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Hexagon Dimensions http://wargame.ch/board/nwc/viewtopic.php?f=5&t=16092 
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Author:  Geoff McCarty [ Wed Oct 17, 2018 9:15 am ] 
Post subject:  Hexagon Dimensions 
https://en.wikipedia.org/wiki/Hexagon https://rechneronline.de/pi/hexagon.php Consider 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 2rank 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? 
Author:  Christian Hecht [ Wed Oct 17, 2018 2:45 pm ] 
Post subject:  Re: Hexagon Dimensions 
Geoff McCarty wrote: What do you think about the hexagon dimensions? They are fancy? Really what's the point about this, is it movement rates, fire casualties, global warming or what? 
Author:  Geoff McCarty [ Wed Oct 17, 2018 3:28 pm ] 
Post subject:  Re: Hexagon Dimensions 
>he doesn't dream about hex porn It is some idea I was kicking around. Could model closer firing distances and further travel distances as I stated. I plan on using it to validate scenario parameters. Normally I had thought of the opposing adjacent lines as 21.13m further back from these hex positions so that they were 100m wide and 100m parallel to each other. I never thought of the angular differences of travel and how that may help specifications. Geometry isn't my strong suit. I don't believe the distance between points of symmetrically placed lines on the short diagonal edge of a hexagon would be twice the the hexside length. Believe the image below is actually the correct dimensions. Not as great a deviation as I hoped for. 
Author:  Christian Hecht [ Wed Oct 17, 2018 6:30 pm ] 
Post subject:  Re: Hexagon Dimensions 
I'm not sure you get anywhere if you try to bring pure logic & math to an abstract system of hexes, turns, etc.. Modeling firing distances in this engine? Well turn of the OR "Optional Fire Results" to have less average results, by this you get more high or low results that could stand for a variety of factors including small/large distance of units in bordering hexes. 
Author:  Geoff McCarty [ Wed Oct 17, 2018 6:58 pm ] 
Post subject:  Re: Hexagon Dimensions 
Every good game should be logical. The best games are card and tabletop classics which are built on totally logical sets of rules despite their representations being total facade. If I'm interested in reducing variations of unit placement, distance between firing units, unit density, and length of travel than I don't see what increasing the variation of firing results might add. It's worth considering though. A 20 digit rand(time) range is better for hit chance resolution than 'damage' I believe so, I prefer OFR on. I'd really like wilder melee resolution except the attack/defense ranges are 80 and 120 digits respectively. That guarantees silly outcomes no matter how the equation is solved at the fire effect end so, OMR is generally better for gameplay and plenty wild. The skewed effect of the optional resolution results presents less abstraction and better simulation overall. 
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