Aw, shucks. Your reaction was exactly mine when I first thought about this, but of course it is true - unless you increase the air pressure, water molecules (at a slim 18 AMU or so) displace N[sub]2[/sub] and O[sub]2[/sub] at 28-32 AMU or so.
I don’t understand what you mean when you say this. You did all your calculations as if you were at sea level, so why would your actual altitude come into the equation?
Humidity is a vital component of calculating density altitude, a life-and-death operation for pilots (especially in the mountains).
This Canadian pilot page has a calculator for density altitude. At 60 degrees F and 30 inches Hg, the difference between 10% humidity and 90% humidity at sea level is about 180 feet. That is, at 90% humidity you have as much air under your wings at sea level as you would have at 180 feet when there is only 10% humidity. Not a huge difference, but worth paying attention to if your life depends on it.
A-ha! A question right up my alley, as a cyclist and geek. Unfortunately, it has not crossed my motivation level to calculate actual numbers by hand. Fortunately, I don’t have to, I can rely on other people as they are always 100% accurate.
This page contains a calculator for times & speeds on a bicycle, taking all the relevant factors I can think of into account - except humidity. Fortunately, from my density altitude calculations, I know the effect! Plugging in identical numbers except one at 0 altitude and one at 180 feet altitude, I get a difference of about 0.25% in speed/time. For a one-hour ride, that’s a difference of 9 seconds. For a 30 minute ride, that’s a difference of 4.5 seconds.
This is definitely a factor, albeit a small one. From this year’s time-trial world championships - from the Results page:
[gold] 1. 3 HONCHAR Serhiy UKR 56:21.75
[silver] 2. 13 RICH Michael GER 56:31.95 + 10.19
[bronze] 3. 8 BODROGI Laszlo HUN 56:45.77 + 24.01
4. 5 BOARDMAN Chris GBR 57:38.08 + 1:16.32
5. 1 OLANO Abraham ESP 57:50.13 + 1:28.37
Note that the top 3 were separated by 10-15 seconds each. Granted 90% to 10% humidity is something that is not likely to happen between a morning time-trial and an afternoon time-trial, but it could be a small factor. Note that even the slightest headwind would be a bigger factor.
Does anyone have any numbers for rolling resistance? It could certainly be a bigger factor, but I just don’t know. Any takers?