03 May 2015

Pythagoras and line of sight

The things I end up doing for this world. So, this happened earlier on today:

I was writing a scene where my main character (the so-called Chronicler) is looking out from a plateau to a sweeping vista below and, since he’s a smart guy, used to conversing with philosophers and mathematicians and explorers and cartographers, I figured he’d know how far the human eye can see on a level plain (or if not the actual distance, at least the means of calculating it.

Now I’m not much of a mathematician myself though I know enough of Pythagoras’ Theorem to be able to calculate this. Luckily my polar/equatorial/mean radius for Elyden have been in place for a while now (seethis post for more statistics for the world), and I could easily (or arbitrarily) calculate the other numbers needed – basically the height of the character and the height of his elevation (since he was on a plateau is reasoned that was 55.5 feet). A bit of tinkering with numbers, and some googling later and I found this.

s = sqrt (2rh + h^2)

I was able to calculate that characters of average height can see an average of 3.54 miles on a clear day, given no intervening terrain. This is more than the 2.9 miles for earth since Elyden is larger. So, all that work (and close to 30 minutes), for a throwaway line that will probably get removed in later edits. At least I have some more information to add to the Encyclopaedia!

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