Hack’s Hardcore Hints #5: Locating Hexes on Master Maps
In Hack’s Hardcore Hints series, David Galster shares some of his scenario design toolkits for Campaign Series: Vietnam, a work-in-progress tactical platoon-scale wargame.
It’s a pleasure, Campaign Series Wargamers,
If you read the article about the Master Map Concept, you may have wondered what method can be used to accurately place overlays in separate, unconnected parts of the map. Here is an explanation of the method I’ve been using.
Map Coordinate Systems
A Master Map must first be set up in either a geographic coordinate system, or Military Grid Reference System, MGRS. Since the Vietnam topo maps all have MGRS grids, I’ll show how it is done that way. The MGRS grids use in rectangular, (x, y) coordinates, while geographic coordinates use degrees latitude and longitude. A method for geographic coordinates exists, but the calculations are more complex.
A reference point for the entire Master Map must first be established. This defines an MGRS reference coordinate, and a corresponding hex coordinate for the CS Map.
With a set of reference coordinates, the process to find a hex coordinate for another MGRS coordinate can be accomplished. The MGRS coordinates usually used are the two digit number shown on topographical maps. These represent the easting, or x coordinate, and northing, or y coordinate, and the units are kilometers.
For example, a reference MGRS coordinate might be 6960 or x= 69 km and y= 60 km, and the reference hex number (118, 29). If another point is given, where another overlay is to be positioned, then the differences in x and y can be easily found. Let’s say that we want to locate a hex number for MGRS 7262. Then we find the differencs such that Δx = 72 – 69 = 3 and Δy = 62- 60 = 2. These can be converted to hex differences because a hex = 250 m. In the vertical direction there are 4 hexes to the kilometer and in the horizontal, 4.619. The reason for this difference is the interlocking of hexes when going from hex to hex in the horizontal direction. (Divide 4 by cosine 30° = 4.619.)
So the hex deltas are Δx = 3*4.619 = 13.856 and the Δy = 2*4 = 8. So the new hex coordinate is reference plus deltas: nx = 118+13.856 = 131.856, and ny = 29 – 8 = 21.
The new hex coordinate is (132, 21). The subtraction is because vertical hexes are numbered increasing downward, while MGRS are increasing upward. If you were trying to accurately place an overlay, you would not go directly in the center of hex (132, 21) but slightly to left of center, since the computed coordinate is a little less than 132.
This can be more conveniently done with an EXCEL spreadsheet and here is an example:
The values are all in column D and labels, symbols, and units to the left. The upper portion is for inputs and the lower for calculations. Once the reference hex and MGRS coordinates are entered, then the target MGRS values are entered in the yellow field.
The calculation section determines the delta distances in kilometers, and then determines the targe hex coordinates, in the blue highlighted fields. Because of the zig-zag of hexagon positions, the vertical values are different depending on whether the horizontal hex coordinate is even or odd. But regardless the center is where the decimals are all zero.
The EXCEL spreadsheet for this may be downloaded here.
Here is a screenshot of the overlay that was positioned based on this calculation:
Overlay Positioned by new Hex Coordinate (132, 21)
I hope this gives you a method you can use for making accurate Master Maps.
Well, CS Wargamers, until next time . . .