Crown Molding Calculations

[Joe Bartok]

Rich, Dragon, et al …
Last night I reviewed my analysis of crown molding related angles, and compiled everything on my hard drive in one document. This question and another one (the log assembly estimate in another thread) have also given me some insight and appreciation as to what you guys go through when someone pops a question on this forum.
What bothered me is that twice since I've elected to participate in this forum, others have used the Crown Molding Calculator, and said that it didn’t seem to work. And I’m wondering, how can it not??? This isn’t “rocket science”, I’ve done my own independent analysis (Page 3), and others have tackled this problem; the answers all agree. Now I’m wondering if I’ve misread and didn’t understand the questions posted, because while I was going over this last night I realised that I’d completely overlooked two possibilities. Check out the diagrams (don’t worry about the formulas if you don’t want to) on Pages 4 and 5. Under the conditions outlined, the definition of wall angle must be modified, and any crown molding calculations require the complement of the spring angle. In terms of the math, we have to replace sin Sping Angle with cos Sping Angle, and multiplication by tan Sping Angle must be changed to a division in the formulas listed in Page 1 (compare to Page 6).
If we apply the procedure Dragon has outlined in another thread, we don’t have to worry about all this trig. But if we use a calculator ... (The calculations shown are in terms of my spreadsheet, that’s all I’ve got to work with since I don’t have the internet on my PC at home.)
Any opinions? Is crown molding installed on vaulted ceilings often enough that this is a concern? Or am I making this too complicated? (If so, just cut this from the forum; this probably should have been posted in the Wood Trim Forum anyhow).

[Tom R]

Joe, - - you provide some really great posts, - - they're great contributions for everyone, - - must really take you some time, - - which I don't have a lot of right now, - - I want to 'delve in' more later, - - but anyway, - - I do believe you are correct about the calculations needing to be based on the 'complement' of the spring angle. I do remember this being a point of confusion, - - at least for me, - - in the past.

[Joe Bartok]

Tom: Keep me posted as to what you think. You guys are the experts, and there's no way I can test the math in the real world. I'm stuck with trying to see this in my "mind's eye", with a little help from a rough sketch. And a lot of numbers! :)

[Rich]

I have to say I've never thought this hard on crown molding :) I agree with Tom - you have some great posts Joe.. and they get me thinking about things I haven't thought about in years.

[Joe Bartok]

Has anyone tried AutoCad to validate the formulas? Not the equations used in the Crown Molding Calculator, we know they work. What about a scenario like the last crown molding topic discussed in the Wood Trim forum? That's a bad one?! Wouldn't AutoCad work on something like that?

[Rich]

Autocad could give x,y, and z coordinates very easily - it has more difficulty with vertical angles but I think I can change the axis of orientation to get them. I'll see if I can come up with something to check them.

[Joe Bartok]

A continuation of the last few posts in Wood Trim (Jan. 29, 2005), but the subject matter is beginning to turn more toward math in general, so Construction Math seems a better place to post this material.
The analysis posted in the Wood Trim forum, with the warped angles returned by the framing angle program isn’t the only way to achieve a joint. Compound joinery is another approach. This is only a preliminary set of notes, a summary of known facts, and it’s not too heavy on the math.
If anyone’s wondering where this is all going at first, hang in there. The original crown molding problem parameters remain the same. Working “in the round” allows us to invoke symmetry; you can’t find anything more symmetrical than a circle. If we can’t accomplish anything with a circular section, then we may as well forget about something like 38/52 crown molding. And yes, O.K., I just had to show off what can be done with the math.
It’s ironic and a bit frustrating that it’s possible to create a joint with three or more irregular pieces, yet matching two pieces at the same joint doesn’t seem to work! The results are still inconclusive. And working with round sections is beginning to highlight a potential problem: despite matching planes and faces, note that the circle section arc lengths are unequal. Perhaps someone else can see something else I’ve overlooked. Any ideas or suggestions?

[Joe Bartok]

It isn't always possible to achieve a compound joint. For example, changing the pitches of one parallel pair of the interlocking trusses to anything other than 8/12 will make a joint using equal diameters impossible. But - it's possible to learn how to recognise these situations. Two-way joints are obviously possible to achieve under some conditions, but not in this particular case. So the question is: how does one know?
The backing angles given on the last page are the values needed to match the edges as the planes turn the corner. But if we assume a cut is made at the 52.62876° angle shown, the arcs on the faces of the ellipses created by the cut won't "fit". Perhaps the cutting plane must be tilted at a compound angle to create a match, and the easiest way of determining the compound angle is to take the backing angles given as pitches meeting at a 90° deck angle, and solve. (Doing this would also be consistent with the definition of the "Line of Convergence" that occurs in the more complex joints). If our assumptions are correct and everything is copacetic, this calculation should return the original 52.62876° and 37.37124° deck angles. That's not what happens, so there is a fatal contradiction somewhere …
This is kind of a bummer. We live in an age of high tech computers and calculators that makes working with numbers quick and painless, and I'm having trouble negotiating a corner with two pieces of wood! It's enough to have baffled Houdini.