Need some math help

[mquan01]

I am to old to remember how this is done, so hopefully someone else can..

I have a 13" diameter circle in which I want I want 15 equal slices (24 degrees each). What is a good way to determine the layout (please show your work to get extra credit)

Thanks in advance

 

[Mike Davis]

I would step off 15 equal spaces with dividers.

or set my Starrett protractor to 24 degrees and mark it out.

or do a print on the computer

or

or

 

[Phil S]

the chord for 13" dia circle with a central angle of 24 is 5.4056"

Just set your dividers to exactly 5.4056" and step off the circle

Hope this help

Sorry I misread and calculated this for a circle with 13" radius instead of a 6.5 radius


The real answer is 2.7028"

Formula is (Sin 12 * 6.5)*2

 

[Bill Clemmons]

Somehow I came up w/ a different number than Phil. Using SketchUp, I came up w/ 2 11/16" for the dividers.

 

[Mike Davis]

Sanity check, 5x15 is 75 that seems larger than the circumference if a 13 inch diamiter circle.

3x15 is 45 I’d say that’s closer.

 

[Dave Richards]

I'd also do it graphically with SketchUp's Pie tool to set up dividers. If I really wanted it to be accurate, I'd print it full size so I could set the dividers off it directly.

 

[Charlie]

13 x 3.1416 = 40.8408 / 15 = 2.72272 will get you close.

 

[Bill Clemmons]

I'd also do it graphically with SketchUp's Pie tool to set up dividers. If I really wanted it to be accurate, I'd print it full size so I could set the dividers off it directly.

If you want it in fractions instead of thousandths, I came up w/ 2 45/64" using Dave's method. SketchUp is a wonderful tool.

 

[Dave Richards]

If you want it in fractions instead of thousandths, I came up w/ 2 45/64" using Dave's method. SketchUp is a wonderful tool.

I started with fractions and got 2-45/64, too. That would be 2.765625. Probably close enough for government work.

 

[Jeff]

The best that you're probably going to get is setting your calipers to 2.70" (2.703" = 2 45/64", +/- 1/64") if you can get that close in the real world. Our pure math carries the decimal beyond what's practical in the shop.

https://www.mathopenref.com/arclength.html

 

[Dave Richards]

Of course printed out to full size, you could pick up the divider setting right off the drawing.
View attachment 24 degrees.pdf

 

[sawman101]

A math problem? No problem for me, I'm just gonna go back to bed.........:wconfused:

 

[Jeff]

Thanks Dave. How do you get a full size PDF file printed? Where?

 

[Dave Richards]

Jeff, that one is just 8-1/2 x 11 so you should be able to print it on your printer at home. When you get set to print it from Adobe Reader or Acrobat make sure you select the correct setting.

 

[Mike Davis]

Thanks Dave. How do you get a full size PDF file printed? Where?

For that particular print 8.5x11 will fit, Most small print shops and even the office supply stores have large format printers now. They charge a lot for a full size 36x48 or some can do even larger but when you really need it...

 

[Dave Richards]

Yes indeed. Larger printing can be had when you need it. I do a lot of woodworking plans on Arch E paper (48 x 36) and when I need to have them printed for myself, I go to Staples.

 

[Gotcha6]

Some UPS stores also carry large format printers. I've had the need occasionally to have full size architectural prints forwarded to me in the field and been able to email the items to the appropriate branch. It was usually ready by the time I arrived, saving me a trip across town and a lot of headaches.

 

[Jeff]

Yes it worked fine on my home printer on 8.5 x 11 paper. Pretty darn accurate with a ruler in 1/64 increments (2 45/64"). Thanks folks.

 

[mquan01]

Thank you all. It would have taken me forever to figure this out by myself.

 

[Mike Davis]

If you don’t know the math or don’t want to bother and don’t have a computer program to work it out you can draw a circle the right size. Any size will work. Take a wild guess and set your compass or dividers. Walk off 15 spaces or what ever number you need. You will probably be over or under the starting point. Now, this is the tricky part. Adjust your divider to 1/15 or what ever number you need smaller or larger. Then walk it off again, you should be a lot closer. Adjust again if you need to then mark each point that the divider touches as you go around the circle. This usually gets me within a few 1/1000ths faster than I can go find a calculator.