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Arc Length of Sinewave calc to find amplitude?

Arc Length of Sinewave calc to find amplitude?

Arc Length of Sinewave calc to find amplitude?

(OP)
Hi all,

Im trying to design a sinewave torroid (Im not sure of its actual name but look up Shark Wheels for reference). To do this I am needing to get a specific arc length across a period, by adjusting the 'amplitude' of the wave.

I know the Arc Length that I need to achieve (for 1 period of X to what would be 2 PI) which is 5.3". The length of a period (0 to 2 PI) is 2.88".

How do I work out what the amplitude y would be? i.e. to fit the Arc Length into that length of period?

Thanks

Matt

RE: Arc Length of Sinewave calc to find amplitude?

On something like that, Simpson's rule and an Excel spreadsheet may get you the answer faster than researching the exact answer.

RE: Arc Length of Sinewave calc to find amplitude?

(OP)
Thanks Guys!

Gregs answer gives me ~ 0.97" for the amplitude and for my purpose this is accurate enough for now. Ill investigate the more detailed answers when I get to that stage.

Thanks for all your help.

RE: Arc Length of Sinewave calc to find amplitude?

quite different to IR's 2.3 ??

another day in paradise, or is paradise one day closer ?

RE: Arc Length of Sinewave calc to find amplitude?

Yes. OK, now approximate each quadrant of the ellipse to a triangle. The length of each triangle is 2.88/4, the height is .97 so the hypotenuse is sqrt(.72^2+.97^2)=1.2, so for 4 triangles we get 4.8 inches. Passes my sanity test!

Cheers

Greg Locock


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