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Name: Melinda
Status: student
Grade: 9-12
Location: CA 
Country: N/A
Date: 4/27/2005


Question:
I am doing a project on similarity for my geometry class. I have to make a small scale replica of the roller coaster Superman the Escape. I know I have to multiply all the measurements by like 1/205 to make it around two feet tall, but how do I figure out the curve of the ride and how wide to make it? Any help would be gratefully accepted!!


Replies:
This is tricky without seeing the plans you are working with -- it could be "trial and error". A relation that might prove useful is: The arc length of a circular arc, call it "L", is given by: L = R x , where "R" is the radius that forms the circular arc, and is the angle expressed in radians. So if you can divide segments of the curved parts into a series of circles -- a French curve may be useful -- then you will be able to construct the curved parts by "n" successive circles: L1, L2, ..., Ln. If you are working from a diagram, and you know (or can find someone who knows) calculus, the length of the arc formed by a function, f(x) from x=a to x=b is: Iab = (1 + [f '(x)]^2) dx, where Iab is the integral from 'a' to 'b', and f ' is the derivative of f(x) with respect to x. If you don't know f(x) you can resort to numerical integration using Simpson's rule, or some other numerical device. A non-mathematical approach would be to use a flexible spline. These are lengths of flexible metal or rubber that can be bent/molded to the desired shape. You can then piece together the model material to fit the spline. These splines can be found at hobby stores or off the Internet if you "Google" search for suppliers that serve model railroading and/or ship building hobbiests. I think one supplier is "Micro Mart" or "Micro Market" -- I forget their exact name. What you are trying to do, model builders do all the time, so you may be able to get some easier way to do what you want to do.

Vince Calder


Small scale models are more of an art form than a science, so please forgive me if some of my answers seem "unscientific". Also, it is not quite clear to me exactly what you have to work from, other than the height of the primary drop.

For the width, I'll assume you have a width of the actual roller coaster. Your best bet is typically to convert this number to a smaller unit of measurement. As I recall, that roller coaster is about 20 feet wide. Dividing that by 205 will yield a small an relatively unusable fraction. Multiplying it by 12 will yield 240 inches wide, which can be divided by 205 to give about 1 11/64ths inches. If the actual ride is closer to 17 feet, it would only need to be 1" wide for the model.

You have correctly judged the curve to be the hardest part to model. If you have a picture of the side of it, you can scale the picture up or down as necessary. If you have the approximate dimensions, you can build that portion of the model separately, using a circular template to build the structure around.

Ryan Belscamper


You are on the right track regarding scale. The accepted practice uses rulers marked off in given distances. An architectural scale,is triangular shape, with 12 different scales. The explanation in words gets complicated.

The scales are used to convert something in feet to inches, either for drawings or models. Something 12 feet becomes at an 1/8 th inch equals a foot scale one and a half inches.

Let us look at your model, you did not mention the height but a guess, say 50 feet. or 50 x 12 = 600 inches. If the model was 1 inch equals 1 inch, that is "full scale" or a 50 foot high model. But if 1/8 inch equals one foot, that is 50 X 1/8 "= 6.25 inches. More convenient for drawings, or models.

The other common scale in use is an engineers scale. Like the architectural it has 12 scales, but instead of feet and inches, it is metric, or in 10 ths. It is used more for larger distances, like trying to make a drawing for something 200 foot long.

Back to your roller coaster. The physical construction related to scale, may be issues. For example, the rails. It could be their width is no more than a line width, will you try for three dimensions, or just opt out for drawing a line. Same goes for the railroad ties , their spacing. Often, it is best to think backwards, how big is the final product, how will you get it to where you want to go. It very well may be partial disassembly. It will be best to make those plans from the beginning. Their is a classic joke of building a boat in your garage, then having to tear the garage down to get the boat out.

James Przewoznik



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