Calculating miter angles

[Cherryville Chuck]

Saw this on an FB post this morning. It's a bit involved but it is one solution. The calculator on your computer or phone will provide the values to plug into the equation. The simplest solution for cutting crown molding angles is to hold the molding against the table and fence of a chop saw at the same angle it will be on the wall. The flats on the backside of the molding will be flush with those surfaces at the correct angle. Then just chop your 45, 22.5, or whatever.

If the molding is too large for that method then you have to make a compound cut. Here's the math:

To calculate the compound miter for cutting crown molding along a 4/12 vault (18.5 degrees), you will need to use trigonometric functions. The compound miter involves both bevel and miter angles. Here's how you can calculate it:
1. Determine the spring angle of your crown molding. The spring angle is the angle formed by the back of the crown molding and the surface it is mounted on. Common spring angles are 38 degrees and 45 degrees, but it's important to know the specific spring angle of your molding.
2. Calculate the miter angle:
- The miter angle is the angle at which the top and bottom edges of the molding meet the wall and ceiling. It is calculated using the arctan function (inverse tangent) as follows:
Miter Angle = arctan(cos(roof angle))
3. Calculate the bevel angle:
- The bevel angle is the angle at which the top edge of the molding is tilted in relation to the wall. It is also calculated using the arctan function:
Bevel Angle = arctan(sin(roof angle) / sin(Miter Angle))
In your case, with a 4/12 vault (18.5 degrees), you can substitute this value for "roof angle" in the above formulas to calculate the miter and bevel angles more precisely.
Once you have the miter and bevel angles, you can set your miter saw accordingly to make the compound cut for your crown molding.
It's important to note that the specific spring angle of your crown molding will affect the calculations, so ensure you have this information before making your cuts.
If you'd like to avoid trial and error, these calculations should help you achieve the correct compound miter for cutting crown molding along a 4/12 vault.

[Herb Stoops]

Back in the day, before Carpenters were aware of Trig. they coped the profile on the end of the angled piece of molding and created the back bevel with a block plane or sanding block, true it wasn't a one-cut operation, and maybe even took longer.
There was a lot more trim used in years past, they have eliminated quite a bit since, and they usually made a miter-box to assure repetitive cuts with a handsaw. A good adjustable miter square helped determine the correct angle cuts to set the miterbox. a lot of the time the numeric value was not even known. this eliminated any field variations that ocured from a calculated angle.
Just saying.........
Herb

[Biagio]

Chuck, in your point 2 you mention a roof angle, but this is not defined?

[Herb Stoops]

Chuck, in your point 2 you mention a roof angle, but this is not defined?

The roof angle is 4/12,i.e.4" rise, to 12" run. or 18.5 degrees.
Or a right triangle of 12" horizontal,to a 4"rise, which creates a pitch of 18.5 degrees. a standard roof pitch.

https://roofonline.com/roof-pitch-to-de ... conversion

Herb

[Stick486]

I cheat..
https://www.boschtools.com/us/en/boscht ... -140461-p/

[Herb Stoops]

My-Oh-My.....The tools today blow my mind!!

How did we ever build anything with 2 sticks and a rubber band????
Herb

[Cherryville Chuck]

Chuck, in your point 2 you mention a roof angle, but this is not defined?

The roof angle is 4/12,i.e.4" rise, to 12" run. or 18.5 degrees.
Or a right triangle of 12" horizontal,to a 4"rise, which creates a pitch of 18.5 degrees. a standard roof pitch.

https://roofonline.com/roof-pitch-to-de ... conversion

Herb

I usually just do it with my desktop computer or phone calculator. Trig is just a ratio of two sides of a right triangle. For a sine of the roof pitch its the vertical rise by the length of the slope which you get with the Pythagorean equation of the square root of the sum of the height squared plus run squared. If you are building your own roof as opposed to ordering trusses you need that number anyway so you know what lumber to buy for the slope.Divide the rise by the length of the slope then find the inverse (-1) sine function of that number. Step by step that works like this:

144 + 16= 160 (sum of the squares for a 4/12 roof)
Sq. Root 160= 12.649 (the length of the slope)
4 (the rise)/12.649= .3162
Hit the inverse function button (INV). The sine function changes to sine-1. Hit the sine-1 button.
The angle is 18.435 degrees.

Easy peasy.

[Cherryville Chuck]

Back in the day, before Carpenters were aware of Trig. they coped the profile on the end of the angled piece of molding and created the back bevel with a block plane or sanding block, true it wasn't a one-cut operation, and maybe even took longer.
Herb

I cope my own baseboards. I'd do it for someone else if they were willing to pay the extra time. A coped corner is far superior to a mitered corner. I did red oak baseboards years ago in my bathroom and the boards shrank and left an ugly gap where you could see to the drywall. A coped joint just shows a shadow line if you have shrinkage and you don't have to worry much about that unless you have two long pieces meet at a corner. A long and a short- you run the long one into the corner and cope the short one.

Coping baseboards is simple for the most part. Cut a 45 bevel on the end and use a coping saw to follow the edge of the bevel. If you saw accurately you'll get a perfect fit.

That wouldn't work on angled crown molding so I don't know if there is an easy trick or not. Maybe saw a bevel at the angle the molding sits at?

[Stick486]

That wouldn't work on angled crown molding so I don't know if there is an easy trick or not.

coped crown corners work well on inside corners...

[Cherryville Chuck]

Maybe if you cut the compound bevels and then follow the edge with a coping saw it works the same as with baseboards. If I had any crown molding scraps around I've give it a try and see. Or maybe you just miter the end to the spring angle and then saw with the saw tilted to the spring angle.

[Nickp]

Dewalt provides a handy-dandy chart for cutting crown...provides miter and bevel angle settings...

https://www.dewalt.ca/why-dewalt/featur ... wn-molding

[Biagio]

Thanks for that, Nick. All those calculations hurt my head.

But how does one set 41.08° and 42.93° on a mitre saw? Do some come with vernier scales?

[DaninVan]

41.08 is 41 in the real world and the other one at 42.93 is 43, if you can see a 1/10th of a degree 8' up a wall your eyesight is waaaay bettern' mine!

[Cherryville Chuck]

Thanks for that, Nick. All those calculations hurt my head.

But how does one set 41.08° and 42.93° on a mitre saw? Do some come with vernier scales?

Mine has digital readout to .1 degree and seems to be pretty accurate but like Dan said, rounding off should work. The fractions tell you which way to round.

[Stick486]

like Dan said, rounding off should work. The fractions tell you which way to round.

.49 - round down...
.50 - your choice...
.51 - round up...

[Biagio]

[/quote]

Mine has digital readout to .1 degree and seems to be pretty accurate but like Dan said, rounding off should work. The fractions tell you which way to round.
[/quote]

Interesting. Which model do you have? Did it come with digital readout, or was that an add-on?

[Cherryville Chuck]

Mine has digital readout to .1 degree and seems to be pretty accurate but like Dan said, rounding off should work. The fractions tell you which way to round.
[/quote]

Interesting. Which model do you have? Did it come with digital readout, or was that an add-on?
[/quote]

Milwaukee 12" SCMS. It came with the digital readout and an led work light to illuminate the cut which works well. It did not come with a laser cut indicator. In really fine cuts I'm not sure how useful the laser is since if they make it a really fine line it'll be hard to see and wider, easy to see and it won't be accurate. Maybe they thought of that and that's why it doesn't have one.

The instructions said it better be dead accurate out of the box. It was and is, for the miter at least. Tilt is analog, not digital, so that part is up to you. It was on sale for $399 at Home Depot, about 1/2 the price of a Bosch glide compound. I've had it for 4-5 years now and I'm extremely happy with it.

[Cherryville Chuck]

A work around for lack of of a laser line. Also acts as some blowout protection as long as the piece you’re keeping is on the left side.

[Biagio]

I have the Bosch glider, accurate out of the box. Best part of it is it takes up virtually no space at the rear.
It has a laser line either side of the blade, but I don’t use them for the reason you mentioned: too broad a line for precision. Also a little proud of the blade, although that gap is adjustable.

I have been thinking of mounting a COB chip to cast a shadow line on the workpiece, but in trying it the shadow was not that distinct. A brighter chip causes glare and may make the pencil mark on the workpiece less visible.
I hate getting old.

[Cherryville Chuck]

I have the Bosch glider, accurate out of the box. Best part of it is it takes up virtually no space at the rear.

I have been thinking of mounting a COB chip to cast a shadow line on the workpiece, but in trying it the shadow was not that distinct. A brighter chip causes glare and may make the pencil mark on the workpiece less visible.
I hate getting old.

The space the Milwaukee takes is an issue. It’s over a metre. I think 42-43”.

Task lighting has become a big issue for me. Shadows are especially a problem. I bought some swing arm lamps at my favourite auction, four for ten bucks. I have one over my lathe and I just mounted another to a table saw and gave one to an uncle for his lathe, and one is spare. I also have mag base LED sewing machine lights on drill press and milling machine. They work well up close. There’s a photo of the lights on the Milwaukee too.

[Herb Stoops]

Those little lights are neat, I have several on different tools.
HErb

[Biagio]

I will have to look for magnetic mains-wired lights like on your drill press. I have tried battery driven Leds, the light is adequate, but keep forgetting to switch them off, dead when next needed.
Have also pondered laser crosshairs for the drill press, but think they may also be too coarse for precision.

[Herb Stoops]

I use the ones with the squeeze clamp that plug in.
Just curious, Biaglo, what is your power rated ,110, 220,AC ? Ours is 110/220 AC
Herb

https://www.google.com/search?client=fi ... 9&dpr=1.88

[Biagio]

We followed the British/European standard of 220v AC., and have stuck with it. Interestingly I have three-phase supply to the house, so with some jigging could run 3-phase power tools. I thought about it years ago, but I neither have nor need any of those. The idea came up when I acquired a knock-off cheap (in every sense of the word) Shopsmith jointer/planer, and needed a motor for it. A patient who was in the electric motor business pointed out that a 3-phase motor cost a fraction of the equivalent single-phase unit, since it has fewer bits.

Generally I think we are better off on 220, the problem is that power tools, for example, cost a lot more than in the USA, because of relative market size. And then there are transport costs. But I understand Canada is in the same position, which makes no sense given the common border. More of Charles ass-hattery, I suppose.

Where we goofed was sticking with the Brit right-hand drive in cars. This makes cars even in UK about 30% more expensive than a left-hand drive equivalent -except Made in Japan cars. Sweden was a lot cleverer - they switched from right to left decades ago. We should have done the same when cars were fewer. Too costly and complicated to do so now.

[Herb Stoops]

I am not an electrician
, but I found this:
https://www.quora.com/Can-I-pull-a-110- ... hase-panel

But Stick would know, he knows everything.
Herb

[Stick486]

We followed the British/European standard of 220v AC

.
we use two 120VAC lines to get 240VAC as where you use a single line carrying 240VAC..
Also.. we have 60HTZ as where you have 50HTZ...
your wiring codes??? (as I remember them from Germany)...
Single Phase Line (Hot) – Brown (220V)
3 Phase, Line 1 – Brown
3 Phase, Line 2 – Black
3 Phase, Line 3 – Grey
Neutral – Blue
Ground – Green with Yellow Stripe

Correct???
.
For the US....
120/208/240 Volt AC Wiring Color Codes in USA used in home and office.

Single Phase, Line (Hot) – Black or Red
3 Phase, Phase 1 – Black
3 Phase, Phase 2 – Red
3 Phase, Phase 3 – Blue
Neutral – White
Ground – Green, Green with Yellow Stripe, or Bare Wire

Plan "B"....
277/480 Volt AC Wiring Color Codes in USA
Common for industrial motors and equipment.

3 Phase, Phase 1 – Brown
3 Phase, Phase 2 – Orange
3 Phase, Phase 3 – Yellow
Neutral – Gray
Ground – Green, Green with Yellow Stripe, or Bare Wire

now for that light you want for your tools..
flex neck plug in the wall desk lamp...
you have these in so many different lamps and styles/configurations...

got shadows... use opposing lamps...
.

image.png

[Stick486]

Interestingly I have three-phase supply to the house, so with some jigging could run 3-phase power tools.

3Ø tools, wiring and motors are cheaper than single phase...
but the electricity use cost way more, as in much more.. as in 3x's as much...

single phase shop, 275~300$ a month..
3Ø shop.. over a thousand dollars a month...

[Stick486]

But Stick would know, he knows everything.

what am I suppose to know???...

[Biagio]

Pretty much as you say, Stick. In practice we run at about 230v for single phase, at 50 Hz, like Europe. The colour code is about as you state it (no grey), with a little leeway: in one installation the colors have to be constant or labeled. This comes about when one needs to run two “lives” in a single protected cable, for alternate location switching of a single light circuit.
For some reason I have not fathomed, the protected cable (like cabtyre, but with an aluminum sheath around the colour-coded conductors) is locally called Norse cable. I guess first imported from Scandinavia, before local production. In same class as traditional armored cable for domestic use, ie conduit not required.

[Cherryville Chuck]

I will have to look for magnetic mains-wired lights like on your drill press. I have tried battery driven Leds, the light is adequate, but keep forgetting to switch them off, dead when next needed.
Have also pondered laser crosshairs for the drill press, but think they may also be too coarse for precision.

The mag base sewing machine lights are great for the DP and would work on a table saw too. On an aluminum top saw you'd have to come up with a work around but I can think of a few. For bench, lathe, and some other jobs the swing arm lamps are hard to beat. The florescent ones I got at auction went cheap because they didn't have holders, just the pins on the ends. Making bases was simple and I made them so they could be clamped to an edge or have a wooden dowel inserted so that I could install them in a bench dog hole. Like you I'm not sure about crosshairs on a DP. I think maybe I'm better off with cross lighting so that there are no shadows. Shadows are really starting to bother me, both physically and mentally.

We share a power grid with the states so ours and theirs are the same Whenever I look at things like lighting on ebay, banggood, etc. I have to make sure it's for our power and not yours. The plug in, if it has one, is one way to tell. They are different and don't interchange.

Our armored cable is referred to as BX cable. That is short for Bronx Cable, the company that I imagine invented it.