over a tank of fuel because you don't know how much time any given person spends sitting at idle. But, you can reliably state that everyone gets "zero MPG" while their car is at rest idling.

Without the quantity (how much time is spent idling?) we can't quantify.

To quantify with any degree of accuracy would be a hassle, too. One would either need to carry a passenger with a stopwatch and a notepad and do several lengthy experiments or take video of same and spend hours reviewing it.

Those of us who have spent time with a ScanGauge honing our driving technique for best MPG already know the answer.

[sbergman27]

Originally Posted by Loren

You can't quantify how much mpg difference it will make over a tank of fuel because you don't know how much time any given person spends sitting at idle.

Last week, individuals certainly seemed capable of making back-of-the-envelope estimates defending their own level of DFCO usage. But this week it is impossible for a person to make a ballpark estimate of how often his engine is at idle?

But, you can reliably state that everyone gets "zero MPG" while their car is at rest idling.

Which is *technically* true, but *practically* meaningless until it is put into the context of total quantity of fuel used.

ScangaugeII does automatically keep track of total fuel used, total miles, and average speed driven on a per day basis. (Among other things.) Say you drive 50 miles in a day, use 1.6 gallons of fuel, and have an average speed of 30 mph. For idling to represent 10% of total fuel consumption, you'd have to be moving for 40 minutes at an average speed of 75 mph, be stopped at idle for an 60 minutes, and get 34.7 mpg while you are moving, for a combined value of 31.25 mpg.

It's certainly possible for a person to ask himself if he thinks he spent 60 minutes idling, and only 40 minutes driving that day... without having to hire on a dedicated stopwatch operator. ;-)

I pulled those numbers completely out of the air, of course. The point being that you can get creative and extract very interesting and useful information out of your ScangaugeII data if you don't just throw up your hands and say that it's impossible, or too hard.

Those of us who have spent time with a ScanGauge honing our driving technique for best MPG already know the answer.

Or at least you think you do. I've seen too many claims of a switch from 5w30 to 0w20 oil yielding an FE improvement of 5%, or jacking tire pressure up to 60 psi yielding 10%, to take anecdotal evidence seriously. Considering wind, temperature, fuel composition (E0, E10, winter, summer) rain and snow, hills, passenger load, etc., fuel mileage logs are mostly noise, and people attribute day to day variations to whatever is on their minds at the time that they expect to make a difference in a particular direction. It's a lot like primitive people's attributing a drought to the displeasure of a particular god.

-Steve

P.S. I should probably also mention that from what I've read of what you've posted on the topic, you seem to drive in a very sensible and reasonable way. Probably a lot like I do, in the city at least. Few people spend as much time on the highway as I do. Highway driving is much simpler to analyze, BTW, which is nice.

[Hershey]

why is it if you coast down a long steep grade in neutral that the ECO-METER gains in overall miles per gallon and when idling at a standstill the mileage decreases ? A sensor for the tranny when coasting in neutral that sends signal to ECO-METER ?

[sbergman27]

Originally Posted by Hershey

why is it if you coast down a long steep grade in neutral that the ECO-METER gains in overall miles per gallon and when idling at a standstill the mileage decreases ?

Could you explain a little more about why that doesn't make sense to you? The eco-meter takes the total distance traveled and divides it by the total fuel used to get the mpg figure. It doesn't know or care if the transmission is in gear or not. The VSS (vehicle speed sensor) indicates forward motion regardless of what gear the transmission happens to be in, including neutral.

-Steve

[Hershey]

o.k. .