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[Zironic]

Or if you want to figure out how many total trees you can cut in a total amount of time - say 2 years - then you need to know how long it takes for trees to grow to be cut agian in that time span/.

[LordZabujca]

If he wants to know how long it takes to clear out an entire map of wood, then yes, knowing the growth rate of new trees is important.

In extremely unlikely cases, maybe - the trees take 3 years to grow from a sapling to a cuttable tree, and your woodcutter should normally cut all available wood in less than 1. So yeah, it pretty much doesn't matter.

Oh, and this "fixed" equation is still very silly. Admit it Ziornic - you just hate math, eh?

[Zironic]

No I love math. This formula is extremely broken because it assumes the dwarf will never get injured, or sleep or have other issues. It was just me and a friend, who took a year of calculus talking about how to calculate woodcutting * JOKINGLY*

-PS I got a 5 on my AP Calc test.

[Keldor]

I noticed a couple problems with your usage of d's.  Namely the ((dC+L+S)-J)/dt bit.

Let's see if I can fix the formula...

let D = density
let M = max trees
let A = area
let T = trees cut
let G = trees grown
let G0 = initial trees on map
let C = base cutting rate
let L = skill level modifier
let S = stat modifier (Agility)
let Rl = base rate of skill gain per trees cut = dL/dT
let Rs = base rate of stat gain per trees cut = dS/dT
let Rsj = base rate of stat gain when doing things other than cutting trees
let Rt = base rate of tree growth
let J = percentage of time actually spent with tree cutting job (including traveling, so if there was no other job than cutting, this would be 1.00 or 100% )

then,

dT/dt = J*(S*D+C*L)
D = A/(G0+G-T)
dG/dt = Rt*(M-(G+G0-T))
dL/dt = J*Rl*dT/dt
dS/dt = J*Rs*dT/dt + (1-J)*Rsj

We can at least do a bit of work on this.

let L0 = initial level
let S0 = initial skill

L = J*Rl*T+L0
S = J*Rs*T + t*Rsj*(1-J)+S0

So can reduce it to two simultainuous differential equations.

dT/dt = J*(A*(J*Rs*T + t*Rsj*(1-J)+S0)/(G0+G-T)+C*(J*Rl*T+L0))
dG/dt = Rt*(M-(G+G0-T))

let Q = current trees standing = G+G0-T

then we can write the equations simply as:

dT/dt = J*(A*(J*Rs*T + t*Rsj*(1-J) + S0)/Q + C*(J*Rl*T+L0))
dG/dt = Rt*(M-Q)

next, differentiate Q

dQ/dt = dG/dt-dT/dt

factor, as much as possible, each equation into terms of T, Q, and G
dT/dt = (J*J*A*Rs*T+J*A*Rsj*t-J*J*Rsj*t+J*S0)/Q + (C*J*Rl)*T +C*L0
Q*dT/dt = T*(J*J*A*Rs+(C*J*Rl)*Q)+t*(J*A*Rsj-J*J*Rsj+(C*L0))+Q*(C*L0)+J*J*A*S0

we end up with something of the form:

Q*dT/dt = (k1+k2*Q)*T+k3*t+k4*Q+k5

differentiate both sides:

QT''+Q'T' = k1T'+k2QT'+k2Q'T+k4*Q'+k3
QT''+Q'T' = (k2T')Q+(k2T+k4)Q'+k1T'+k3

further solving is left as an exercise for the student.

[LordZabujca]

Wait, what? You're calculating the density by dividing the AREA by the number of trees, not the other way around? How does that make any sense?

[Zironic]

I noticed a couple problems with your usage of d's.  Namely the ((dC+L+S)-J)/dt bit.

Let's see if I can fix the formula...

let D = density
let M = max trees
let A = area
let T = trees cut
let G = trees grown
let G0 = initial trees on map
let C = base cutting rate
let L = skill level modifier
let S = stat modifier (Agility)
let Rl = base rate of skill gain per trees cut = dL/dT
let Rs = base rate of stat gain per trees cut = dS/dT
let Rsj = base rate of stat gain when doing things other than cutting trees
let Rt = base rate of tree growth
let J = percentage of time actually spent with tree cutting job (including traveling, so if there was no other job than cutting, this would be 1.00 or 100% )

then,

dT/dt = J*(S*D+C*L)
D = A/(G0+G-T)
dG/dt = Rt*(M-(G+G0-T))
dL/dt = J*Rl*dT/dt
dS/dt = J*Rs*dT/dt + (1-J)*Rsj

We can at least do a bit of work on this.

let L0 = initial level
let S0 = initial skill

L = J*Rl*T+L0
S = J*Rs*T + t*Rsj*(1-J)+S0

So can reduce it to two simultainuous differential equations.

dT/dt = J*(A*(J*Rs*T + t*Rsj*(1-J)+S0)/(G0+G-T)+C*(J*Rl*T+L0))
dG/dt = Rt*(M-(G+G0-T))

let Q = current trees standing = G+G0-T

then we can write the equations simply as:

dT/dt = J*(A*(J*Rs*T + t*Rsj*(1-J) + S0)/Q + C*(J*Rl*T+L0))
dG/dt = Rt*(M-Q)

next, differentiate Q

dQ/dt = dG/dt-dT/dt

factor, as much as possible, each equation into terms of T, Q, and G
dT/dt = (J*J*A*Rs*T+J*A*Rsj*t-J*J*Rsj*t+J*S0)/Q + (C*J*Rl)*T +C*L0
Q*dT/dt = T*(J*J*A*Rs+(C*J*Rl)*Q)+t*(J*A*Rsj-J*J*Rsj+(C*L0))+Q*(C*L0)+J*J*A*S0

we end up with something of the form:

Q*dT/dt = (k1+k2*Q)*T+k3*t+k4*Q+k5

differentiate both sides:

QT''+Q'T' = k1T'+k2QT'+k2Q'T+k4*Q'+k3
QT''+Q'T' = (k2T')Q+(k2T+k4)Q'+k1T'+k3

further solving is left as an exercise for the student.

Alas I said: This formula is very basic and many things are left out or assumed.  I would differentiate both sides - however I lack the time or patient for a large problem. But taking quick glimpses of your formula. Ok Now assuming the k's are constants - because it just makes sense.

So far, Q= [Q'(K2T+K4-T')+K1t'+k3]/(T''-K2T')

I run into trouble further when trying to figure out what the K's represent as constants.

However I remember the question is of the rate of trees cut so T' needs to be solved for too.

T=[T'(Q'-K1-K2Q)-K4Q'-K3+QT'']/(K2Q')

T'=[Q'(K2T+K4)+K3-QT'']/(Q'-K1-K2Q)

[Torak]

Takes about half a second for a legendary dwarf with Mighty strength to cut a tree down at 100-105 fps, so I'd assume that in a 1x1 local tile,s he can cut all of it down in about 1500-1600 frames.

Not taking into account movement and sleep. (what was the fancy word for this, dead-something)

[Draco18s]

Not taking into account movement and sleep. (what was the fancy word for this, dead-something)

Dead heading.  Heading, as in direction, dead as in useless.

[axus]

Thanks for sharing