RCT2 maths

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File: 1444910147729.jpg (283.95 KB, 658x502, 329:251, op.jpg)

RCT2 maths 10/15/15 (Thu) 11:55:47 No.3207

Dear /sci/entists

Not sure just how /sci/ this is. Hopefully its allowed.

I'm working on a project in RCT2 but it requires some maths beyond my understanding. Hoping some anon can help me out.

Back story of the project. I've discovered a new way to go slow and I think I’ve made the longest ride possible. I found out that if you have a coaster running on a perfectly level track it will keep going indefinitely (even round corners) with its speed decaying in a regular way towards zero but importantly never getting to zero. Eventually its average speed would be far lower than the normal "vintage cars" (see mr. Bones et al) method of going slow. Exploiting this I made a giant spiral track on the largest map size possible (256 by 256) with the train starting on the out side edge and slowly working its way into the centre. When it get to the centre there is a tiny hill and it then rolls back the way it came.

I need help with 2 problems

1 how long is the spiral I've made?

2 given the total length of the spiral how long will the train take to complete a run?

OP 10/15/15 (Thu) 11:57:04 No.3208

File: 1444910224682.jpg (51.6 KB, 1266x260, 633:130, problem 1.jpg)

Problem 1

I think i've got something useful of the spiral length but i don't know how to simplify this further.

OP 10/15/15 (Thu) 12:03:53 No.3209

File: 1444910633760.png (51.91 KB, 1298x702, 649:351, problem 2.png)

>>3208

Problem 2

I recorded some data of the train slowing down over time.

top left table is the raw data i collected from watching the train slow down after it left the station. I recorded the time (in minutes) and how many tiles from the station the train had traveled. from that I calculated the trains speed (tiles per minute) and did a plot of that, right graph. from that i found the a line of best fit. the table at the bottom is this equation and its values.

Am i using the right kind of line of best fit or is there a better kind. I tried log and exp but they didn't fit as well as this powers.

10/15/15 (Thu) 14:44:51 No.3210

>>3208

>how to simplify this

Look at length of two consecutive sections instead.

(x+(x-1)) + ((x-1) + (x-2)) + ((x-2) + (x-3)) + … =

= (2x - 1) + (2(x-1) - 1) + … =

= Σ (1 to x) (2x - 1) = Σ (n < 2x; n odd) =

= x^2

Somewhat unsurprisingly, as your path passes through each single plot on a surface of x^2.

>>3209

>Am i using the right kind of line of best fit

log is definitely not the right fit for this. Theoretically, exp should be the right one; if deceleration is proportional to speed, the solution to your differential equation should be exponential deceleration towards zero. But from your plot it looks like your speed doesn't go down to zero, but to some constant value different from zero.

OP 10/15/15 (Thu) 16:16:31 No.3211

File: 1444925791526.gif (1.25 MB, 245x246, 245:246, sensible anguish.gif)

>>3210

>its simplifies to x^2

god dam it im retarded

>..but to some constant value different from zero

yeah it does seem to do that. however, If i ever let it run for a really long time eventually the coaster just creeps along. moving one pixel every few seconds. maybe i just need to get more data for a better exp fit.

OP 10/15/15 (Thu) 17:39:21 No.3213

>>3209

ok so for the sake of argument lets use that equation i got.

Y = 25.526650366 X^-0.35828871

with Y being Speed and X being Time.

now the length of the track is 256(size of the map in tiles) squared which is 65,536. but because the coaster will roll back the real length is double that, so 131,072 tiles long. if that a speed/time graph then the area under the curve should be distance, right? if i can put that distance in and work back i should be able to get the time? I have a feeling im going to need calculus for this.

10/15/15 (Thu) 20:23:18 No.3214

>>3213

Yes, you're going to need Calculus for this.

http://www.wolframalpha.com/input/?i=solve+integral+from+0+to+t+of+25.526650366+x^-0.35828871+dx+%3D+131%2C072&dataset=

Wolfram says t=303383 minutes, or around 210 and a half days, for a round trip.

OP 10/15/15 (Thu) 20:28:41 No.3215

File: 1444940921337.png (12.21 KB, 338x281, 338:281, smug peep.png)

>>3214

>210 days for a round trip

now we're talking

if you're interested mr. bones wild ride takes 70 minutes to finish, the wheel of life and death takes 60 hours to finish and this one takes 210 days.

10/15/15 (Thu) 20:53:33 No.3216

>>3215

To be fair, it looks like your fit from >>3209 underestimates the speed at later times, so 210 days is probably an overestimate.

OP 10/15/15 (Thu) 21:16:45 No.3217

>>3216

yeah I know but I don't know how to get a better fit. exp should work, according to >>3210

better but for some reason it makes a straight line.

10/15/15 (Thu) 21:36:03 No.3218

>>3217

Yeah because you should use exponential+constant fit, not the bare exponential fit. But I don't think excel can handle this.

I use Mathematica for stuff like that because I have student's license.

10/15/15 (Thu) 23:47:56 No.3219

>>3207

> When it get to the centre there is a tiny hill and it then rolls back the way it came.

When it gets to the centre hill, how do you know that won't change things and cause the car to stop?

OP 10/16/15 (Fri) 09:08:43 No.3221

File: 1444986523254.png (43.65 KB, 1440x900, 8:5, zoomed out.png)

>>3219

I tested it on a smaller scale and it always rolls back even when it has a really tiny speed. its kind of a moot point anyway because I'm not planning on leaving it run the full 200 ish days so there might be some other things i've not considers that will eventually stop the train. At some point the game probably doesn't measure the really tiny speed that well and would just round it down to zero and the train would stop. but as far as im aware it would take a long time to get to that point. I've left it running for a few hours and its still going but so slowly that it kind of jitters forwards, one animation frame at a time.

OP 11/22/15 (Sun) 19:13:16 No.3519

File: 1448219596887-0.jpg (33.51 KB, 580x544, 145:136, random walk in a 2d box.jpg)

File: 1448219596948-1.jpg (229.48 KB, 761x450, 761:450, box maze.jpg)

me again.

I think I'm onto something here. something slower but, again, its a bit beyond my level.

my idea is to have a hedge maze which is just a large box (no paths / dead ends / corridors etc) and have the guests start in one corner and finish in the opposite corner. Guests walk randomly a bit like 2 gases mixing. I need to know any equations or laws that govern this kind of random walk experiment.

Also how does it scale with box size? If the guests knew the way out than the time it took them to get out would be 2n with n being the box length (guests can't walk on the diagonal so it would not be √(2n^2) as they can't use the hypotenuse). so doubling the size of the box would double the walking time in the is best case. also some really unlucky guest could be trapped in there forever but I really want to find out what the average escape time would be and how that scales with box size.

also if i had say 100 guests in the maze and measured the time it took for them all to get out would it resemble radio active decay?

11/22/15 (Sun) 19:36:44 No.3520

>>3519

What you're looking for is called Brownian Motion. It's a well studied phenomenon and some of the known properties are likely to help you.

https://en.wikipedia.org/wiki/Brownian_motion

OP 11/22/15 (Sun) 19:52:54 No.3521

>>3520

Thanks. I'll have a look into it.

11/23/15 (Mon) 00:54:36 No.3522

>>3519

pure random walk scales with square of box length