How big is a hex?

[hcobb]

The problem with ITL 55 is that it treats the Megahex as being 3.33 as long as the underlying hex when it is actually only 2.5 times as long. This 33 percent error is compounded at every step up.

[swampthing]

Originally Posted by hcobb

The problem with ITL 55 is that it treats the Megahex as being 3.33 as long as the underlying hex when it is actually only 2.5 times as long.

How do you figure? It quotes 4 feet for a hex, and 3 yards (9 feet) for a megahex. 9/4 is 2.25, not 3.33.

I make the center-to-center distance between two adjacent megahexes to be about 10.6 feet (two 4-foot hexes over, plus one more up at an angle), which is about 2.65 times as much as a hex.

[hcobb]

I have a detailed table showing the error on page ITL 55 here:

https://www.hcobb.com/tft/Megahex_scale.html

[David Bofinger]

Originally Posted by hcobb

I have a detailed table showing the error on page ITL 55 here:

https://www.hcobb.com/tft/Megahex_scale.html

Yes, but your ratio 2.5 is also wrong. I don't know where you got it from but the correct ratio is the square root of 7. We can prove this either by coordinate geometry or just by noticing that the area scales up by a factor of 7 each time so the linear ratio must be the square root of that. The hex size sequence, with a bit of rounding, should be:

• hex "combat": 4 feet
• megahex "labyrinth": 10 feet or 11 feet or 3.5 yards (it's actually about 10.6 feet)
• megamegahex "village": 10 yards
• mega^3hex "town": 25 yards
• mega^4hex, between "town" and "city": 65 yards
• mega^5hex, between "city" and "county": 175 yards
• mega^6hex, bit larger than "county": 1/4 mile
• mega^7hex, close to "barony": 2/3 mile
• mega^8hex, bit larger than "duchy": 2 miles
• mega^9hex "province": 5 miles

Which nicely takes us to the scale of the Elyntia map, telling us Elyntia is mapped in megamegamegamegamegamegamegamegamegahexes, rather than megamegamegamegamegamegamegamegahexes as RAW would claim. :-)

It is, incidentally, weird that a barony is larger than a county.

Should we care about larger hexes then we have:

• mega^10hex: 13 miles
• mega^11hex: 35 miles
• mega^12hex: 90 miles
• mega^13hex: 235 miles
• mega^14hex: 625 miles

Which should be enough even for Cidri cartographers.

[hcobb]

Area increases by 7, but you're not on a 45 degree angle, so it's not sqrt(7) distance. (Note that the coordinate system rotates on each step.)

[BobP]

Did anyone notice that the Pocket Box maps are not 1" hexes? They're 15/16" hexes ... a wee compromise to still fit everything onto the sheet.

[FireHorse]

Geometry is purty.

5 Layers of Hexes. So this could be Combat at the smallest and City at the largest, or City at the smallest and Province at the largest. Or any other five consecutive layers of zoom.