|Apr29-12, 08:31 PM||#1|
Calculate number of turns in Archimedes spiral
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:
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.
|Apr30-12, 05:58 AM||#2|
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:
hope that helps a bit!
|Apr30-12, 06:06 PM||#3|
Ok, I'll see how I go. Thanks a lot.
|Similar Threads for: Calculate number of turns in Archimedes spiral|
|Fluids: calculate pressure loss due to turns in pipe flow||Mechanical Engineering||9|
|How to Calculate the Number of Turns of Wire needed on a Iron Core Magnetic Solenoid||General Physics||3|
|Coil turns number||Classical Physics||17|
|Number of Turns on a Loop||Introductory Physics Homework||3|
|Calculate a diver's turns in air||Introductory Physics Homework||1|