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Scientific Performance Testing
Power Models  :  Regression Method CdA Estimation
Wind Speed (KPH)
Kilos (Rider + Bike)
Bearing Refers To
Temp (Deg C)
Average Grade (%)
Rel. Humidity (%)
Results & Sanity Checks
There was an unexpected error or your calculations exceeded the allowed time. Either one or more of your parameters is beyond the realms of probability or the server is extremely busy right now. Double check the parameters and try again.
The Chung method is an excellent way to estimate a riders CdA using power data collected on the road. It doesnt require a velodrome or even a flat course, and if you use a circuit then light winds are unlikely to have a significant impact on the result. But it is not the only way to estimate CdA with a power meter. Before the Chung method came the regression method and the model here implementents the methodology of
Martin et al (2006)
So how does it differ? Well this a test which must be done on a velodrome, a flat piece of road, or else a nearly flat road for which the gradient is known with some precision. An outdoor test also requires recording of the wind conditions (strength and bearing) experienced at that location when the test is being run. Unfortunately these are not things you can discern with amazing accuracy from a simple weather report, however basic hand-held anemometers (wind speed meters) go for small change on ebay.
Carrying out the test on a road requries that you first locate a straight stretch of tarmac long enough to ride at a smooth pace for ideally a minute or more. You need to know the compass heading or bearing of the road (eg North = 0 degrees, South = 180 degrees), followed by the wind strength and bearing. As with the Chung method it's also essential to record the data that will be used to calculate the relevant air density (temperature, pressure, humidity) although these can come straight from a weather report.
The test methodology is to ride up and down the road, at least 6 times is recommended, using a range of different speeds. Somewhere in middle of the stretch e.g. the middle 1 minute if the road is taking about 2 minutes to cover and just when the riders speed and power at at their smoothest the applicable speed and power data will be used to estimate CdA. How you decide to identify these critical sections of power meter data is upto you, but this model tries to make things as easy as possible because you feed it with a 3 column file where columns 1 & 2 are speed and power data. In column 3 you simply "tag" the important sections of you data (eg 1-6) while any other data is ignored. There is an example of a suitable 6 sector test file
although in a real test the power and speed numbers would not be constant through each sector as they are in this simplified example which also uses just 10 second sectors.
Carrying out the test on a velodrome is easier because you can assume a flat "road" and zero wind. In this case you might collect data every 4 laps of 8, using the time in between the test sections to adjust speed. Remember that maintaining a smooth speed and power through the test sections is just as important so in the track case you might want to stay on the black line throughout. Anybody who has seen "The Final Hour" (a documentary about Chris Boardman's preparation for the Athletes Hour Record) will have seen Boardman & Peter Keen using a very similar procedure to evaluate the aerodynamic merits of various equipment choices and this is, of course, an excellent application of this kind of testing.
So how is the data converted into a CdA? Basically the model uses a form of the same theoretical power model used elsewhere on this site to decompose the forces affecting the rider into components representing acceleraton, climb, rolling reistance, and aerodynamic drag. Arrranging this model in a clever way and feeding it with speed and power data allows the riders CdA to be estimated from a regression on all the different observations.
Ride Data File
Data File. Create and select a text (.txt) or comma separated values (.csv) file having three comma separated columns of ride data in the same format as the example. Column 1 should be the speed data, column 2 the wattage data, and in column 3 you should tag the critical sections of the test. For example if you rode a 6 sector test tag all of the rows representing sector 1 data with "1", "s1" or similar in column 3, then do the same for all other sectors. Rows that are not tagged will simply be ignored. A "txt" file can be created easily on most computers while the "Save As" menu in Excel is the easiest way to create a "csv" file from 3 simple columns of spreadsheet data.
Speed In. Select the unit of speed applicable to the recorded data (KPH or MPH).
Interval (Sec). Select the recording interval of your power data in seconds.
Rider + Bike Weight (Kilos). Input total weight in kilos (e.g. 80).
Pressure (Millibars). Input the ambient air pressure in Millibars (e.g. 1013). You can get this number from any good weather forecast.
Temprature (Deg C). Input a temperature in degrees Celcius (e.g. 20)
Relative Humidity (%). Input the ambient air humidity in percent (e.g. 20). Again you can get this number from a weather forecast.
CRR (Rolling Resistance). Select the coefficient of rolling resistance applicable to the course. Typical values are .004 (Asphalt) and .008 (Rough Tarmac).
The following inputs can all be left as "0" or the default values in the case of a test on a velodrome.
Wind Speed (KPH). Input the wind speed in Kilometes per hour (e.g. 5).
Wind Bearing. Select the applicable wind direction as a heading (e.g. NW) or else input a wind bearing between 0 and 255 degrees. This is the direction the wind is blowing from, not to.
Course Bearing. Select the bearing of the course consistent with your choice of "Bearing Refers To"
Bearing Refers To. Is the bearing you provided the direction you were riding in on the odd numbered sectors, the even numbered sectors, or if you always covered the road in the same direction select "All Sectors"
Average Grade (%). Specify the average grade of the road, in the direction of the course bearing, as a percentage. eg 1.5 = 1.5%
Outputs – Sanity Checks
Before focussing on the CdA estimated by the model it is important to check that the ride data file fed into the model has been read in a way that makes sense. Based on the contents of the file and your parameter inputs each of the summary numbers in this section should make sense. If not, double check everything and try again.
Outputs - CdA & R^2
CdA is the metric of aerodynamic drag (
rag x frontal
rea) calculated in respect of the rider and bike combined. The figure is expressed in metres squared. Typical but not exceptional cycling values are in the range .25 to .40 and you should expect to see a value within or close to this range, otherwise the validity of the test may be questionable. To see some typical CdA values have a look a the
. R^2 (R squared) expresses the explanatory power of the regression used to estiamte CdA in the range 0-1 where 1 is ideal and significantly lower values may suggest an unreliable test.
This test is all about relating the riders realised speeds with the power outputs applied to achieve those speeds and then "backing out" the applicable CdA. If the data is good then there will be a clear relationship between the speed and power averages collected from the 6 or more test sectors and you should check for this here in a visual sense. Each test sector is represented by a diamond, hopefully all close to the the blue trend line. On a theoretical level aerodynamic drag force increases at the square of speed so this is the relationship you should observe on this graph.
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