Aero Torque/Watts to Spin

This aero torque topic has been on my list for a long time. I've tried many different ways of gaining insight into the deal over the years:

1) reported texas a&m wind tunnel motor measurements
2) srm power meter driving rear wheels in calm air
3) coast down of wheels in a truing stand with a fan blowing
4) srm power meter driving rear wheels with a fan blowing
5) srm power meter driving rear wheels while I stood in the bed of my pickup and my wife drove around at 30mph

more recently:

6) on a really windy day (30mph gusts) I did the srm power meter thing
7) monitoring the motor (that is used to spin the wheels) power during wheel/tire tests in the san diego wind tunnel
8) using all six force and moment component data from the wind tunnel balance during same test described in #7

I've found several independent references on the internets:

http://www.recumbents.com/WISIL/MartinDocs/Validation%20of%20a%20mathematical%20model%20for%20road%20cycling.pdf

estimated two wheels need additional 3-4 watts at 40kph 6-7 watts at 50kph

http://www.soton.ac.uk/~aijf197/Wheel%20Aerodynamics/Results%20and%20Discussion.htm

estimated one wheel to need additional 5-9 watts at 40kph

http://journals.pepublishing.com/content/g1463815454723l0/

estimated a single wheel requires more than listed above (research funded by a wheel manufacturer)

There also used to be a thesis from the same university as the latter link above that included CFD work here:

http://ir.canterbury.ac.nz/handle/10092/1800

(research funded by a wheel manufacturer)

But they have since removed the document until October of 2010. The first time I followed the thesis link in maybe December of 2008, I was able to download, save, and read the paper and the rotational watts are similar to what was reported above – though, they include wind tunnel measurements (translational/rotational) for the zipp 808 and hed three spoke. The manner in which these researchers gathered their rotational power data is clever (the motor they use to spin the wheel in the tunnel is mounted on a force platform that monitors things), and does not use the data acquired from a six component balance.

Based on my SRM tinkerings, I’ve really not been able to discern more than a few watt difference between wheels – independent of whether or not there is ambient wind present (and the numbers on the plot below include drivetrain losses):



This past time in the tunnel, I made the mental commitment to reduce the wind tunnel force and moment data in such a way that it not only reflected the translational resistive force, but also the aerodynamic torque – or “watts to spin”.

I won’t bore you with math and whatnot related to how I independently approached this topic using force/moment wind tunnel data (I'm not the sharpest tool in the shed, so I reckon it took me quite a bit longer to figure this one out compared to the big dawgs at the wheel company's - and I probably stuffed something up along the way :-0 ), but it seems as if the rotational watts can account for a chunk of the whole "fastest wheel" deal. For an estimate on the magnitude I came up with you might want to check out the insider's forum for discussion/further insight.

I’m not sure what to make of this independent finding. It’s encouraging that one is able to use force and moment data to repeatably measure this aerodynamic torque value and this fact will more than likely prompt me to investigate wheels that are different than the three spoke and the 1080 in the future. I would expect wheels like the HED 90 and 808 and shallower rim/longer spoke wheels to get rotationally bad at a relatively faster rate.

So, maybe the data here:

http://journals.pepublishing.com/content/g1463815454723l0/

Is on target?