Tinker's Equation: Making Math Fun Again

[John Out West]

Hey There,

I recently made rules for the Tinkering craft, where players can make mundane contraptions. Contraptions like Automatic Crossbows and Grapple Guns, not sentient spinning tops of doom or iron golems that obey your verbal commands. You can see the whole craft here (https://storage.googleapis.com/wzukusers/user-28883749/documents/5c30e57457f09gL3Ggbo/Tinkering%201.2.pdf).

As part of my series on "Crafts for Adventurers," this craft is supposed to be used while adventuring and not during downtime. Its another zero gold system. Creating a contraption takes only an hour if you have the parts, and creating a schematic takes a week of pondering (Thinking about it) with an hour of writing each night. Tinker's can't create their own raw materials, so they need to hire or become a Blacksmith to create gears, cogs, and sprockets.

The craft itself is simple. You take a mundane item, like a Grappling Hook or an Axe, and give it an augment. This augment may be to let it use itself or to spin wildly to give you an advantage in battle, among other options. Players use the Tinker's Tinkering Skill when using a Contraption, so even if you have a -1 to strength, a Gas-Powered Grappling Gun will let you use the tinker's +7. This does not translate to attacks.

After the Augment is added, you add the contraptions Power-source, Triggers, and Faults. These are not determined by the Player, but by the Tinker Character who is actually solving the engineering problems of the design, so they are chosen randomly from a list. Players can choose their Power-source or Trigger, but this strain on the Tinker causes more Faults to show up in the design. Faults are the unresolved issues with the contraption, such as overheating, making noise, or the design itself being finicky. Every design as at least one flaw.

With this Tinkering System you can make Grapple Guns, Portable or Stationary Traps, Automatic Crossbows, and Chainsaw Swords. The current Tinkering system is essentially non-existent, which is why this is necessary.

- - - - - - - - - - - - - - - - - -
The Tinkering craft seems to work well, as far as I can see, but I'm adding in a new system for calculating how to deal with the Powersources. The model i was using before was too simplistic, but I fear this new version might be too complex, or that I might be missing something. I'll post it below, and if you have any suggestions I would love to hear them!

- - - - - - - - - - - - - - - - - -

Powersource
Whenever an Augmentation on an contraption is used, such as a gun rotating a barrel or a shield unfolding, the stored units are expended to make the action possible.

Power Requirements.
The equation to determine the amount of Units a contraption needs, you must determine the Contraption’s weight and the distance it moves. The equation is as such:
(Size Units) x (1 + Distance Units) = Unit Requirement

Ranged:
For some contraptions, the purpose is not to move itself but to propel something else. In this case, the Unit Requirement of the contraption is added to the Unit Requirement of the ammunition. The equation is as such:
(Unit Requirement) + (Ammo Size Units) x (Ammo Distance Units) = Ranged Unit Requirement

Size Units:
1/2 Unit = Tiny (Palm Sized) : about 1/4lb
1 Unit = Light (Two-Weapon) : about 1lb
2 Units = Medium : about 4lbs
4 Units = Large (Two-Handed) : about 8lbs
8 Units = Large, Heavy : about 16lbs
16 Units = Huge, Mounted : about 32lbs

Distance Units
1 Distance Unit is added to the contraption for every 5ft the contraption is required to move, always rounding down to a multiple of 5. If the contraption doesn't move, but rather pivots, then measure the furthest angled distance that the pivoting edge has to travel and treat it as a straight line.

Unit Capacity
Each contraption can only hold a certain amount of Units safely. Most Tinkers put in safeguards to prevent the item from exceeding their unit capacity.
Each contraction has a Unit Capacity that is 10x their Size Units.

Units Generators
These generators will convert energy into Units that the contraption can use to activate its features. The energy transferred from the generator will negate from its origin, reducing total damage or movement in exchange for the units. This cannot reduce the damage from incoming attacks, however, if an attack is blocked and the contraptions function is to defend, it may be able to absorb the appropriate amount of damage or movement.

Generators
Roll 1d6 to determine the Generator randomly, or choose your Generator and add a fault to your design. Reroll on a six.
(1) Impact: This lever turns kinetic energy into mechanical energy.
Gain 1 Unit per Strength or Force damage.

(2) High Gear: This tiny gear requires a lot of strength to wind.
Gain 1 Unit per 5x Strength Check.

(3) Low Gear: This huge gear need a lot of winding to rotate.
Gain 1 Unit per 5x Dexterity Check.

(4) Pull: This cord is almost impossible to pull without anchoring it first.
Gain 1 Unit per 5ft movement.

(5) Boiler: Steam pours out of these superheated vessels. Requires a heat source and 1 ounce of water per 100 units.
Gain 1 Unit per Fire damage.

[aimlessPolymath]

Hey There,

I recently made rules for the Tinkering craft, where players can make mundane contraptions. Contraptions like Automatic Crossbows and Grapple Guns, not sentient spinning tops of doom or iron golems that obey your verbal commands. You can see the whole craft here (https://storage.googleapis.com/wzukusers/user-28883749/documents/5c30e57457f09gL3Ggbo/Tinkering%201.2.pdf).

As part of my series on "Crafts for Adventurers," this craft is supposed to be used while adventuring and not during downtime. Its another zero gold system. Creating a contraption takes only an hour if you have the parts, and creating a schematic takes a week of pondering (Thinking about it) with an hour of writing each night. Tinker's can't create their own raw materials, so they need to hire or become a Blacksmith to create gears, cogs, and sprockets.

The craft itself is simple. You take a mundane item, like a Grappling Hook or an Axe, and give it an augment. This augment may be to let it use itself or to spin wildly to give you an advantage in battle, among other options. Players use the Tinker's Tinkering Skill when using a Contraption, so even if you have a -1 to strength, a Gas-Powered Grappling Gun will let you use the tinker's +7. This does not translate to attacks.

After the Augment is added, you add the contraptions Power-source, Triggers, and Faults. These are not determined by the Player, but by the Tinker Character who is actually solving the engineering problems of the design, so they are chosen randomly from a list. Players can choose their Power-source or Trigger, but this strain on the Tinker causes more Faults to show up in the design. Faults are the unresolved issues with the contraption, such as overheating, making noise, or the design itself being finicky. Every design as at least one flaw.

With this Tinkering System you can make Grapple Guns, Portable or Stationary Traps, Automatic Crossbows, and Chainsaw Swords. The current Tinkering system is essentially non-existent, which is why this is necessary.

- - - - - - - - - - - - - - - - - -
The Tinkering craft seems to work well, as far as I can see, but I'm adding in a new system for calculating how to deal with the Powersources. The model i was using before was too simplistic, but I fear this new version might be too complex, or that I might be missing something. I'll post it below, and if you have any suggestions I would love to hear them!

- - - - - - - - - - - - - - - - - -

Powersource
Whenever an Augmentation on an contraption is used, such as a gun rotating a barrel or a shield unfolding, the stored units are expended to make the action possible.

Power Requirements.
The equation to determine the amount of Units a contraption needs, you must determine the Contraption’s weight and the distance it moves. The equation is as such:
(Size Units) x (1 + Distance Units) = Unit Requirement

Ranged:
For some contraptions, the purpose is not to move itself but to propel something else. In this case, the Unit Requirement of the contraption is added to the Unit Requirement of the ammunition. The equation is as such:
(Unit Requirement) + (Ammo Size Units) x (Ammo Distance Units) = Ranged Unit Requirement

Size Units:
1/2 Unit = Tiny (Palm Sized) : about 1/4lb
1 Unit = Light (Two-Weapon) : about 1lb
2 Units = Medium : about 4lbs
4 Units = Large (Two-Handed) : about 8lbs
8 Units = Large, Heavy : about 16lbs
16 Units = Huge, Mounted : about 32lbs

Distance Units
1 Distance Unit is added to the contraption for every 5ft the contraption is required to move, always rounding down to a multiple of 5. If the contraption doesn't move, but rather pivots, then measure the furthest angled distance that the pivoting edge has to travel and treat it as a straight line.

Unit Capacity
Each contraption can only hold a certain amount of Units safely. Most Tinkers put in safeguards to prevent the item from exceeding their unit capacity.
Each contraction has a Unit Capacity that is 10x their Size Units.

Units Generators
These generators will convert energy into Units that the contraption can use to activate its features. The energy transferred from the generator will negate from its origin, reducing total damage or movement in exchange for the units. This cannot reduce the damage from incoming attacks, however, if an attack is blocked and the contraptions function is to defend, it may be able to absorb the appropriate amount of damage or movement.

Generators
Roll 1d6 to determine the Generator randomly, or choose your Generator and add a fault to your design. Reroll on a six.
(1) Impact: This lever turns kinetic energy into mechanical energy.
Gain 1 Unit per Strength or Force damage.

(2) High Gear: This tiny gear requires a lot of strength to wind.
Gain 1 Unit per 5x Strength Check.

(3) Low Gear: This huge gear need a lot of winding to rotate.
Gain 1 Unit per 5x Dexterity Check.

(4) Pull: This cord is almost impossible to pull without anchoring it first.
Gain 1 Unit per 5ft movement.

(5) Boiler: Steam pours out of these superheated vessels. Requires a heat source and 1 ounce of water per 100 units.
Gain 1 Unit per Fire damage.
Always a fan of your work!

Two things-

First, your energy equation doesn't describe rate very well; if I spend energy in two expenditures, I go less distance than I do for a single expenditure of twice as much. Relates to this, it doesn't seem to function very well for cases where momentum plays a large factor; once I have my buzzsaw blade "spun up", it takes very little power to leave it spinning as long as it isn't hitting something; a battlewagon in motion tends to stay in motion unless acted on by an outside wall, etc.

Second and far more minor, I have a wording change for the low/high gear power sources:
"This requires an action and a Str/Dex ability check, providing one Unit per 5 points of the check"

[John Out West]

Always a fan of your work!

Two things-

First, your energy equation doesn't describe rate very well; if I spend energy in two expenditures, I go less distance than I do for a single expenditure of twice as much. Relates to this, it doesn't seem to function very well for cases where momentum plays a large factor; once I have my buzzsaw blade "spun up", it takes very little power to leave it spinning as long as it isn't hitting something; a battlewagon in motion tends to stay in motion unless acted on by an outside wall, etc.

Second and far more minor, I have a wording change for the low/high gear power sources:
"This requires an action and a Str/Dex ability check, providing one Unit per 5 points of the check"

Danget Polymath, you ruined my weekend by making me do all the changes. Which i have done. Thanks for that by the way. Always nice to get a kick in the butt in the right direction.

I made some changes based on the feedback:

Unit Requirement
( Unit Weight) x (1+Unit Distance) = Unit Requirement

Ranged Unit Requirement
(Unit Requirement) +(Ammo Unit Size) x (Ammo Unit Distance)

Inertia Calculation for Vehicles.
Assuming your vehicle is well oiled and causes negligible friction, the distance your vehicle travels in a given round will be its Current Speed + any new speed your vehicle generates - The Worlds Gravity x Friction Coefficient. The worlds gravity is 10 (9.8 but lets be simpler) and a normal paved road's Friction is 0.5. (0.2 on Ice, 1.0 in rough terrain) Typically, most vehicles will lose 5ft per round. For now we'll ignore adding the additional weight of the Rider. The calculation is:
(Speed + Acceleration) - (Gravity x Friction)

New Figures
Although the calculations are the same, we now measure by weight instead of by weight class. Now, for each 2lbs of an item, it has 4 Unit Capacity and 1 Unit Size, which can be summarized in: The Unit Capacity is twice the contraption's weight, and the Unit Size is half the contraption's weight.
---------------------------

I've made a small list of items below to show an example of the kind of things you can do, as well as the calculations that go along with them. Remember that its the weight of the original item that is taken into account for Unit Size and Capacity, or in the Grapple Gun's case, a custom item built to fire the Grappling Hook that was given a custom weight specifically to fire the Hook.
-------------------------
Weight . Capacity . Units Size . Distance . Unit Distance Name
6 . . . . . . 12 . . . . . . 3 . . . . . . 0 . . . . . . 0 . . Chainsaw Sword
100 . . . 200 . . . . . . 50 . . . . . 15ft . . . . . . 3 . .Motorwagen
10 . . . . . 20 . . . . . . 5 . . . . . . 0 . . . . . . 0 . . . . Crossbow
1/8 . . . . x . . . . . . 1/16 . . . 80 . . . . . . 16 . . . . . . Bolt
36 . . . . . . 72 . . . . . . 18 . . . . . 0 . . . . . . 0 . . . . Grapple Gun
10 . . . . . . x . . . . . . 5 . . . . . . 50 . . . . . . 10 . . Hook+Silk Rope
250 . . . 500 . . . . . . 125 . . . . . . 0 . . . . . . 0 . . . Bolt Launcher
8lbs . . . . x . . . . . . 4 . . . . . . 300 . . . . . . 60 . . . . . Huge Bolt
------------------------
Math:
(Size Unit) x (1 + Distance Unit) = Total Unit Cost
------------------------
Chainsaw Sword
(3) x (1+0) = 3 Cost Per use. With Capacity 12 thats 4 uses per tank.
--
Motorwagen
(50)x(1+3) = 200 Cost per use. With capacity 200 that's 1 use per tank. Speed loss is (Speed) - (Gravity x Friction) or (20) - (10x0.5) = 5ft per round lost. Fill tank back up to 200 every 3 rounds or stop moving.
--
Crossbow
(5) x (1+0) + (1/16 x 16) = 5 + 1 = 6 Cost Per use. With Capacity 20 that's 3 shots per tank.
--
Grappling Gun
(18) x (1+0) + (5x10 = 50) =68 Cost per Use. With capacity 72 that is 1 use per tank.
--
Bolt Launcher
(125) x (1+0) + (200) x (4) = 355 Units per use, with a capacity of 500 you can fire it once before recharging.
----------------------

I think that all sounds rather doable, but i would love to hear your opinions! It seems to scale well with small and large items, allowing you to fire large bolts 300ft accurately, and easily making a repeater crossbow or even a basic vehicle.

For the Motorwagen, dealing 200 points of fire damage isn't as difficult as you think, as most trains would have multiple vents to absorb the fire. The real question is: How do you calculate the surface area. If the fire dealt 10d10 Fire damage, for an average of 5, you would need 40 "targets" to have guaranteed full power every round. If it were calculated by Square Inches, you would only need to devote an 8x5 space to it, which is reasonable.

Edit: One thing i like to remember is Horse Power, which in this would be twice their movement per round. which is 120 or 24 Units. So Something like the Bolt Launcher could be recharged by a Horse in about a minute. Good for sieges.

[John Out West]

Okay, the numbers are getting really exciting.

The problem I have now, if you can call it a problem, is that regardless of the weight of the Contraption, it can move a maximum of 15ft per round.

The current equation is:

( Unit Size ) x (1 + Distance/5) = Unit Requirement

The problem is that the Unit Requirement will always be four times the Unit Size, so the max distance any contraption can go, regardless of its size or weight, is 15ft. Another way to put it is:

( x/2 ) x (1 + y/5) = 2x
X = Contraption Size, y = Distance

I've created some solutions to this, including lighter materials that will decrease the Unit Size, and Augments that increase the amount of Units a device can hold, but i'm still not a fan of the idea that I can know for certain that each device can move a maximum of 15ft on its own.

I'm looking for opinions on the matter. If it seems like a silly problem than good, but if it seems like a problem that I need to solve then I would like to hear it. If you have some ideas on how to solve this problem I would also like to hear those.

This is the newest version (https://storage.googleapis.com/wzukusers/user-28883749/documents/5c3700a9e9204Z26y75b/Tinkering%201.3.pdf).

[aimlessPolymath]

I think you can partially resolve this in multiple ways within the established rules, either with vehicle acceleration or projectile rules. Maybe combining them.

First, projectiles. If the object that is being launched is smaller than its power supply, then you can make it move much faster. Perhaps the chainsword is 3 Size Units, but only 1.5 Size Unit of that is actually the moving parts- this lets you nearly double the number of uses by halving the cost.

Edit: Upon a reread, I misunderstood the math behind projectiles. In combination with the Speed change, this could work for handheld contraptions in which only some portion is "active", but is probably not worth the effort to calculate for arbitrary devices.

Second, a straight-up modification of the maximum capacity of contraptions will improve maximum speed very easily. As evidence that such a change may be needed, I point to the Crossbow that can only fire at a range of up to 75 ft- this is an absurdly low range.

A more outlandish move (which I personally like as it speaks to my physics class) is to take the vehicle rules and replace current measurements of Distance units with Speed, then generate some general figures for deceleration over time. This lets you break that gap by powering up over time.

One example entirely within your existing system: assuming an average wheeled object decelerates at 5ft/rd in standard Material Plane terrain, that means that if you activate it each round (producing 15 ft of speed each time), you actually accelerate by 10ft/rd2, which lets you build up speed over time. (Technically, you can do so indefinitely, so I suggest including a maximum speed somewhere for sanity- round-by-round movement does not really handle high-speed chases or driving at indefinite speed)

Presumably, this system would come with a couple general categories of machine depending on how they interact with the environment- your Chainsword might only lose 5 ft/rnd of speed per round while not hitting anything, but each attack takes off 20ft/rnd of speed. Its maximum belt speed might be 100 ft/round. Some example categories would be Geared, Wheeled, Launched, Impact(direct/glancing). This could also be a place for materials to matter, since they will have different tolerances and friction coefficients.

One major benefit of this is the ability to convert efficiently into a damage table, using a tool I built for 3.5- the size categories can be converted into Size ranks, if needed.

Take the bite attack of a creature of the size of the creature that would use the weapon (or projectile) as a two-handed weapon (1d6 for Medium creatures), then scale it up or down in size based on the Speed Table(taken from an older work):



Speed(/rnd)
20 ft
30 ft
40 ft
60 ft
80 ft120 ft



Adjustment
-1
+0
+1
+2
+3+4



Something along these lines, anyway- I was never quite satisfied with how the rules worked out.

This lets you roughly determine a damage for a two-handed Chainsword for a given size category- suppose it spins at 100 fr/rnd. We round it down to 80 ft, so +3 size categories for a Medium bite attack brings it to a 3d6 weapon- assuming it can be properly powered.

A one-handed Chainsword would be a two-handed weapon for a Small creature, so the damage scales down a step to 2d6.

A 75 ft range crossbow generates a speed bonus of +2, but Tiny creatures use the bolt as a two-handed weapon- so it cancels out to 1d6 damage per bolt. Not particularly scary- according to a Google search, the actual velocities were more like 1800 ft/rnd, which would be something like 2d6 damage (based on where the chart caps out)