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.
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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.
Jim
Today
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