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Old 05-25-2009, 06:38 PM   #15 (permalink)
Ernie Rogers
Ernie Rogers
 
Join Date: Feb 2008
Location: Pleasant Grove, Utah
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Recalculated Crr for head wind

The last time, I analyzed Darin's coast-down data on the assumption that he described a tailwind. The results suggested too much friction in the drive train, and I assumed the cause was a misunderstanding on the wind direction. I repeated the calculation assuming a headwind instead.

With a headwind that adds to aero drag, it became necessary to include a drag term in the analysis, and that imposed guessing some parameters about the car. Here are the ones I used--

Frontal area = 19.5 sq.ft.
Cd = 0.32
Car weight = 2,000 lb
I used a "constant" headwind, the RMS of wind speed (6 mph at 22.5 deg = 5.5 mph) and the reported max air speed (11.5 mph + 5.5 mph) = 12.6 mph RMS. Here are the results, Crr versus tire pressure--

P___________Crr_
20............0.01348 (extra digits are carried for fitting to formula)
25............0.01188
30............0.01086
35............0.01015
40............0.00957
45............0.00919
50............0.00889
55............0.00863

These Crr values very closely fit the following formula--

Crr = .0059 + 0.15 /P

It's amazing to me that only the constant term changed in considering a head wind instead of a tail wind. I don't know the physical significance of the constant term, except that it does incorporate friction of drive train components which would not change with tire pressure.

If one guesses that the constant term is due entirely to actions outside the tire, then you get an eye-popping Crr for the tire only of 0.0033 at 45 psi.

Note to the casual observer: A coast-down test doesn't produce significant heat in the tire (I think) so low-pressure results can be somewhat higher (because the tire is cooler) than in a measurement at normal tire speed.

Ernie Rogers

Quote:
Originally Posted by Ernie Rogers View Post
Darin had two sets of data at his web site. I graphed the numbers for the first case (the Metro), then curve-fit them by eye and studied the results.

It appears from his description that the tests may have had a tail wind close to equalling the average speed in this coast-down test. If so, the aero drag is close to zero and only rolling resistance stopped the car. For the case of no wind, the rolling resistance coefficient is equal to the average slope of the road. Here are the Crr numbers I got for pressures from 20 psi to 55 psi--

20............0.0147
25............0.0131
30............0.0121
35............0.0114
40............0.0108
45............0.0104
50............0.0101
55............0.0099

These Crr values very closely fit the following formula--

Crr = .0071 + 0.15 /P

Ohh, my! Maybe I had the wind in the wrong direction. I can do that calculation but maybe someone else would like a turn.

Ernie Rogers

Last edited by Ernie Rogers; 05-27-2009 at 01:52 AM..
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