# Working with radius's **URL:** \ **Category:** Factual Questions\ **Created:** [March 17, 2018, 2:58am UTC](https://boards.straightdope.com/t/working-with-radiuss/810709 "2018-03-17T02:58:09Z")\ **Posts on this page:** 17\ **Page:** 1
**Author:** ![HoneyBadgerDC](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/honeybadgerdc/32/1033_2.png) [@HoneyBadgerDC](https://boards.straightdope.com/u/HoneyBadgerDC)\ **Post date:** [March 17, 2018, 2:58am UTC](https://boards.straightdope.com/t/working-with-radiuss/810709/1 "2018-03-17T02:58:09Z")
Trying to figure out if there is some kind of process I can look up on line for something I am doing. I am creating forms for archery bows and trying to create as smooth as possible transitions. I want to play with quite a few so trial and error to some extent is expected but if there were some kind of online calculator it would be easier. Visualize a drum say 4ft or 6 ft in diameter just for example. I tie a string to it say 10 ft long for a starting radius and as soon as I start to draw my circle the string starts winding around the drum tightening up my radius. I am wondering if there might be some kind of simulator available so I don’t have to make so many drums. I don’t know the name of the process I am looking for to look it up. ---
**Author:** ![beowulff](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/beowulff/32/542_2.png) [@beowulff](https://boards.straightdope.com/u/beowulff)\ **Post date:** [March 17, 2018, 3:01am UTC](https://boards.straightdope.com/t/working-with-radiuss/810709/2 "2018-03-17T03:01:28Z")
Sounds like one of the many forms of a [Spiral](https://en.wikipedia.org/wiki/Spiral). ---
**Author:** ![HoneyBadgerDC](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/honeybadgerdc/32/1033_2.png) [@HoneyBadgerDC](https://boards.straightdope.com/u/HoneyBadgerDC)\ **Post date:** [March 17, 2018, 3:03am UTC](https://boards.straightdope.com/t/working-with-radiuss/810709/3 "2018-03-17T03:03:37Z")
> [@beowulff](#): > > Sounds like one of the many forms of a [Spiral](https://en.wikipedia.org/wiki/Spiral). I actually got the right word for it here a few years ago but can’t remember. I will check out spirals. ---
**Author:** ![HoneyBadgerDC](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/honeybadgerdc/32/1033_2.png) [@HoneyBadgerDC](https://boards.straightdope.com/u/HoneyBadgerDC)\ **Post date:** [March 17, 2018, 3:31am UTC](https://boards.straightdope.com/t/working-with-radiuss/810709/4 "2018-03-17T03:31:11Z")
I found the old thread, it is called an in volute, I will try and search that. ---
**Author:** ![HoneyBadgerDC](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/honeybadgerdc/32/1033_2.png) [@HoneyBadgerDC](https://boards.straightdope.com/u/HoneyBadgerDC)\ **Post date:** [March 17, 2018, 3:37am UTC](https://boards.straightdope.com/t/working-with-radiuss/810709/5 "2018-03-17T03:37:04Z")
I did find a calculator but I don’t believe it will work for what I am doing. I don’t have enough background to use it. ---
**Author:** ![Qadgop\_the\_Mercotan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/qadgop_the_mercotan/32/83_2.png) [@Qadgop\_the\_Mercotan](https://boards.straightdope.com/u/Qadgop_the_Mercotan)\ **Post date:** [March 17, 2018, 3:43am UTC](https://boards.straightdope.com/t/working-with-radiuss/810709/6 "2018-03-17T03:43:37Z")
Radius’s _whaaaaaat?_ Or do you mean _radii_, or perhaps radiuses? 😛 ---
**Author:** ![HoneyBadgerDC](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/honeybadgerdc/32/1033_2.png) [@HoneyBadgerDC](https://boards.straightdope.com/u/HoneyBadgerDC)\ **Post date:** [March 17, 2018, 3:44am UTC](https://boards.straightdope.com/t/working-with-radiuss/810709/7 "2018-03-17T03:44:50Z")
> [@Qadgop\_the\_Mercotan](#): > > Radius’s _whaaaaaat?_ > > Or do you mean _radii_, or perhaps radiuses? > > 😛 I spelled it the way you did and spell check corrected me! ---
**Author:** ![DPRK](https://avatars.discourse-cdn.com/v4/letter/d/4491bb/32.png) [@DPRK](https://boards.straightdope.com/u/DPRK)\ **Post date:** [March 17, 2018, 4:05am UTC](https://boards.straightdope.com/t/working-with-radiuss/810709/8 "2018-03-17T04:05:17Z")
> [@HoneyBadgerDC](#): > > I did find a calculator but I don’t believe it will work for what I am doing. I don’t have enough background to use it. You never said exactly what you wanted to do. Are you using a CAD program where you can define a curve using a parametric equation? Do you just want to sketch smooth curves? (the free Inkscape supports at least Euler spirals, which are good enough for railroads and photonic integrated circuits if you believe Wikipedia.) ---
**Author:** ![HoneyBadgerDC](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/honeybadgerdc/32/1033_2.png) [@HoneyBadgerDC](https://boards.straightdope.com/u/HoneyBadgerDC)\ **Post date:** [March 17, 2018, 4:26am UTC](https://boards.straightdope.com/t/working-with-radiuss/810709/9 "2018-03-17T04:26:15Z")
> [@DPRK](#): > > You never said exactly what you wanted to do. Are you using a CAD program where you can define a curve using a parametric equation? Do you just want to sketch smooth curves? (the free Inkscape supports at least Euler spirals, which are good enough for railroads and photonic integrated circuits if you believe Wikipedia.) My first post explains what I am doing. Designing archery bow limbs with smooth transitions in the curves, I will be working from 6" radiuses into 150" radiuses and everything in between. I don’t have any kind of background in the drawing programs or much math so a lot of the time I have to just do things by hand. Sometimes I get lucky and can find internet programs I can use. ---
**Author:** ![DPRK](https://avatars.discourse-cdn.com/v4/letter/d/4491bb/32.png) [@DPRK](https://boards.straightdope.com/u/DPRK)\ **Post date:** [March 17, 2018, 7:10am UTC](https://boards.straightdope.com/t/working-with-radiuss/810709/10 "2018-03-17T07:10:07Z")
So, for mechanical reasons, you want to use circle involutes rather than other spirals or smooth curves, and you are not using any CAD or computerized sketching programs. Besides using spools and string, you could plot the required curve using a free plotting utility, and then output the result on a printer or plotter. [Here](http://mathworld.wolfram.com/CircleInvolute.html) or [here](https://www.mathcurve.com/courbes2d.gb/developpantedecercle/developpantedecercle.shtml) you can find parametric equations for the curve. To generate a plot on the computer you could use matplotlib, and I’m sure people will have even better suggestions. NB in an Euler spiral, the curvature varies linearly with length. In your spirals, it will be proportional to the inverse square root of the length. ---
**Author:** ![HoneyBadgerDC](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/honeybadgerdc/32/1033_2.png) [@HoneyBadgerDC](https://boards.straightdope.com/u/HoneyBadgerDC)\ **Post date:** [March 17, 2018, 12:27pm UTC](https://boards.straightdope.com/t/working-with-radiuss/810709/11 "2018-03-17T12:27:56Z")
> [@DPRK](#): > > So, for mechanical reasons, you want to use circle involutes rather than other spirals or smooth curves, and you are not using any CAD or computerized sketching programs. > > Besides using spools and string, you could plot the required curve using a free plotting utility, and then output the result on a printer or plotter. [Here](http://mathworld.wolfram.com/CircleInvolute.html) or [here](https://www.mathcurve.com/courbes2d.gb/developpantedecercle/developpantedecercle.shtml) you can find parametric equations for the curve. To generate a plot on the computer you could use matplotlib, and I’m sure people will have even better suggestions. > > NB in an Euler spiral, the curvature varies linearly with length. In your spirals, it will be proportional to the inverse square root of the length. Thanks, this is what I was looking for. I will need to do some studying to learn how to figure it but I think I can do that. Involute of an ellipse is actually what i will be doing. The smooth transitions of a curve are very important in an archery limb as it is drawn back. Mastering this program would be very helpful in trying different layouts. I will call in a friend to coach me a little on the math. ---
**Author:** ![DPRK](https://avatars.discourse-cdn.com/v4/letter/d/4491bb/32.png) [@DPRK](https://boards.straightdope.com/u/DPRK)\ **Post date:** [March 17, 2018, 3:22pm UTC](https://boards.straightdope.com/t/working-with-radiuss/810709/12 "2018-03-17T15:22:41Z")
I hope it helps. Please be aware, though, that simple plotting software will give you a nice plot of various curves, but it will not do any kind of finite-element analysis of the behaviour of actual structures under load. ---
**Author:** ![HoneyBadgerDC](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/honeybadgerdc/32/1033_2.png) [@HoneyBadgerDC](https://boards.straightdope.com/u/HoneyBadgerDC)\ **Post date:** [March 17, 2018, 10:12pm UTC](https://boards.straightdope.com/t/working-with-radiuss/810709/13 "2018-03-17T22:12:05Z")
> [@DPRK](#): > > I hope it helps. Please be aware, though, that simple plotting software will give you a nice plot of various curves, but it will not do any kind of finite-element analysis of the behaviour of actual structures under load. Thanks, I understand that about the analysis. Being able to generate these shapes just makes it a lot easier when playing with different designs. ---
**Author:** ![TreacherousCretin](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/treacherouscretin/32/476_2.png) [@TreacherousCretin](https://boards.straightdope.com/u/TreacherousCretin)\ **Post date:** [March 17, 2018, 11:01pm UTC](https://boards.straightdope.com/t/working-with-radiuss/810709/14 "2018-03-17T23:01:24Z")
> [@HoneyBadgerDC](#): > > I spelled it the way you did and spell check corrected me! Which spellchecker was that? _Radius’s_ is not the plural of radius. ---
**Author:** ![DSeid](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dseid/32/20194_2.png) [@DSeid](https://boards.straightdope.com/u/DSeid)\ **Post date:** [March 17, 2018, 11:05pm UTC](https://boards.straightdope.com/t/working-with-radiuss/810709/15 "2018-03-17T23:05:55Z")
> [@TreacherousCretin](#): > > Which spellchecker was that? _Radius’s_ is not the plural of radius. Maybe the grocer has them on sale? ---
**Author:** ![HoneyBadgerDC](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/honeybadgerdc/32/1033_2.png) [@HoneyBadgerDC](https://boards.straightdope.com/u/HoneyBadgerDC)\ **Post date:** [March 17, 2018, 11:53pm UTC](https://boards.straightdope.com/t/working-with-radiuss/810709/16 "2018-03-17T23:53:01Z")
> [@TreacherousCretin](#): > > Which spellchecker was that? _Radius’s_ is not the plural of radius. Maybe I just thought I spelt it that way ---
**Author:** ![DavidwithanR](https://avatars.discourse-cdn.com/v4/letter/d/3bc359/32.png) [@DavidwithanR](https://boards.straightdope.com/u/DavidwithanR)\ **Post date:** [March 18, 2018, 12:47am UTC](https://boards.straightdope.com/t/working-with-radiuss/810709/17 "2018-03-18T00:47:07Z")
A spellchecker often doesn’t know whether you need a plural or a possessive. Its helpful to remember that word’s naming group’s of thing’s usually dont have apostrophe’s. But its not alway’s easy. 😃