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How do I calculate an angle?

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  • How do I calculate an angle?

    Hi all,

    My current wood working project is to make an aquarium stand for what's known as a bow front aquarium. It's called that because the front of the aquarium bow's outwards in a horizontal arch (versus vertical arch)about 4" out in the center.


    In making this unit, I'll be using a number of vertical .75x1.5 pieces of wood (slats) up front to curve around this arc.

    My question is, how do I figure out what kind of angle I'll need for them? I want to put an angled rip cut into the slat's to allow them to nessle tightly against each other.

    Any idea's on how I can figure out the right angle? (I was thinking trial and error with a number of 1/2" long cross cut pieces.)

    Am I taking the right track with this one??

    Any idea's on an easier way to do this more precisely??

    TIA,

    BB

    [ 10-01-2001: Message edited by: Bubba Blue ]

  • #2
    There is, I believe, a pretty good explanatin of this in a book called "Router Magic." From memory (I'm not at home), it goes something like this:

    The curved side of your acquarium base is actually a segment of a many-sided box.

    The subtended angle of two sides of a box is equal to 360 divided by the number of sides. For a 4-sided box, the subtended angle between two sides is 90 degrees; for a 6-sided box, the aubtended angle between two adjacent sides is 60 degrees.

    The bevel for joining two sides of a box is equal to half the subtended angle. Bevel 45 degrees for the sides of a 4-sided box, and 30 degrees for the sides of a six-sided box.

    The hard part for your problem is to figure out how many sides there would be if the box went all the way around. Do this by figuring out the angle between the two end pieces. If you have them mocked, take two straight boards, tack them to the sides so that the overlap one another in the back, and measure the angle. Divide that angle into to 360 and hope that it comes out even. Multiply the result by the number of sides you plan for the front of your base.

    For example, if you planned 12 sides for the front and the angle between the end pieces is 60 degrees, this would be the same as a 72-sided box. 360/72 is 5, which is the subtended angle between the front slats, and 2.5 degrees would be the bevel.

    For the life of me, though, I can't remember how to figure the bevel between the left and right most slats and the end pieces.

    Good luck.

    Comment


    • #3
      RGAD,

      Based on my extremely foggy recollection of my Jr. High Geometry class, I think recall (extremely vaguely) how one could what you're saying.

      The problem I have is the sides are not at the angle I want. The aquarium has a rectangular footprint with the exception of the front arc and which, if I understand your idea correctly, they need to be at an angle going back to the center, right?

      This being the case, can I can't use that proceedure without getting the correct angle right?

      Hmmm... thinking this through further, can I trace the arc out on a large piece of paper/wood and use a T-Square to figure out where the center would be (by placing perpendicular to both of the arc's ends and drawing the line in to the center of the arc?

      I can probably find the location of the center to some degree of accuracy.

      My other thought was to call the manufacturer and ask what the arc is. The only possible drawback is they may not be willing to tell.

      Thanks.

      Comment


      • #4
        Ijust read rgad's reply Man I thought this woodworking was pretty simple
        Semper Fi <BR>Chuck<BR>USMC 66-70

        Comment


        • #5
          If the two sides join the back at a 90-degree angle, they are parallel and, you're right, you can't get the angle between them by extending them.

          The straight line between the front edges of the side panels (i.e., what the front would be if it were flat) is known in trig terms as a "chord". If you measure the length of the chord (distance between the front edges of the side panels) and the depth of the chord (distance between the center of the chord and center of the curved section, i.e., how much the curved section hangs out in front of where a flat front would be), there are formulas that will tell you the angle of the chord. From there you can proceed with what we talked about yesterday.

          Somewhere I have a trig book with the right formula. I have doubts I could find it, but if you get me the measurements for length and depth of the chord, I'll look.

          Comment


          • #6
            Do mean the distance of the arc and not the width of the aquarium? Here's a quick graphic of what I think you mean. Because it's a geocities account, you'll need use without the "http://" but with "www."

            geocities.com/ca_woodworker/tank_dimensions.jpg

            Darned geocities!!

            Comment


            • #7
              Let me play with this and I'll get back to you.

              Chuck: Nuthin's simple.

              Comment


              • #8
                Got the sketch.

                The arc you've labelled "A" is the "length of the arc."

                The dimension you've labelled "B" is the "depth of the chord"

                The unlabelled line that starts at the front edge of one side and (if extended) would go to the front edge of the other side, is the chord and its length is the "length of the chord".

                Get me any two of the above and I can calculate the subtended angle of the chord.

                Then tell me how many pieces (slats) you intend to use to form the arc, and we can caculate the bevel angle (approximately).

                If you are going to depend on edge gluing the slats toghether, the bevel angle is critical and you're going to have to do some experimenting. If you're going to fasten the slats to something else, such as the curved edges of the top and bottom panels, then you can arbitrarily increase the bevel angle (undercut), so as to get a tight fit.

                By the way, I gave up looking for a trig book. I remembered that you can use a CAD program to draw the chord and depth of chord, then draw a three-point circle to enclose the chord, and then AutoCad will calculate the subtended angle of the chord for us.

                Not "simple," but neat.

                Comment


                • #9
                  <BLOCKQUOTE>quote:</font><HR>Originally posted by RGad:
                  Got the sketch...

                  The unlabelled line that starts at the front edge of one side and (if extended) would go to the front edge of the other side, is the chord and its length is the "length of the chord".


                  huh? Do you mean the width of the tank?

                  Get me any two of the above and I can calculate the subtended angle of the chord.

                  Then tell me how many pieces (slats) you intend to use to form the arc, and we can caculate the bevel angle (approximately).

                  If you are going to depend on edge gluing the slats toghether, the bevel angle is critical and you're going to have to do some experimenting. If you're going to fasten the slats to something else, such as the curved edges of the top and bottom panels, then you can arbitrarily increase the bevel angle (undercut), so as to get a tight fit.

                  By the way, I gave up looking for a trig book. I remembered that you can use a CAD program to draw the chord and depth of chord, then draw a three-point circle to enclose the chord, and then AutoCad will calculate the subtended angle of the chord for us.

                  Not "simple," but neat.
                  <HR></BLOCKQUOTE>

                  Ah the wonders of Autocad!! [img]smile.gif[/img]

                  Not sure on number of slats, but i'll have a number when I get home.

                  Regarding the other numbers, I'll measure that when I get home also.

                  One last thing... I got an email response from the manufacturer. They explained the design of their stand and tank as follows...

                  There is an upper and lower collar which supports the aquarium and gives a larger foot to the stand. The body of the stand is approximately 1.25" less than the perimeter of the tank frame. Trace the bottom frame onto a piece of paper or cardboard and subtract 1.25" all around. The collars extend approximately .25" beyond the frame of the tank, giving there support. All slats are planed to .76" thick. The radius of the 46 gallon Bow front is 44.925"

                  Hope this helps. I'll get you the other measurements this evening or in the morning.

                  Thanks for your help!!

                  [ 10-02-2001: Message edited by: Bubba Blue ]

                  Comment


                  • #10
                    I'll wait for the numbers and see what I can do.

                    It occurs to me that there is another way to approach this problem. There is a form of joint called a "canoe joint" or something like that which consists of bullnoses on one edge of a slat and coves on the other, both milled with a router. Insert the bullnose of one slat into the cove of the adjoining slat and you have what amounts to a hinge. This might be easier than trying to bevel the edges and have them come out perfect enough to take a good glue joint.

                    Comment


                    • #11
                      <BLOCKQUOTE>quote:</font><HR>Originally posted by RGad:
                      I'll wait for the numbers and see what I can do.

                      Thanks, I really appreciate your help with this problem

                      It occurs to me that there is another way to approach this problem. There is a form of joint called a "canoe joint" or something like that which consists of bullnoses on one edge of a slat and coves on the other, both milled with a router.

                      so kinda rounded on the edges with one being concave and the other being convex??

                      If only had a router with the required bits!! Home depot does rent them right?
                      <HR></BLOCKQUOTE>

                      Comment


                      • #12
                        It occurs to me that there is a 2nd way that I can make this unit and that is to curve a piece of wood around the arc instead of using thin slats. Would this be easier or more difficult to do?

                        I do want to put a couple of cabinet doors in front there as well.

                        TIA

                        Comment


                        • #13
                          You can go to Sears and get one of those bendable,or shapeable rulers and just place it around the shape up want to duplicate and then place it onto a board and trace it. The ruler holds the shape you put it in...Donny

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                          • #14
                            Ridgidrock,

                            Sorry for not being clear... transfering the shape is easy enough (it's only 36" across) and only weighs 10lbs when empty, so I can easily place it over a piece of wood to build a gig.

                            I'm currently considering two options in building the front facia of this stand...

                            1) Build it using numerous vertical slats ripped with the appropriate angle to give a tight seamless fit.

                            2) Build it using one to three pieces of wood curved to match the arch of the front of the aquarium.

                            Sorry everyone, I'm still thinking this through and I think that instead of option #1, I'd prefer the looks of option #2.

                            So now my question is... how do I actually bend the wood to create the front of the stand?

                            Well, I did some online research last night and found the most prevelent answer as focussed on bending planks by enclosing them a container that you pump full of steam. Kinda tough to do that with a +40" wide sheet of wood.

                            I do recall when I was younger (vaguely... it was soo long ago) a couple of friends who build a skateboard 1/4 pipe ramp using 2x4's and plywood. They soaked the plywood with the garden hose and bent it too the 2x4 frame and nailed it in place.

                            Would doing something similar with maple plywood sheets work? I'd probably use a gig to hold it in the right shape until it dries.

                            Again, sorry for the shift in this thread, but as I said, I'm still thinking through this.

                            Comment


                            • #15
                              Bubba, there is stuff called "bending plywood". Does just what you are asking for (I think, I'm a little dizzy from the math ), no steam, water, fuss or muss. It's an eighth inch thick, if memory serves. You laminate as many thicknesses as desired, then veneer over it.

                              Dave

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