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Um... I'd like to know how far across, one side to the opposite side, is an exploration hex.
According to Ultimate Campaign p. 154 "Each hex... is 12 miles across from corner to corner... an area just under 95 square miles."
Okay, that sounds like each side of the hex is 12 miles long. Unfortunately, per the math on Hexagon Wikipedia, Paizo's math doesn't work.
I expect there is something wrong with my assumptions.
I'm the GM and I'm planning for the party to travel to a distant city exploring the map on the way. To get the distance right, and I'm ok with approximately, I need to know how far it is across each hex.
Thanks!
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12 miles is the distance between opposite corners, making each side 6 miles long, for an area of about 93.5 square miles.
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1) Ultimate Campaign says a hex is 12 miles corner to corner, not 12 miles flat-to-flat.
2) From Wikipidia: "The longest diagonals of a regular hexagon, connecting diametrically opposite vertices, are twice the length of one side."
3) Because that long diagonal is 12 miles, the length of one side (t) is 6 miles.
4) From Wikipedia: The area (A) of a regular hexagon of side length t is given by A = 2.598 * t^2 = 93.528 square miles, which the book rounds off to "just under 95."
5) From Wikipedia: Another alternative formula for the area if only the flat-to-flat distance, d, is known, is given by A = .866 * d^2.
6) From 4 and 5 we can determine that
A = 93.528 = .866 * d^2
108 = d^2
d is therefore approximately 10.4.
So the flat-to-flat distance across each hex is 10.4 miles.
Favoriting all the posts that contain people doing math for me =)
10.5 Miles across. Cool. Thank you very much!
Or just ten miles if you want a number that's very easy to multiply by. (30 hexes are 300 miles, not 315 or 312 if you're a sticker for accuracy).
1) Ultimate Campaign says a hex is 12 miles corner to corner, not 12 miles flat-to-flat.
2) From Wikipidia: "The longest diagonals of a regular hexagon, connecting diametrically opposite vertices, are twice the length of one side."
3) Because that long diagonal is 12 miles, the length of one side (t) is 6 miles.
4) From Wikipedia: The area (A) of a regular hexagon of side length t is given by A = 2.598 * t^2 = 93.528 square miles, which the book rounds off to "just under 95."
5) From Wikipedia: Another alternative formula for the area if only the flat-to-flat distance, d, is known, is given by A = .866 * d^2.
6) From 4 and 5 we can determine that
A = 93.528 = .866 * d^2
108 = d^2
d is therefore approximately 10.4.So the flat-to-flat distance across each hex is 10.4 miles.
This is why he designs games for a living and I just play them...
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This is why he designs games for a living and I just play them...
Chemistry major, almost a math minor. I'm a multiclassed nerd. :p
One thing which came into my mind the first time I read the exploration rules:
The avarage (KM) Group will have horses at level 2-3, so they will explore each field within one day (by foot 2 days avarage).
For me this is a little bit fast (95 square miles!) if I think of dense forests or mountains. Did I miss something? (Example: Washington DC has 68 square miles, can you explore it (including caves/cellar etc. within one day)?
The alternative is that the players will spend months of game time exploring each hex, which seems,.... uncinematic.
Why in the name of all that is holy would you base the hex size on something that doesn't correlate to the movement rates for overland travel in your own game??? This hex size makes absolutely zero sense. 12 miles center to center, now that would make sense, though 6 miles center to center would be better.
One thing which came into my mind the first time I read the exploration rules:
The avarage (KM) Group will have horses at level 2-3, so they will explore each field within one day (by foot 2 days avarage).For me this is a little bit fast (95 square miles!) if I think of dense forests or mountains. Did I miss something? (Example: Washington DC has 68 square miles, can you explore it (including caves/cellar etc. within one day)?
Exploration isn't in-depth investigation. It's more "quick overview". I haven't fully crunched the numbers, but the basic premise of the exploration rules is that you wander around the hex (presumably efficiently) until you've seen all of it - which might just be "hey, I think there's a cave in that cliff-face!" or "huh, smoke, probably a village over there...", and the players get to choose what they actually investigate, which takes extra time.
Personally, I would have preferred exploration times measured in hours, like the travel-through times: it would have allowed more scope for working out what happens when players interrupt their explorations to investigate something in detail.
Why in the name of all that is holy would you base the hex size on something that doesn't correlate to the movement rates for overland travel in your own game??? This hex size makes absolutely zero sense. 12 miles center to center, now that would make sense, though 6 miles center to center would be better.
Good question, really, and I suspect the answer is "because near as damnit it makes no difference" with a side-order of "it makes hex-sides a nice round number in length". Remember that exploration tends to happen in trackless wilderness, which even on plains means you only move at 3/4 normal distance. At speed 30, that means you can expect to cover no more than 18 miles on plains in a day. So to traverse a plains hex face-to-face takes 4 hours 40 minutes and vertex-to-vertex takes 5 hours 20 minutes. That's an average of 5 hours. Using the larger hex size, face-to-face takes 5 hours 20 minutes, and vertex-to-vertex takes 6 hours 13 minutes, which averages to the horribly untidy 5 hours, 46 minutes, 40 seconds (which I guess you'd round up to 6 hours).
I'll have a play with all of the numbers later, see if the results are overall tidier one way or the other.