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Made by CamBam => Members Projects => Topic started by: Bubba on May 07, 2018, 20:07:21 pm



Title: This really stumped me..
Post by: Bubba on May 07, 2018, 20:07:21 pm
To all you geometry, trigonometry, calculus experts.
I need to route template out of plywood based on 18"diameter sheet metal pipe that is squished to an ellipse of 14" minor axis dimension. How to calculate major axis dimension? It should be the same circumference measured as round or ellipse, no? The circumference of the 18" dia pipe is 56.548667,calculated. Help greatly appreciated.    


Title: Re: This really stumped me..
Post by: lloydsp on May 07, 2018, 20:27:30 pm
The interior circumference of the 14" section would be (ideally, without 'creasing') 43.982".

The exterior circumference of that depends upon whether or not the metal just compressed or 'creased' when rolling to the smaller diameter.  If it did not crease, then the circumference would be (14"+material-thickness)*pi.

If it did crease, the best way is just to measure it with a tape.

A disc to fit inside the 14" minor diameter would be 14" in diameter.  A disc to fit inside your major (18") diameter would be 18" in diameter.  Both probably need to be increased by a few thousandths to 'fit tight' -- say 0.030", and chamfered on one face so as to able to be hammered into the pipe tightly.

Is that what you were looking for?  Or, did I miss the actual question?

Lloyd


Title: Re: This really stumped me..
Post by: Bubba on May 07, 2018, 20:38:01 pm
Hi Lloyd, thanks for quick reply. I haven't formated my question correctly, sorry. Just edited my original post, hopefully it make more sense of what I'm after. When squeezing 18" dia pipe to 14" it's shape becomes elliptical, with minor axis 14" and major axis is?  ;D

BTW, this template be used as mockup on construction job site, and it shoud pretty close about.125" play accepted.

Thanks.   


Title: Re: This really stumped me..
Post by: lloydsp on May 07, 2018, 20:48:06 pm
AH!  Ok, there are formulae for that, too.  Let me look it up.

Lloyd
(give me a few)


Title: Re: This really stumped me..
Post by: lloydsp on May 07, 2018, 21:11:02 pm
Ok...
This formula is only accurate to (at worst) about 2%, but you might have to 'adjust' figures to get it to come out exactly right.

The perimeter ('circumference', which is really only a term for circles) of an ellipse is thus.

ellipse perimeter = (approx) pi [ 3(a+b) - sqrt((3a+b)(a+3b))]

Substitute terms to get one or the other axis.

Lloyd


Title: Re: This really stumped me..
Post by: Bubba on May 07, 2018, 23:34:04 pm
Thanks for the formula, Lloyd.

Could you give me the numbers, minor major axis dimensions?
 Thanks


Title: Re: This really stumped me..
Post by: Garyhlucas on May 08, 2018, 00:48:51 am
Bubba,
I just did something like this, using a bit cheating. Any Cad program will draw a mathematically correct ellipse and measure the circumference. Set both axis to size and measure the circumference. Adjust the long axis until you have the circumference you want.


Title: Re: This really stumped me..
Post by: lloydsp on May 08, 2018, 00:56:52 am
Gary's suggestion is a good one!

Bubba, I haven't had time to explore the solution.  I was busy with <heh> 'actual work' today.  I'll fiddle with it this evening, if time permits.  Again, just to be 'irritating'... substitution of terms is the way one arrives at a solution.

Lloyd


Title: Re: This really stumped me..
Post by: Bubba on May 08, 2018, 02:11:16 am
Lloyd,Gary,

 That's exactly what I was thinking knowing the circumference of 18" pipe and try to mach the
 elipse circumference knowing the 14" minor axis size. The problem is the I don't have any other CAD program that will measure this. other than Viacad, CamBam is the only cad program I use, and as far as I know neither have the capability to measure circumference. Thanks for helping.


Title: Re: This really stumped me..
Post by: Bubba on May 08, 2018, 02:55:13 am
Gentleman,

I got it done, after spending little more time reading help menu in ViaCAD I have learned the 'Verify' dropdown menu has option called 'Length'. So after tweaking the unknown Major axis (minor is 14"dia) and arriving on its 21.590" value the circumference is close enough..

18" dia  pipe circumference  =  56.548"
21.590" x 14" circumference = 56.542"

 ;) :D ;D     


Title: Re: This really stumped me..
Post by: lloydsp on May 08, 2018, 04:02:53 am
21.5938" is what I come up with.

WHEW!  I haven't done ellipses since HIGH SCHOOL!

Lloyd


Title: Re: This really stumped me..
Post by: Bubba on May 08, 2018, 12:00:55 pm
Thank you Lloyd for verifying this.

I was surprised that I was able to arrive at similar number by tweaking the Major axis just a bit a couple of times.

It once again, this group proves that you ask you shall receive help if you willing to cooperate and do your part.  ;D


Title: Re: This really stumped me..
Post by: lloydsp on May 08, 2018, 12:02:52 pm
BTW,
For others... If you don't wish to do difficult math on such projects, the TurboCad Learning Edition (freeware) will also allow you to draw and freely adjust axes on ellipses, and displays all the properties in a side-bar window.

All you'd need to know is the correct circumference of the original pipe, and the 'compression width' -- just as we started with here.

There are also all sorts of 'math aids' out there -- on-line calculators for difficult expressions.  However, most of them are simply 'click bait' to sell commercial math packages.

One that has a useful formula evaluator and DOESN'T refuse to answer until you've purchased is https://www.mathpapa.com/algebra-calculator.html

'Hope that all helps.

Lloyd


Title: Re: This really stumped me..
Post by: Bubba on May 08, 2018, 14:07:53 pm
Lloyd,
Thanks for this, just typing this while watching Turbocad downloading.  ;D


Title: Re: This really stumped me..
Post by: lloydsp on May 08, 2018, 14:27:30 pm
My pleasure, Bubba.

I also 'really struggled' with the problem.  I had to re-learn some more-or-less 'basic' algebra I haven't had to use for more than 40 years.  But it was a good exercise.

Oh... and just a side-bar note about ellipses:  There are NO purely-algebraic solutions that will give an exact answer.  Ellipses are one of those few figures in geometry that can only be accurately-solved by 'successive approximation'.  That is best-solved on paper with The Calculus.  It can also be done by computer algorithm, using an iterative process.

Technically speaking, there is NO 'exact' answer (ever), but you can get to the precision of correctness you need with enough iterations.

Lloyd


Title: Re: This really stumped me..
Post by: Garyhlucas on May 08, 2018, 16:27:34 pm
Yep,
No matter how much pi you eat you will never get an exact answer.


Title: Re: This really stumped me..
Post by: Bubba on May 08, 2018, 18:08:54 pm
That much a was aware of trying to calculate this.. I wish I was paying more attention in school, it was long time a go trig, geometry and  calculus learned (or attempted to learn) in early/mid sixties back in the fifth grade. Retained most of trig and geometry because my line of work required this.. I guess, as the saying goes 'if you don't use it you loosed'  ;D ;D