Tuesday, September 12, 2017

Rivers: Where the water goes and where it doesn't

Last time I had worked out that an inch of annual rainfall on a square mile translates into 1.5 cubic feet per minute of runoff all year on average.  So where does this runoff go?

Well, downhill obviously, and most wide-area maps show mountains and oceans, so obviously it ends up running into rivers and flowing to the ocean.  Wherever a river is shown on a map is by default the lowest spot in the immediate area, but even hexes without rivers marked will have creeks, streams, rivulets, and rills draining the excess rainfall out of the lowest point in the hex and toward the ocean.

If water flows toward the lowest point, then it follows that water flows away from the highest points.  The line connecting the highest points in an area (of whatever size, from a square foot to a continent) is the local divide.  The divide can run along a mountain ridge, a line of hills, or simply an area of slightly higher ground on otherwise flat terrain.  All rain falling in an area bounded by divides will flow eventually into the same body of water; this is the watershed.


Three watersheds, separated by divides running along mountains and hills



Using what we know about rainfall and the flow of water from higher to lower elevations, we can now work out the total flow of water in a river.  This will define the amount of water that flows past a given point in the river each minute, but doesn't show whether it is a wide, slow river or a narrow, cascading one.  We'll worry about that detail later...for now, we'll look at the total flow.

For simplicity's sake, I'm going to assume all the hexes on the following map receive the same amount of rainfall...let's say 50" per year.  Obviously when using an actual campaign map, forest gets more rain than grassland (although our 50" falls within both temperate forest and grassland), which gets more than desert.  For terrain types not specified in the last post, use an approximation based on the surrounding terrain; a bare, rocky mountain rising from the midst of a steaming jungle will probably get as much rain as the surrounding jungle.  An oasis in the desert probably gets no more rain than the desert itself (most are fed by groundwater).  A mountain hex serving as a divide might get more rain on one side than on the other, due to the rain shadow effect, and this will affect the water drainage on each side.


We know each square mile gets 50" of rain, and since each inch of annual rain translates to 1.5 cubic feet of flow per minute, we have a flow rate of 75 cubic feet per minute for each square mile on our map.  Let's say each hex is 20 miles across, but how many square miles are in a 20 mile hex? 

I've found a super easy link to help with that: https://rechneronline.de/pi/hexagon.php Whatever hex size you choose (20 miles in this case), input that into the "short diagonal" or d2 window (notice d2 goes across the hex from one face to the opposite face...exactly the distance we use in RPG mapping).  For a 20 mile hex we get 346 square miles, and that means we get 26000 cubic feet per minute of water flow per hex, rounding off because we're not interested in making this math any crazier than we have to. 

Ok, this next part is a little tedious.  Now we add up the total flow for each river hex. So for the furthest north branch of this river (hex 0601), we'll have the hexes to the north (0500, 0600, 0700) flow into it.  0400 looks like it would flow into 0500, so we'll add that too; same goes for 0800 flowing into 0700.  Lastly, the rainfall running off of 0601 itself will end up in the river in 0601, so we have six hexes worth of flow.  Since we're using the same rainfall for all hexes, it's going to amount to 156,000 cubic feet of water per minute flowing out of 0601.

Similarly, 0602 will have 0200 flowing into 0300, which flows into 0401, which flows into 0501, which finally flows into 0602.  This is mirrored on the other side with 0701 through 1000.  The rain running off 0602 ends up in the river.  Lastly, all the water in the river at 0601 ends up here, for a total of 390,000 cubic feet per minute. 

For hex 0603, we do the same thing (I vastly oversimplified this water flow, just running in parallel lines of hexes like this...for greater realism and more satisfying detail, there should be low spots that local area hexes drain into, which then drains into the river).  In this case, since there is another branch of the river to the west, some of the hexes that would otherwise have ended up here instead drain towards the other branch.

Here is a table summing up the drainage area feeding each hex and the total water flow.  For each entry, if a river hex feeds into another river hex, I marked it in red, so I'd remember to add the river's total flow instead of counting it as another hex of rainfall runoff.  I ended this table before hex 0708, as that hex is fed by both branches of the river.

0601
0400, 0500, 0600, 0601, 0700, 0800
156,000
0602
0200, 0300, 0401, 0501, 0601, 0602, 0701, 0801, 0900, 1000
390,000
0603
0301, 0402, 0502, 0602, 0603, 0702, 0802, 0901, 1001, 1100, 1200
650,000
0604
0403, 0404, 0405, 0503, 0504, 0603, 0604, 0703, 0803, 0902, 1002, 1101, 1201
962,000
0704
0505, 0604, 0605, 0704, 0804, 0903, 1003, 1102, 1202
1,170,000
0705
0606, 0704, 0805, 0904, 1004, 1103, 1203
1,326,000
0706
0705, 0806, 0905, 1005, 1104, 1204
1,456,000
0707
0706, 0807, 0906, 1006, 1105, 1205
1,586,000

 And the same deal for that western branch.  You can see some of the drainage patterns get a little thrown off by the bends in the river:

0103
0000, 0001, 0002, 0003, 0100, 0101, 0102, 0103, 0201, 0202, 0203, 0302
312,000
0104
0004, 0103, 0104, 0204, 0303
416,000
0105
0005, 0104, 0105, 0205, 0304
520,000
0206
0006, 0105, 0106, 0206, 0305
624,000
0306
0206, 0207, 0306
676,000
0407
0007, 0107, 0208, 0306, 0307, 0406, 0407
832,000
0507
0407, 0506, 0507
884,000
0607
0507, 0607
910,000
0608
0408, 0508, 0607, 0608
988,000

And now the lower reaches of this river, after the two branches meet up:

0708
0608, 0707, 0708, 0808, 0907, 1007, 1106, 1206
2,730,000
0809
0708, 0809, 0908, 1008, 1107, 1207
2,860,000
0810
0609, 0709, 0809, 0810, 0909, 1009, 1108, 1208
3,042,000
0811
0409, 0509, 0610, 0710, 0810, 0811, 0910, 1010, 1109, 1209
3,276,000
0911
0811, 0911, 1011, 1110, 1210
3,380,000
0912
0611, 0711, 0812, 0911, 0912, 1012, 1111, 1211
3,562,000

If you looked closely, you probably noticed that I didn't get all the hexes in there.  I decided it was all too regular and patterned (even though I was going for a simple illustration), and decided to add another small river in the west.  Here's the new map, and the chart for the new river:





 

0109
0008, 0009, 0108, 0109, 0209, 0308
156,000
0110
0010, 0109, 0110, 0210, 0309
260,000
0111
0011, 0110, 0111, 0211, 0310, 0410
390,000
0212
0111, 0311, 0411, 0510
468,000


All right...all done here.  Now we know the total flow in these rivers for each hex, but like I said earlier, that doesn't tell us whether the river is narrow, shallow, and fast or wide, deep, and slow, or somewhere in between.  This gives us a start, though, and once I tease apart the effects of the slope of the riverbed, we'll be well on our way to getting a clear picture of these rivers.

Tuesday, August 8, 2017

The Care and Feeding of Rivers

In 1804, noted Quest-Giver (and President of the United States) Thomas Jefferson sent Meriwether Lewis and William Clark on a hexcrawl to find a water route across North America to the Pacific Ocean.  Along the way, they had to portage their boats around rapids, and eventually cache them, moving forward in smaller canoes more suited to shallower water.  Eventually, they had to leave these as well, traveling overland across the continental divide until reaching a river on the other side deep enough to float a canoe in.

I have rarely (as in, "never that I can remember") seen a published adventure or RPG supplement which dealt with the changing nature of a river as you travel up or downstream, with varying currents, depth, and hazards.  For the most part, in an RPG, a river is a blue line on a map, and any interpretation of what that blue line means is left to a GM's personal experience.  For me as a teenager, that meant a blue line on a game map meant a body of water that was too deep and wide to cross without a bridge except by very strong and unencumbered swimmers, navigable by ocean-going ships, and potentially hiding giant water monsters of some sort.

A river
Of course, even then I knew there were other kinds of rivers, but I had no kind of feel for how a given river might vary from what I considered "the norm".  Heck, even now, I have a few generic fall-backs  that don't really cover the full range of possibilities for a river, and don't necessarily reflect reality all that well.  So I'm doing something about it.

A river
First, a river has to be fed by rainfall.  We can infer how much rain falls in a given area from the vegetation found there.  We're kind of reversing cause and effect here, but I've never seen an RPG map start with rainfall levels and just kind of imply that a forest exists in this area from there.  We work with the tools we have.

A river

Working off of this table (and converting units to imperial units, because metrics just doesn't say "fantasy", also rounding roughly for simplicity's sake):

We get the following for inches of rain per year:

 
Tundra 0-40
Cold Desert 0-10
Hot Desert 0-20
Grasslands 20-55
Shrublands 20-55
Savannah 20-55
Thorn Forest 20-55
Boreal Forest 15-50
Temperate Forest 25-95
Temperate Rainforest 75-100
Tropical Dry Forest 50-100
Tropical Montane Forest 100-140
Tropical Rainforest 100-180

Now, about 2/3 of this water will return to the atmosphere as vapor, from direct evaporation into the air or transpiration as a result of plant photosynthesis.  The rest of it is absorbed into the ground (where it slowly flows and returns to the surface as springs) or runs off into streams.  An inch of rain on one square mile of land produces 2,323,340 cubic feet of water, so each inch of annual rainfall translates into about 1.5 cubic feet of water per minute flowing off of each square mile of land year round (again, majorly simplifying).

And this is about as far as I've gotten.  The Dungeoneer's Survival Guide has some flow velocities based on the slope of the stream, and I originally considered this might be good enough to work with, since knowing total flow and flow velocity will give you the numbers you need to work out the size of the stream.  For example, if you know you have 1000 cubic feet of water flowing each minute, and you know it's flowing at 20 feet per minute, you can easily see that the stream will have a cross section of 50 square feet.  While I was trying to figure out how to structure that cross section (is it 5' deep and 10 across? 2 deep and 25 across?  deeper?  shallower?), I came across a discussion of water flow that showed that velocity is based on slope *and* cross section...a wide, shallow stream will move slower than a deeper one of the same cross-sectional area.  While I could ignore this, and it might not even matter for small rivers that only drain a couple dozen hexes, I'm afraid that really long rivers like the Streel River of the Known World/Mystara would end up ridiculously deep and wide as they flowed slowly through plains and marsh in the final few miles to the ocean.  Like miles wide.

So I'm looking into some numbers, trying to come up with a simpler solution for RPG rivers than applying Manning's equation with its fractional exponents to every hex.  I'll be back later.

Sunday, July 9, 2017

Parnax the Mighty

Inspired by Joseph Manola's hexcrawl In the Shadow of the Great Machine.
http://udan-adan.blogspot.com/2017/07/in-shadow-of-great-machine-hexcrawl.html

A crazed outcast, Parnax the Mighty has exposed himself to uncontrolled energies of the Great Machine in order to turn himself into a superman.  His results have been very mixed.

Parnax's plan was to give himself a powerful physique to match his unparalleled intellect and magical prowess.  He is now of prodigious size, but his musculature and skeletal structure have not quite kept up. His elephantine bulk requires him to move about on all fours, taking a full round to shift into a sitting position to cast spells.  Returning to all fours for movement takes no time.  If an arm or leg is injured, his movement rate is reduced by 1/2; if two limbs are injured, he is barely mobile, effectively immobile for tactical purposes.

Additionally, his tremendous bulk causes him to take double damage from falls, taking 1d6 damage even if he trips, although this might be hard to pull off given his four-limbed gait.

DCC Stats: Init -1; Atk fist +7 melee (1d8+8); AC 15; HD 10d8; hp 53; MV 30’; Act 1d20 or 2d20 (when spell casting); SP spell casting as level 7 Wizard, melee crits use Giant table; SV Fort +7, Ref +1, Will +4; AL C.

Thursday, June 29, 2017

Examples for NPC Corruption

I don't know if my original posts about how to do this are clear enough, so here's a few walk-throughs.

I'm making a level 8 wizard as the main villain for an adventure.  I have no strong theme for him that would suggest a series of linked mutations, so I'm going to corrupt him randomly.  His spell list is as follows: Runic Alphabet, Mortal; Sleep; Color Spray; Patron Bond (King of Elfland), and therefore Invoke Patron (King of Elfland); Choking Cloud; Nythuul's Porcupine Coat; ESP; Breathe Life; Dispel Magic; Lokerimon's Orderly Assistance; and Control Ice.  I roll an 86 on Table I, resulting in 22 failed rolls. 

The first failed casting I roll up is Control Ice.  At this point it's obvious that if you wanted more accurate detail you could develop the system so that the first few failures are 1st level spells, with the 4th level failures only coming in towards the end of the list, but this is good enough to suit me.  At any rate, rolling on the results for a spell check of 1 for Control Ice, I get a 4, which is a misfire.  Nothing of lasting interest.

Next, I roll up Sleep, and roll a 3 on Sleep's chart, resulting in another misfire.

Next is Patron Bond.  This results in automatic patron taint, so rolling on that table I get a 3.  This wizard becomes aloof and indifferent to mortal concerns.  This is no big deal, so I'll let it ride.  The wizard loses 1 Personality and I move on.

The next roll turns out to be a misfire, but after that a failed Color Spray leads to the caster having his skin changed to a rainbow pattern.  That attracts a little too much attention, so I use one of my (8/2) 4 bonus Luck points to ignore that.  The very next roll is a failed Lokerimon's Orderly Assistance, resulting in the caster becoming overly helpful to anyone who asks unless he passes a Will check.  That makes for a very poor villain, so I use another bonus Luck point to nix that.

Twenty two failures is a lot to detail, but I go on in this manner, throwing out a good many of the failures because they were simple misfires, spending bonus Luck to eliminate a few particularly bad corruptions/taints, and having to deal with the rest.  At the end of it all, this wizard has an aloof and indifferent manner (-1 Personality), horrid pustules on his face (-1 Personality), becomes withdrawn from mortal concerns (the same patron taint a second time, and another -1 Personality), shimmery sheen to his skin which has a green tone (two separate results), painful lesions and sores, flesh that flows and reforms on his legs, and a longing for Elfland.  Now he's nicely weird, as a level 8 wizard should be.


Later, the characters are looking for a wizard in town to sell some weird magic reagents to, and he seems like he'll be a recurring NPC, so I stat him up quickly.  Using the quicker method from part 2 of this series of posts, I roll a 78 for a level 5 wizard, giving this guy 5 failures.  Since I'm using Table II, these are all corruption or patron taint, and I don't have to deal with misfires. 

This guy's spell list is Charm Person, Magic Shield, Ekim's Mystical Mask, Flaming Hands, Ventriloquism, Shatter, Detect Invisible, and Write Magic.

The first failure is Ekim's Mystical Mask.  I roll a 3 on the corruption table (this guy has no patron, so no patron taint), and find that he's taken to wearing hoods or masks in order to not reveal his true face.

The second failure is the same.  No point worrying about it now...even if I had spent Luck on it before, he'd have to deal with it again.

Next is a failed Flaming Hands, resulting in a -2 on spell checks for any cold based magic.  Since he has no cold based magic, this is nothing to worry about.

I still have two more failures to roll, and two bonus Luck points to spend, so I'm done. 


Lastly, the PCs encounter a group of bandits with a wizard among the leadership.  This is another 5th level guy, and I don't want to spend a lot of time on detailing him, so using the quickest method, I roll a 95, or 7 failures.  I'm spending my two bonus Luck points to knock this right down to five failures.

First failure is 1 Minor, with a result of 7, chills.  Next is 6 Greater with a result of 3, bull head.  Next is Minor, painful lesions; Major, deep blue skin; and lastly Minor, hair falls out.  Quick and dirty, but done in about a minute. 

NPC Wizard Corruption, Part II

That last method of determining wizard corruption can take a while, especially as the wizard's level goes up.  That can take way too long to do at the table for those wizards who are rolled up as a random encounter.  Here is a couple of quicker methods.

Table II is used for these methods.  It is similar to Table I except that it excludes misfires from the results (I estimated that about half of failures result in a misfire...this may not be 100% accurate, but it's eyeball close.)

Table II
#failures Level 2 Level 3 Level 4 Level 5 Level 6 Level 7 #failures Level 8 Level 9 Level 10
0 01-60 01-28 01-10 01-03 01 0


1 61-91 29-64 11-34 04-13 02-04 01 1

2 92-99 65-87 35-61 14-32 05-12 02-03 2 01

3 00 88-96 62-81 33-54 13-26 04-09 3 02
4 97-99 82-92 55-73 27-44 10-19 4 03-06 01
5
00 93-97 74-86 45-62 20-33 5 07-13 02-04 01
6
98-99 87-94 63-76 34-49 6 14-23 05-08 02
7
00 95-98 77-87 50-64 7 24-35 09-14 03-04
8
99 88-93 65-76 8 36-49 15-23 05-08
9

00 94-97 77-86 9 50-62 24-34 09-13
10



98-99 87-92 10 63-74 35-46 14-21
11

00 93-96 11 75-83 47-57 22-30
12

97-98 12 84-90 58-69 31-41
13

99 13 91-94 70-78 42-52
14


00 14 95-97 79-86 53-62
15





15 98 87-91 63-72
16



16 99 92-95 73-80
17



17 00 96-97 81-86
18



18 98 87-91
19



19 99 92-94
20





20
00 95-97






21 98






22 99






23 00


Quicker Method:
  • Roll on Table II for the number of spell failures that resulted in corruption or patron taint.
  • Subtract the wizard's Luck bonus from the number of spell failures (negative Luck bonus results in more corruptions).
  •  Approximately 1/3 of the remaining failures will be patron taint.  Randomly determine a spell from the wizard's spell list and roll on its corruption results table (or use the appropriate patron taint table).
  • Luck can be burned to avoid corruption effects as usual.  As an option, the Judge can allow up to 1/2 the wizard's level in bonus Luck to avoid corruption.

Quickest Method (use for minor characters):
  • Roll on Table II for the  number of spell failures that resulted in corruption or patron taint.
  •  Subtract the wizard's Luck bonus from the number of spell failures (negative Luck bonus results in more corruptions).  
  •  Luck can be burned to avoid corruption effects as usual.  As an option, the Judge can allow up to 1/2 the wizard's level in bonus Luck to avoid corruption.
  •  Roll remaining corruption results on the the generic tables (1-3 Minor; 4-5 Major; 6 Greater).

NPC Wizard Corruption in DCC

Well, I won't be winning any awards for regularity in posting...

It occurred to me that there is no system in place for determining corruption for NPC wizards in DCC.  Judges running a hexcrawl with wandering monster checks could roll up an NPC wizard in any of several ways (master of a random castle, member of a bandit gang or pirate crew, etc), and whether that wizard has any lingering corruption from his dealings in magic depends largely on how creative (or lazy) the Judge is on the fly.  But that's just not good enough for me...if there are numbers to crunch, I have to crunch them.

So, it seems to me that the average number of XP gained in an encounter is 2, not simply because the possible outcomes range from 0-4, but also due the dangers involved.  A character who only ever deals with 0XP encounters won't gain any levels, but those who only ever deal with 4XP encounters (generally involving fatalities) are unlikely to live long enough to gain many. 

I further estimate that a wizard will cast about one spell per encounter.  Easy encounters might not need any spellcasting, and desperately dangerous ones might require more than one, but given that, in many cases, spell effects from one casting can carry over into multiple encounters, one spell per encounter doesn't sound too far off.  Summoned creatures can hang around for quite a while, charmed characters will stay charmed for at least a day with a spell check of 14+, etc.  Also, wizards can use magic items without gaining corruption (usually).

Given these estimates, a wizard who goes from level 1 to level 2 has had on average (50-10)/2=20 encounters and cast 20 spells, each with a 1 in 20 chance of a spell fumble.  There's a good chance that he'll get away without any corruption, and a vanishingly small chance that he'll end up with 20 corruptions.  Without going into all the mathematical details, this is a pretty standard binomial distribution, and working out the percentages isn't all that difficult.  Table I shows the range of possible spell fumbles experienced by wizards of different levels, expressed in percentile terms.


 Table I
#failures Level 2 Level 3 Level 4 Level 5 Level 6 Level 7 Level 8 Level 9 Level 10 #failures
0 01-36 01-08 01



0
1 37-74 09-28 02-06 01



1
2 75-93 29-54 07-17 02-03



2
3 94-99 55-76 18-34 04-08 01



3
4 00 77-90 35-53 09-17 02-03


4
5
91-96 54-71 18-30 04-07 01


5
6
97-99 72-84 31-45 08-13 02

6
7
00 85-92 46-60 14-22 03-04

7
8
93-97 61-73 23-33 05-08 01

8
9

98-99 74-83 34-46 09-14 02
9
10

00 84-90 47-59 15-22 03-04

10
11

91-94 60-71 23-31 05-07 01
11
12

95-97 72-81 32-42 08-11 02
12
13


98-99 82-88 43-53 12-17 03 13
14


00 89-93 54-64 18-21 04-05 14
15



94-96 65-74 22-30 06-08 01 15
16



97-98 75-82 31-40 09-12 02 16
17



99 83-88 41-50 13-17 03 17
18



00 89-93 51-60 18-23 04-05 18
19



94-96 61-69 24-30 06-07 19
20




97-98 70-77 31-38 08-10 20






99 78-83 39-47 11-14 21






00 84-88 48-56 15-19 22






89-92 57-64 20-25 23






93-95 65-72 26-32 24







96-97 73-79 33-40 25







98 80-85 41-48 26







99 86-90 49-56 27







00 91-94 57-64 28







95-96 65-72 29








97 73-78 30








98 79-84 31








99 85-87 32








00 88-90 33








91-92 34









93-94 35









95-96 36









97 37









98 38









99 39









00 40


 At this point, you need to randomly determine which spell from the caster's spell list was being cast when the failure occurred.  Roll on that spell's table for a spellcheck of 1 to figure out whether that failure ended up with corruption, patron taint, a misfire, or all three.  (Misfires are so fleeting in effect that we're not generally concerned with them here.)  Don't forget the effects of Luck, not only on the chances of a misfire instead of corruption, but also burning a point of Luck to avoid a corruption effect.  As an option, the Judge can allow the NPC wizard a few points of additional Luck only for the purposes of avoiding corruption and patron taint; this should probably not be more than about half the wizard's level, or only the highest level wizards will ever be corrupted.  At any rate, the Judge must decide for the wizard whether to burn Luck to avoid this corruption before moving on to the next corruption roll.


Tuesday, May 16, 2017

One Page Dungeon: Underworld Turf War

I meant to post this forever ago, and for whatever reason just never did.  Well, here is my 2017 One Page Dungeon Contest entry.  I went mapless this go-round.  It's an underground city with mazy streets, easy to get lost in, and until your characters have been around to a few landmarks enough to know their way, they're basically wandering randomly.

Due to the "no OGL" rule for this year's contest, I had to make a change to my original concept.  I wanted to use Dark Creepers and Dark Stalkers from the Fiend Folio as the main creatures in the adventure, but ended up changing the name to "morlock" to meet the rule requirements.  Generally I think of morlocks as a little less intelligent and crafty than Dark Creepers, but space was kind of an issue as well.  "Underdweller" was going to make me have to drop more material than I wanted.

At any rate, my daughter ran it for some people with 1st level characters using kobold stats, and there's no reason you couldn't run it for name level characters using giant stats, I guess.  Make it your own...that's the point of RPG gaming.

https://drive.google.com/open?id=0B3lpDs7zrq1nckNNS0t4UDV0a3c