Slope example

This slope system seems pretty straightforward to me, but since I've been doing this sample area, and will continue doing it as I get into the next major stage of this river-building project, I might as well work out the details on the slope.

For ease of reference, here is the map again:

Oh, look at me...I just now realized that when I started this river project, I set this map at 20 miles per hex, but when I worked out my rough slope system, I went with 24 mile hexes as standard.  Okay, no big deal.  I'll lop off about 20% of each increment.

I'll start from the lower end of the rivers and work my way up, going in the opposite order to how I worked out the total flow of water.  First, the small river to the west:

hex	die roll type	result	elevation
0212	d4	1	0
0111	d4	4	160
0110	d4	3	240
0109	d4	2	240

I used hex 0212 as my baseline, even though it isn't really a coast.  Whenever I decide to extend this map to the coast, I'll work out the elevations to sea level and find 0212's true elevation, and then add that amount to the other hexes of the river.  The same goes for this other river, with 0912 as the baseline:

hex	die roll type	result	elevation
0912	d4	4	160
0911	d4	3	240
0811	d4	1	240
0810	d4	4	400
0809	d4	3	480
0708	d4	2	480

That gets us up to the convergence point.  Now for the western branch:

hex	die roll type	result	elevation
0608	d4	1	480
0607	d4	2	480
0507	d4	1	480
0407	d4	3	560
0306	d4	2	560
0206	d4	1	560
0105	d4	1	560
0104	d6	1	560
0103	d8	1	560

And the eastern branch:

hex	die roll type	result	elevation
0707	d4	3	560
0706	d4	3	640
0705	d4	1	640
0704	d4	1	640
0604	d4	2	640
0603	d4	2	640
0602	d6	6	1040
0601	d8	4	1200

So now we just have to go back and work out the slope using the general formula (change in elevation)/(change in horizontal distance), keeping in mind that a 20 mile hex has (20*5280 = 105,600) horizontal feet.  For that matter, since we're using discrete increments, we don't even have to calculate the slope on each hex individually; every roll of 3 is an elevation increase of 100 feet, resulting in a slope of (80/105,600 = 0.0007).  We could just add this to the slope table I published last post.  Also, since we need a non-zero slope in order for the water to flow, I'm putting some fairly negligible numbers for the negligible elevation change results:

Die Roll	Slope
1	0.0001
2	0.0003
3	0.0007
4	0.0015
5	0.002
6	0.004
7	0.006
8	0.01
9	0.02
10	0.03
11	0.04
12	0.05
13	0.08

Now, this results in our river sections looking like this:

hex	die roll type	result	elevation	slope
0212	d4	1	0	0.0001
0111	d4	4	160	0.0015
0110	d4	3	240	0.0007
0109	d4	2	240	0.0003
0912	d4	4	160	0.0015
0911	d4	3	240	0.0007
0811	d4	1	240	0.0001
0810	d4	4	400	0.0015
0809	d4	3	480	0.0007
0708	d4	2	480	0.0003
0608	d4	1	480	0.0001
0607	d4	2	480	0.0003
0507	d4	1	480	0.0001
0407	d4	3	560	0.0007
0306	d4	2	560	0.0003
0206	d4	1	560	0.0001
0105	d4	1	560	0.0001
0104	d6	1	560	0.0001
0103	d8	1	560	0.0001
0707	d4	3	560	0.0007
0706	d4	3	640	0.0007
0705	d4	1	640	0.0001
0704	d4	1	640	0.0001
0604	d4	2	640	0.0003
0603	d4	2	640	0.0003
0602	d6	6	1040	0.004
0601	d8	4	1200	0.0015

If you're using some other system for determining elevations of your hexes, you'll have to do the math to work out the slope values. Still, it's not that hard...change in elevation, divided by change in horizontal distance.  If you're getting numbers that don't look anything like what I have on this table, you might want to check your math, or else realize your world is craggy and rugged as all get out.