Crown molding

[that_guy]

I'm a DIYér, so go easy - my terminolgy is often wrong....

I have crown molding - 5 1/2", designed to cover a ceiling/wall corner 3 7/8"x 3 7/8" and I'm trying to figure out what angle cut I need on an outside corner. I can create some type of jig (home-made mitre box) to place the molding in, I would place it into the box on an angle and then cut at 45 degrees. But I would like to use a mitre saw, I'm just having trouble figuring out the angle if I lay the molding flat.

Thanks.

[that_guy]

Ok... so I asked a stupid question because I'm having trouble using the calculator and since my question is a common set-up I thought someone would know. In my scenario, I typed in a wall angle of 315 and a spring angle of 45. I got a mitre angle of 59.64. Did I do this right, and if so, how do I set the mitre for 59.64?

[Rich]

You'll probably have to use 75 - or included wall angle. Test fit a couple short pieces.
If you don't want to cut it flat - hold the portion of the crown that goes against the ceiling against the fence of the saw and the portion of the crown that goes against the wall against the table of the saw. Then cut a 45 - or half the wall angle.

[that_guy]

Thanks Rich...

Placing the piece on an angle and then cutting it, seems much easier (no angles to calculate) and this is how I've cut trim in the past. However, I can't place the moulding on an angle because the fence is barely 2" tall. But maybe I'll try jigging something to increase the size of the fence. I want to cut it flat but the mitre saw I borrowed will only cut to 45 degrees and I don't think it can cut a piece that is 5" wide. If neither of these options work, I'm going to have to create a home-made mitre box.

Thanks again for your help.


P.S. This isn't rocket science, is there mitre saws (or mitre boxes) out there that can handle something (apparently) this simple?

[Rich]

There are definately saws that can handle it - but again try the 75 degree angle in the calculator if you can't get a decent jig made up.
For the jig - get some 1/2 or 3/4 mdf and put a stop on the table portion at 3-7/8" - make the fence part 4 or 4.5" tall from the mdf table. Should lay right in there.

[Dragon]

You can't really get enough control with a miter box to make a good cut. Too much blade slop.

You might try attaching 4" wide boards to the face of your fence, raising it that way.

If your crown is 38 degree spring angle set crown stops at 3 5/8" out from the face of the fence. This should give you 4 1/4" down from the ceiling to the bottom edge of the crown.

[that_guy]

Rich...that's great advice for the jig.

...And I'm obviously using the calculator wrong. I'm assuming the mitre angle is the angle at which you make a cut on a flat piece (is this right)? But what is a bevel angel and the angle from level?

[Joe Bartok]

Lots of interesting posts today.
I ran this problem through my own calculators; the online html progams employ vector products, the LAG Excel worksheet is trigonometric. Same answers as posted by that_guy, so the calculator is being used correctly. But here’s what I think is happening.
Check out my Pentagonal Roof pdf posted in Roof Framing, and look at the backing angles (corresponding to the Crown Molding bevel) created when a deck angle exceeds 90 degrees. Also at my website, under Miscellaneous Notes, look at the tables of angle values. The manual calculations, the worksheet, and the javascript calculators all returned different values for certain angles, though all are related to one basic value. What happens is: imagine two pitches meeting at 90 degrees, creating a Hip rafter. Now imagine “dragging” the Deck angle (which corresponds to the Wall angle for the crown molding) to a value of 270 degrees. The Hip is now a Valley, or worse, like the roof in my pdf’s, a blend of both!
This is what I think the problem is with the crown molding, and here’s how I solved it (I think?!):
Total Wall angle / 2 = 157.5 degrees (Oh-oh! That definitely exceeds 90 degrees). So, our outside corner “Hip” is a “Valley”.
157.5 – 90 = 67.5, and we need the complement of this, or 22.5, (or, 180 – 157.5 = 22.5, either way, a Total Deck angle of 45 degrees which gives the same results as 315 degrees). By the way, I have a question: why use 75 degrees?
The remaining calcs I did step by step on a calculator, and got the same results.
Bevel = Blade angle as read on the gauge = 40.78947 degrees, with the molding oriented to make the back face short.
Angle from level means the complement of the Bevel value.
Miter = Angle the arm of the saw swings left/right = 59.63881 degrees. And here’s the catch (maybe!). Because of the initial Wall angle value exceeding 90 degrees, we need the complement of the miter angle, or 30.36119 degrees.
If anyone cares to try this and experiment with a piece of scrap and let me know how you make out. I’d appreciate some feedback; if you’ve checked out the diagrams referenced above, you can see these roofing scenarios are a bit of a cross. Despite having literally hundreds of equations at my disposal, the change of trig functions from positive to negative with such large angles makes them difficult to deal with. And there’s no way any calculator can be “fixed” to work in these situations.
By the way, I’ve got a Crown Molding file including the formulas, but didn’t want to post it, as there’s already a calculator at this website. Also, Dragon has some pics posted (I can’t remember exactly where) on his method of cutting crown molding. Very ingenious, and no fooling around with calculations. Too bad this normally isn’t an option for me; I have to deal with 14 inch logs or 10 by 12 timbers to be cut with chain saws, and it’s pretty hard to get those on a jig!

[that_guy]

Thanks Dragon, Joe and Rich.

I'll tryout some of what you all suggested.

It's great to have a place to go to when you have a problem/question!

[Rich]

Whoa 75?.. LMFAO @ myself. I was saying 75 because I was thinking.. well let's just say I wasn't thinking. :) I really am laughing at myself too.

[Rich]

Should've been 45 - 360-315 = 45.. the necessary numbers come out the same - just positive. Well said Joe. I'll see if I can change the calculator to take that into account. If angle > 90 angle = 90-angle. I believe I can even make the change to the calc to handle an iniitial half angle over 90.

[Joe Bartok]

Rich, I don't know if your calculator needs any adjustment.
I did some more sketching last night (images attached), and what I was thinking might be “wrong” yesterday due to changes of sign with angle value just doesn’t apply here. The “deck” angle used in the formulas never really exceeds 90°. Here’s a step-by-step analysis, with results exactly same as returned the Crown Molding Calculator.
315° INSIDE CORNER = VALLEY
Longest face of molding is the back face
45° of the ceiling is visible
The equivalent of the total deck angle between “Valley ridges” is 45°
The required wall angle for calculation is 45° ÷ 2 = 22.5°
315° OUTSIDE CORNER = HIP
Longest face of molding is the visible face
315° of the ceiling is visible
The equivalent of the total deck angle between “Hip eaves” is 45°
The required wall angle for calculation is 45° ÷ 2 = 22.5°
The following formulas call for 90 – Spring angle; in this case the angle is still 45°. These are the same equations used in the framing angle calculators to solve values for a Purlin meets Valley cut. (With respect to the ceiling, the crown molding has the same orientation as a purlin does in a Hip/Valley roof).
“Hip” angle = R1 = arctan (tan 45° × sin 22.5°) = 20.94102°
Bevel = C5 = arctan (sin 20.94102° ÷ tan 22.5° = 40.78947°
Miter = P2 = arctan (cos 45° ÷ tan 22.5° = 59.63881°
Same answers as yesterday!
The following more direct formulas are modified versions of the log/timber joinery equations and also return Bevel = 40.78947° and Miter = 59.63881°. Wall angle means half the total wall angle measured.
tan MITER = sin SPRING ANGLE ÷ tan WALL ANGLE
sin BEVEL = cos SPRING ANGLE × cos WALL ANGLE
And, I revisited my calculators one more time. The Excel worksheet uses the trig formulas given above. The online calculator employs vector products: totally different and lengthier formulas with lots of square roots. Both calculators will accept either 315° or 45° and return the same reults as above.
So, the only thing I can think of is: are the angles we’re starting with in the "real world" indeed 315° and 45°?

[that_guy]

woa!! I started this out thinking "this can't be rocket science"... but apparently, it is!!!

[Joe Bartok]

This isn't rocket science, and don't worry about all those formulas. I was "thinking out loud", and trying out a variety of methods to test the answer and make certain the numbers you got yesterday were correct, regardless of whether the wall angle was greater than or less than 180 degrees. Also, ignore my idea posted yesterday about using the complement of the miter angle; it doesn't apply here.
As for the dreaded rocket science: crown molding angles, timber framing angles, calculations for saw blade angles in general, hip/valley roof calcs, these all employ nothing more than the Pythagorean Theorem in three dimensions, the "Hip Model" composed of four right-angled triangles shown in the diagrams. Nor does it matter if we call the solution a geometric development, or use trigonometry or vector products: it's still right angled triangles and Pythagoras. Just a few simple formulas, but with a lot of applications. :)

[that_guy]

[that_guy]

Okay thanks Joe.

So let me ask you one last question, as I won't get a chance to try this out for a couple of days and we can hopefully put this issue to rest. I always like to work with examples... Since we're talking about angles > than 90,

If I input a wall angle of 270 and a spring angle of 45, the caculator tells me that I need the following:

mitre -35.26
bevel -30
ang. from level 120

This then means that I swing the saw to -35.26 (more or less, I guess) and I angle it from perpendicular to -30.... did I interpret this right?

Thanks for all your help.

[Joe Bartok]

I didn't realise this calculator would return negative values under these conditions, but it doesn't matter. The values are correct, and so is your interpretation of the meanings of miter and bevel. As for what's "positive" and "negative", imagine cutting a compound angle on a piece of work. One of the mating pieces will have "positive" angles, the other "negative".
With a wall angle of 270° we have an outside corner, therefore the 30° bevel must be oriented to cut the molding so the back face is the shortest face.
Well, let's see if this post gets through. I'm having trouble with logging in and out, posting and editing.

[Joe Bartok]

This diagram will explain what I meant yesterday with regard to positive and negative angles. There’s an opposite hand involved at each joint, so the question of whether a value is plus or minus under these conditions is a moot point. It’s the number that counts (yeah, I know what I said).
Now I have a question for you guys. It’s going to be a couple of days before I can get a sketch ready, and I want to double-check my numbers, but here’s a description:
We begin with the usual two walls and a ceiling mutually perpendicular to one another, but there’s a catch. Before the ceiling meets one wall, it deviates from the level at 30°, thus meeting the wall in question at 60°. (This has been discussed in this forum before, hasn’t it? Is the 30° called the rake angle?). Say we want 38/52 crown molding following the ceiling/wall joint. I threw the numbers in my calculators, and the returns for the joint where the ceiling is 60° are scary (one of the bevel angles is 77°!). Matching the widths on the visible faces isn’t a big problem, what bites my @$$ is that crown molding has a finish. How do you deal with matching that as it turns the corner? Surely the bevel angles can’t be simply set equal, as this will involve the miters.
So what’s the solution? There must be a quick-and-dirty (and accurate) way to cut molding in these situations. This thread's getting kind of long, so I'll start this anew in the Construction Math forum when I've got everything together.

[Dragon]

Joe the 30 degrees you asked about is called the Spring Angle.

However, most crown will made for either 38 or 45 degree Spring Angle.

As for the quick, dirty, and accurate way to cut crown, refer to my posts in another topic in this sub-forum. Using miter and bevel while cutting crown flat is fine for the occasional cut and the do-it-yourselfer. But if you're in this to make a living, there really is a better, faster, more accurate way.

[Joe Bartok]

Dragon: I've read your posts on cutting crown molding, it's a neat method, and I'll have to try it out on this strange joint (and it's not theoretical, I'm looking at these planes and angles on the ceiling as I type this!). My description in my last post wasn't very clear, so I've attached a rough sketch. The angle of the molding with respect to the wall, or spring angle, is 38° throughout. The entire plane of the ceiling revolves at 30°. The one joint is no problem to figure out, the headache is in the upper corner.
Using the ceiling as a reference plane, there is a plane with a pitch angle of 52° meeting another plane with a pitch angle of 82° at a deck angle of 90°. (I know these aren't the normal definitions of the spring angles, but this is what my calculators require as inputs). In fact, I was thinking of your method of cutting to deal with this, and it would probably work here as well (make a fence to the pitch angle, miter in this event would be the "deck angle" returned by my calculation). What bugs me is how to match the finish as the molding turns this corner. Will cutting the molding your way automatically match the edges where the two pieces of molding meet? I could be wrong here, but my thinking is that whether the angles are calculated, or the cutting is done in a way to eliminate "miter" and "bevel", the two methods amount to the same thing, and the resulting angles on the molding come out the same. But, using trig, I find that the mating edges can be matched, but not the widths, and hence, neither can the finish. Or, am I overlooking something?

[Joe Bartok]

Dragon, I reviewed your posts again, especially the photos. To apply your method, we don't worry about the strange twists and turns the molding makes. Regardless of the ceiling slope at the joint, I still set the molding up at it's spring angle (corrected for slope if necessary) and cut with the saw turned left/right at 45 degrees. This this should automatically create the correct bevel angles, and more importantly, create equal angles on the molding faces. (This of course is where I'm screwed trying to use the trig; each piece has it's own "natural" angle returned by the calculators, and there's no way to keep things equal as we go around the corner!) If these were angles in a complex roof system, I'd be wary of making changes like this, as they would have other major repercussions, but with the molding there's only the two faces to worry about.
So, into the trig tonight, starting with the assumptions that the angles are split equally as a premise. I'm probably "overthinking" something that's really very straightforward, and makes sense to me when I look at the images you've posted. Oh well! :)

[Dragon]

Ok, you now have too many angles.

If I'm following your drawing correctly you have a vault starting at an outside corner. If you follow the flat ceiling elevation around then you cant meet at your inside corner and follow the same line from the ceiling around. Its time for a transistion box at the inside corner, and a filler above the crown from outside to inside corner between the crown and the ceiling.

I think what is throwing you here is the elevation. Remember that it is figured where the crown meets the ceiling. Once you go onto a vaulted ceiling, the elevation rises until you get into the corner and start going up the rake.

Or, you can stop the crown at the outside corner and pick it up again at the inside corner with none in between.


I have one builder who has a bad habit of putting a 45 degree wall in a room with a vaulted ceiling. To date he has never understood why I keep telling him that I cant crown the entire room in one continuous run without losing the spring angle on the crown. I even built patterns and stuck them into the corners. His eyes glaze over.

[Joe Bartok]

Ok, you now have too many angles.
Yes, that is the problem! I'm still going to pursue all the options as I know them, and post the numbers and a better drawing in the Construction Math forum, hopefully tomorrow.
One idea that may work is to treat the corner as a compound joint. Another option is "half-splitting" all the angles; this would be the equivalent of offsetting a hip rafter to equalize the overhangs when unequal pitches are involved.
By the way, I don't do this for a living. And there may not be a satisfactory resolution in terms of the numbers, your transition box (or, custom cutting some of the pieces? is that an option?) may be the only answer. But it's worth the effort to try, as the insight gained from the attempt can often be applied to other similar problems. I always like to see things for myself.

[Dragon]

No, custom cutting is not an angle. You have to keep in mind that once you go around the outside corner your ceiling height is no longer the same. You are no longer dealing with a right angle. Well... you are, but the right angle is behind the sheetrock instead of at the joint between wall and ceiling. The only way to keep the profile lined up is to keep the crown at the same height, away from the ceiling. Once you get to the inside corner and travel up the vault you can't go back to the ceiling with a continuous run. You HAVE to put a transition box in.

[Joe Bartok]

I believe! This is something I had to see for myself, but enough's enough! It's time to cry "uncle". Here's the math, if anyone's interested. Perhaps this deserves the title already given to another thread: Crown Molding Horror!
To recap; The 38/52 molding follows the wall-ceiling joint along a 30° slope, then turns at a right angle and follows a level line. The sketches (not to scale) detail the angle values returned for the joint, and some of them are fearsome. Check out the 77 degree bevel angle! At least the difference in the dimensions here is hidden (assuming there’s a saw that can tilt to such an angle to make this cut). What’s worse is that it isn’t possible using the “natural” angles to match the finishes on the faces. Life would be a lot simpler if we could make all the angles equal, as the crown molding calculations normally do. But I can’t seem to accomplish that in a satisfactory fashion. Frustrating, to have calculators and programs that will cope with a compound joint in 3D, and then be foiled by two pieces of molding!
I don't understand the transition box, though (I've never had to deal with this in the real world). Or does it have one set of exterior angles to conform to the walls and ceiling, and another to accomodate the molding?
Any pix?

[Dragon]

Oh heck I can run that easily in a continous run.

That drawing looks much different than the last one.

For some reason I was seeing you turning a wall at the point where the vault started before.

All you have to do to run crown in that drawing is change the spring angle from vertical and allow it to run more toward the horizontal on your upper piece of crown. you'll still cut it for 38 degree, it just wont go on the wall at 38 degrees. It will vary by the degree of the slope of the ceiling.

[Joe Bartok]

Well, after I had given up on trying to solve this riddle, you say it can be done! So I went back at it, but haven't come up with a successful resolution yet. (But then, my only claim to experience at working with crown molding is having watched someone install it last summer, and implementing a solution in my worksheet. Hardly a stellar track record!). The math is beginning to deviate from the topic of crown molding, so the preliminary notes (Joinery_Summary.pdf) are posted in the Construction Math forum. But the problem parameters remain the same, and perhaps the sketches are a little clearer. :)