Charlie, two full tenths is low 9.70s, not low 9.60s. Which did you mean?
While I know Mureika’s calculator is not always highly regarded here, it puts Bolt at 9.80 with no wind, and 9.71 with +1.9m/s, with no change to the altitude. I was skeptical of the calculator until I read through how it works, and now I think it does a pretty good job. It has a few problems (not all of them are mentioned here, some are part of further discussion):
-It requires you to enter an altitude, which it then uses to calculate a “corrected time”. If you want to know what it thinks someone would have run on the same track with a different wind (which is what I did for the numbers above), you have to play guess & test a little bit.
-It assumes a the same drag ratio for all runners, which isn’t true. Not everyone’s body shape is the same, and, the heavier someone is, the less of an effect drag becomes. These assumptions are not that significant.
See Canadian Journal of Physics 79, 697-713 (2001) at http://arxiv.org/pdf/physics/0007042v1.
The mathematical model produced, based on race data from 88OG, 97WC, and 99WC, gives the following splits for a 9.85 runner.
0.15
1.71
1.04
0.93
0.88
0.86
0.85
0.84
0.85
0.86
0.88
9.85
Something else that Charlie didn’t mention is that the effect of wind is stronger for headwinds than it is for tailwinds. Since the drag (force from wind) is proportional to the square of the difference in speeds (the speed of air that the runner actually feels), this results in a bigger change for headwinds.
Example (forgive me for getting technical here): At some point Bolt will be running at 12m/s. Consider the wind speeds of -2, 0, and +2. At -2, he will feel a 14m/s wind. At 0, he feels a 12m/s wind, and at +2, he feels a 10m/s wind.
Since the drag force is proportional the square of the speed:
-2m/s gives 14m/s, which gives 196
+0m/s gives 12m/s, which gives 144
+2m/s gives 10m/s, which gives 100
So, in normal wind we get 144.
This increases to 196 at +2m/s, which is a 36.1% increase in wind drag.
This decreases to 144 at -2m/s, which is a 30.6% decrease in wind drag.