Wednesday, January 31, 2018

New River Spreadsheet and a Note on Meanders

Ok, I said I'd make a spreadsheet to figure out the velocity of floodwaters, so here it is:

https://drive.google.com/open?id=1ywgbsL2LDHmilJcopdpemxe4GkGTVJMf

It's just a quick and dirty calculation, assuming a triangular river cross-section, and absolutely not taking into account that the slope of the riverbed at its normal height and the slope of the adjacent area might not be the same, but it'll get you close enough for game purposes.

Note that if you already know the width, depth, and slope of a river, you can use the flood calculation pages to work out the velocity; just fill in the yellow areas and the green area will be your output.  It doesn't even have to be a flooded river, just any flowing water with known parameters.  The other cells in the spreadsheet are really just intermediate calculations that I didn't bother hiding.  It's just easier that way.  Besides, this calculation is a lot more straightforward than the first two pages, so a couple of unimportant but visible cells isn't going to busy up the spreadsheet too bad.

All that said, I was going to write a post working out all the details of meandering rivers.  Meanders follow certain mathematical rules, and knowing them can help you draw more realistic rivers.  But I'm not going to, because this guy has already done it.  Thanks, Dave Richeson.

Monday, January 29, 2018

Entrenchment

Entrenchment is the last major characteristic in the Rosgen classification system. It is expressed as a ratio, giving the new width of the river if it were to be twice as deep as normal (as might happen in a 50-100 year flood).  This, not coincidentally, helps describe the immediate area surrounding the river.


The lower the entrenchment number, the deeper the river is cut into the landscape.  The higher the number, the more it lies along the general surface, spreading wider during a flood event. 

 For example, in our sample river map we've been following for the last several posts, the river in hex 0306 is ~90 feet deep, ~1950 feet across, and is type F, which is a deeply entrenched river type.  We find the entrenchment ratio is 1.2, so during a major flood event, the river in hex 0306 will be (90x2 = 180) 180 feet deep and (1950x1.2 = 2340) 2340 feet across.  The velocity should also be recalculated...I guess I should add a flood page to the spreadsheet.

Looking closer at this info we just found, you can see that if you move directly away from the river (perpendicularly), assuming that the river spreads equally to the left and right as the floodwaters rise, the land rises 90 feet (the added flood depth) in the course of 195 feet (half the added width of the floodwaters), giving the land there a slope of (90/195 = .46) .46, a very steep grade.  Tributaries flowing into the river here could easily be type Aa+ (remember that this river type isn't randomly generated in this system), although if they run in at an oblique enough angle the steep slope might be mitigated.  Also, characters will have an extra hard time crossing the river here.  As steep as the slope is, there probably isn't a road running down to the river, so no ferries or bridges either; if they have to get across the river right here, it'll mean a climb down to the river, a long swim, and then a climb back up on the other side.

Also worth mentioning, a 50 year flood, by definition, has a 2% chance of occurring in any given year, and a 100 year flood has a 1% chance.  Therefore, if you are using an annual events table to shape your campaign, there should be a 1-2% chance of needing to use the entrenchment ratio each game year...

This is the last addition to the river generation table, which is as follows:

 
Die Roll Slope DA C E F D B G A Aa+
1 0.0001 x x x x x


placed as needed
2 0.0003 x x x x x



3 0.0007 x x x x x



4 0.0015 x x x x x



5 0.002 x x x x x



6 0.004 x x x x x



7 0.006
x x x x



8 0.01
x x x x



9 0.02



x x x

10 0.03



x x x

11 0.04




x
12 0.05






x
13 0.08






x












Sinuosity 1 Min 1.4* Min 1.5* Min 1.4* 1 Min1.2* Min 1.2* 1.0 – 1.2 1.0 – 1.1

WDR 2d20 (d10x2)+12 d12 (d10x2)+12 (d10x4)+40 (d10x2)+12 d12 d12 d12

Entrench. >2.2** >2.2** >2.2** (d4/10)+1 1 (d8/10)+1.4 (d4/10)+1 (d4/10)+1 (d4/10)+1






















* For these river types, roll 1-6 d6, divide by 10, and add 1, for a total of 1.1 to 4.6.  If this result falls under the minimum listed, use the minimum instead.
** These river types are associated with floodplains. If obvious floodplain boundaries (hills, mountains, etc) are apparent on the map, the river will fill that area during a 50-100 year flood. If boundaries are not apparent for whatever reason, the entrenchment ratio can be simulated by rolling an “exploding” d6 (ie, if a 6 is rolled on d6, keep it and add another d6, continuing to add d6s as long as 6s are rolled), dividing by 10, and adding to 2.2 (or (d6X/10)+2.2)

Thursday, January 25, 2018

River Sample take 2

In the original river sample I ran, I used 50 inches of rain as the average per hex, which is a little on the high side.  In US terms, only the deep South and Pacific Northwest get that much in a year.  Thirty inches is the national average, and closer to Europe's average annual rainfall as well (although still a little high).  With that in mind, here is the river data with 30 inches of rain per hex.

hex flow slope river type wdr sinuousity adjusted slope depth width velocity
0109 93600 0.0003 D 60 1 0.0003 25.7 1542.7 4.7
0110 156000 0.0007 E 7 1.6 0.00044 65.5 458.5 10.4
0111 234000 0.0015 DA 20 1 0.0015 40.5 810.5 14.2
0212 280800 0.0001 DA 23 1 0.0001 68 1572 5.2










0601 93600 0.0015 D 76 1 0.0015 17.4 1322.4 8.1
0602 234000 0.004 C 28 2.7 0.00148 35.8 1002 13
0603 390000 0.0003 C 20 2.1 0.00014 49.7 994.4 15.8
0604 577200 0.0003 C 16 3.1 0.000097 103.4 1653.9 6.8
0704 702000 0.0001 E 12 2.6 0.000038 147.9 1775.3 5.3
0705 795600 0.0001 E 5 1.5 0.000067 196.5 982.7 8.2
0706 873600 0.0007 E 9 2.1 0.00033 119.6 1076.2 13.6
0707 951600 0.0007 C 14 1.7 0.00041 100.1 1401.4 13.6










0103 187200 0.0001 C 16 3.1 0.000032 83.4 1334.9 3.4
0104 249600 0.0001 DA 23 1 0.0001 65 1504 5
0105 312000 0.0001 DA 34 1 0.0001 61.4 2088.3 4.9
0206 374400 0.0001 F 14 3.3 0.00003 115.2 1612.8 4
0306 405600 0.0003 F 22 1.9 0.00016 73.1 1608.2 6.9
0407 499200 0.0007 C 20 2.2 0.00032 71.9 1438.6 9.6
0507 530400 0.0001 C 28 2.3 0.000043 94.4 2644.4 4.2
0607 546000 0.0003 E 6 3.3 0.00009 150 900 8.1
0608 592800 0.0001 C 28 1.8 0.00005 95.7 2680.1 4.6










0708 1638000 0.0003 F 24 1.7 0.00018 116.8 2803.1 10
0809 1716000 0.0007 DA 33 1 0.0007 81 2695 15.5
0810 1825200 0.0015 F 22 2.8 0.00054 102.3 2250.3 15.9
0811 1965600 0.0001 DA 13 1 0.0001 176 2287 9.7
0911 2028000 0.0007 C 14 2.6 0.00027 143.8 2012.9 14
0912 2137200 0.0015 DA 27 1 0.0015 83 2240 23

These are still pretty deep and wide, supporting my earlier observation that, on a 20 mile-per-hex map at least, if a river is marked, it is a major obstacle.  Bridges, ferries, or magic are needed to get across. 

Sunday, January 21, 2018

Sample River Update

Going back to the sample river I've used to illustrate my thinking throughout this river project...



I'm going to start with this small river to the west.  So far, we know this much:

hex flow slope
0109 156000 0.0003
0110 260000 0.0007
0111 390000 0.0015
0212 468000 0.0001

None of the slopes dictate a river type for any of these hexes, and there are no terrain types that suggest a river type, so I'll roll randomly from among the possible types (DA, C, E, F, and D), and then determine the width-to-depth ratio and adjust the slope value due to sinuousity for each hex.

hex flow slope river type wdr sinuousity adjusted slope
0109 156000 0.0003 E 7 1.6 0.00048
0110 260000 0.0007 D 60 1 0.0007
0111 390000 0.0015 DA 20 1 0.0015
0212 468000 0.0001 DA 23 1 0.0001

So, we can see already that this river is going to go from a relatively narrow, deep river to a wider, shallower river and dropping a bunch of sediment.  I might have to go back and change this; it doesn't make much sense to drop sediment with the slope increasing.  If anything the river should speed up and erode more. For now we'll press forward and run these values through the spreadsheet.  Since I didn't work out every possible WDR outcome for the spreadsheet, I've just used the average of the results for WDR 22 and 24 to find the results for WDR 23 in hex 0212.  For what it's worth, the only significant difference it made was in the width.

hex flow slope river type wdr sinuousity adjusted slope depth width velocity
0109 156000 0.0003 E 7 1.6 0.00019 76.9 536.7 7.6
0110 260000 0.0007 D 60 1 0.0007 32.2 1930.6 8.4
0111 390000 0.0015 DA 20 1 0.0015 49.1 981.6 16.2
0212 468000 0.0001 DA 23 1 0.0001 82.9 1904.8 5.9

Looking at these final results, I'm going to go back and switch river types between hexes 0109 and 0110.  If the river speeds up, as it does here, there's no way for it to drop its sediment and form a type D stream in hex 0110.  Switching the two river types then gives us:
 
hex flow slope river type wdr sinuousity adjusted slope depth width velocity
0109 156000 0.0003 D 60 1 0.0003 31.1 1868.4 5.4
0110 260000 0.0007 E 7 1.6 0.00044 79.3 555.3 11.8
0111 390000 0.0015 DA 20 1 0.0015 49.1 981.6 16.2
0212 468000 0.0001 DA 23 1 0.0001 82.9 1904.8 5.9

All right then, moving on, here is the other major river, with its two main tributaries broken out separately as before.  At this point, I have two observations: 1) type D rivers show up more often than they should, given the circumstances required for their formation (you should either move them to a better position as I did for the small river above or just reroll the river type if type D comes up in an inappropriate spot); and 2) if you have a river marked on a 20 mile hex map, its probably impassable without a boat or a bridge.

hex flow slope river type wdr sinuousity adjusted slope depth width velocity
0601 156000 0.0015 D 76 1 0.0015 21 1601.7 9.2
0602 390000 0.004 C 28 2.7 0.00148 43.3 1213.7 15.1
0603 650000 0.0003 C 20 2.1 0.00014 92.7 1854.6 7.6
0604 962000 0.0003 C 16 3.1 0.000097 125.2 2003.1 7.8
0704 1170000 0.0001 E 12 2.6 0.000038 179.2 2150.1 6.1
0705 1326000 0.0001 E 5 1.5 0.000067 238 1190.1 9.4
0706 1456000 0.0007 E 9 2.1 0.00033 144.8 1303.5 15.4
0707 1586000 0.0007 C 14 1.7 0.00041 121.2 1697.3 15.4










0103 312000 0.0001 C 16 3.1 0.000032 101 1616.7 3.8
0104 416000 0.0001 DA 23 1 0.0001 79.3 1822.5 5.8
0105 520000 0.0001 DA 34 1 0.0001 74.3 2529.2 5.5
0206 624000 0.0001 F 14 3.3 0.00003 139.5 1953.4 4.6
0306 676000 0.0003 F 22 1.9 0.00016 88.5 1947.8 7.8
0407 832000 0.0007 C 20 2.2 0.00032 87.1 1742.3 11
0507 884000 0.0001 C 28 2.3 0.000043 114.3 3202.7 4.8
0607 910000 0.0003 E 6 3.3 0.00009 181.7 1090 9.2
0608 988000 0.0001 C 28 1.8 0.00005 115.9 3246 5.3










0708 2730000 0.0003 F 24 1.7 0.00018 141.5 3394.9 11.4
0809 2860000 0.0007 DA 33 1 0.0007 99 3266 17.7
0810 3042000 0.0015 F 22 2.8 0.00054 123.9 2725.5 18
0811 3276000 0.0001 DA 13 1 0.0001 213.6 2770.6 11.1
0911 3380000 0.0007 C 14 2.6 0.00027 174.1 2437.9 15.9
0912 3562000 0.0015 DA 27 1 0.0015 100.5 2712.2 26.2

Well, this is a pretty broad river by the time we get to the lower reaches on this map. Right around a half mile across.  This table was made using 50 inches of rain annually in each hex, which is kind of on the high side, apparently.  I'll recalculate all this with 30 inches of annual rain and see what difference it makes, leaving the river types and slopes unchanged.  But I'll do that in a later post...this one has waited too long as it is.

Wednesday, January 17, 2018

Excuses excuses

Well, between the holidays, out of town travel, a bout of the Captain Trips, and weather that's been too cold for normal life in this drafty old house, I haven't done anything here for a while.  That's not too unusual, I guess, since I tend to work pretty slowly churning out posts, but in this case I've worked zero for several weeks.  I'm getting back on it (although the house is still drafty, and it is still too cold for comfort), and should have a real post fairly soon.