Before I bungle the math

[Merc465]

Has anyone already crunched the numbers regarding the square kilometrage or hectarage for the planetery mapping units in the T5 "Traveller Mapping System" (TMS) for the different sized hexes?

DIAM. MAPPING UNIT SQ.KM HECTARES
100m "100m" Hex ? ?
1 km Single Hex ? ?
10 km Local Hex ? ?
100 km Terrain Hex ? ?
1000 km World Hex ? ?

 

[Ulsyus]

If my maths is right, and W is the width of the hex from one straight side to another, the area should be...

(3^0.5/2)*W²

If that's correct then:

1000km hex = 866,025km²
100km hex = 8,660km²

...and so on. Gross error check anyone?

 

[pendragonman]

Area A of a hexagon:

A=3^(3/2) divided by 2 times the side length squared. You have the square root of 3 in your formula.

So a hex with a side length of 1000 km is ~2,600,000 km squared

And 100 km side length is ~25980.76 km squared

 

[aramis]

If my maths is right, and W is the width of the hex from one straight side to another, the area should be...

(3^0.5/2)*W²

should be
(3^1.5)/(2*W²)
per Pendragonman's notes.

 

[OjnoTheRed]

World Hexes are 1000km from side-to-side; divide that by the square root of three to get the length of each of the six sides of the hex.

To help develop the World Mapping generator for T5 (see link in my signature block) I crunched the numbers for all 20 world sizes to see how much of an approximation this was.

It turns out that dividing world radius for each size (PI * World Size * 1,610) by the number of hex-widths at the equator gives 1,010km for each hex from side-to-side consistently. Good enough to round to 1,000 km for me.

 

[Ulsyus]

Area A of a hexagon:

A=3^(3/2) divided by 2 times the side length squared. You have the square root of 3 in your formula.

Yeah, I was using the width of the hex, not the length of one of its sides, as the variable. I did that based on the idea of the hexes generally being measured across-wise and not normally having their side lengths determined in world-building.