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Calculate number of turns in Archimedes spiral 
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#1
Apr2912, 08:31 PM

P: 4

Hi,
I'm an engineer designing a spring system for a garage roller door. I need to know the number of turns of the door for all the size combinations. I've found this page which gives a good equation for finding the length if you know the number of turns, starting radius and gap between spirals: The equation of the spiral is r=x+yθ, so x=starting radius, y=gap/2∏, and to find L we're taking the integral from a=0 to b=2∏n (where n=turns). When you know n, this is straightfoward, and even I could work that out. But it's been a decade since I've done anything like this, so I was wondering if anyone could help me find an expression for n in this: L=∫[itex]^{2∏n}_{0}[/itex] [itex]\sqrt{(a+bθ)^2+b^2}dθ[/itex] Lord help me, my way of solving this is to find L for n=1,2,3,4,5 etc, graph it in excel and use "find trendline" to get an equation. Any help appreciated, thanks. 


#2
Apr3012, 05:58 AM

P: 169

Hey!
If you're only looking for the answer, you can use this. For methodology, you can do two substitutions: first [itex]v=a+b\theta[/itex] Then you need to make a second substitution v=b*sinh(u). Donīt forget the derivatives. For more information you can visit this topic: http://www.physicsforums.com/showthread.php?t=157980 hope that helps a bit! 


#3
Apr3012, 06:06 PM

P: 4

Ok, I'll see how I go. Thanks a lot.



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