Thursday, January 10, 2019

Notes on Artillery

I posted a bunch of artillery pieces a while back, but gave little or no information about what each one was.  Here is a little more description for each one.

Swivel Gun (Murtherer): I listed this piece with the small arms in the price list and damage tables because it can be loaded and fired effectively by one person.  It is essentially a high powered musket, but is too heavy to be fired from the shoulder.  It is usually mounted along the rails of a ship, at the bow of a boat, or on the walls of a fort, but can be mounted on a wagon or cart, or possibly even fired like a regular musket by a large enough creature, like an ogre.  Murtherers are generally between .70 to 1 inch in caliber.  The number that can be mounted on a given vehicle or fort is left to the individual DM, although I would recommend no more than one every five feet of distance.  The sheer cost should keep the actual numbers in a game well below this level, though.

Rabinet: The smallest crew-served weapon on the list, the rabinet is basically a heavier version of the murtherer.  Due to the extra crew member involved in loading this weapon, there should be no more than one per 10' when mounted on a ship.  Rabinets fire a 1" ball which weighs about half an ounce; the gun itself weighs about 120 lbs.

Falconet: These are generally mounted on a carriage, but can be mounted on a sturdy fort wall like a murtherer.  Falconets are used in small, hard to supply forts (easy to pack in, easy to keep supplied with powder and shot) or in larger boats or small ships as chasers (guns mounted in the bow or stern to fire ahead or behind) or occasionally as a broadside weapon.  They fire a 2" ball weighing 1 lb, and weight about 200 lbs including the gun and carriage.

Minion: Minions (and all larger guns) are always mounted on carriages.  On ships, minions are used as primary broadside weapons on small ships or as secondary weapons on larger ships (ships mounted their bigger guns on the lower decks and smaller guns on higher decks for stability).  On land, they are often called Grasshopper Guns for the way they jump with recoil when fired.  They are often used to defend wilderness forts, and are typical light artillery pieces taken out with an army on maneuvers.  Minions fire a 3 1/2" ball weighing 6 lbs, and weigh in at 1500 lbs with carriage.

Quartocannon:  In naval use, quartocannons are medium weight guns, used as primary weaponry on medium sized ships and secondary weaponry on the largest of warships.  In military use, they are the standard size for field artillery.  They fire a 4 1/2" 12 lb ball, and weigh 3600 lbs.

Demicannon: The heaviest guns in general naval use, serving as primary weapons on the largest warships.  On land, guns of this size and larger are usually used as defensive weapons in coastal forts or as siege guns for destroying fortress walls.  They fire a 6 1/2" ball weighing 32 lbs, and weigh 6000 lbs.

Cannon: Proving too unwieldy for shipboard use, cannons are usually used to attack or defend forts.  They fire an 8" 50 lb ball, and weigh 7000 lbs.

Basilisk: Named (aptly) for a terrible monster, this is the largest direct fire gun in use.  They are almost always used as siege guns by wealthy nations against the mightiest enemy strongholds.  A basilisk fires a 10" ball weighing 90 lbs, and weighs 8000 lbs.

Mortar:  The smallest of the indirect fire guns.  All indirect fire guns have very short barrels with thick barrel walls, and fire an explosive shell in an arc that can bypass walls and defensive earthworks.  The mortar fires a 6" 20 lb shell and weighs 1800 lbs.

Pedrero: Named after a weapon of a previous era which fired stone balls, this is a larger version of the mortar.  It fires a 10" 50 lb shell and weighs 3500 lbs.

Heavy Mortar: The heaviest indirect fire gun.  It fires a 15" 200 lb shell and weighs 4500 lbs.

In general, all of these artillery pieces come with a carriage (included in the price). Carriages come in two types: field carriages and naval carriages.  A field carriage has high wheels (for getting across ground rougher than a road or level floor) and long trailing pieces on each side for hitching to a team of horses or oxen.  A naval carriage is for use on a ship or fort, where it isn't expected to be moved very far or very often.  A naval carriage has small wheels to help maneuver it for loading and firing (not very good for rolling across grass or dirt), and no trails.

I chose these names and these particular sizes for color and gameability.  There were guns made in all shapes and sizes, and given all kinds of different names, and the names given here were often applied to guns that don't resemble my descriptions at all.  You can ignore all this ambiguity and use just what I have listed here, or you can take advantage of it and have sakers, culverin bastards, and demiculverins which all are functionally equivalent to quartocannons if you feel that it would add something to your game to do so.

Thursday, January 3, 2019

Weapon Mastery: Firearms

I've never made Weapon Mastery tables for the D&D Rules Cyclopedia before.  There are some pretty arbitrary-seeming decisions to be made, especially as far as Primary and Secondary target types.

Well, these may not be up to RC standards, but since I haven't been able to figure out what criteria they used on the RC tables for various weapons, this is better than nothing.  I tried to minimize the funky DCC style dice for this table, but since I already used d5s for the basic fowling piece, d7s snuck in here too.

Weapon Level Ranges Damage Defense Special Effects
Pistol BS 25'/50'/100' 1d6 -- 4 rounds to reload
[P=A] SK 30'/60'/100' 2d4 -- 3 rounds to reload
1Hand; small EX 35'/70'/100' 2d6 -- 2 rounds to reload
missile MS 40'/80'/110' 3d4+2 -- 1 round to reload
Enc: 20 cn GM 50'/90'/120' 3d6+3 -- 1 round to reload; automatic initiative

Fowling Piece BS 30'/70'/150' 2d5# -- 4 rounds to reload
[P=A] SK 35'/80'/150' 2d6# -- 3 rounds to reload
2Hand; medium EX 40'/90'/150' 2d7# -- 2 rounds to reload
missile MS 45'/100'/160' 2d8# -- 1 round to reload
Enc: 50 cn GM 50'/110'/170' 2d10# -- 1 round to reload; automatic initiative

Musket BS 50'/100'/200' 1d8 -- 4 rounds to reload
[P=A] SK 60'/110'/200' 2d6 -- 3 rounds to reload
2Hand; medium EX 70'/120'/200' 2d8 -- 2 rounds to reload
missile MS 80'/130'/210' 3d6 -- 1 round to reload
Enc: 80 cn GM 90'/140'/220' 3d8 -- 1 round to reload; automatic initiative

Rifled Musket BS 75'/150'/300' 1d10 -- 5 rounds to reload
[P=A] SK 85'/160'/300' 2d8 -- 4 rounds to reload
2Hand; medium EX 100'/170'/300' 2d10 -- 3 rounds to reload
missile MS 110'/180'/310' 3d8 -- 2 rounds to reload
Enc: 80 cn GM 120'/190'/320' 3d10 -- 2 rounds to reload; automatic initiative

# Fowling pieces do both dice of damage at short range, the higher of the two dice at medium range, and the lower of the two at long range

Saturday, December 1, 2018

Mighty Deeds of Firearms and Firearm Fumbles

I don't see any reason that any class shouldn't use any given firearm.  Sure, most of them aren't going to want to lug around a musket, and thieves would just find matchlocks inconvenient for sneaking around, but in the right circumstances, any class should have the ability to use any firearm.  But it's warriors (and dwarves) that really should get the most out of them.

Of course, they already get quite a lot out of firearms.  Their deed dice give them greater chances of hits and more damage when they do, and they can use existing Mighty Deeds to make Precision Shots, Disarm a foe, or even make Pushbacks or Throws if appropriate.  But gunpowder weapons are slow to reload, and a pistoleer or musketman is vulnerable to enemy attack while reloading.  These new Mighty Deeds aren't meant for attacking, per se, so no attack roll is needed while attempting them.  Only the deed die needs to be thrown.

Mobility - Rather than having to stand in one spot receiving no Agility bonus to Armor Class while reloading, the warrior may move and dodge.

3 Character can either retain his Agility bonus to Armor Class or move up to 5' per round while reloading
4 Character can either retain his Agility bonus to Armor Class and move up to 5' per round or move up to 10' per round (without Agility bonus) while reloading
5 Character can retain his Agility bonus and move up to half his normal rate per round while reloading
6 Character can retain his Agility bonus and move up to ¾ his normal rate per round while reloading
7+ Character can retain his Agility bonus and move up to his full normal rate per round while reloading

Speed - The character is able to reload faster than lesser trained marksmen.

3 Reloading takes the normal amount of time (4 rounds, or 5 for rifles), but the character automatically wins the initiative on the round he is able to fire
4 Reloading takes one less round than normal
5 Reloading takes two less rounds than normal
6 Reloading takes three less rounds than normal
7+ Reloading takes three less rounds than normal, and the character automatically wins the initiative on the round he is able to fire

Fumbles are different for firearms.  Armor worn doesn't matter; just roll 1d10 and modify with the firer's Luck modifier.

1- Misfire: weapon doesn't go off, try again next action
2-3 Pan flash: the priming goes off but doesn't light the charge. Spend 1 round repriming and try again.
4-5 Hang fire: weapon doesn't go off yet, but will in 1d4 rounds. If the character isn't still aiming the weapon, roll randomly to see where the shot goes.
6-7 Hang fire: weapon doesn't go off yet, but will in 2d6 rounds. If the character isn't still aiming the weapon, roll randomly to see where the shot goes.
8-9 Squib: the charge wasn't strong enough to propel the bullet from the barrel. It'll take some out-of-combat time to dig it out.
10+ Explosion: the charge bursts the weapon open, destroying it and inflicting its damage on the firer.

At the Judge's option, fumbles may be rolled as normal in the DCC rules 50% of the time, and using this table the other 50% of the time.  Also, this table may be used for weapons that have been double charged or double shotted.  In this case, a roll of 8+ with a double shotted weapon with a single powder charge will always be a squib, and a roll of 8+ with any double charged weapon (regardless of whether it has a single or double shot) will be an explosion.

Tuesday, November 13, 2018

Yet Another Set of Musket Rules

I've seen some interesting and inspiring frontier fantasy or pirate fantasy posts here and there on the internet lately, and it got me thinking about a frontier fantasy setting I created years ago for Hero System.  Of course, these types of fantasy often allow for gunpowder weapons, and I've seen several takes on muskets and cannons in gaming, but there are some things you can do with old-fashioned muzzleloading arms that you can't do with more modern ones, and games often overlook these options.  Here, I've converted my Hero rules over for use in Dungeon Crawl Classics or the D&D Rules Cyclopedia edition.  RC players will have to either use funky DCC dice for some damage rolls here, or use a workaround with the standard polyhedral dice; I can provide help with that if anyone needs it.

Matchlock Musket 75 Matchlock Pistol 35
Wheellock Musket 100 Wheellock Pistol 50
Matchlock Fowling Piece 80 Wheellock Fowling Piece 110
Rifled Musket (wheellock) 200 Grenado Gun (matchlock) 150
Bullets (12) 3 Powder, 1 pound horn 15
Bullet Mold 9 Lead for 12 bullets 2
Grenado 20 Match/foot 3
Swivel Gun/Murtherer 300

 Any pistol, musket, rifle, or fowling piece may be made in a double barrelled version for an additional 75% of cost.  Additional barrels add another 75% of cost each. Any musket may be made in a volleygun version for an additional 50% cost. A single-barreled fowling piece may be made with a flared bell muzzle for an additional 10% cost.

Rabinet 750 Ammo 1
Falconet 1500 Ammo 3
Minion (Grasshopper Gun) 3000 Ammo 15
Quartocannon 7000 Ammo 35
Demicannon 12000 Ammo 90
Cannon 25000 Ammo 150
Basilisk 50000 Ammo 250
Mortar 3000 Ammo 50
Pedrero 10000 Ammo 225
Heavy Mortar 20000 Ammo 325
Serpentine Powder, 5lb keg 35 Corned Powder, 5lb keg 75
Serpentine Powder, 10lb keg 60 Corned Powder, 10lb keg 140
Serpentine Powder, 20lb keg 110 Corned Powder, 20lb keg 250

Any artillery piece can be built as an organ gun for an additional 50% cost and 50% weight per barrel. Artillery pieces of Quartocannon size or larger can be built as a carronade for no additional cost or weight. All ammunition costs the same, whether it's a ball, grapeshot, bar shot, chain shot, or expanding shot.


DMG Range
Pistol 1d6 25'/50'/100'
Musket* 1d8 50'/100'/200'
Rifled Musket* 1d10 75'/150'/300'
Fowling Piece* 2d5# 30'/70'/150'
Grenado 1d6+ within 10' 10'/20'/30'
Grenado Gun* as grenado 30'/70'/150'
Swivel Gun/Murtherer+ 1d12 75'/150'/300'

Rabinet+ 1d14 100'/200'/400'
Falconet+ 1d16 110'/225'/450'
Minion (Grasshopper Gun)+ 1d20 125'/250'/500'
Quartocannon+ 1d24 135'/275'/550'
Demicannon+ 1d30 150'/300'/600'
Cannon+ 1d30+6 160'/325'/650'
Basilisk+ 1d30+12 175'/350'/700'
Mortar+ 1d12^ within 15' (150')/300'/600'
Pedrero+ 1d20^ within 20' (160')/325'/650'
Heavy Mortar+ 2d14^ within 25' (175')/350'/700'
Serpentine Powder, 5lb keg 1d10 --
Serpentine Powder, 10lb keg 1d14 --
Serpentine Powder, 20lb keg 1d20 --
Corned Powder, 5lb keg 1d14 --
Corned Powder, 10lb keg 1d20 --
Corned Powder, 20lb keg 1d30 --

* Two handed weapon (d16 initiative in DCC; lose initiative unless opponent is using a two handed weapon in RC)
# Close range damage: 2d5; medium range damage: higher of 2d5; long range damage: lower of 2d5
+ Mounted weapon (lose initiative unless fighting against mounted weapons or siege weapons)
^ Save for half damage (Reflex save vs attack roll for DCC; Dragon breath for RC)

New Rules:
Firing at ships – Artillery firing at ships do 1/5 normal damage, applied against the ship's hull points (see D&D Expert set or Rules Compendium).

Firearms vs. Armor – Firearms are very effective against normal armor, generally punching right through.  Disregard the value of any worn armor when determining Armor Class of the target.  Magic armor still adds in its magic bonus, characters still get Dexterity bonuses, and small targets still get their bonuses for size (pixies, stirges, etc) when being fired on by a regular ball-firing weapon.  Creatures with natural armor still get their normal AC; you won't take down a dragon just because you brought a pistol.

Fowling Pieces – Made for hunting ducks, quail, and other fowl, a fowling piece fires a handful of small shot rather than a large ball.  These shot are relatively ineffective at penetrating armor (normal AC for worn armor), but are very good at hitting small, agile targets.  The target of an attacker with a fowling piece gets no Dexterity or size bonuses when fired on by a fowling piece.

Reloading – Small arms (up to the size of the swivel gun) generally take 4 rounds to reload, firing on the 5th round.  During this time, the loading character can't move and does not get their Dexterity bonus.  Rifles take an extra round to load, due to the tight tolerance between the bullet and the barrel.

Powder usage – Most small arms get 12 charges from a pound of powder. Swivel guns get 10 charges from a pound. Grenado guns fire a grenado with ¼ pound of powder.  Multiple barrel weapons must use a charge and a ball or shot for each barrel. All small arms use corned powder.

Cannons and mortars can use either serpentine powder or corned powder. If using the less powerful serpentine powder, a rabinet gets 3 charges per pound of powder, a falconet gets 1 charge per pound, a minion uses 6 pounds per charge, a quartocannon uses 12 pounds per charge, a demicannon 32 pounds, a cannon 50 pounds, and a basilisk 90 pounds. A mortar uses 8 pounds, a pedrero 40 pounds, and a heavy mortar 75 pounds. Corned powder is twice as powerful, so a rabinet gets 6 charges per
pound, a falconet 2 charges per pound, a minion uses 3 pounds per charge, a quartocannon 6 pounds, etc.

Match burn rates – Quickmatch comes in several varieties, with burn rates ranging from 10-100 feet per second. Slow match burns at 1 foot per hour. Characters may specify which type they want when they buy it. Match found while adventuring will need to be tested in order to determine how fast it burns, in most cases. Using match without testing it can be embarrassing or even very dangerous.

Flared Bells – A fowling piece may be built with a flared bell muzzle. This reduces reload time by one round. Only a single barreled fowling piece may be made with a flared bell.

Volley Guns – A volley gun is a multi-barreled smoothbore musket with one lock. Firing the weapon fires all the barrels at the same time, each barrel getting a separate attack roll. Due to the added recoil, the attack rolls of a volley gun are decreased by 1 for a two barreled version, by 2 for a 3-4 barreled version, and by 3 for a 5-8 barreled version (the maximum size).

Variant ammunition – Black powder weapons can be loaded in many different ways: with shot, with ball, with stones, with shot and ball, with two balls, or with a double charge of gunpowder. Cannons have even more options available. The weapons table shows the ballistic characteristics of the most common type of ammunition for the weapon type, assuming that fowling pieces are loaded with shot, that mortars are loaded with shells, and that all other weapons are loaded with a single ball. Variants follow:

Double shot: Loading two of the standard type of ammunition is called "double shotting".  Double shotting a weapon takes extra time (lose a die step to initiative for DCC, -1 initiative penalty for RC)  and confers two attack rolls for one attack action. Both attacks must be made against the same target or against two adjacent targets.  If the attacker rolls a 1 on the attack roll, the powder charge was not powerful enough to move the extra ammunition from the barrel, and it will take at least several minutes, if not hours, to clear the weapon.

Double charge: Loading an extra ration of gunpowder into the weapon is called "double charging". Double charging takes no extra time, and gives the weapon an additional +1 to hit, additional range (+5' to close range, +25' to medium, +50' to long), and +1d4 damage. If the attacker rolls a 1 on the attack roll, the powder charge blows the weapon apart, causing the same damage to the attacker as would have been inflicted had the weapon hit. If a weapon is double shotted and double charged, then this failure result takes precedence.

Loading shot into a ball-firing weapon: This can be done with all small arms, and artillery pieces up to minion in size.  Loading shot into a ball-firing weapon reduces range to 30'/70'/150' regardless of what it is when firing ball ammunition. Armor now gets full value vs this attack, but Dexterity and size are ignored.  Damage works as with the fowling piece (2 dice at close range, higher of 2 dice at medium, lower of 2 dice at long) and is as follows:
ball damage shot damage
1d6 2d3
1d8 2d4
1d10 2d5
1d12 2d6
1d14 2d7
1d16 2d8
1d20 2d10

Loading a ball into a fowling piece: Loading a ball into a fowling piece gives it a damage of 1d8.  Worn armor is no longer considered in Armor Class, but Dexterity and size now are.

Loading stones, nails, glass, or other junk: Loading stones or junk into a firearm (whether a ball-firing weapon or a fowling piece) is similar to loading it with shot.  Since stones and steel junk are not as heavy as lead, when rolling damage, 3 dice are rolled and the highest die is discarded, with the other 2 dice being read as for shot.

Mixing shot and ball: When mixing shot and ball in any firearm, the attacker gets two attack rolls per action. If only one attack hits, it is assumed to be the shot, and damage is inflicted as normal for shot fired from that type of weapon. If both attacks hit, the ball also hits, doing damage as normal for ball ammunition fired from that type of weapon. The weapon is considered to be double-shotted for misfire purposes.

Bar shot, chain shot, and expanding shot: These are all different types of shot for naval artillery. They are only made for Quartocannons and larger, and cost the same as a regular ball. These types of shot are are designed to cut sails and rigging.  Damage for shots fired against the rigging is tracked separately for purposes of reducing movement, but this damage can not sink the ship.  These kinds of shot do full regular damage to personnel and 1/10 damage to the ship's regular hull points.

Grapeshot: Grapeshot is a case of large balls (each equivalent to a minion ball) fired from a Quartocannon or larger, essentially turning it into a large blunderbuss. Grapeshot covers a cone shaped area reaching out to the gun's close range, with a base of 1/2 the close range distance.  Anything within this cone suffers the gun's normal damage (save for half damage: Reflex save vs attack roll for DCC, save vs Dragon Breath for RC).  Grapeshot does 1/2 damage against structures and 1/10 against the hull points of a ship, and as such, is usually used against personnel. A canister of grapeshot costs the same as a ball for the same weapon.

Red-hot shot: Many coastal fortresses have furnaces for heating balls to a glowing red heat. These red-hot shot can set a ship aflame if they lodge in the hull, with a 1 in 10 chance per round for d10 minutes (d10x6 rounds). Dousing the shot with water prevents the shot from starting a fire as long as it is actively doused; each round of dousing also reduces the time it could start a fire (reduce the d10 minutes rolled earlier by 1 minute per round that the shot is doused). Ships set afire will take one point of hull damage per turn for the first two turns, then damage doubles each turn afterwards.  A ten crew member fire fighting detail can reduce this damage by 1d6 points per turn; if this is more than the damage that would have been inflicted, the fire is out.

Crew-served weapons – Most artillery is crewed by more than one man. The crew sizes listed are the minimum effective crew sizes. Military units will tend to have larger crews; the extra men tend horses while the weapon is in action. Naval gun crews will adhere more strongly to the minimum effective crew size. Artillery which is crewed by fewer than the minimum effective crew will have their reload time increased as listed.

Artillery Normal Crew Normal Reload Crew -1 Crew -2 Crew -3 Crew -4 Crew -5
Rabinet 2 5 rounds 10 rounds -- -- -- --
Falconet 2 10 rounds (1 minute) 2 minutes -- -- -- --
Minion (Grasshopper Gun) 2 3 minutes 4 minutes -- -- -- --
Quartocannon 3 5 minutes 10 minutes 15 minutes -- -- --
Demicannon 3 6 minutes 12 minutes 18 minutes -- -- --
Cannon 4 8 minutes 12 minutes 18 minutes 24 minutes -- --
Basilisk 6 10 minutes (1 turn) 15 minutes 20 minutes 25 minutes 30 minutes 35 minutes
Mortar 3 2 minutes 3 minutes 4 minutes -- -- --
Pedrero 4 4 minutes 6 minutes 8 minutes 12 minutes -- --
Heavy Mortar 6 6 minutes 12 minutes 18 minutes 25 minutes 30 minutes 35 minutes

Organ Guns – Any cannon-type gun can be built as an organ gun -- a gun with multiple barrels. This gives the weapon a number of attacks equal to the number of barrels used. Each barrel must be reloaded separately, at full standard reload rate each. An organ gun does not have to fire all of its barrels at once.

Carronades – Artillery pieces of quartocannon size and larger can be constructed as a carronade, if desired. A carronade has a shorter, heavier barrel, giving it reduced range as compared to a long gun, but it can hold a heavier charge. A typical carronade charge is 50% heavier than a powder charge for a comparably sized long gun. This carronade charge can be doubled, following all normal rules for double-charging. A carronade has a range equal to the next lower size of artillery, damage equal to the next larger size (a basilisk sized carronade does 1d30+18 damage), and costs the same as a comparable long gun.

Use of firearms vs non-firearm wielding opponents – Using firearms against opponents without them has some important effects on morale. Minor NPCs facing opponents armed with firearms must make a morale check each time they are fired on if their side does not have firearms as well, surrendering or retreating as best fits the situation.  PCs and major NPCs aren't subject to this, but at the DM's option must succeed at a saving throw (DCC: Will save vs opponent's attack roll; RC: Save vs Death) in order to make any aggressive action (moving toward the enemy and/or attacking)

Naval Gunfire – Because of the action of the ocean's waves in rocking the ship, gunners on a ship suffer an additional penalty to attack rolls equal to (the wind's Beaufort number minus 4) x2. For example, in a gentle breeze (Beaufort number 3) the penalty would be (3-4 = -1 which is less than 0) no penalty at all, but in a strong gale (Beaufort number 9) the penalty would be (9-4 = 5 x 2 =10) -10 to all attacks.

Thursday, October 4, 2018

Robert Manning Deep Under Taboo Island

In a memorable scene from the classic adventure The Isle of Dread, the party is wading through a flooded underground temple when they open a door into a dry area and are swept away as the water drains down into the cavern below.  At least, that's how the circumstances are set up; I suppose some parties get lucky or have made better plans based on paranoia, divination, or secretly reading the adventure beforehand.

It occurred to me a while back that Robert Manning's equation could be used to figure out the flow rate of water moving in a man-made channel (like a dungeon corridor) and I thought it might be fun to compare my cursory knowledge of fluid mechanics with the wild guesses of David Cook and Tom Moldvay.

So here's the map:

We have 101.5 10' squares filled five feet deep with water (most of area 2 is deeper than that, but only the top five feet is able to drain off; also the half square comes from the stairs leading up and over the dry section of corridor into area 4).  Once the door in the north wall of room 7 is opened 50,750 cubic feet of water starts draining down the stairs into the cavern below.  The adventure estimates that the water will flow for two minutes, or 12 ten-second rounds.  Let's see what Manning has to say.

Manning's equation requires us to know the cross sectional area of the "river", which in this case will be the width and depth of the water flowing through the doorway.  It also requires the slope of channel the water flows down, and the "Manning's n" value representing the friction the channel exerts on the flowing water.

My previous spreadsheets used a triangular cross-section to represent the shape of a natural stream, with shallow water by the banks and a deeper channel further out.  Because this is a man-made corridor, with floors and walls squared off, the numbers are going to come out a little differently, and a lot easier.  The cross-section of the stream will be the width of the doorway multiplied by the depth of the water, while the wetted perimeter will be the width of the doorway added to twice the depth of the water (see diagram).  No Pythagorean theorem here!

It should also be noted that this water isn't being replenished from groundwater or rains far upstream.  As it flows out, the level of the water will drop, which will affect the flow rate as both the cross-section of the stream and the wetted perimeter drop.

The hallway that the water will drain down has about 40 horizontal feet worth of stairs.  We'll assume that this temple/cavern complex was built according to standard US building codes, and the stairways are made up of 7 inch risers and 11 inch treads, for a slope of .6363 (repeating).  For what it's worth, that puts level 3 about 25 feet below level 2.

Normally, in a dungeon passage carved from stone, I would assume the flow channel is pretty smooth, and choose a low value for Manning's n, but the description specifically mentions all the dangerous debris hidden in the water for characters to stumble and hurt themselves on if they're not careful, so I'm going to go with 0.035 here.

I'm going to assume that the door here is eight feet tall by three feet wide.  That's pretty big for a regular interior door in a home, but houses don't typically have 10' wide and tall passages either. 

And with that, we can start looking at the flow rate through the doorway.  Punching it all into the spreadsheet gives us a flow of 37 feet per minute, or about 6 feet per 10 second round.


That's not fast at all.  What went wrong here?

I'm going to guess that this slow rate comes from the fact that the formula is supposed to be for a steady flow, whereas this is water suddenly released.  That slope we got above is pretty steep for a natural stream, and 6' per round is pretty fast compared to some of the flow speeds we've looked at earlier, but consider this: at the instant the door is opened, the water in the doorway extends ZERO feet past the doorway and 5' high, giving it infinite slope.

Well, infinite slope doesn't help out a whole lot either.  There's no way to input infinity into the spreadsheet without getting a Division by Zero error, and even if you could, you'd just get infinite flow, which is as absurd as the leisurely 6' per round flow.  Just pulling a number out of the air, let's go with slope equal to the depth of the water, or 5 in this case.  That's a pretty significant jump from .64 without getting too crazy.

So with a slope of 5, we end up with a flow rate of 105' per minute, or 17.5' per round.  That's plenty to sweep the character opening the door into the portcullis beyond with a fair amount of force. Maybe not 1d4 damage worth of force, although getting knocked down by suddenly gushing water combined with the debris strewn down the passage might account for that.

At the end of the first round, then, the flooded area has drained off (3' x 5' x 17.5 =) 262.5 cubic feet of water.  That's pretty negligible compared to what's there, so it's going to flow like that for several rounds.  To drain off a single foot of water would take over 10,000 cubic feet of water, so we don't have to recalculate the water depth just yet; five feet is still close enough.

The water in that corridor is going to slow down somewhat.  The corridor is wider, so a lot of that energy is going sideways.  If the water has shot out 17.5' and settled into the 10' wide corridor, the total amount of water that has drained in the first round will average about 1.5' deep past the door.  Round 2 begins in this situation.

In round 2, punching in the numbers in the spreadsheet (assuming a slope equal to the water depth since there's no previous sustained flow) gives a velocity of 57' per minute, or about 9.5' per round.  That starts the flow down the stairs, but let's keep it simple and not take that into account just now.  The front edge of the water flow is at 27' past the door.

Looking at the door, now we have some previous flow, but not sustained flow; there's still more water pouring out the door than there is on the other side.  The flow will slow down, but still not be as slow as a regular stream.  We've been taking the depth of the water as the slope for water flowing into a dry area, so let's take the difference in water depth for this situation.  Five feet inside the door vs 1.5' outside the door gives a slope of 3.5, which then gives a velocity of 87.6' per minute, or 14.5' per round.  In this round, 217.5 cubic feet of water drain from the flooded area, for a total drainage of 480 cubic feet. At this point the water past the door averages 1.8' in depth.  Let's call that 2'.

Round 3 begins now.  Running down the stairs, we have the stairs themselves sloping downward at .6363, and 2' deep water flowing into it, giving a total slope of 2.64 and a flow rate of 105.2' per minute or about 17.5' per round.  The front edge of the flow is 44.5' past the door, off the level 2 map and spilling down into level 3.

Coming through the door, we have a new slope of 3, giving a velocity of 81' per minute, or 13.5' per round.  202.5 cubic feet of water drain this round, totaling 682.5 cubic feet in all.  Thanks to the water picking up speed down the stairs, the average depth drops to 1.5'. 

Ok, round 4.  Running down the stairs, the slope is now 2.14 (1.5' deep plus .64 stair slope).  The velocity is 68.5' per minute, or 11.4 (let's call it 11.5) feet per round.  The front edge is 56' past the door, almost to the bottom of the stairs.

Flowing through the door, with a slope of 3.5, the water is moving at 87.6' per minute (14.5' per round).  217.5 cubic feet of water drain out, for a total drainage so far of 900 cubic feet.  The average depth down the corridor is still about 1.5'.

For round 5, all the inputs remain the same.  The front edge runs out to 67.5' past the door, and starts spreading out into the cave.  At this point, I'm going to assume that the flow is established down the stairs.  The depth of the water doesn't add to the slope anymore, given that there's water all the way down now.  The water will continue to spill into "dry" areas on level 3 until it goes over the edge into the mud pits, but I won't bother tracking it per se.

Water comes through the door at a rate of 217.5 cubic feet once again, increasing total drainage to 1117.5.  The average depth down the corridor is still about 1.5'.

In round 6, since the flow is now established, the slope down the corridor is just .64.  The flow rate is now 37.4' per minute, or about 6' per round.  (6 x 10 x 1.5 =) 90 cubic feet of water flow out of the corridor into the cave.  217.5 cubic feet of water pour out through the door, making the total drainage from the flooded area 1335 cubic feet.  Water isn't flowing out as fast as it was, so the depth of water in the corridor is increasing (but still rounds to about 1.5 for now).  One minute has passed.

Round 7 is going to look a lot like round 6.  Flow rates are unchanged.  Total drainage is now 1552.5, and water depth in the corridor is now 2'.

With the water beginning to back up in the corridor, round 8 sees a little bit of tweaking.  Flow rate in the corridor is now 43.1' per minute (7.2' per round), with 144 cubic feet flowing into the cave.  The rising water in the corridor slows the flow through the doorway to 81' per minute (13.5' per round).  Total drainage is 1755.  Depth in the corridor remains at 2'.

At this point, the water levels reach a pattern of slow but steady decline, with the water running down the stairs remaining at just under half the depth of the flooded area of the dungeon and water velocity dropping proportionately.  It takes just over 10 minutes for the water level of the flooded area to drop below four feet, and nearly a half hour before it drops below three feet.  By the end of an hour, the flooded area is down below two feet, and after a total of two hours of draining, it's down below a foot, with the water running down the stairs just a few inches in depth and the velocity of the water only about 1/4 what it was during the first rush as the door was opened.

I'm not going to run the numbers past this, because while it's somewhat interesting as rapid changes occur, it's very tedious once everything slows down and the numbers quit changing as fast.  I tried changing scales, and when I went from round by round to minute by minute it worked out okay, but trying to scale up to 10 minute blocks makes things go all weird.  Somehow the water (according to the numbers) starts running in spurts, with the depth in the stairway going from almost nothing to deeper than the flooded area.  Well, after two hours, even the shortest halfling is in no danger of being swept away, and it's safe to say that some noticeable water flow will continue for a day or two afterward, probably long after the PCs have finished looting and left the place forevermore.

For what it's worth, I'm adding a page to this river spreadsheet to work out flow rates in square-bottomed corridors, in case anyone ever needs to flood a party of PCs out of a dungeon.

Here's the link:

Monday, September 3, 2018

A Useful Cipher

Years ago, when I was still in the Army and working at NSA, I came across an article with obvious use in game (at least if you're the type of DM who likes to make maps with cryptic notations or other similar props).  Luckily, it was not only unclassified, but also available on their external website. 

I don't know what made me think of it today, but here it is.  Enjoy.