Geometry help...

I didn’t get far in geometry…
I want to use a pencil on the end of a string to draw the arc in the pic I posted. How long should the string be? Or, how long is the radius of the circle segment shown in the pic?.. I am debating a 22" or 23" width for this board.

Thanks in advance for any help

I think I know - draw a straight line from one portion of the arc to another, say end to middle.  Bisect that line and draw a perpendicular line out from there.  Now, do the same thing at another place in the arc.  At the inersection of those two perependicular lines, that is the center of the radius.  This all pre-suposes that that arc is indeed part of a perfect circle.

Hope this helps & happy 4th!

here’s a pic

This is an old carpenters trick, chrisp.  You’re going to need a few nails or screws and a couple of small pieces of wood prob about 4’ long for your 82" length. Draw yourself a line 82" long. Square up your 4 3/4" at each end and set a nail or screw at those points. Mark your middle and square up your 11". Set a nail or screw there. Get your battens and lay one touching the nail at each of the 4 3/4 and 11" marks. Take the other board and lay it on the first board touching the 11" nail. At the other end measure up past your 4 3/4" mark up to 11". What you’ll have is one board resting at an angle and the other running parallel to your baseline, just 11" up. Take two nails or screws and fasten the overlaps in your boards at those points. Now take your pencil and holding it at the intersection of where your two boards join you’ll slide your boards,

always keeping against your “set” nails. So your mark will start at one 4 3/4 poinclimbing to your middle 11" point and back down to the other 4 3/4 point at the other end. Perfect every time. It’s far easier than my explanation, I’m pretty poor at teaching.




You’ll need a twelve-foot tape. Edited to add quarter points if you don’t want to use string.

ARC Radius127.8935, Length 83.4738

ARC Radius 137.6050 Length 83.2645

Biggreen, cool trick!

 

Thanks for all the quick replies fellas, just what I needed and I learned some cool things too.
I knew I could count on you guys…

Now to see how it looks on my blank.

every wood planked board I have ever built speaks to me …“Gee I’m a tree”.

A string on a pivot point is a bad idea. Any string is going to stretch or go slack and you will not get an even curve. Sloppy way to do it. Biggreen’s method looks good, though you might have trouble figuring it out if you’ve never used it before. Once you do get it, it’s pretty simple.

Does this curve represent your wide point and outline?

I see what you did there BB30 hahaha

Sammy, I was planning to actually use a pencil in the “hook” part of a tape measure but, Biggreen’s method looks like it is the go…

I had a hard time picturing it when he described it but, the pictures cleared it up for me.

And, yes, this curve is potentially for an outline… I need to get it on the blank though before I decide if I like it or not… I am shooting for a funky snubnose double ender

Yeah, sorry chrisp. I couldn’t figure how to modify my post to place the pictures with the description. The method is, however, really pretty quick, easy, and accurate.

Nice method biggreen.  It took a couple of reads but with the pictures I think I get it.

Simple and practical.  Another pearl found at Swaylocks…

Thanks Biggreen!  This method really works well.

Here is a pic from my second try, notching the jig to place the tip at the intersection and bracing the pen resulted in more accuracy. First attempt I held the pen by hand in the corner, spun the jig with the other,  and was under by about 1/16".

-J

http://www.mathopenref.com/arcradius.html

Maybe I missed something, but it sounds/looks like you’re looking for the formula to calculate the radius of an arc segment.

My math skills are pretty rusty, but this looked like it might be useful.

that is very nice, bg, very clean and easy!