The barrel vault of the bookcase in Woodsmith 274 (page 40 of the article) is made of two sheets of Bendy plywood that are epoxied together. First you’ll have to make a form that shapes the barrel exactly to fit the top of case.
Build the form. Cut out and shape one of the four MDF ribs of the form (use a trammel and plunge router). Notice that the rib is a half circle with a 3" tail. Use this rib as a template for the other three. Cut the filler blocks for the top and bottom of the form ribs. After cutting the pieces to size, glue up the two bases (three pieces of MDF). Cut the notches for the ribs. Then round over the bottom edges to make it easier to attach the band clamps. Glue in the outer two ribs using clamping squares. Then glue in the inside ribs using the filler blocks to ensure they’re square. Finish up by adding the fillers at the top of the ribs.
To make the vault, you’ll coat two sheets of 3⁄8" plywood with epoxy and clamp them to the form.
Cut the sheets 1” wider than needed for the final vault and lay them out in the shop. First, you want to moisten the surfaces with water. Then mix the epoxy and add thickener (to the consistency of peanut butter). Apply the epoxy with toothed applicator to the wet surfaces (Figure 2 above). After setting the epoxy tools aside, flip the sheets together and lay them across the forms. Apply band clamps first, then the F-clamps and clamping blocks. It’s important to transfer trim line locations to the barrel. Leave the barrel in the clamps overnight (Figure 3).
Set the Stage. Lay out and pre-gap all the clamps needed to clamp the barrel to the form. Set the form on blocks so you can fish the band clamps underneath. The clamping blocks ensure that once you’ve trimmed the ends of the vault they will align to the sides of the case.
Trim to Size. Next, it’s time to trim the barrel to final size and add grooves to join with the case. Also cut the rabbet for back. You want the vault to be stable while trimming the ends square at the trim line. Figure 4 above shows how to do this. Placing the vault on a sacrificial board allows you to cut completely through the vault in one pass. For the sake of a square cut, the guide block lifts the saw base plate above the curve of the vault (Figure 4a).
Grooves. Next, you need cut the grooves in the edges of the barrel to mate with the tongues on the case. To do this safely and accurately, use double-sided tape to attach the plywood base to the saw as you see in Figure 5. First, position the rip fence as shown in Figure 5a. Then raise the blade to the proper height. This setup provides complete support for the barrel as you make the grooves.
Rabbet Next. Routing the rabbet along the back edge of the barrel to receive the plywood back is best done at the router table. Attach a temporary support black for greater control while routing.
More Veneer. Now it’s time for the big match — veneering the case. The best way to win the battle against this long, floppy, piece of veneer is to not fight it. To do that you’ll lay the case on its back, lifted off the floor with blocking. Then you can apply contact cement to both surfaces. When the surfaces are dry, stand the veneer on edge. With the help of a trusted friend or two, press the veneer place. After it’s trimmed flush it’s time to install the face frame.
Shaping the Arch. After you’ve glued up the segments of the arch, hold it in place on top of the case edging you previously installed (Figure 8 above). Detail 8a shows tracing the outside profile on backside of arch. At the band saw, cut out the profile to the waste side of the line. Now you can tape the arch in place on the case and use a trammel to draw the inner arc profile. Remove the waste and sand it smooth at the spindle sander. Glue the arched edging to the bookcase and when it’s dry, use a flush trim bit in your router to clean up outer the edge.