# Method for drawing very large radius?
**URL:** https://boards.straightdope.com/t/method-for-drawing-very-large-radius/756486
**Category:** Factual Questions
**Created:** [June 4, 2016, 1:04pm UTC](https://boards.straightdope.com/t/method-for-drawing-very-large-radius/756486 "2016-06-04T13:04:56Z")
**Posts on this page:** 16
**Page:** 1
### Author:  [@HoneyBadgerDC](https://boards.straightdope.com/u/HoneyBadgerDC)
#### Post date: [June 4, 2016, 1:04pm UTC](https://boards.straightdope.com/t/method-for-drawing-very-large-radius/756486/1 "2016-06-04T13:04:56Z")
Is there a method I could use for example to draw a 40 ft radius on a 3 ft piece of wood without building a 40 ft compass? Maybe some kind of radius compounding device?
---
### Author:  [@naita](https://boards.straightdope.com/u/naita)
#### Post date: [June 4, 2016, 1:08pm UTC](https://boards.straightdope.com/t/method-for-drawing-very-large-radius/756486/2 "2016-06-04T13:08:17Z")
A string, a nail and a pencil. Refine as required by your desire for precision.
ETA: Right. That’s not what you asked. But it’s still likely the easiest way.
---
### Author:  [@naita](https://boards.straightdope.com/u/naita)
#### Post date: [June 4, 2016, 1:11pm UTC](https://boards.straightdope.com/t/method-for-drawing-very-large-radius/756486/3 "2016-06-04T13:11:15Z")
Except of course for these methods: [Marking large-radius arcs](https://woodgears.ca/shop-tricks/large_arc.html)
---
### Author:  [@naita](https://boards.straightdope.com/u/naita)
#### Post date: [June 4, 2016, 1:13pm UTC](https://boards.straightdope.com/t/method-for-drawing-very-large-radius/756486/4 "2016-06-04T13:13:53Z")
Except of course for these methods: [Marking large-radius arcs](https://woodgears.ca/shop-tricks/large_arc.html)
The most accurate of which uses the relationship between periferal and central angles (illustration in link):
> [@](#):
>
> Drive a nail at each end of the desired arc. Then attach two straight strips of wood to each other at an angle. Trace your arc with a pencil positioned at the intersection of the strips, sliding the strips and the pencil along both nails. To set the angle of the two pieces of wood, hold the pencil at the desired midpoint of the arc and attach the strips of wood to each other so that they both touch the pencil and the nails.
>
> A neat property of this method is that the angle covered by the arc is exactly equal to twice the change in angle between the two strips of wood. To make an arc that covers 90 degrees for example the angle between the strips should be 135 degrees (180 - 90/2).
>
> For very shallow arcs, I prefer the first method though.
---
### Author:  [@enipla](https://boards.straightdope.com/u/enipla)
#### Post date: [June 4, 2016, 1:48pm UTC](https://boards.straightdope.com/t/method-for-drawing-very-large-radius/756486/5 "2016-06-04T13:48:33Z")
So… we know the chord length and radius. Now all we need to do is find the length of the arc. I’m looking online for a calculator to do this.
If we have arc length, you could cut a strip of paper to that length, and lay it on its side and curve it to match the chord endpoints. Then trace along the arc of the paper on the wood.
---
### Author:  [@Chronos](https://boards.straightdope.com/u/Chronos)
#### Post date: [June 4, 2016, 2:05pm UTC](https://boards.straightdope.com/t/method-for-drawing-very-large-radius/756486/6 "2016-06-04T14:05:04Z")
> [@](#):
>
> So… we know the chord length and radius. Now all we need to do is find the length of the arc. I’m looking online for a calculator to do this.
It’s straightforward trigonometry. Picture (draw it if it helps) the sector (pie slice). Draw the chord, and draw another line down the middle of the sector (bisecting the angle). You now have a right triangle (a pair of them, actually) formed by the radius, half of the chord, and most of the bisecting line. The angle of that right triangle is half of the sector’s angle, and the sine of that angle is half the chord length divided by the radius.
So if we take half the chord length, divide it by the radius, and take the inverse sine, then double the result, we’ll have the sector angle. If we got the angle in radians, then just multiply it by the radius to get the arc length. If we got it in degrees, then multiply it by π/180° times the radius.
---
### Author:  [@HoneyBadgerDC](https://boards.straightdope.com/u/HoneyBadgerDC)
#### Post date: [June 4, 2016, 2:06pm UTC](https://boards.straightdope.com/t/method-for-drawing-very-large-radius/756486/7 "2016-06-04T14:06:04Z")
> [@naita](#):
>
> Except of course for these methods: [Marking large-radius arcs](https://woodgears.ca/shop-tricks/large_arc.html)
>
> The most accurate of which uses the relationship between periferal and central angles (illustration in link):
This is perfect, I am making barrel staves for non standard decorative barrels. I think I need to cut my staves on somekind of radius.
---
### Author:  [@HoneyBadgerDC](https://boards.straightdope.com/u/HoneyBadgerDC)
#### Post date: [June 4, 2016, 4:43pm UTC](https://boards.straightdope.com/t/method-for-drawing-very-large-radius/756486/8 "2016-06-04T16:43:41Z")
Once I started figuring actual radiuses they are very manageable, much smaller than I was thinking for some reason. But I was curious as to how you would solve the problem anyway.
---
### Author:  [@Napier](https://boards.straightdope.com/u/Napier)
#### Post date: [June 5, 2016, 12:02pm UTC](https://boards.straightdope.com/t/method-for-drawing-very-large-radius/756486/9 "2016-06-05T12:02:45Z")
> [@HoneyBadgerDC](#):
>
> This is perfect, I am making barrel staves for non standard decorative barrels. I think I need to cut my staves on somekind of radius.
You wouldn’t need them to have circular edges. It depends on how you want your barrel to taper. Perhaps you could find a cooper to guide you?
---
### Author:  [@HoneyBadgerDC](https://boards.straightdope.com/u/HoneyBadgerDC)
#### Post date: [June 5, 2016, 1:09pm UTC](https://boards.straightdope.com/t/method-for-drawing-very-large-radius/756486/10 "2016-06-05T13:09:26Z")
> [@Napier](#):
>
> You wouldn’t need them to have circular edges. It depends on how you want your barrel to taper. Perhaps you could find a cooper to guide you?
```
For some reason it is very difficult to find stave patterns on line.
```
---
### Author:  [@Thin\_Ice](https://boards.straightdope.com/u/Thin_Ice)
#### Post date: [June 5, 2016, 6:12pm UTC](https://boards.straightdope.com/t/method-for-drawing-very-large-radius/756486/11 "2016-06-05T18:12:56Z")
For what it’s worth, here’s a short video on cutting barrel staves:
[https://www.youtube.com/watch?v=yX8kXZ6Lpmo](https://www.youtube.com/watch?v=yX8kXZ6Lpmo)
---
### Author:  [@HoneyBadgerDC](https://boards.straightdope.com/u/HoneyBadgerDC)
#### Post date: [June 5, 2016, 7:18pm UTC](https://boards.straightdope.com/t/method-for-drawing-very-large-radius/756486/12 "2016-06-05T19:18:55Z")
> [@Thin\_Ice](#):
>
> For what it’s worth, here’s a short video on cutting barrel staves:
>
> [https://www.youtube.com/watch?v=yX8kXZ6Lpmo](https://www.youtube.com/watch?v=yX8kXZ6Lpmo)
That was good! No one ever show the exact method for shaping the sides of the stave. I am going to try using a portion of a circumference method.
---
### Author:  [@Thin\_Ice](https://boards.straightdope.com/u/Thin_Ice)
#### Post date: [June 5, 2016, 9:38pm UTC](https://boards.straightdope.com/t/method-for-drawing-very-large-radius/756486/13 "2016-06-05T21:38:51Z")
Here’s a YT link to barrel making vids. I haven’t watched any of these but you might find some useful info in one or more of them.
[https://www.youtube.com/results?search\_query=barrel+making](https://www.youtube.com/results?search_query=barrel+making)
---
### Author:  [@Kevbo](https://boards.straightdope.com/u/Kevbo)
#### Post date: [June 6, 2016, 6:50pm UTC](https://boards.straightdope.com/t/method-for-drawing-very-large-radius/756486/14 "2016-06-06T18:50:53Z")
The method used by ancient Greek architects/masons to gauge the correct large radius bulge on their columns was to draw a shortened model with a shorter radius, then transfer the sagitta at a given point scaled to the full length column using something like a caliper or dividers.
This was a bit of mystery until the templates were found still scribed on the floor of an unfinished building.
Suppose you want the finished piece 6 feet long with a 1/2" saggita. Make a curve 6" long with the same 1/2" sagitta, and then measure points 1/2" apart and transfer them to locations 6" apart on the full sized piece.
---
### Author:  [@Dr.Strangelove](https://boards.straightdope.com/u/Dr.Strangelove)
#### Post date: [June 6, 2016, 9:51pm UTC](https://boards.straightdope.com/t/method-for-drawing-very-large-radius/756486/15 "2016-06-06T21:51:12Z")
For short arc lengths, a parabola is a very good approximation of a circular segment.
Suppose for the moment that you want a curve that is 32 inches wide and 1 inch tall, and centered (i.e., it intersects the points [0, 1], [16, 0] and [32, 1]). Then, it’s easy to calculate the remaining points, since they go with x[sup]2[/sup]. [8, 0.25] and [24, 0.25] are points on the curve, as are [12, 0.0625], [20, 0.0625], [4, 0.5625], and [28, 0.5625]. You can repeat this process with as many points as you need to achieve smooth interpolation.
---
### Author:  [@Colophon](https://boards.straightdope.com/u/Colophon)
#### Post date: [June 7, 2016, 7:00pm UTC](https://boards.straightdope.com/t/method-for-drawing-very-large-radius/756486/16 "2016-06-07T19:00:58Z")
> [@Napier](#):
>
> You wouldn’t need them to have circular edges. It depends on how you want your barrel to taper. Perhaps you could find a cooper to guide you?
If these are small decorative barrels, you probably want a Mini Cooper.