A visitor asked how I made the hopper. I was going to reply as a comment, but figured I’d write a full post to show how I made it.
The easy way is to use SketchUp. I’ll use the dimensions Tom is asking about for his hopper. 40″ x 24″.
First, draw a rectangle in SketchUp that is 40″ wide by 24″ deep.
Next, use the Push/Pull Tool to give it some height. This is what we don’t know yet, so let’s just use 24″.
Pan to the underside of our newly created 40″ x 24″ x 24″ box, since the trap door is on the bottom.
Next, use the Tape Measure tool to draw some guide lines. Make sure it’s in Guide mode by having the + sign in the cursor. Use the Ctrl key to toggle the tool mode. Now, click on the green axis line and let’s place a guideline at 20″, half the width of the box. Draw a horizontal guide using the red axis and place it at 12″. You can use one of the edges and let the tool select the midpoint of the line.
There may be an easier way to do this, but this works for me.
Using the Tape Tool, create horizontal guidelines that are offset from the horizontal mid-line by 2″, and 1.5″ offset for the depth mid-line. It should look like this.
Put the model in Wireframe mode, and draw lines from the 3 x 4 rectangle to the 40 x 24 rectangle at the top. In my picture I drew two of the lines to the wrong corners. It’s easy to see this mistake when you start deleting lines. Just undo in SketchUp to correct any mistakes you make.
Using the Eraser Tool, erase the 40 x 24 rectangle on the bottom. Be sure to take it out of Wireframe mode when you’re done.
OK, this gives us our plenum, but how tall should it be. If we imagine a right triangle that starts at the center point of the 40″ side, travels along the top face of the plenum, and stops at 10″ back, which is 1/2 the depth of the plenum, less 1/2 the depth of the bottom face. Then the triangle takes a right angle and travels vertically down, it will arrive at the midpoint of the front edge of the bottom face. The hypotenuse of this triangle would be the height of the 40 x 3 trapezoid shape. In case my explanation doesn’t make sense, I’ve drawn it out.
Now that we’ve drawn this triangle, we can ask SketchUp to give us the height of this 40 x 3 trapezoid shape. Comes out to 26″. But how do we know this is enough or not? TP Tools also sells a pickup tube, or you can make your own. In my case, I measured the length of their pickup tube, added some extra for good measure to arrive at the length. I don’t remember how long I made mine, but let’s say in this example, that we want this hypotenuse to be 30″.
Using a2 + b2 = c2 (a squared + b squared = c squared), we know the hypotenuse we want, 30″, we know one side, which is 10″. So how tall would this plenum be to make this work out. Solving for B gives us b2 = c2 – a2, or b2 = (30 * 30) – (10 * 10), or b2 = 900 – 100, or b2 = 800. Taking the square root of 800, gives us 28.28″.
Knowing this, we can now solve for the side. The triangles top edge is (40 / 2) – (3 / 2), or 20 – 1.5 or 18.5″. The height will still be the same, 28.8, so now we know a and b, this gives us a2 + b2 = c2, or (18.5 * 18.5) + (28.8 * 28.8) = c2, 342 + 829.44 = c2, or 34.22″.
Now that I have my dimensions, I can draw them in SketchUp. Select the face that is 40 x 3, right click and choose Select -> Bounding Edges. We’ll make a copy of this face using the Move tool in Add mode (Ctrl key) and drag it to the Origin.
Using the Rotate Tool, rotate this face to lie flat on the earth plane. We need to rotate around the red axis, so make sure the Rotate tool is in the right orientation.
Once rotated, it should be lying on the earth plane. This is the starting shape of the front side of the hopper. But we need to make it easy to mount inside the cabinet, and we need an way to mount the trap door and we need to have the sides edges line up with the other pieces. So let’s create some flanges (not sure if that’s the right word).
I’ll use a 1.5″ flange on top, a 1″ flange on the sides, and a 1″ flange on the bottom which we’ll mount the trap door to.
After drawing some guidelines and drawing some lines, this is what you end up with.
If we bent this shape using a sheet metal brake, this is how the shape would look.
After all this, it might be easier to take your steel to a local HVAC company and tell them you want a plenum that is 40 x 24 that reduces to 3 x 4, has a 1.5″ flange on top, a 1″ flange on bottom with the 40″ side having a length of 28.8″, or round up to 29″.
How I mounted the trap door, was once I had the 3 x 4 opening with a 1″ flange, it fit inside the plastic part from TP Tools. I then drilled some holes through the plastic and steel and use cap screws or rivets to attach the trap door to the steel hopper.