Hello,
Here are some coast-down numbers for those that like mathematics...
For me, this started right after MetroMPG posted some numbers of his boat tail improvement. The thought of doing coast downs and checking for any kind of an aero gain was too good to pass up.
So with this in mind, several roads on the way to work were chosen for their inherent flatness as discovered by Google Earth.
The data collection device is a Garmin hand held GPS, that is currently set to collect data every 2 seconds.
Before a run, the Garmin is turned on about one mile before the event to allow it to get tentative satellite information and settle down in it's readings.
Two types of testing were initially thought as being important:
1) High speed, as in starting at about 60 mph.
2) Low speed, as in below 15 mph or so.
The high speed is obvious; we use the high air resistance to determine air drag, or Cd.
The low speed option is meant to determine the overall rolling resistance of the vehicle, including losses in the drive train, as well as tire rolling resistance, or Crr.
------ Low Speed Rolling Resistance ------
Shown below is the raw output data from the GPS device. It spits out:
X-data (Latitude)
Y-data (Longitude)
Z-data (Elevation)
...data for each run.
The data is extracted via a custom Visual Basic program, which is used primarily for keeping track of bicycle ride data, but is also useful for coast down testing as well shall see.
This raw data is then converted to world Geodetic data that simulates the outer crust of the Earth, as shown in the data below:
The graph below shows both the raw GPS readings and a "smoothed" set of data.
Note that this GPS device is not an industrial quality unit, such as those used for building bridges and such. Because of this, the data yielded is pretty rough and needs to be messaged for our purposes. Fortunately there are ways to do this, such as low order curve fitting.
For the "smooth" curve on this graph, the GPS raw data was smoothed by a process known as polynomial curve fitting, either first order or second order equations. A first order equation is also known as linear regression or y=mx + b. The graph below has data smoothed by first and second order polynomials.
The graph is a low speed run in town on a flat street with little traffic in either direction. The velocity is shown in meters/second, but can be estimated in MPH by doubling the numbers.
The next picture is on the same street, but going the opposite way.
Now the numbers are converted to effective Crr. This picture shows us heading with the wind. Remember that this was in town, so the houses partially block the wind.
And here is the same run, but in the opposite direction. The true Crr based on these two graphs, is a sloped line somewhere between the two shown here.
From these two graphs, several things become obvious:
1) The basic Crr of the vehicle does not go to zero at zero speed.
2) As the vehicle velocity picks up, the effective Crr goes up as well.
So it can be seen that Crr is not a fixed value, as outside temperature and vehicle velocity
do affect our vehicle Crr. Notice in the graphs, Crr is defined as Crr (v * t), since vehicle velocity and outside temperature also affect this number. As more data is collected, their effect on Crr will become more apparent.
This changing Crr as the vehicle speed increases is already well documented by of all things, a bicycle rider named John Tetz. Below is graph of very thoroughly documented coast downs from his bicycle collection.
John has discovered that Crr is variable, and not constant as alluded to in the article posted on the "instructables".
Measure the drag coefficient of your car
John Tetz Bicycle Coast Down Crr's
------ High Speed Air Drag ------
Several high speed runs have been analyzed as well. Since the vehicle Crr is not fully defined at this time due to a lack of supporting data, the high speed coast down data is only showing velocity and resultant deceleration, and no attempt is made to compute Cd.
This graph shows the coast down numbers for two runs on the same morning on the way to work. Watching the weather, this day was chosen for it's outside temperature and lack of winds.
It had snowed earlier in the week, but the road conditions were dry since the salt had done it's job. One road had the car facing east and the second about 20 minutes later, facing south.
These two runs show a difference of about 7%. The Google Earth and elevation data from the GPS show these roads to be extremely flat, although the second road is flat within 3 feet over the 1/2 mile stretch used for the testing.
It is obvious that wind is a factor in these two graphs. Even though posted weather data for the area showed calm wind conditions, this was definitely not the case here. One or both of the roads had to have some wind present for this large of a data variation. Ideally it would be nice to measure air speed during the tests, but this would involve another data collection device besides the GPS.
Of course measuring wind speed would not account for side winds and the resultant change in effective Cd of the vehicle. It may be more effective to keep collecting data until numerous runs with similar data can be compiled, and data not fitting within a certain percentage, discarded. Actually this last approach has been alluded to by AeroHead in a different conversation, so it certainly has some merit.
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At this point, I'm not sure if back to back testing on the same road and the same day would yield acceptable results for testing our aero mods.
For testing my under body smoothing panels in an A-B-A fashion, it would take the better portion of a day:
1) Do the first run with the GPS
2) Drive back home, jack the car up 8 inches and remove all the panels
3) Go back to the same location and hope the temperature, traffic, and so on is the same as before
4) Perform the coast down tests
5) Drive back home again, jack up the car and put the panels back on
6) Drive back out again for another round of testing.
In the summer time, this type of test would present some variables that would make it hard to get repeatable results; i.e. temperature gain and air thinning plus the change in Crr because of this.
Of course, if one were a night owl, all of this could be done in the wee hours with hopefully better results.
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With that being said, these coast down tests will continue, as the hope is to determine the major factors that go into performing testing that shows progress made to our vehicles.
It may be that we will find only one road that is flat enough for these tests to show reasonable repeatability.
John Tetz mentioned the use of a graded road instead of a flat road for his bicycle coast downs. It may turn out this is an option as well.
Jim.
Today
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