While my pier columns are setting it was time to move on to the next question: How to set that 40^{o} angle for the solar panels?

I attended 12 different public schools growing up. I don’t know how many math classes I failed or squeaked by in, but they were legion.

Makes me a little angry, too, because whenever somebody tried to teach me something allegedly useful like geometry, the question I kept asking was “What would I use this for?” And I kept not getting an answer. Many years later in tech school when I learned how to calculate the cubic inch displacement of a gasoline engine? Same formulae, now actually applied to a real-world thing, no problem. I’m not stupid. Just not interested in public school theoreticals uncoupled to anything in reality, taught by bored teachers who didn’t even know the answer to my very simple question – and who seemed offended that I’d dared ask.

This trip down memory lane doesn’t have a point, it has an angle…

But that’s the wrong angle.

I’m aware that it should be simplicity itself to calculate the lengths of the two parallel sides of an irregular rectangle – no idea what the name of that is – with two 90^{o} angles and two 40^{o} angles. If only I’d stayed awake or stopped reading science fiction during any one of those long-ago math classes, I would not now be having this problem. That sepulchral laughter in the background is coming from myriads of retired geometry teachers, most no doubt long gone.

Late last week I tore apart one of my friend T’s comically overbuilt battery shelves and found myself richer by four 6-foot 4X4s and 3 2-footers. No way those weren’t going into my new rack. I knew the 2-footers would turn out to be too long – since the 6-footers couldn’t get longer – but I didn’t know how much too long they were. And I could only think of one way to find out.

Sticking the 8-foot 2X6 to the uprights temporarily with screws, I ended up setting it with three different short uprights and measuring the angle before I got in the ballpark where I wanted to be.

A halfway decent math student would have been inside and drinking beer long before I was half done. But there wasn’t anybody like that around here. I finally got it done…

…and of course the other one will be much easier, when I build it in a couple of days.

##
About Joel

You shouldn't ask these questions of a paranoid recluse, you know.

1, 1, square root of 2. Oh, wait, that’s for a 45 not 40. Eh, close enough. I’m gettin’ a beer.

Actually, there’s an app for that. There are free apps for either Android or Apple phones/pads that turn your pad into a spirit level, and will happily read out an angle relative to level ground. In my cheap off-brand Android smartphone, I use an app called “Clinometer”.

Now that you mention it, there must be apps for trig also.

I think your plumb line angle thing is very clever. I’ve never seen that done before.

Well, I think what you have there is not a rectangle. It is a right trapezoid. (Does it have thermometer taste?) And, it wouldn’t have 2 40 degree angles either. This is a case of divide and conquer. Think of it as 2 shapes. A triangle sitting on top of a rectangle. The sum of the angles in a triangle is always 180. So, if one corner is 90 deg. and another is 40, that leaves 50 for the other. Oh, I can see how you can get to 40 for both, because you’re referencing level, instead of level for one, and plumb for the other. Anyways, at that point, you recite the magic incantation, SOHCAHTOA, and Bob’s your uncle!

But, I’d do it pretty much as you described. Really. Lots of people will use tape measures and do their figures, and that’s fine, but if I need to cut something to fit inside a space, I hold it up to the space, and mark it. Same exact method as using a story pole. It’s quicker, and more accurate.

The other thing to do is make a scale drawing. As long as your scale is big enough, your error won’t be big enough to matter much. Last place I worked, std. scale was 1/24, and that was fine for almost all purposes. When it wasn’t, I’d draw the area of interest at double or triple that, and take measurements from my drawing. Well, I’d check using a formula too, and be very very close.

Also, you can get pretty far without SOHCAHTOA, by dividing and using Pythagora’s rule. (Still referred to as a “theorem”, but if it’s been proved, is it still a theorem?)

Gosh I really enjoy this blog. Very clever solution. Joel you are way cool. I do the hold it up and mark it thing too.

Hey, Ben! I don’t think in terms of apps but that would have been a great thing thing to have. My neighbor S builds all sorts of solar panel rigs, and he’s got a compass app on his smartphone that he can reset for declination for true south. Not really easier to use than my actual compass, I personally think, (maybe it’s got other features) but an angle app would have been much easier than the protractor and sinker on a string.

40 degrees actually has a shortcut, built right into your square. 40 degrees is a 10/12 roof pitch, so for every 12 inches of horizontal travel, you have 10 inches of vertical travel. Knowing how far apart your posts are, figure the ratio- for posts 6 feet apart, that’s 5 feet of drop. Subtract that from the height of your tall post, and you have the height of the small one. We carpenters (or properly, our ancestors) invented that system many years ago because math sucks in the field when you should be building things. It’s why roofs use weird angles that don’t work out in even degrees.