I need some help.

[Tim Brooks]

I want to build my daughter one of the dollhouse bookcase I saw posted here a while back but I need someone to point me in the right direction. Here is a picture of the bookcase to which I am refering:

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I am still learning my way around the workshop I have in my garage and am having trouble with calculating some of the angles for the top of the bookcase as well as how to calculate the length of the top pieces. I'm sure this problem is very trivial to all of you but I was lucky to get through geometry and dropped trigonometry in high school.

I have cut to length the three shelves but have reached a point where I need to get some advice from the experts. Where the vertical pieces meet the roof, I will need to cut a few dados. I will need to know how to determine what that angle would need to be for the proper cut on my table saw.

I am accepting any advice you would like to pass along concerning a project like this. I am using ¾” birch ply and I will be joining the shelves using dado cuts, glue, and possibly screws. Thanks in advance for you help and input.

To summarize:
1. How do I calculate the angles for the dados where the vertical pieces meet the top (roof)?<O:p</O:p
2. How do I determine what the length needs to be for the two top pieces?<O:p</O:p
3. How do I calculate the angle for where to two top pieces meet at the peak?
<O:p</O:p<O:p</O:p

[Steve Wargo]

This is a very simple answer... Sliding Bevel gauge. You can buy a cheap one at HD for $9. No calculation needed.

[Art Mulder]

1. How do I calculate the angles for the dados where the vertical pieces meet the top (roof)?
2. How do I determine what the length needs to be for the two top pieces?<o></o>
3. How do I calculate the angle for where to two top pieces meet at the peak?

#1 and #3 are the same question. High school geometry: Add up the angles in a triangle and the total is? The sum of the three angles inside any triangle always add up to 180 degrees. (and yes, I googled that to be sure, since high school was a few years ago...:D)

So, pick an angle for the top... from the photo I'd say it is more than a right angle, so let's just pick a number and call it 110 degrees... then the other two angles have 70 degrees total, and since they are equal, that is 35 degrees each. (and of course, I'd draw it out on paper first, to decided it 110 degrees looks nice or not.)

But you also need to cut the miter where the top two pieces meet. That should just be 110 degrees cut in half. Test on scrap first.

#2... Errr, did I mention that high school was a long time ago? I think that the pythagorean theorem is the one you want here. Drop an imaginary vertical from the peak, until it insersects with an imaginary line connecting the top of the two sides. This gives you a right-angled triangle. So then it is "the square of the hypotenuse (the lengthy you want) is equal to the sum of the squares of the other two sides (those two imaginary lines we talked about)."

Hope that helps.

...art

[Tim Brooks]

So, pick an angle for the top... from the photo I'd say it is more than a right angle, so let's just pick a number and call it 110 degrees... then the other two angles have 70 degrees total, and since they are equal, that is 35 degrees each. (and of course, I'd draw it out on paper first, to decided it 110 degrees looks nice or not.)

...art[/quote]

So what you are saying is as long as I like the 110 degrees at the top, I will adjust the bevel on my table saw to 35 degrees to cut the dados that the vertical pieces sit in, right? I really am making this much harder than it has to be...

[Bob Childress]

Art,
If you think high school was a long time ago for you! :eek: Well. . ..

Art has the idea, Tim. You might approach it this way for simplicity.

#s 2 & 3 go together: For the sake of symmetry, you might want to plan for an isosceles (sp?) triangle, where all the sides are equal. So, decide how much you want the roof to overhang the sides on each end and cut a board to that overall length. That is the length now of the roof pieces. Since all the sides will be equal length, each angle is 60 degrees (3 x 60 = 180), so the roof angle is 60 degrees divided by two or 30 degrees on each board edge.

# 1: Although I sort of intuitively think they would now also be 30 degrees (or maybe 60 degrees), I can't prove it, so do what Steve said and get a bevel scale to be sure.:)

Now my head hurts and I'll have to go back to bed.

[Kyle Kraft]

Just for clarity, a triangle with all three sides congruent is an equilateral triangle. The iscoceles has 2 equal sides and 2 equal angles. Minor technicality, as long as the bookshelf turns out the way you like.

[Julio Navarro]

just my 02's

draw a full size sketch of the angles and use a protractor.

The dados I think would need to be chiseled out by hand, I can't visualize how to make them at such angles with the TS or router.

Just MHO

[Scott Kuykendall]

I made the same bookcase for my daughter. I am no good at figuring angles either. The way I did it was to draw it out on a piece of plywood laying flat on a table or saw horses. Cut the roof pcs long and just eyeball it. I didn't cut any dados for the sides that meet the roof, just nailed them and it worked out fine.
Scott

[Bob Childress]

Kyle, darn it, of course it is equilateral, not iscoceles. I told you it was long ago.:o I can feel Mrs. Smith's keen eyes looking over my shoulder right now and she does not look pleased:mad:

[Kyle Kraft]

In the words of Mr. Mattson, "Geometry is fun, d@^* it!!"

[Art Mulder]

Kyle, darn it, of course it is equilateral, not iscoceles.

Bob, go look at that photo again... that is NOT an equilateral triangle, and I would surely NOT recommend him making it so. An equilateral triangle would probably add a foot to the height of that peak!! :eek:

[Art Mulder]

The dados I think would need to be chiseled out by hand, I can't visualize how to make them at such angles with the TS or router.

The way I did it was to draw it out on a piece of plywood laying flat on a table or saw horses. Cut the roof pcs long and just eyeball it. I didn't cut any dados for the sides that meet the roof, just nailed them and it worked out fine.

Y'know, I've never tried cutting a dado on my TS that was NOT set to 90 degrees. I would think that you could, but I never have. You'd certainly need a new sacrificial insert for the saw.

I wonder if Scott has the right idea. If I look at that photo again, the roof overhangs the front of the bookcase by a few inches. So instead of cutting an angled dado in the roof, you could cut an angle on the top of the sides. So first, make the roof (the peak joint) then tack on a few boards to hold that stiff, and then put it on the sides and glue/nail it into place.

As a final step, you reach for the putty to fill the nail holes, as well as any other cracks or gaps that happened due to those darn complicated angles, and give thanks that you are painting this project! :rolleyes:

[Julio Navarro]

Y'know, I've never tried cutting a dado on my TS that was NOT set to 90 degrees. I would think that you could, but I never have. You'd certainly need a new sacrificial insert for the saw.

Perhaps a birds mouth dado? just a slight angle to the dado blade and a complimantary angle of the board to make a birds mouth cut to the board then the verticle divider would fit nicely onto the roof.

[Julio Navarro]

Y'know, I've never tried cutting a dado on my TS that was NOT set to 90 degrees. I would think that you could, but I never have. You'd certainly need a new sacrificial insert for the saw.

Perhaps a birds mouth dado? just a slight angle to the dado blade and a complimantary angle of the board to make a birds mouth cut to the board then the verticle divider would fit nicely onto the roof.

[Dan Stuewe]

As a final step, you reach for the putty to fill the nail holes, as well as any other cracks or gaps that happened due to those darn complicated angles, and give thanks that you are painting this project! :rolleyes:

Ding Ding Ding! That's the correct answer :rolleyes:

The example in the picture happens to be my attempt at saving $$$ instead of buying from Pottery Barn. I can take some measurements when I get home. But There was a good amount of covering up done on this one. As for the sides to roof. I simply nailed the roof to the sides (with glue). I know it isn't an ideal joint, but I'm sure it will last long enough. Maybe not for generations, but for at least a generation.

[Louis Brandt]

The triangle in the photo is simply isosceles (two equal sides and two equal angles), but not equilateral (three equal sides and three equal angles).
Louis

[Bob Childress]

Bob, go look at that photo again... that is NOT an equilateral triangle, and I would surely NOT recommend him making it so. An equilateral triangle would probably add a foot to the height of that peak!! :eek:

Art,

I didn't day THAT one was equilateral, just that he COULD use one. That one clearly isn't. But the EQL would work fine if the bookcase were made narrower, for example. :)

[Tim Brooks]

Wow, thanks so much for the input. I have just purchased a set of dado blades so I'm not very experienced with using them but explain to me why I could not use the bevel on the TS when the dado is installed? Because the board will be laying flat all the way across the TS, why would you have to use an insert? What are the dangers of not using an insert? I realize I'm showing my ignorance but this how one learns!!!!!!

Dan, I apologize for not giving you credit for the picture but thanks. It wasn't long after I saw your post and the one that someone else posted before yours about the bookcase, that my wife found the one at the Barn and asked me about making one. What better way to learn, right?

Again, thanks to everyone for the input. It is like having all of you in my garage mentoring me. Thanks a bunch!

[Julio Navarro]

The insert is needeed if you are dadoing an end cut as for a tenon. if you are cutting a dado across a long board the insert is not as important.

I still think a birds mouth dado is an easy solution to your roof joint. If you dont use an insert you can tilt the blade slightly while rasing the board slightly to give you the needed angle for the vertical side.

Here is a sketch

Upload didnt work so heres a link:

http://www.tarnsmanoftreve.com/images/birdsmouth.bmp

[Marvin Keys]

You could do what I did when I built mine, which is keep guessing until the angles all work. :rolleyes: Trial and error may not be the smartest way to go, but it does work eventually.

[Jesse Cloud]

Hey Tim,
First, on the geometry... anytime I make anything with angles or curves or just complicated joinery, I draw a full scale drawing first. Just get some packing paper or a side of a cardboard box and draw it to scale. That will help you find a pleasing slope and show what the angle should be.

Secondly, the deal with the insert for the dado is that your sawblade goes through a removeable insert in your saw. The insert that came with the saw is just a little larger that your 1/8th inch thick regular blade. A stack of dado blades just won't fit. You can pay $$$ to get a manufactured insert from the maker of your tablesaw, or pay fewer $$ to get a plastic insert from Woodcraft or Rockler or whoever, or pay nothing by making your own. Just get a board close to the thickness of your current insert and plane it to just the right thickness. Put the insert on top and draw the shape on your board. Use a jigsaw, bandsaw, handsaw - whatever to cut out the shape. Sand the edge smooth. Then put the new insert in the saw with the dado blades all the way down. Securely clamp a 2x4 or something sturdy over the insert. Turn on the saw and slowly raise the blade until it has cut through the insert. If you will be cutting at a angle, set that angle on your blade before you begin the cut.

If you make an insert, might as well make a few blanks to use later while you are at it.

Hope this helps.

[Barry Beech]

I haven't read all the responses but I built this bookshelf for my daughter and I cut the angle at 35 degrees.

Also, I used dados at a 35 degree angle for the sides and center support.