Friday, November 13, 2009

Chung Method Aerodynamic Testing

I've always wanted my own wind tunnel. Now I sort of have one.

A couple of years ago I read Robert Chung's presentation, "Estimating CdA with a Power Meter," on aerodynamic testing using nothing more than a known road profile, internet weather info, a bathroom scale, and a power meter.

I remember finding it interesting at the time; but I didn't follow up because I didn't have a power meter on my TT bike. And I didn't really care what my CdA was on my road bike.

A few weeks ago, I read about Colin Griffiths's recent Chung testing in the UK. I now have a Power Tap wheel that I can easily move to my Cervelo TT bike, so re-enter Chung testing.

Basically, Robert Chung took the equation for all the forces acting on a rider: power, air drag (CdA), rolling resistance (Crr), and gravity:

w = wrr + wPE + wKE + waero
w = Crr m v g + s m v g + a m v + CdA ρ vair 2v / 2

and he solved the equation for slope:

s = w/(m g v) – Crr – a/g – (ρ CdA v2)/(2 m g)

Then he used slope and known horizontal position at each time interval to build a virtual profile (using a spreadsheet). By adjusting values of CdA and Crr until the virtual profile matches the real world profile, you are able to solve for both.

Lucky for me, I'm an engineer and a surveyor (lucky in this example, anyway - most of the time I'd rather be a rocket scientist or the base player for the Stones). And lucky for me, a few years ago I designed and staked out a new subdivision street about a mile from my house, so I know the EXACT profile of the road. And lucky for me, the developer has barely sold a single lot in the subdivision, so there is ZERO traffic. And lucky for me, the profile is a perfect U shape with cul-de-sacs at each end so that I can turn around at both ends without touching the brakes. And lastly, the road is very well protected by tall pines, reducing any minor breezes that might interfere with my results.

So as a test run, today I Chung-tested my Tarmac, and I got perfect results. Here's the procedure:

  • Get on the web and get the temperature, pressure, and humidity for the test location.

  • Dress for riding and weigh yourself with your bike, bottles, everything.

  • Ride a known profile (really all you need to know is the elevations of the high points and low points).

  • Keep EXACTLY the same position on the bike for the duration of the test.

  • Do not ever touch the brakes - the formula can't account for deceleration due to braking).

  • Record several runs over/through the known profile.

  • Return home and record weight and weather data again and average start/finish numbers.

  • Set up a spreadsheet to plot a virtual profile of your course using the Chung Method.

  • Adjust the CdA and Crr until you get a constant amplitude and crest height.

  • Here's a screen shot of the spreadsheet I created to do all of this. Download it from my eSnips account if you want a copy.

    It worked like a charm. I did three runs of the course in each of three different positions: 1 - on the hoods; 2 - on the "horns" (hands wrapped around the tops of my Shimano shifters and elbows sort of low; and 3 - in the drops.

    I did a trial-and-error adjustment the CdAs for all three positions to get an almost perfect and consistent profile. What little profile variation I saw was likely due to a very light breeze or hitting a rock in the road. A little tweaking of the Crr (rolling resistance coefficient) got the amplitudes right.

    Here's what it looked like when I was done. Remember, this is a VIRTUAL profile. It's not measured elevations, it's calculated elevations assuming all the different forces on the rider. It looks to be so accurate and precise that I could literally use it to perform asbuilt surveys on finished roadways (Causey will find that idea intriguing, I think).

    The fact that it worked is cool enough. But now comes the fun part: using the new technique to play around with different positions and equipment on my TT bike.

    I also learned something very interesting and useful that I will use while training and racing on the road bike. I've always wondered how much more aerodynamic it was to ride in the drops as compared to on the horns. On the horns is so much more comfortable and seems more powerful, too. I turns out that my CdA on the horns is a LOT lower than on the hoods (somewhat expected), and only very slightly less aero than riding in the drops (I was surprised the difference was so little).

    So there will be no more training or riding in the drops for me. The almost immeasurable benefit isn't worth the more aggressive, less comfortable position. I'll just ride on the horns. I guess I'll only use the drops for standing and sprinting.


    Colin Griffiths said...

    I'm glad to read that you've started testing, I could do with a bit of help. Your first results are a lot better than mine were, I had a lot of "getting my head around it" to do before I got anything usefully consistent. If only your street was a bit closer to Leicester! It seems like a perfect venue.

    Robert said...


    Very nice. Glad it's working out for you. While googling around a while back I found your badger3 spreadsheet.

    1. I think you're plotting elevation in feet, not meters, and the x-axis doesn't appear to be distance. Nonetheless, I'm guessing your venue has maybe a 4.5 to 5% slope?

    2. You may want to use the refined version of the acceleration calculation rather than dv/dt. Also, I don't have any experience with the new PT's but I wonder if you couldn't just get away with assuming 1 sec intervals.

    3. Speaking of surveying, you know Coggan's 1 km "flat" road? I think he found a consistent 20cm dip on it.

    Robert Jordan said...

    You are correct, sir - thanks for pointing out those problems. When I converted everything from meters to feet, I forgot to update the chart y axis. And the x axis was row number in my spreadsheet instead of feet - all that's fixed now. The long steep slope is actually 7.78%. That gives me lots of speed on the way down and very little aero resistance on the way back up, which allows me to better separate CdA from Crr.

    I will search for the refined version of the acceleration calculation.

    When I export the PT data from WKO+, the time increments are 1.02 seconds, 1.02 seconds, 0.96 seconds, repeat. Strange because I understand that PT collects data every 1.26 seconds.

    Funny you mention Coggan's flat road. I have suspicions that the grading contractor might have missed the elevations by a foot or two on the road I designed and staked, so I plan to resurvey it to be sure. Eliminate unknowns whereever you can, right.

    Last thing - I suspect my bike odometer might be measuring long by as much as 1%. If that's true (I plan to recalibrate it), it would raise my CdAs a little, which would seem more realistic.

    Thanks again for the input.

    Robert said...

    I will search for the refined version of the acceleration calculation.

    When I export the PT data from WKO+, the time increments are 1.02 seconds, 1.02 seconds, 0.96 seconds, repeat. Strange because I understand that PT collects data every 1.26 seconds.

    As you can see, speed measurement is used both to derive v and also a. If tire circumference is off, it affects both. The 1.02 and 0.96 time intervals are puzzling -- I had presumed you were using one of the newer ANT+ PT's and hadn't gone through WKO+ but rather used Poweragent or something else.

    The acceleration correction doesn't make a big difference but as long as you're looking for precision you might as well try. Adam Haile originally noticed that estimating a with (delta v)/(delta t) has a slight bias when "true" a changes sign when speed is reported for the preceding interval. He proposed a=diff(v^2)/(2*v*timeinterval). An alternative is a=diff(v,2)/(2*timeint) but they give essentially the same VE over every interval I've looked at.

    I'd be very interested if you ever re-survey that road and find out that the contractor was off. That'd be cool.