Math Help, Please!

[JackLeg]

I was never a great math student, and sometimes I wish I had paid more attention. Like now!

Here's my question. Building a swing stand. Sides (legs) are 72", want a 60" base. Using a 2 X 6 header. What is a simple way to determine what angle I should cut the legs to meet the header.

(I've figured it out using "Reggie Math") but I suspect there's a fairly easy and accurate way. Thanks in advance for your help. :notworthy:

 

[Gotcha6]

This is like laying off rafters - only a little more complicated. 60" base means 30" each side of the ridge centerline. Deduct 1/2 of ridge thickness (3/4") for a net run of 29-1/4". Use a framing square next. divide 29-1/4 by 3 for a quotient of 9 -3/4". Divide 72" by three for a quotient of 24". Set the zero end of the tape on the short leg of the square at 9 - 3/4" and swing it up on the long leg until the tape reads 24". The intersection with the long leg will be the rise. Be sure & use the same side of the tape measure on both ends. This should give you the cut for the top and bottom.

 

[FredP]

If the reggie math dont work you could try FRED math!:rotflm: I would think 10 - 15 degrees would look good but thats just a WAG on my part.:gar-La; the one I did was much larger and I dont remember the angles used but if you run the top through the sides so it sticks out on the ends you could put the struts on the outside out of the way and get a different look. but I havent tried that either YET...... just always thought it would look cool.:widea: 1 + 2 = 3.768? :no:

 

[Bas]

65.4 degrees, if I picture the swing stand correctly. Not sure why the size of the header matters for the angle. cos(65) = 0.42 = (60/2) / 72.

Hope I got that right. If not, eh, well, that's because it's metric, and you need to convert it!

 

[Bas]

You're going to be sorry you asked.... :rolf:

 

[DaveO]

OK if I am reading this correctly the legs of the swing are going to be 72" long and they will be 60" apart at the base. So you can break that down into a right triangle calculation, by splitting the base in half.
Your upper angle will be 65.38º, and bottom angle will be 24.62º and the middle angle which won't exist, but is just being used for calculation purposes is 90º.
Check out this calculator - http://www.csgnetwork.com/righttricalc.html

Personally I would make it a 30º/60º/90º triangle and adjust your length accordingly. make the base 72" wide also if you want to stay with 72" legs.

Dave

 

[Alan in Little Washington]

I was never a great math student, and sometimes I wish I had paid more attention. Like now!

Here's my question. Building a swing stand. Sides (legs) are 72", want a 60" base. Using a 2 X 6 header. What is a simple way to determine what angle I should cut the legs to meet the header.

(I've figured it out using "Reggie Math") but I suspect there's a fairly easy and accurate way. Thanks in advance for your help. :notworthy:

We will call the angle you want X

sine X = 30/72 or .41666.... (You need the arcsine of .41666 . . . . (angle whose sine is .41666) ).

from a calculator or trig tables:

X = 24.62 degrees (approx)

Here are some good explanations and diagrams.

 

[JackLeg]

Whew!! I'm on "info-overload!" THANKS to all! Especially DaveO for the calculator. It came up with the same answer as Dave and Bas.

Saved the link in my Shop Notes folder.

Now, I just need to remember to take the laptop to the shop!!!

:rotflm:

 

[Threejs]

Uh, yeah what they said. An upper and of 65 degrees and a lower angle of 25 degrees. (as long as it adds up to 90 and is close to that, you are good)

 

[FredP]

hmmmmmmmm........... :eusa_thin think I read wrong or sumpin!:rotflm: I was thinkin bout the splay? the greater the angle the longer the legs gotta be to keep the swing off the ground. or you hafta shorten the chains. or grow shorter legs else yur gonna wear out ur shoes!:gar-La; when I did mine I just layed the legs on the ground and formed a "V" spread em till it looked right and scribed a line. set the miter saw to that angle and cut all four the same length. :embaresse math aint my high point either. I rank math right up there with spelling!:rotflm:

fred

 

[RayH]

I'm with Fred. If it looks right, that must be the right answer.:icon_thum Lay it out on the ground and go with that.

rayH

 

[Gotcha6]

Guys, I was tryin' to keep it simple ...... I figured with a handle like JackLeg he'd have a framing square, but maybe not a calcuator with trig functions on it.:eusa_danc Took me some time to learn to use one myslf. Besides, he's gotta mark the board with something and he 's building a swing, not a raised panel door. Oh, well, a good example of how the folks here'll come together to give a guy some help.
BTW, I'm savin' that link too! Thanks, DaveO!:icon_thum

 

[junquecol]

Do it the almost idiot proof method. On a flat surface, make a full size template. Using either a Wixey protractor, or a Swanson Speed Square read actual angle. Works for this idiot- most of the time that is. :rotflm:

 

[sawduster]

Boy, did this one lose me quick !! :icon_scra

 

[TracyP]

Boy, did this one lose me quick !! :icon_scra

Me Too, Also:rotflm:

 

[JackLeg]

Bruce: That's exactly what I did. Just put them on the table and evened my tops, spread the legs out to 60", and then took my trusty old (and I mean OLD) T-Bevel square and matched the angle.

SO, maybe this is the way to go.

Dennis, I REALLY appreciate the framing square tip. I've always wanted to know more about how to use a framing square. When I was a kid, my Dad told me that if a man knew how to use all the info on a framing square, he wouldn't need a college degree, he'd be a self taught engineer!

Thanks to everyone for the tips.

:notworthy:

 

[Bas]

The Windows calculator has built-in trig functions. I can't remember 90% of the math I took, but this stuff has proven useful over the years. It enables me to calculate exactly where and by how much I screwed up.

Common sense math works here as well. The angle is somewhere between 45 (not enough) and 90 degrees (too much). (90 + 45) / 2 = 67.5. Close enough

 

[Alan in Little Washington]

Looks like a bunch of us got the right "numbers" 24.62 and 65.38, we just differ in terminology. As far as actual angles created at the leg-base intersection and the leg-ridge they are 65.38 and 24.62 degrees respectively. When you cut the legs on a mitersaw (if you could cut 65 degrees) the "cuts" will actually be reversed since 0 on a mitersaw is actually at 90 deg to the 2 X 6 long axis you would cut the bottoms at 24.62 and the top end at 65.38. Clear as mud? :icon_scra:icon_scra

I used the Win calculator by trial and error by computing the sine of various angles and comparing that to the known value of the sine, since the calculator won't give you arcsine.

 

[gdoebs]

I'd draw it in SketchUp!

 

[Bas]

Looks like a bunch of us got the right "numbers" 24.62 and 65.38, we just differ in terminology. As far as actual angles created at the leg-base intersection and the leg-ridge they are 65.38 and 24.62 degrees respectively. When you cut the legs on a mitersaw (if you could cut 65 degrees) the "cuts" will actually be reversed since 0 on a mitersaw is actually at 90 deg to the 2 X 6 long axis you would cut the bottoms at 24.62 and the top end at 65.38. Clear as mud? :icon_scra:icon_scra

Yeah, 24.62 is probably the better woodworking answer. The only angle that works regardless of tilt direction/ perspective is 45 degrees This is kind of project is probably better suited to a circular saw though

I used the Win calculator by trial and error by computing the sine of various angles and comparing that to the known value of the sine, since the calculator won't give you arcsine.

Actually, it will , but it's not intuitive. Enter the sine, check the "Inv" box it's all the way on the left), then click sin. Square root function works the same - click Inv, then x^2

Make that TOTALLY not intuitive. :icon_scra