Sunday, November 15, 2009

Chung Spreadsheet - Better Acceleration Calculation

The CdAs I calculated for my road bike seemed a little lower than what I would have expected. After reading 106 miles on my Power Tap odometer yesterday for a Claxton Century course that was advertised as 104 miles, I figured the problem might be my PT odometer. I did a very accurate 3-revolution, weighted calibration of my PT wheel this morning and found the circumference to be dead on 2100 mm. I had had the PT programmed to 2098 mm. That means I'm going 2100/2098=1.00095 times as fast/far as I'd thought. Not only is that probably insignificant, it would LOWER my CdA calculations, not raise them. (A quick check revealed that my fastest CdA - when I was in the drops - was lowered by 0.001 m^2 by accounting for the PT circumference change). So I can scratch that as a significant source of error, although the fact that I picked up any change in CdA at all from a 0.095% change in speed is surprising - this method really does provide incredible data resolution).

Then I read Dr. Chung's comment on my last post: He noticed that I had used a simple approximation of acceleration in my Chung Method spreadsheet. To calculate acceleration, I used: change in velocity from T1 to T2 divided by the time interval a = (t2-t1)/dt.

That seemed correct to me. But he suggested I use a more robust approximation suggested by Adam Haile: a = (t2^2-t1^2)/(2*t2*(t2-t1))

As you can see in the highlighted columns in this screen shot of my spreadsheet, the two methods result in very similar, but differing, values of a.

It turns out those differences are enough to change my CdA calculations significantly. My road bike CdAs for hoods, horns, and drops changed from 0.310, 0.245, and 0.240 to 0.338, 0.258, and 0.255, respectively. Those numbers seem more realistic, although they are still lower than I would have guessed.

My Crr changed from 0.0054 to 0.0055 (a difference that is probably not within the resolution of the method).

I think I have everything ready now to do some baseline TT bike tests. Then I'll begin to tinker with my position and see what happens.