There is a lot of interest regarding aero drag coefficients in TTs, and AFAIK there aren't any good protocols for determining this if there is wind. So I put something together that seems to work. I've only done one series of tests though. Unfortunately I've discovered that a flatish section of road with a steady grade may be even more difficult to find where I live than a windless day! I've used this on several people's TT files lately... which isn't the best way to use it, but if that is all you have it will give you a ballpark idea of your drag coefficient.
Anyway... ask questions, give it a try if you are interested, and let me know how it goes.
Updated 2013.06.29 with entrance and exit speed inputs to account for momentum.
http://www.whitemountainwheels.com/CdA_Calc_2013_06_29.xls
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You need a section of road with a consistent grade (~zero is best), where you can ride at a consistent power and speed. You'll do out-back runs over this segment and record average power and speed. Around 1 mile long is probably best, so you can have enough data points in each run and still do several "laps". If you have a GPS, it's easy to create these segments in Strava.
No traffic... unless you want to know how traffic effects your drag.
You need to be fully up to speed before you enter the segment. I recommend allowing at least .25 miles for this.
How hard should you go? Up to you. Power to overcome wind drag is porportional to speed ^3, so don't go too slow. If you wish you can make this an interval workout, or ride below FTP if you are tired. Varying your speed between runs can be instructive for looking at other variables, but that is more of an advanced topic.
Even though wind is allowed, it's best if the wind speed and direction are consistent during the runs. Also, strong winds are inherently more variable in their effect and will increase the variability of results.
Crr needs to be input. I assume a value of .004 (85F baseline) for the "good" tires (like Vittoria Corsas and Conti Supersonics) with latex tubes on nice pavement, and scale from there based on roller tests. Crummy pavement can increase Crr substantially. Also note that Crr is effected by temperature, and hot pavement can boost your tire temperature well above ambient. A ballpark guess for the temperature effect is ~0.8%/F... but don't worry if you are unable to measure it. So long as it isn't varying a lot during your runs, at least your numbers will be consistent. If you are trying to determine CdA on two different days when the tire temperature is likely to be very different, then you should consider it.
The Crr number also includes bearing friction, but if your bike is well maintained and adjusted, this should only be a few watts... around 10% or less of the total rolling resistance.
Environmental conditions can be found at a nearby airport, or other good weather station if no airport is near.
Regarding wind speed, at bike level the wind is usually < 50% of airport data and could be much less if the road is sheltered.
I assume an 8 watt drivetrain loss if you have a crank PM. This should be a good approximation for power >100W or so.
Pay attention to and keep track of the wind speed and wind direction (qualitatively at least). For each out-back you will input a guess for wind speed and direction. Even if you feel it was calm, don't input zero for the wind... start with at least 1 mph. It is also best to start with the wind guess not directly in line with your riding direction.
The calculation assumes that the wind was constant for each out-back, and adjusts wind speed (with angle fixed at your input), and then wind angle (with wind speed fixed at your input), so that the equations of motion are satisfied in both directions. If the calculated CdA for the out and back segments match, then you know it converged.
Unless you got lucky though, the CdAs for the two cases where wind speed and angle were adjusted will *not* be the same on your first try. You then have the choice of changing your guess for wind speed, wind angle, or both.
There is more than one "correct" solution for wind speed and direction and this will effect your calculated CdA a small amount, so make sure that both are realistic. For instance, say you end up with a 4 mph wind that is 45 deg from your direction of travel. An 8 mph wind that is closer to perpendicular would also solve the equations and result in a slightly different CdA number.
When all 4 calculated CdAs match and the wind speed and direction numbers look realistic, then you are done with that run.
Averaging more runs will reduce the random errors (the wind mostly)... I'd suggest at least 4 out-backs if you want a good number. Accuracy? Don't know yet. Even if all your inputs are perfect, the wind will still be variable, so it depends.
Yaw will effect your CdA so don't expect to get the same value if yaw changes significantly.
Anyway... ask questions, give it a try if you are interested, and let me know how it goes.
Updated 2013.06.29 with entrance and exit speed inputs to account for momentum.
http://www.whitemountainwheels.com/CdA_Calc_2013_06_29.xls
............................................
You need a section of road with a consistent grade (~zero is best), where you can ride at a consistent power and speed. You'll do out-back runs over this segment and record average power and speed. Around 1 mile long is probably best, so you can have enough data points in each run and still do several "laps". If you have a GPS, it's easy to create these segments in Strava.
No traffic... unless you want to know how traffic effects your drag.
You need to be fully up to speed before you enter the segment. I recommend allowing at least .25 miles for this.
How hard should you go? Up to you. Power to overcome wind drag is porportional to speed ^3, so don't go too slow. If you wish you can make this an interval workout, or ride below FTP if you are tired. Varying your speed between runs can be instructive for looking at other variables, but that is more of an advanced topic.
Even though wind is allowed, it's best if the wind speed and direction are consistent during the runs. Also, strong winds are inherently more variable in their effect and will increase the variability of results.
Crr needs to be input. I assume a value of .004 (85F baseline) for the "good" tires (like Vittoria Corsas and Conti Supersonics) with latex tubes on nice pavement, and scale from there based on roller tests. Crummy pavement can increase Crr substantially. Also note that Crr is effected by temperature, and hot pavement can boost your tire temperature well above ambient. A ballpark guess for the temperature effect is ~0.8%/F... but don't worry if you are unable to measure it. So long as it isn't varying a lot during your runs, at least your numbers will be consistent. If you are trying to determine CdA on two different days when the tire temperature is likely to be very different, then you should consider it.
The Crr number also includes bearing friction, but if your bike is well maintained and adjusted, this should only be a few watts... around 10% or less of the total rolling resistance.
Environmental conditions can be found at a nearby airport, or other good weather station if no airport is near.
Regarding wind speed, at bike level the wind is usually < 50% of airport data and could be much less if the road is sheltered.
I assume an 8 watt drivetrain loss if you have a crank PM. This should be a good approximation for power >100W or so.
Pay attention to and keep track of the wind speed and wind direction (qualitatively at least). For each out-back you will input a guess for wind speed and direction. Even if you feel it was calm, don't input zero for the wind... start with at least 1 mph. It is also best to start with the wind guess not directly in line with your riding direction.
The calculation assumes that the wind was constant for each out-back, and adjusts wind speed (with angle fixed at your input), and then wind angle (with wind speed fixed at your input), so that the equations of motion are satisfied in both directions. If the calculated CdA for the out and back segments match, then you know it converged.
Unless you got lucky though, the CdAs for the two cases where wind speed and angle were adjusted will *not* be the same on your first try. You then have the choice of changing your guess for wind speed, wind angle, or both.
There is more than one "correct" solution for wind speed and direction and this will effect your calculated CdA a small amount, so make sure that both are realistic. For instance, say you end up with a 4 mph wind that is 45 deg from your direction of travel. An 8 mph wind that is closer to perpendicular would also solve the equations and result in a slightly different CdA number.
When all 4 calculated CdAs match and the wind speed and direction numbers look realistic, then you are done with that run.
Averaging more runs will reduce the random errors (the wind mostly)... I'd suggest at least 4 out-backs if you want a good number. Accuracy? Don't know yet. Even if all your inputs are perfect, the wind will still be variable, so it depends.
Yaw will effect your CdA so don't expect to get the same value if yaw changes significantly.
