Math Question...

[Guest]

I need to find the formula for measuring the length of the perimeter of an ellipse.
If memory serves me correctly... pi x D works for a circle, but I'm clueless about an ellipse which has two different diamaters at the major and minor axis.

If you're wondering why I need this formula... I got some current prices on copper yesterday...

[mikeschn]

The ellipse is a geometrical entity that does not permit calculation of the perimeter very easily, as with a circle. To calculate the perimeter, one must:

Write the elliptical equation:

Solve Eq 1 for y in terms of x:

Use arclength formula to calculate length for positive portion of Eq 2 and multiply by 2 to account for the negative half of Eq 2:

Using Eq 3 and 4, and a = 7/16 and b = 49/128, we obtain for the perimeter of the inner ellipse for the disk:

Arclength’ = Perimeterellipse = Pe = 2.579952 . 2.58 inches

Use this perimeter (circumference in terms of a circle) to calculate the radius, R, of the circle:


solving Eq 5 for R:


Ri = 0.41062 inches

For aid in drawing, R can be approximated as Ri = 105/256, introducing an error of only 0.11%. This R is the radius of the inner ring of the circle, the outer ring can be found by adding a wall thickness of 1/32 giving Ro = 113/256 .



or you can do it the easy way and give me the dimensions of your ellipse, and I'll calculate the perimeter for you on the cad system...

Mike...

[San Diegan]

Mike is right on. For more than you ever wanted to know including the history of various approximations, see

http://home.att.net/~numericana/answer/ellipse.htm#elliptic

Tom

[Guest]

Mike,
I've even had my coffee this morning and that eqaution still looks like a foreign language to me...



My biggest concern right now is how long the copper needs to be from the forward lower ellipse, up and around to the galley hatch hinge.

Alumawood just doesn't have that same ring to it...

BTW- Here's the scoop on what I've been able to locate on copper sheet sizes...3' x 10' in stock, 4' x 10' special order.
If 4' x 10' is indeed the largest sheet size out there, 3' x 10' will work with a seam right down the middle running lengthwise and unfortunately, another seam running across the 5' width somewhere in the cabin area.
Cost:
3' x 10' (Thinner than what I want) $107.00 per sheet
3' x 10' (Thickness I want) $205.00 per sheet

Perhaps it's time to consider a "Full-Woody"...
(I could still use copper accents)

[mikeschn]

Hey Dean,

For the line that you have in red on your layout, here are the results...

Date : 3/31/2005 12:28:12 PM
Current work part: C:\Documents and Settings\Desktop\arc length.dwg
===============================================
Information Units Inches
Total Arc Length = 231.351667389590

Does that help?

Mike...

P.S. A woody? You can't pee on a Woodie!

[Guest]

Thanks Mike,
At least that is under 20', now if I can just accept the fact about seams...

BTW- Haven't you read Yellow River, by I. P. Freely?

[Sarge]

This kind of math reminds me of the old question:

How many cops does it take to throw a cop-killer down a flight of stairs?


Answer: None. He slipped.


As you were,

-Sarge

[Arne]

I use graph paper, common pins and a piece of string and some multiple to convert it..... you do have a drawing, right?

[Jiminsav]

you can put cooper wires in it..