need a little math help please

[Ralph D]

I have to make a new base for my mega tree...it’s a ten foot tall mega tree. I want to make the base out of 2x4's in the shape of a 10 sided star it’s called a decagon. I’d like to make the base 6 feet around. So my question is, how long does each piece of wood have to be and what angle do i make the cuts at? I’m not the greatest at math or measuring so i thought the best place to ask would be here.

Thanks,

Ralph

[ItsMeBobO]

You only need 3 8 foot 2x4s and will have half of one left over.

10 pieces of 2x4's with all 20 ends cut to 18 degrees (off 90).
18x20 = 360 making a full circle.

The longest side of each will be 22.62 or 22 5/8 inches to end up with a 6 foot diameter base.



http://www.sonoma.edu/users/w/wilsonst/courses/math_150/projects/decagon.html

[Ralph D]

Bobo! thanks so much, could you do the same for me for 5 feet around, not sure which i will be doing, I will be making it thursday and just might make both and when setup starts on the 7th see which ones works best. lol I went to the link you gave me and remembered why math is not my thing. lol but thanks so much. youd the man!

Ralph

[amcdonald307]

The math in that link almost made me faint!

Your 18deg angle is going to be the same, no matter your final diameter for a 10 sided "circle", so that is a constant.

To figure your outside length per each board, take the diameter you want times PI and divide by the number of sides. So:

5' diameter = 60"
60*3.14159/10 = 18.85" for each outside edge, then cut 18deg "inward" on each of those ends.

Don't get too hung up on the fractional measurement, just make sure each of the 10 are the exact same length. For instance, if you have 90" of usable stud (a stud isn't actually 96", right?) and you want to get all your pieces out of just 2 studs, cut 5 pieces 18" long from each. That will give you a little wiggle room for a buggered end and still give you roughly a 5' diameter.

[ItsMeBobO]

No problem Ralph. FYI I detest most complex math, but I like logic and puzzles. Have fun with your project.

To build 5 feet diameter with 10 sides use 18 7/8.
Or use all of two 2x4s at 20 inches for 5' 4"

[Ralph D]

ok! not my day, I made both and didnt like either or them. Bobo i pm you. so now I need some help with a 7.5 wide base please

[Ralph D]

ok everyone i'm going to ask is this calculation right.

my new base will be 7.5 feet round.

so 7.5 x 12 = 90

90 is my diameter.

90*(PI) 3.14159/10(the number of sides) = 28.27 (which is the long side(outside) of the board)

so at the edge or 28.27, i cut inword 18 degrees, and do the same to each board i cut. all said and done, I shold have a new base for my mega tree at 7.5 round.

Right?

[Nova5]

according to CADD the angle of the first leg turn up and pointing right from the bottom flat is 36. making both cuts 18deg each. 18 will always be the cut angle regardless of size as its a function of number of pieces.

CADD makes this easy. give it a 10 sided poly (heck I could to 9 or 50 if i wanted.) and a radius, it'll pop the poly up, then just pull a dimension on the sides. bing all done.

[Nova5]

amcdonald307 wrote:

The math in that link almost made me faint!

Your 18deg angle is going to be the same, no matter your final diameter for a 10 sided "circle", so that is a constant.

To figure your outside length per each board, take the diameter you want times PI and divide by the number of sides. So:

5' diameter = 60"
60*3.14159/10 = 18.85" for each outside edge, then cut 18deg "inward" on each of those ends.

Don't get too hung up on the fractional measurement, just make sure each of the 10 are the exact same length. For instance, if you have 90" of usable stud (a stud isn't actually 96", right?) and you want to get all your pieces out of just 2 studs, cut 5 pieces 18" long from each. That will give you a little wiggle room for a buggered end and still give you roughly a 5' diameter.

Studs are 8f - (minus) 4.5" to accomodate a double top plate and single bottom plate.

a true 8' is 96" there is also one cut to allow single top and single bottom. cost per foot is probably less on the stud due to its high use/demand/stock.

[Ralph D]

Well thanks everyone! God I’m so upset I didn’t get to make my base today, and IM still teetering between 6 1/2 and 71/2 base...can't make up my mind! But I did get to make 2 brand new radio sign’s ( I make them from scratch) and I made to pvc sign holders, cleaned them, painted them white and even toped it off with a candy cane stripe. Working alone isn’t fun. I did get a little help, my youngest daughter Samantha and her boyfriend…very nice boy came out and leaned a hand for about 30 min’s. Man it takes so much longer alone, but at least it’s another thing off my check list of things to get done.

[Ralph D]

Ok this is a new question but it still has to do with the mega tree base. I’m going to use I hooks around the base to hook my light strings to. I want to make them look as equaled spaced as I can. So I have a 3 color mega tree r/w/g, 16 channels per color. How do I figure out the distance between hooks?

[Bob VandenBoom]

Assuming 48 strands going from the base to the top: Spacing = (diameter X 3.1416)/48

If you are going to use one strand to go from the base, over the top, and down to the base on the opposite side then you will need: Spacing = (diameter x 3.1416)/96

[Ralph D]

ok what is 4.7 on a tape measure

[jbzeus]

About 4 45/64" :-)

[Nova5]

Figure out what 4.75 is and work back.

[Bob VandenBoom]

Closest would be 4 11/16. Anything close to that will be fine. If you can get your strands within a 16th of an inch you are doing pretty good.