The computational cyclist.
Steve Gribble   ·   gribble [at] gmail [dot] com

Crr and Cd·A solver

This tool allows you to estimate your coefficient of rolling resistance (Crr) and your aerodynamic drag coefficient times frontal area (Cd·A). To use the tool, you need to get out on your bike and perform a number of coast-downs from speed on flat ground and then upload the resulting Garmin .tcx file into the tool. As well, you need to estimate air density (rho) using meteorological data from the time you rode, and you need to provide an accurate measurement of the total weight of you and your bike.

Crr and Cd·A Solver

Enter the air density, in kg/m3. If you need it, you can use our air density calculator.
Enter the total mass of the rider and bike (in kg).
Select a .tcx file to upload.

Instructions

Find a long stretch of flat road, and pick a windless, rainless day. It's important that the road is pancake flat: if the altitude varies at all, the tool will reject the data you gather.

Gather data from a set of coast-down sections into a single .tcx file. Your Garmin computer should only be recording data while you are actually coasting down. I recommend you set your Garmin to gather data every second, rather than using smart recording, so that you have plenty of data for the tool to analyze. For each coast-down section, follow this procedure:

If you have a power meter on your bike, you don't need to press start/stop for each coast-down section. Instead, the tool will automatically detect sections of your ride where you are not applying power. So, if you do have a power meter, start recording, accelerate to 20mph, coast down to 4mph, and repeat as many times as you like while continuing to record.

If you want, you can perform a number of different experiments on your aero position while gathering data. For each position, create a separate .tcx file, and gather a set of coast-down sections in that position within the .tcx file.

Once you've gathered your data, head home and upload your .tcx file to your computer. (If you performed multiple position experiments, you'll have multiple .tcx files.) Next, use weather data from the web to determine the temperature, air pressure, and dew point while you were gathering data, and use our air density calculator to estimate the air density rho. Finally, measure the total weight of you and your bike, including any equipment you were carrying during the data gathering, such as your helmet, clothes, water bottles, and bike tools.

The physics behind the tool

First, remind yourself of the physics of the forces affecting a cyclist. For details, read the section at the bottom of this page. During a coast-down test on flat ground, there are two forces affecting the cyclist: aerodynamic drag and rolling resistance. Newton's second law states that F = m · a, where a is the acceleration and m is mass (i.e., weight). The total force acting on the cyclist at any moment in time is the sum of the rolling resistance and aerodynamic drag. Given these facts, the following relationship holds:
a (m/s2) = 9.8067 · Crr + V2 · ( (Cd · A) · Rho ) / (2 · W)
or, simplifying for exposition:
a = c1 + c2 · V2
During a coast-down test, your bike is gathering a number of data points. Each one contains a timestamp and a velocity, as well as other data. By looking at neighboring data points, the tool calculates the average deceleration over that time period, as well as the average velocity. In this way, the tool generates a set of (velocity2, acceleration) pairs based on your measured data in your .tcx file. Using the above equation, the tool uses linear regression to curve fit a straight line against the (velocity2, acceleration) pairs. The slope of this line is c2, and the intercept is c1. From these, you can calculate Crr and Cd·A.

This technique works as long as your data is clean. Calculating acceleration from velocity pairs can be noisy, so the Crr estimate is probably more accurate than the Cd·A estimate.