"How to calculate an angle for a two-winged support?" Topic

That's probably a confusing title, but here's the situation:

I need to build an upright support piece that slopes at precisely 72 degrees. The support is in two parts, "winged" as it were, to be self- supporting, with the slope formed by the joined corner of the two wings.

If you look down from the top, this would make a V shape, with the point of the V being the part that slopes up and back. From the side, it would look like this: /_ (Sort of a bent L). If that's unclear, imagine folding a piece of paper along the diagonal and standing it on edge, with the diagonal fold as the slope.

Here's my problem: The angle of the slope is affected by the width of the spread of the two wings (the angle of the two sides of the V). The wider that angle, the lower the resulting slope of the join. I have a limit of area that V can cover, which means that I have to cut the angles of the two V halves exactly so that when the two sides of the support are joined together, the standing support will angle back at 72 degrees, no more and no less.

How do I calculate what the angle of the base edges should be to the slope edge so that when fitted together I get that 72 degree slope?

It's not just simple trig. A simple slope-to-base of a triangle is easy, but I've got to take that triangle and pull it out (and push it back) in a third dimension to produce the actual slope-to-base relationship.

Right now I know the length of the final slope (20"), the angle of the final slope (72 degrees), and the limits on the angle of the V (53 degrees, max), and the length of the V's legs (the base) as 4.5" each (though they could go to 6"). But what is the angle of each leg (each base side) to the adjoining slope?

Why do both sides of the slope piece have to match? Can you leaver the outside sloped side at 72 degrees and the inner at vertical (or some other angle) to match the V pieces?

I am embarrassed to say this, but I'd use trial and error. There is a mathematical way to do it, and I'm usually handy with math. I love trigonometry. But I'd just grab and index card and a pair of scissors and make a couple of trials.

You should google for "compound mitres" and see if someone hasn't written up an easy method, though.

Lay out a cardboard template with the base V then add a vertical template with the 72deg slope, now lay a piece of paper against it in the position of the finished piece and mark the angle.

Robert

So, you are trying to "join" two right triangles that measure (4.5", 19.5", 20") along the hypotenuse with the resulting angle between the edge formed by the joined hypotenuses and the table being 72 degrees?

Following on from Andrew Walters post, I've seen a number of compound mitre calculators on line where you just input the known angles and it calculates the needed cuts are simple angles. They are all woodworking sites and deal with cutting moulding for frames, boxes and furniture. Chris Schwarz has published a few recent blogs on his Popular Woodworking and also Lost Art Press sites on 'resultant angles' when calculating leg angles for stools and chairs which might be of use

I just didn't save the URL's as I didn't need to do the calculations for any of my projects.

I'd have no trouble with the maths but can't be sure that I've understood how it is constructed.

I'm having trouble visualizing it. Can you build a mock up with card stock or index cards and take some pictures?

jansson.us/jcompound.html

Or

link

To be clearer.

If viewed from the side, the angle produced by the support will be a right triangle with a height of 16" and a base-to-hypotenuse angle of 72 degrees.

The physical support itself will effectively be two triangles (not necessarily right triangles) joined along one edge (which will be the hypotenuse above). The join will be an angle (two miter cuts attached to each other, like the edges of a wood box). That angle created between these two halves is currently planned to be 53 degrees. What I'm trying to determine is what the angle between the base of these halves and the join edge should be to cause the joined edge to slope at 72 degrees as described above. Keep in mind that these two halves will flair out in a V from the join, with their bases forming the bottom of the support.

Think of it like this: Fold a piece of paper longways, then fold in two of the corners diagonally to meet the fold, like making a paper airplane. If you then stand the paper up on these diagonals, the longways fold will make a slope. The angle of that slope will depend on how far apart the two halves of the paper are (the angle formed by the long fold). The wider it is, the flatter the slope; the narrower, the steeper the slope.

In the case of the paper I've described, the angle of each diagonal is of course 45 degrees. However, let's say the interior angle of the V had to be a specific limit (53 degrees) and the slope of the fold is also a specific angle (72 degrees). What then should be the angle of the diagonal folds to produce this result?

That's what I'm trying to do, only with plywood.

I was composing while wakenney was typing. So I'll say thanks for the links. I think what I need may be there.