Chicagoist Takes On...Ask Tom
By Margaret Lyons in News on Jul 12, 2004 4:41PM
Chicagoist loves the Ask Tom Why column in the Tribune, where people write in 'weather' questions and meteorologists answer them. (Tom gets a little help from the weather crew.) In general the questions don't need to be answered by a weather expert; they just need to be answered by someone who's relatively well informed or who can look things up in an encyclopedia. For example, it turns out people don't know what a 40 percent chance of rain is, so they ask Tom. We're glad he helps out with stuff like that.
Every so often, though, we can get our geek on. For example, how far away is the horizon? Oh. Oh, yes. Oh sweet and velvety geometry. Tom says that you should multiply the square root of your height by 1.3 to get the distance to the horizon. Other sources say multiply by 1.17. Wanna do a little math? Do we ever!
The earth is a circle with radius r = 6378.1 kilometers, or 3963.1676 miles, or 20,925,524.9 feet. Your distance from the center of the earth is r + h, where h is your height (well, the height of your eyes). The horizons distance from the center of the earth is r. So we have a triangle, with legs r, r + h, and d, where d is the distance from your eyes to the horizon. (Help, I'm a visual learner.) We all remember that the angle drawn by a tangent line and radius is a right angle, so we luckily have a right triangle. Still with us? So fun. Nothing gets the juices flowing on a Monday like a little Pythagorean theorem. Yum.
So boiling down the hoohah, we get d = sqrt[(r + h)^2 r^2]. Were going to assume that h << r, so we simplify to d = sqrt[2rh], which we simplify further to say d = 6469.239 x sqrt[h] in feet. So with the conversion...it works out...to...wait, hang on...um, OK. Converting from feet to miles, that works out to 1.223 x sqrt[h] miles. We're going to chalk these differences up to refraction. Nerd alert.