Today we're going to look at a simple technique for figuring out the radius of an arch, so you can mark it out cleanly and get a nice cut. This particular arch will be 6 inches below our top plate, and it will be 12 inches high and 36 inches wide, but this process will work for any dimensions.
Here's how you do it:
1. From one end of a 4-foot wide sheet of plywood, measure down 6 inches on both sides and draw a line across; this will be the top of the arch.
2. Measure another 12 inches down from that line and draw a line across the plywood (18 inches total from the end of the plywood); this will define the bottom ends of the arch.
3. Make a mark 6 inches in from each side (taking away a total of 1 foot, since we're making a 36-inch wide arch on a 48-inch wide sheet), and make one more mark in the middle of the sheet, on each of the lines above.
4. Draw a line from each of the outer marks (the ones that define the width at 36 inches) on the line that is 18 inches from the edge of the plywood (the bottom edges of the arch) to the center mark on the line that is 6 inches from the edge (the top of the arch), making a triangle.
5. Measure the length of the angled lines you just made (the two lines that go from the center of the top of the arch to the two bottom points of the arch), and find and mark the center of each (in this case, 10-13/16 inches is the distance from one end to the center of each line).
6. Put a screw at the center of the top of the arch (the center of the line 6 inches from the end of the plywood), and one screw at each of the bottom points of the arch (the marks 6 inches in from each end of the line that is 18 inches from the end of the plywood). Each screw should be located so that the end of your tape measure will be directly over the mark on the plywood when hooked over the head of the screw.
7. Pick a measurement that is more than half the length of the angled lines of the triangle; in this case we're using 20 inches.
8. One at a time, hook your tape measure over each of the screws you just placed, hold your pencil at the measurement you just picked (in this case, 20 inches) and make an arc. Draw these arcs so that they cross each other near the middle of the plywood.
9. Use a straightedge to draw a straight line from one of the line midpoints you marked in step 5 to where the arc you just drew from the top of the triangle and the arc you drew from the same side of the plywood cross. Do the same for the other midpoint from step 5.
10. The two lines you drew in step 9 (perpendicular to the angled lines in the triangle you drew in step 4) should cross in the middle of the plywood below the bottom of your arch. Put a screw at the point where these lines cross.
11. Hook your tape measure over the head of this screw, and use your tape measure and pencil as a compass, connecting the marks where you previous screws (in step 6).
Now you've drawn your arch — all you need to do is cut it out.
Note: if this process seems a little complicated, you can alternatively use a framing square to draw the perpendicular lines that extend down from the ceter marks you made in step 5. With that done, you can jump right to step 10, place a screw in the point where these perpendiculars cross, and complete your arc with yor tape-measure "compass".