Yet another compound miter question

[mjd]

have done some searching and will continue to do so, but if anyone has some tips it would be greatly appreciated: I'm starting an arts&crafts clock w/QSWO, copying from a magazine ad, and trying to determine the cleanest way to join the face and sides. There are two slightly-tapered (3 degrees) face pieces that form the front (in between them is a door with the clockface attached). I've beveled the bottom and tops of each side piece to the same degree, but in order to avoid leaving the end grain of the face exposed, instead of butting the face to the side I'm thinking of mitering them, but I know I need to adust for the taper and bevel. Front view, right-hand front piece looks like this

| \ | \ | \ | \

the right side piece is beveled top and bottom so it can lean up and stand flat along with the front which is straight up vertical (not beveled on the bottom). Due to the taper, I (think) I can't just cut the edges 45 degrees the way I could if it were two sides of a straight up box. I've looked at some calculators and formulas and seen things like how to figure similar cuts for sheathing the roof of gazebo, but in those cases all the pieces lean in at the same degree.

Is this going to be too tough for my aging brain 30 years removed from any formal math training? I could just butt-join the side to the back of front piece and not care that the edge shows, but I'd like to have a seamless look of the ray-flecked white oak all the way around.

[Chris Friesen]

Actually, you can. Assuming that the top and bottom of the clock are rectangular, then the joint between the front and side pieces is still

90 degrees.

Chris

[mjd]

you know, I kept looking at these pieces and thinking the same thing, but then I got this nagging feeling I was missing something. I was probably reading too much into it? I'll try it out first on a couple scrap pieces. Thanks very much for your help.

[Tom Veatch]

Not sure I understand the configuration correctly, but assuming a flat rectangular piece at the top and bottom and a flat tapered piece on each side, 45* miters may or may not be appropriate.

Assuming that the edges of the joint are supposed to meet at the inner and outer corners, then 45* miters will work if and only if the width of the bottom piece is the same as the maximum width of the tapered side and the width of the top piece is the same as the minimum width of the tapered side .

Otherwise, the miter angles cannot be 45*. The correct angles, will be:

Miter Angle for Bottom Piece = inverse tangent (Maximum width of side piece/width of bottom piece) Miter Angle for Side Piece at the Bottom = 90 - Miter Angle for Bottom piece.

Miter Angle for Top Piece = inverse tangent (Minimum width of side piece/width of top piece) Miter Angle for Side Piece at the Top = 90 - Miter angle for Top Piece.

Note 1) Miter angles defined above are the standard definition where the angle of the cut is measured relative to the square end. e.g., 0* miter angle equal a square cut

Note 2) If the two mating pieces have the same width, the equations above reduce to the common 45* mitered corner.

Note 3) For the tapered piece, the inside edge should be the reference face placed against a miter gauge set to the calculated angle.

Note 4) The above calculations can be used to determine the miter angles for any joint in which the members have different widths.

For the top angle

Tom Veatch Wichita, KS USA