Calculator Programs For Coasters

[jimths08]

[CENTER][CENTER][FONT=&quot]Calculator Programs for Coasters[/FONT][/CENTER]
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[CENTER][CENTER][FONT=&quot]The Basics[/FONT][/CENTER]
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Okay, so here we are with no lives. Soooo, what more to do than make something you’ll never use. For the next 30 minutes or so, were going to be building programs in graphing calculators. Though it’s not tested, these programs should work on most [I]Texas Instruments[/I] calculators. I personally have a TI-83. Most people in school now have a TI-83Plus which will work as well. The models I’m going to walk you through are the TI-83, and TI-83Plus. If you have a different model, PM or IM me and I’ll try to help you out.

[CENTER][CENTER][FONT=&quot]Building the Beast[/FONT][/CENTER]
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Now that you know how to access your programs area, we’ll being making our first program. During this first program, I’ll describe each and every detail so that you understand how it works and what each part does.

1: turn on your calculator and press the PRGM button

2: using your directional pad, press the ‘right’ button 2 times until ‘new’ is highlighted

3: press ‘enter’ and name the program ‘CSTRDROP’ by typing in each letter with the green super-scripts above most of the buttons. for example, to get CSTR, press ‘PRGM’ then ‘LN’, ‘4’, and ‘*’ as in multiply.

4: once you get it named it will take you too a screen that says PROGRAM: CSTRDROP
:
5: now I’m giving you an idea of what the end process will look like. here goes,
Disp “SOLVE FOR”
Disp “1 SPEED:”
Disp “2 HEIGHT:”
Input “”,A
If A=1
Goto 1
If A=2
Goto 2
Lbl 1
Input “DROP HEIGHT:”,L
‘square root of’ ((H*.3048*9.81/.5))*2.2369363*.864+L=V
Disp “DROP SPEED IS:”,V
Stop
Lbl 2
Input “DESIRED SPEED:”,v
Input “LIFT SPEED:”,L
(((V/2.2369363)2 *.5/9.81)+L)*3.2808=H
Disp “HEIGHT IS”,H
looks pretty sickly doesn’t it? its not.

6: you can see the first thing we need is a ‘Disp’ command. ‘Disp stands for display and enables what-ever you put in parenthesis to be seen when you run the program. Those of you familiar with HTML will understand this a bit better but I’m telling it as if you all are dumb and idiots.

7: make sure you’re still in the program called CSTRDROP (your calculator probably shut off while I was jabbering) and press ‘PRGM’. what comes up is a list of words which we’ll use later. press the ‘right’ button once till you see that ‘I/O’ is highlighted. now press ‘3’. it takes you back to the PRGM screen with ‘Disp’ shown. now we can start typing.

8: what you put here really doesn’t matter since it doesn’t interfere with the calculations of the formula, you could be “TRIGONOMETRY SUCKS” for all I care, but every time you run the program, that will pop up on your screen. whether or not your moma will like seeing that when you show her this, is your own risk that I don’t take blame for. I would type “SOLVE FOR” since that tells you your going to try and solve for something. one trick you need to learn, if you press ‘2nd’ and then ‘ALPHA’. with the 83Plus you can hit ‘ALPHA’ twice to make it lowercase.

9: now press ‘ENTER’ which will take you to the next line. press ‘PRGM’ and hit the ‘right’ button once, then press ‘3’ to get ‘Disp’ again.

10: type ”1 SPEED:” and make sure you have the quotations.

11: press ‘ENTER’ and get another ‘Disp’. on this one type “2 HEIGHT:”.

12: now were going to press ‘PRGM’ and the ‘right’ (I’m going to call it > for now on) button and make sure ‘1:’ is highlighted. press ‘ENTER’. ‘Input’ shows up in the PRGM area, now type “”,A. its odd yea, but it tells the calculator that the number you push next is going to be a branch where each leads in different directions.

13: now click ‘PRGM’ and then ‘ENTER’. you can see that ‘If’ was placed in the program, type ‘A’.

14: here is a tricky part, press ‘2nd’ and then ‘CATALOG’ which is the 2nd button from the left on the bottom row. using the ‘up’ and ‘down’ arrows, scroll until you see the ‘=’ sign. when the little black arrow is pointing at it, hit ‘ENTER’.

15: now hit ‘1’ and then ‘ENTER’. press ‘PRGM’ and then ‘0’. you get ‘Goto’ on the program screen. next simply hit ‘1’.

16: repeat numbers 13,14, and 15 but instead of ‘1’ hit ‘2’ in the spots required. in the end it will look like this: ‘If A=2
Goto 2

17: now we can do some more logical non-technical stuff. press ‘PRGM’ and then ‘9’. ‘Lbl’ comes up, now hit ‘1’and then ‘ENTER’ what we have just done is told the program that the next few lines we write will be the sub-program for the whole program. imagine it like a tree that splits from the single trunk to 2 branches. the two branches never interact yet they came from the same source, that’s how this works. we had one program where you decided what you wanted to do, now you will input numbers to solve for variables. for you younger kids, a variable is a number that can change, for instance, (3.14)R where you can change R to get a different number when multiplied by 3.14.

18: next hit ‘PRGM’ and ‘>’. hit ‘ENTER’ and you get ‘Input’. ‘input’ stands for a number that you are pressing. your giving input to the calculator. type “DROP HEIGHT”,H. what will be displayed is ‘DROP HEIGHT’ and ,H is what we will put in the formula to stand for height. consider it a tag or label.

19: now we’re going to do the same thing as above but instead it will turn out as Input “LIFT SPEED”,L. remember to get the ‘Input’ go to ‘PRGM’, hit ‘>’ and then ‘ENTER’.

20: here is the fun part; the formula! don’t you feel like a mad scientist? the formula is ‘square root of’ H*.3048*9.81/.5)*2.2369363*.864+L=V. to get the ‘square root of’, hit ‘2nd’ then ‘x2’ which is the first button 5 rows up from the bottom. to get the ‘(‘, hit the side-by-side buttons in the 5th row, 3 and 4 columns from the left. to get the ‘=’ at then end, don’t hit ‘ENTER’, that will just take you to the next line. instead, hit ‘STO->’ which is 2nd row from the bottom, first button. it will give you a symbol similar to ‘>’, then type V.

21: now that we’ve got our formula written, we have to display the answer! it doesn’t do it on its own so we have to tell it to. to do this, type ‘DROP SPEED IS:”,V’. I’m pretty sure you know how to type all of that. what that line does is take the answer from our formula, V, and attaches it to the line ‘DROP SPEED IS’. once again, you see that the ,V is a tag that tells what and where from to pull something.

22: the first branch of our program is almost done, all that needs left is to close it. to do this, hit ‘PRGM’ then ‘ALPHA’ and finally ‘F’. ‘Stop appears in your program. what the ‘ALPHA F’ did was select the correct direction and it wasn’t a number since ‘Stop’ was so far down the list of directions.

23: one branch down, one to go. for this next one, I won’t be as detailed as the first so stay focused and pay attention. type in ‘Lbl 2’. remember that ‘Lbl’ is a direction so you hit ‘PRGM’ then ‘9’

24: here is the 2nd branch of the program;
Lbl 2
Input “DESIRED SPEED:”,V
Input “LIFT SPEED:”,L
(((V/2.2369363)2 *.5/9.81)+L)*3.2808=H
Disp “HEIGHT IS”,H
Stop
you should be able to copy that down without any problem or issues. just remember that to get ‘Input’ you go ‘PRGM’ ‘>’ twice and ‘ENTER’. same for Disp except instead of ‘ENTER’ you hit ‘3’. don’t forget the 3 tags at the ends of the ‘Input’s and ‘Disp’.

25: test the formula by turning off your calculator and turning it back on. hit PRGM and then find the program titled ‘CSTRDROP’. highlight the number next to hit and hit enter. it will ask you the questions and if you will plainly input the answers you need and want. for a test, run the program and hit ‘1’ then ‘ENTER’. it asks you the drop height, put 208 in and hit ‘ENTER’. then it asks for the lift speed, hit ‘6’ then ‘ENTER’.

[CENTER][CENTER][FONT=&quot]Complaint Department[/FONT][/CENTER]
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If your having trouble with the formulas or how to work with your calculator, talk with me on AIM, MSN, or PM/E-Mail me. I’d be happy to help. These formulas are great at working with elementary; they tell you what the train will do in different situations. Remember that the drop height isn’t the height of the structure. For instance, Raging Bull is only 202’ tall but the drop is 208’ tall. So I would put 208 for the H variable. The lift speed is exactly what it sounds like. Put it at 6 and hit enter. Tada! 74.16414787 comes up. That’s in mph and all the inputs you make such as height and speed are all to be in imperial fashion. Speed=MPH, Length=Ft, ect. This particular formula was made to be accurate with B&M hyper coasters in NoLimits and real life ones such as Raging Bull and Apollo’s Chariot. They may not work correctly with Intamin or Vekoma coasters. Reason being, they have different friction rates, which is the rate of speed lost over a given distance. I have it set for B&M at 0.864 at the moment and to change it, just find those numbers in the formula and change it as needed. I’ll post the Intamin, Vekoma, and wooden friction rates as I calculate them. The reason there are 2 programs is that one of them calculates the speed at a drop from you giving a height. The other is the opposite; you give a speed and it tells you how high you need to be to get that speed. The 2nd program has some issues and isn’t 100% accurate. It should be within 1-5 feet though. The first program is only off by 1 or so mph so its pretty accurate. Reason for its in-accuracy could be different lift speeds and friction rates between coasters. Well that wraps it up for this tutorial, 2 more are to come; G-forces and launches! Happy programming!

[jimths08]

*I had to post this after the above post because it was too big. 10,000 char. limit. :sick:

Well, here they are. I've been working on them off and on for about 2 months now. If your having trouble getting them to work properly or something of the sort, PM/Email/IM me and we'll work it out.

Credit:
Jimmy-building and programming
John-walking me through glitches
Oscar-reversing the formula
Dirk-formulas (I found them on his site)

[Forrest Gump]

Wow, this is.... very interesting.

Now I can finally prove my physics teacher wrong on some incorrect statistics he gave us. ;o) Or not, I'm not that much of a jerk.

[CP Maverick]

Ok so you accounted for friction, what about air resistance? On a coaster, especially taller ones, you're going to have more resistance from air than from the wheels. How does your program compensate for that? :)

Remember, drag is a function of velocity squared and the velocity in that function would be dynamic (changing) so you'd need to program a differential equation to figure the drag force throughout the drop.

[jimths08]

Though you are right, wind is a variable that is always changing. Lift speed stays the same, and height stays the same. If you carry a little wind speed thing when you go to a park then I back down, but in a program like this, its not a thing that really makes a difference.

With the resistance changing at different speeds, I've not an idea how to math that or what ratio to change it so its better that I don't try to. The difference really would only be about 1 foot or mph.

Also, in NL, I'm pretty sure that wind isn't a factor. These things aren't meant for you to rely on building a contraption in your backyard, just for fun and entertainment. :)

[CP Maverick]

I wasn't talking about weather generated wind, I was talking about drag caused by the motion of the vehicle. Air is a fluid like water, move your hand quickly through water and you'll feel a force pushing back at you. That's the force that dictates terminal velocity.

Drag force = 1/2 drag coefficient * frontal area * fluid density * velocity²

Terminal velocity is when the drag force and the force due to gravity are equal.

[Jimmy B]

[QUOTE=jimths08]With the resistance changing at different speeds, I've not an idea how to math that or what ratio to change it so its better that I don't try to.[/QUOTE]


Wait until you take courses like Differential Equations (DE), Linear Systems, and Engineering Mechanics, then you'll find out how remarkably simple it is to mathematically analyze first-oder DE's by employing methods of separation of variables in the most general cases. Although numerically modeling the changing speeds can be quite a challenge, but yield more precise results. This can be done on mathematical software or even on MS Excel.

And yes, air resistance actually does make a big difference, in fact it is the primary force that limits the speed of all moving objects, especially coaster trains.

[jimths08]

Well as the programs are now, they represent B&M hypers pretty accuratly. If there is a difference, its only by 1mph or less in most cases. Some of you will go and try to test this, its not possibly unless you know the lift speeds of the coaster.

An example: Silver Star at Europa Park has a 210.75' drop and hits 78.9 mph(its probably more depending on when the tested it, usually its in winter w/o anybody on the train) If you plug 210.75' with a 6mph lift into the program, it comes out with a speed 74.6 which is the biggest fault of the program not sporting wind resistance. Say you up the lift speed to 9 though suddenly it comes out at 77.6mph. Closer yet; for all we know the lift speed may be 8 or 9 mph.

Another example: Raging Bull at SFGAM has a 208' drop with a lift speed around 6 mph and hits 73mph. Plug those numbers in and you get 73.6mph. Right on, I've ridden it and can say the lift speed is pretty accurate so the end result is also close. Its not perfect no, but its within 2-3 mph in the end. It works even better with NL, test it on your own and see.

One thing you may notice in both of these is that Silver Star is only 2 feet taller yet poses 4mph more. I'm not as experienced as many of you are but I'd say its A: lift speed B: varying friction resistance due to maintenance C: varying directions at which the wind hits the train.

[CP Maverick]

Once again, we weren't talking about wind you feel standing in one place. Lift speed will have minimal effect on the final velocity of a real working vehicle.

[jimths08]

Of course lift speed makes a difference. The lift speeds is simply added to the final speed. You could have a coaster that was 100' tall go 70mph, but the lift speed would have to be around 25mph. If your going X speed X high, you just do the formula for a drop and add the speed you allready had at start of the fall. If it works in real life then how much can it be wrong in a formula? The things you guys are talking about are things that matter yea, but I can guarantee that for the people who do use this, it will work fine with them, because what they use it for will effect gs and so only 0.1 or less. If you revised it and made it fool proof, then hats off to you. I've not taken a physics class and right now are just in Trigonometry, whether it makes a difference or not.

[CP Maverick]

Why go through all of what you did and just use an equation like

(g-a)h + v1²/2 = v2²/2
g = gravity
a = drag (because you're keeping the equations simple, calculate drag as an average of the numbers)
h = height
v1 = lift
v2 = final

a = 0.35 * sqrt(v1²+2gh) ..[metric]
v2 = sqrt(v1²+2[g-a]h)

Input h, v1
calculate a
calculate v2
output v2

[jimths08]

The formula I put togther was basically from [url=http://members.home.nl/ermen.dirk/Website/gforcecalculations.html]here[/url] just altered to fit Imperial. I talked with several people who were in upper level maths and physics but non of them knew of any different so I just went with it. I guess that one would work just the same, whats there is there though.

[Joseph]

[quote=CP Maverick]Why go through all of what you did and just use an equation like <snip>
[/quote]

Because coasters travel in 2 (and usually three) directions so that forumla would be rendered fairly inaccurate.

Good stuff Jimmy, I like when people do inteesting stuff like this :)

[CP Maverick]

Those equations were based off momentum equations, so I'm not sure what you're getting at... Like I stated before, wheel friction has little effect on ride speed.

[Joseph]

Explain how you derived it then because I've never seen a momentum equation based upon acceleration.

Do you think that momentum is scalar?

[Montu Man]

[quote=jimths08]Of course lift speed makes a difference. The lift speeds is simply added to the final speed. You could have a coaster that was 100' tall go 70mph, but the lift speed would have to be around 25mph. If your going X speed X high, you just do the formula for a drop and add the speed you allready had at start of the fall. If it works in real life then how much can it be wrong in a formula? The things you guys are talking about are things that matter yea, but I can guarantee that for the people who do use this, it will work fine with them, because what they use it for will effect gs and so only 0.1 or less. If you revised it and made it fool proof, then hats off to you. I've not taken a physics class and right now are just in Trigonometry, whether it makes a difference or not.[/quote]

Lift speed does have an impact. If you had a 100 MPH lift hill verses an 8 MPH one, the coaster with the 100MPH lift will have a higher velocity at the end of the first drop.

[CP Maverick]

I was referring to the minimal difference in speed a 5mph lift and a 15mph lift make.

Momentum is a vector, but none of those equations are concerned with direction. What you're telling me is that a coaster with a drop to the left and a coaster with a drop to the right of the same length will have different speeds, that's completely inaccurate. They will have different velocities, yes, but only in the sense of direction, not magnitude. All those equations give you is magnitude, aka "speed"...

Any other questions?

[Jimmy B]

[QUOTE=CP Maverick](g-a)h + v1&#178;/2 = v2&#178;/2
g = gravity
a = drag (because you're keeping the equations simple, calculate drag as an average of the numbers)
h = height
v1 = lift
v2 = final

a = 0.35 * sqrt(v1&#178;+2gh) ..[metric]
v2 = sqrt(v1&#178;+2[g-a]h)

Input h, v1
calculate a
calculate v2
output v2[/QUOTE]


I don't believe I've seen that equation explicity either, but that looks more like a kinetic energy per unit mass equation, which is derived from momentum.

The system of differential equations that model the vertical and horizontal velocity, respectively, of the train as a function of time is

d&#178;y/dt&#178; = a*(dy/dt)&#178; - g

d&#178;x/dt&#178; = a*(dx/dt)&#178;

a = drag coefficient
g = gravitational acceleration

Simply employ the separation of variables method for solving them; for that second DE, you'll get an inverse linear function, and for the first one, you'll get a hyperbolic [i]arctan[/i] function. You could also solve the DE's further to acquire the position functions with time.

[Joseph]

What I'm trying to say is..

If you are going to use momentum, you have to find all three components to come up with the magnitude, since there is movement in more that one direction and the magnitude of the velocity in the y-direction is not always the same as the x-direction. (only at 45 degrees, ignoring friction). Plus, if you have a "turning drop", even if ever so slightly, that z-component may be small but again different in magnitude.

[CP Maverick]

^ Did you read his original problem? All he was solving for was speed and/or height. Why would you need all three vectors to determine that?

Jimmy, is that the same drag coefficient used in my drag force calculations? It almost seems overly simplified.

[jimths08]

My drag is really simple. All I did was times the answer by 0.864 to get the final answer. I found 0.864 by using heights and speeds from Raging Bull, Apollo's Chariot and Nitro. I've talked with another guy who is a mechanical engineer trainee with 2 or 3 years at SFSTL who says he knows the coefficent is 0.13 for B&M but I've not tested it yet.

[CP Maverick]

0.13? Wow that's really low if its the same as the drag coef I'm using. Most cars fall into the 0.3x catergory.

[redunzelizer]

[quote=jimths08]Of course lift speed makes a difference. The lift speeds is simply added to the final speed. You could have a coaster that was 100' tall go 70mph, but the lift speed would have to be around 25mph. If your going X speed X high, [B]you just do the formula for a drop and add the speed you allready had at start of the fall[/B]. If it works in real life then how much can it be wrong in a formula? .[/quote]
[COLOR=Red][B]You're soooo dead wron[COLOR=DarkOrchid]k[/COLOR]!!! :sick:[/B][/COLOR]

Please stop confusing people like that. Thanx! :sadface:

redunzelizer

[jimths08]

He didn't say what type of B&M though, just B&M was all I heard.

lol, What Red? Explain that out.

[redunzelizer]

[quote=jimths08]lol, What Red? Explain that out.[/quote]
Nothing to "lol" about. I had posted the underlying (frictionless) equations exactly 16 hours ago on another board, within the thread [I]you[/I] started about the very same topic (even with the same wording).

If you are either not willing or capable of reading, and at the same time attempt to provide a bloated program for a simple one line formula, with [I]your [/I]formulas even being wron[B]k[/B], I can only suggest:

Stop this crap. Immediately! And better apologize for your obvious ignorance.

redunzelizer

P.S. I tried to help a bit [I](16 hours ago)[/I] like i usually try to.
And you now are "lol'ing" at me. I *will* remember that next time. Promised!