Determine the size of your wing chair by referring to some construction plans. If you do not have plans, use photos of a wing back chair to determine its size. Get photos that show a side and front view of the wing back chair. Study the photo for details like the curvature of the chair legs.
Draw 1-inch squares on the photo with a marker and a ruler. This will allow you to see the curves that have to be cut into the wood to create the legs and other curved parts of the chair.
Using the plans or photos, transfer your measurements to the appropriate pieces of mahogany wood. Draw the shapes that need to be cut onto the wood. Use the band saw to cut out all the pieces. These include two front legs with their own curvature, four pieces of wood for a seat, two curved pieces for the back, two sets of three-piece projecting "wings," two back legs with their own curvature, and two sets of a two-piece construction armrest.
Attach the four pieces of wood for the chair seat. Screw in place all four corners with a drill. Cut out four small blocks of wood and glue the cubes onto the tops of the front legs of the chair.
Use a drill press to make a mortise in all four corners of the chair seat, on the underside. The mortise should be large enough that the wood blocks on the chair legs can fit into them. Slide the blocks of the chair legs into these to attach the legs to the seat.
Screw the back legs and back pieces onto the chair seat. Assemble the three-piece projecting “wing” structures and screw them into the back.
Screw the two-piece construction armrests together and attach to the chair seat and back.