Length of a curve

Brief sysnopsis: I need to get some steel pipe rolled to match the inside of an eliptical canopy roof structure and I do not know how to calculate for the actual length of pipe required. Pythagora doesn't seem to cut it when "c" follows a curve.

Thanks in advance for any help I get

What a delight to see such a question. The students who frequent this sight can have answered, right before their eyes, "When will I EVER use this stuff?!"

The Pythagorean Theorem COULD be adequate, but only in very small sections. To do the whole thing, that is a non-trivial problem. I do not think I would have put it under "Geometry". I think it would require calculus.

Can you supply the exact measurements you are trying to match? Is it exactly half an ellipse or is it less than half? Is it truly elliptical or is it just not quite a circle?

If you want a general answer about general stuff, a brief answer could be given. If you're building a real structure, you'll have to be substantially more specific. I't not a famous aviary with lights strung up on each beam, is it?

Let's see what you have?

If it is half an elipse you might be entertained by
http://mathforum.org/dr.math/faq/formul ... lipse.html

Thanks guys;

Here's the information that I have, picture 5 points along a horizontal line (consider the line to be the base 0.0' elevation). Labelled Left to Right (a-e). Points "a" and "e" are the exterior columns where the canopy begins, they are both at base elevation. Points "b" and "d" are 26.5' above base. Point "c" is the centre point along the line and the highest part of the main canopy at 56.5' above base. Assuming point "a" is 0'-0" along the base line, "b" is 58.5', "c" is 119.5', "d" is 180.5' and "e" is 239 across from "a."

So what you are looking at is a two tiered canopy consisting of two lower, 1/4 elipse outside sections and one main, 1/2 elipse canopy section starting at the high ends of the lower tiers. Kind of like this:

______ g
(**|**) ______ h
(**| |**) ______ i
a b c d f

a to b- 58.5'
b to c- 61.0'
i= 0.0'
h= 26.5'
g= 56.5'

I'm not sure what other information is required to figure this out, if I have it (and understand what I'm being asked :? ) I'll provide it, I have some scans of the original blue prints that I would be more than happy to attatch to an email if they would be any help

P.S. No this isn't an aviary, this is proposed to be a waterpark ontop of a parking garage up the street from a big famous aviary...closer to the casino.

Thanks again
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First Try:

Using your measurements, unfortunately they do not suggest a perfect ellipse. If it were, 'h' would have to be in the neighborhood of 48.6'.

As I recall, the top of "the" aviary is not flat, it comes to a point. Also, the edge of the canopy is not vertical, suggesting only sort of an ellipse, or maybe just a portion of the to, rather than all of it.

So, there are several options. We can use various shapes to determine minimum and maximum arc lengths for the four sections. An ellipse may not be the best choice. You haven't built it, already, have you? If you have, maybe you can just go throw a cable over the top and measure it. It's been done?

Oh, there is one other important factor. You provided only one cross section of the structure. Is that the only one getting a pipe? Does the rafter stay the same size the entire length or does it taper? As I recall, "the" aviary stays the same width most of the way, but has the ends closed off differently.

What's the chance we're talking about the same aviary?

So, where does that leave us. This is an excellent example for showing the difference between textbook problems and real-world problems. If you're actually going to build it, you have to abandon all your simplifying assumptions.