We discussed this before, but after I talked to my math teacher, I had to post this. The angle of ascent on Magnum's hill is not done with the trig function sine, becuase since the drop is only 194'8", the triangle is not a right triangle. Sine only works with right triangles, so you would have to use a different trig function. The same goes for MF and how long the first hill is. My math teacher told me that he wouldn't tell me how to do the problem and that I would learn how to do it next year.
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Counting Down the days until June 22
Jeff Young
Isn't that when you use the inverse of sine and cosine and all that good stuff on your TI-86 calculator?
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Raptor Flights: 12
Force Rides: 9
Actually... if you know the angle the lift or hill makes w/ the ground [or, at least, the mean of it], you can solve for the total ride length of the hill. Trust me. =)
Without actual ride plans, or if you can't get there with a nifty angle of inclination device (can't remember proper technical term--inclinometer or something to that affect), you can only get with in a few degrees (read on for explanation). The easiest, most acurate method of finding angle of inclination with total height and lift length IS USING inv sin proportions. By doing this, a vertical leg of a triangel is simply being drawn down to connect with the second leg from the lift hill's highest point. Using the drop even with any other laws of sines rule is pretty much useless because of the roll- over at the top and the pullout at the bottom. The reason even the basic trig method is even thrown off slightly is once again due to the roll-over at the peak of the hill given the fact that the leg and the hypotenuse do not form a perfect point at this imaginary point. Not to mention, the coaster starts ascending from the base of the hill from a height greater than zero. Although, as I sit here thinking about it, if the added hypotenuse obtained from the height of the base of the lift off the ground was added to the overall length of the lift, this would mostly compensate for the roll-over radius at the peak. --Given radius of the roll-over curve, though, you COULD also calculate the theoretical maximum peak of the triangle for a true angle calculation more accurately but making sure as to subtract the base of the lift's height fromt total height. At that point, though, you might as well have the plans in your hands.
Physics day Mganum angle as posted by Dave Althoff: 28 degrees.
Angle obtained using supposed exact length of lift hill not counting height of base or rolloever in standard inv sin relationship(**althought we found we may have iterated an already skewed value**for all intensive purposes, disregard this as there was no proof.): 30 degrees
Pretty close,thoug, ehh?
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-Dave Kochman
Pittsburgh
I always use 30 for my quick and dirties, as it's just as inaccurate as not accounting for rollovers on entry and exit.
Safely agreed as you could see. :)
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-Dave Kochman
Pittsburgh
But how could it be using inverse sin if there is no right angle in the problem? Since the lift hill is 205 and the drop is roughly 195, there is no right angle in the triangle.
I don't know about you but I'm more worried about the drop then the accent. I would much rather let my TI-85 do the work for me anyway ;)
Jeff -- there IS a right angle, the plumb line ;)
We've been making so many assumptions and rounding (like ignoring the curves, etc.) to begin with, that making a few more won't kill us (we're not BUILDING these rides, after all ;) )
Look at it this way: the lift doesn't take you 205 feet up from where you START anyway -- don't forget, the track is already elevated before you ever get to the lift. That 205 figure is from ground height, not track height. Without plans, we don't know how much you actually get elevated by the LIFT (as opposed to up the stairs getting into the station, then down the little dip out of the station, then up the lift, which apparently totals roughly 205 feet ;) )
We also don't know how far down the drop takes you *compared to where the lift started*, so saying we don't have a right triangle because the drop isn't as high as the lift doesn't really matter. (We can factor the drop right out -- drop a plumb line from the top of the hill, and draw a line extending the track at the bottom of the lift parallel to the ground. We now have a right triangle with the side opposite the "30 degree" angle, call it length X, being SOMEWHERE in the 200 foot ballpark. Without plans we don't know the exact length of this virtual line)
So for simplicity, let's argue that the first drop goes down to the same level as the start of the lift. That gives us 195 feet as a number to plug into X. Earlier messages were using 200 or 205 for these calculations (because that's "the height of the lift"), but the net difference in what amounts to ballpark figures isn't THAT much.
Tell your teacher a CMU grad says he's trying to overcomplicate our assumptions... ;)
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--Greg
http://www.pobox.com/~gregleg/
MF count: 2
*** This post was edited by GregLeg1 on 5/28/2000. ***
All this is much easier with a photograph and a protractor. Precision is only for theoreticians anyways.
-- Harley
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CP fan since 68.