https://en.wikipedia.org/wiki/Hexagonhttps://rechneronline.de/pi/hexagon.phpConsider the following image: If the soldiers are assembled in a 100m line on the short diagonal edge of a hexagon firing at an adjacent opposing line of soldiers the distance between forces point to point (equal to hexside length) is only 57.74m. If each file of a 100m line were a pace or 75cm apart 133.33 men could fit in a rank. 399.99 men could fit in a 3 rank line. The distance between moving from one short diagonal in a hexgrid to a symmetrical position in an adjacent hexagon is 115.47m (long diagonal distance) which would be the integer of every additional hexagon ranging from a firing point (hexside + long diagonal). Range 2 fire would be 173.21m, 3 would be 288.68m, etc.

If the distance between opposing soldiers point to point is increased from 57.74m to 100m then the linear distance of the short diagonal edge will be 173.21m. At one pace per file 230.95 men could fit in each rank and 692.85 in a three rank line. The distance of moving between hexagons would be 200m. The distance between a firing point 2 hexes away would be 300m, range 3 at 500m, etc. I like these patterns alot better than the first example.

If the point to point adjacent hex firing distance were 75m then the short diagonal edge is 129.9m. 173.2 men per rank and 519.6 men could fit in a three rank line at this scale. The long diagonal distance between hexes is 150m. At range 2 225m, range 3 375m, etc.

The firing resolution distances assume that the opposing forces are facing each other though. I'm leading up to dropping 2-rank line and skirmisher nonsense in order to better simulate light infantry. A central aligned short diagonal formation is more natural but, this forward offset allows for increased distances beyond adjacent positions. It is also how the isometric sprites are displayed. What do you think about the hexagon dimensions?