Shivering Sine Wave
Okay, lemme see if I focus and find the real identities of this equation...
If you take the sine of way too much pi, it gives you ST. ST being our constant... Constant source of airtime... We then find there really is no limit the A factor. So we then recenter this equation around the CF axis, and plug that into our TI-Whatscomingin03 calculators... And what do we get?? Fun²!!!!
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-Jon
I'd Rather Be Riding Roller Coasters
Think of it as (f[un])^2. Thus, the square of the function of 'un'. But I digress.
Hills, while largely sine in appearance, I'm willing to bet are actually semi-klothoid in nature.
[this is explained for loops nicely here:
http://www.pen.k12.va.us/Anthology/Pav/Science/Physics/book/Loops.f/Loops.html]
You see, a standard sine curve works fine, but it is too wide on top and/or too tight on the bottom.
Round curves can be fun, too.
*** This post was edited by Wolf on 8/23/2002. ***
Michael Darling said:
If you're at a constant slope, you have a constant derivitave (Oh, my God... calculus!) so you're not going to leave your seat.
I never thought I'd actually find myself adding to this conversation, but here goes nothing:
If you're at a constant slope, then the equation is nothing more than a constant. Thus, the derivative of the slope is NOT a constant, but rather ZERO. I believe what you meant to say was that the slope of the line was linear in nature, in which case the first derivative WOULD be constant. It's really quite easy to understand, because calculus is so awesome.
I mean, look at me, I'm a moron and I can see this whole thing very clearly. I can "secant" you?
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[Nitro Dave -- 100 Laps] [Track Record: 56 and counting...]
"Honesty or mystery, tell me? I'm not scared anymore...
I've got no secret purpose...I don't seem obvious, do I?" -- The Authority Song
*** This post was edited by Davie the Luv Monkey on 8/25/2002. ***
ST chick said:
Not the Fun² thing, please not the Fun² thing! By the way, why isn't it Fun quantity squared, or (Fun)²? I mean, wouldn't Fun² just be Funn?
It's better than hearing the "song." I'm sure someone can guess what song I'm talking about…
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“If you give a enthusiast a footer.......He’ll want a coaster!!!"
Ya know, I come here on my last day of summer vacation to get my last online coaster fix, and I run into school and math stuff!
e
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Tommy Penner - Variable X
Cedar Point FanBoy since 2001.
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[Nitro Dave -- 100 Laps] [Track Record: 56 and counting...]
[Proud Coasterbuzz Club Member, Credit Whore, & Jr. Gemini Double-Lapper]
Gemini -- It's no Millennium Force, but it's twice as nice!
*** This post was edited by Davie the Luv Monkey on 8/26/2002. ***
If you're at a constant slope, then the equation is nothing more than a constant. Thus, the derivative of the slope is NOT a constant, but rather ZERO. I believe what you meant to say was that the slope of the line was linear in nature, in which case the first derivative WOULD be constant. It's really quite easy to understand, because calculus is so awesome.
y=2x has a constant slope, and the equation isn't a constant. y=4 also has a constant slope, and it is, indeed, zero. Hopefully calculus will become a bit more awesome for you in the future--keep applying it to coasters.
Right. A constant slope has a constant derivative. (d elevation/d time). A flat piece of track has a zero derivative.
Airtime is really dictated by the second derivative of elevation/dt^2. Thus, the perfect floater hill comes down in an actual parabola (quadratic) (note that a sin wave is not a parabola). A sin wave's second derivative is a negative sin wave, so you'd get the most air cresting the top of the hill but not so much down the second half of the back side.
Calculus is fun.
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A rollercoaster? What's that?
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