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3-Wheeler 12-21-2011 04:15 PM

Coast Down Testing - 2000 Honda Insight
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There have been those posting on EcoModder, discussing how people were able to determine not only the Cd of their vehicle, but also the effects of large and small modifications.

It was with this curiosity that this author recorded numerous coast down tests via a hand held GPS, during the time period of January 04th, 2010 through April 01st, 2010.

A section of road on the way to work was examined using Google Earth for flatness, and found to be suitable for coast down testing. The elevation of the road in feet above sea level is shown below.

The two vertical red lines indicate the primary section of road used for the coast downs, and within an elevation change of about two feet.

The graph below shows not only the digital elevation in feet, but a polynomial curve fit of the road surface as well.

Once it was determined that coast down testing would be tried, a method for recording the coast down data was needed.

Reading the speedometer and recording time via stopwatch was considered, but not the most desirable approach.

A hand held GPS was already used for hiking and such, and thus considered ideal for exact recording of speed and time. The unit is a Garmin Legend eTrex and is set to record speed data every two seconds.

The GPS is started about two minutes before taking coast down data to allow the GPS unit to sync with the satellites and create stable readings.

Below is graph showing the raw output from the hand-held GPS in the coast down zone on the road. Note how much deviation the data has. As noted this is with the sample rate of two seconds.

This amount of speed variation between speed samples has been consistent over all the coast downs, and this graph is typical of that variation.

Since the speed variation is so high, it is desirable to “smooth” the data via some mathematical method. The graph below shows what a smoothing method called “Linear Regression” looks like, as signified by the thicker red line.

And here is what the resultant deceleration curve looks like, in response to the Linear Regression smoothing.

The rolling resistance portion of the overall deceleration is shown below, again, based on a Linear Regression coast down smoothing.

Note that the Crr portion of the energy loss should be something closer to a straight line, not the downward sloping curve as shown below.

With the above three curves in mind, another approach to smooth the raw GPS data is shown in the form of a second order polynomial that has three coefficients.

Note that the curve fit to the raw data seems much closer than the linear regression line above.

And from this data smoothing, we can calculate what the resultant deceleration curve looks like. It appears that the deceleration curve shape is almost a straight line with a steep upward slope.

This curve is closer to what the deceleration curve should look like, but not quite.

And from the above deceleration curve, we can then determine what the rolling resistance portion of the total energy loss looks like. It is certainly closer to a straight curve.

From the above, it does not appear that applying either Linear Regression or a low order polynomial yields the desired smoothing, as the deceleration curves do not approach the ideal shape.

In order to smooth the raw GPS data without altering the true change in coast down speed, maybe another smoothing approach can give us an answer.

The screen shot below is from a custom Visual Basic program who’s sole purpose is to smooth rough GPS data as shown. The smoothing method in this case is a single pass, 5 point data averaging method, and one can clearly see that the raw GPS data, represented by red circles is indeed smoothed by presence of the blue line segments.

However, this data is still too rough in nature to allow proper deceleration of the vehicle to be calculated properly.

So we take the process above and loop the freshly calculated output data a total of 2000 times to produce the very smooth curve shown below.

This smooth curve is now placed along side the raw GPS data below.

And the resultant coast down deceleration is shown below.

Well, now it seems we have a deceleration curve that is starting to have the characteristic curve of combining the rolling resistance and velocity squared aero component.

If we then calculate the effective rolling resistance portion of the total energy loss, we end up with a curve that is shown below. This seems to indicate that the rolling resistance portion of the deceleration load is constant with speed.

To be quite honest, I am not sure if on a theoretical level, this is actually the case or not.

The data below shows the entire mathematical process of taking the raw GPS data, smoothing it, calculating the Total Deceleration, Aero Force in Newtons, the Crr Force in Newtons, and finally the calculated deceleration (model).

In this case, the actual Total Deceleration and the Model Deceleration had the best match with the following settings:

Cd: 0.234; Crr: 0.0134; Wind: -1.16 m/s

During the coast down testing over the winter of 2010, 39 coast down runs were recorded and the deceleration of each run is shown below.

Looking at the graph, one can easily see that there is quite a bit of variance in the data. The heavy red curve represents the “average” of all 39 coast downs, and this curve is surprisingly close to the “ideal” coast down deceleration curve.

So what does the “average” curve tell us? The car apparently has a Cd of 0.228, a Crr of 0.0137 in cold Wisconsin winter conditions. Remember that the Cd probably is very close to actuality since the stock Insight has a Cd of 0.25 and this car has, at this point in time, fiberglass under-body smoothing panels, with about 70% coverage. Several of the panels next to the rear wheels are not created at this point in time.

It is also obvious from the data that the moving velocity in which the aero effect equates to the same rolling drag is close to 20 m/s (44.7 mph).

What the data in this study also tells us is that, even though the coast down testing is performed on the same section of road during the drive to work and the car fully warmed up for 20 miles before reaching this location, the data between each run is highly variable.

It is this author’s opinion that the conditions and/or measurement methods during these coast down tests are still too variable to be of much use regarding aero improvements to our cars.

One possible improvement would be to arrange for the collection of much more data, maybe in the hundreds of data points, and utilize a method that is not so prone to speed variance, such as the GPS unit is now.


I can see why Aerohead gave up on this sort of testing long ago, as he has already made mention of in the past. It will take some dedicated equipment to record enough data, and with enough consistency, to really add value to our aero endeavors at EcoModder.


gone-ot 12-21-2011 05:31 PM

...can't "explain" ALL the variances, but these 'variables' came to mind:

• differences in wind velocity
• differences in wind direction
• differences in driver control (we're seldom 100% repeatable)
• differences in air temperature
• differences in air density (cold/dry winter vs. hot/humid summer)
• differences in GPS satellite lock-on's (jumping between different satellites?)

...individually, these might be small, but their "interactions" might be significant?!?

...what kind of regression correlation coefficent (R^2) do you get when you tell the Trendline function to "set intercept = 0", which forces the "average" line to go through zero at Y = X = 0.

slowbro 12-21-2011 05:32 PM

Wow. This is very interesting. I've been wondering myself about the reliability of my testing. Does anyone know of the reliability of this compared to measuring fuel economy while holding speed to test improvements? I suspect coast down testing would be a little more reliable, but as many of us know, even the tiniest variations in a driving commute can contribute significant variations in fuel economy. Ideally, it would be nice to average 39 runs in A-B-A style for testing, but that is very time (and gas) consuming.

gone-ot 12-21-2011 05:41 PM

...this posting needs to be "STICKIED"!

Fr3AkAzOiD 12-21-2011 06:14 PM

I could barely follow this but I'm geeking out over your details. lol

JRMichler 12-21-2011 08:55 PM

Your most accurate fit to the data is from a least squares fit of a quadratic equation to the raw data. Filtering the raw data makes look prettier while reducing accuracy. The lost accuracy comes from the phase characteristics of your filter.

Your road has enough slope to fuzz the results. I regularly drive a route of about 60 miles. One end is 800 feet higher than the other end, for an average slope of 13 feet per mile. Average mileage is about 5 MPG higher going downhill.

Your top speed was only 40 MPH, which is not fast enough for accurate results. A 5 MPH headwind increases aero drag by 27% at 40 MPH, and more at lower speeds. A 5 MPH head or tailwind will change my trip mileage by about 2 MPG.

Averaging several runs is good. Starting at a much higher speed is even better. The best starting speed is where the aero drag is at least ten times higher than the rolling resistance. Coasting down until almost stopped will also improve accuracy.

MTA: OK, I see that you already spotted some of this. You calculated that air drag is equal to RR at a speed higher than your highest test speed. That means that it is difficult to accurately estimate Cd from your data. Your Crr should be pretty good because the test data is almost all rolling resistance, with very little contribution from air drag.

drmiller100 12-21-2011 09:12 PM

seems to me there are 3 major uses of fuel.

One is overcoming aerodynamic drag.
One is overcoming rolling resistance.
One is accelerating the vehicle.

Of the three, I suspect the middle one is the least significant.

I agree aero drag would be MUCH easier to calculate at higher speeds.

Also, I suspect some of your curve is actually from the wheels energy being non linear with respect to speed - the wheels are rotating, so they give energy to the system as a function of the square of the mph.

accelerating the vehicle is a function of rotational inertia and weight of the vehicle.

Cd 12-21-2011 09:38 PM


Originally Posted by Old Tele man (Post 275683)
...this posting needs to be "STICKIED"!

I'll second that !
Please make this a 'stickie'

NeilBlanchard 12-21-2011 10:04 PM

Holy moly Batman! That is some serious data crunching.

How did you determine the Crr? In my coastdown tests using the Instructables spreadsheet, this is the hardest part to get -- it is basically an educated guess?

@drmiller100 -- I suspect you are correct. The aerodynamic drag swamps everything else at a constant speed. And accelerating (from a stop and/or uphill) is huge but if you can limit the time it lasts in proportion to the whole drive time, then it becomes less critical.

jime57 12-21-2011 11:11 PM


Originally Posted by 3-Wheeler (Post 275678)
I can see why Aerohead gave up on this sort of testing long ago, as he has already made mention of in the past. It will take some dedicated equipment to record enough data, and with enough consistency, to really add value to our aero endeavors at EcoModder.


Thanks for the interesting and very thorough report. I have been affraid all along that some of the techniques we hold so dear don't render accurate results without considerable control and considerable data. I don't think any one could have exercised much more dedication than you have and I compliment you on your effort.

I have felt for a long time, since 2008 when I first joined, that the easiest measurement would be MPG improvement over long two way courses. With such controls as low wind, constant driving techniques, constant average speed, the small variations of conditions and driving technique average out if the course is long enough. I have achieved good repeatability with this technique. True that it doesn't serve up the number we would all like to get - the improved Cd - but it does point to which mods work and relatively how well they work.

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