Summary: Cut a 1" length of 1-1/4" ID PVC pipe, for the pulley groove. Cut another length, 22-1/8"+kerf, for the drum axle. At 2-5/8" to 2-1/4" from one end of this axle, cut it at an angle of 14 degrees. The beveled cut makes it easier to re-erect the braced and laced drum, after it's been collapsed for storage.
1-1/4" I.D. PVC pipe with precisely squared ends, length 23-1/8" + 2 kerfs. (Kerf = saw blade thickness, typically 1/16" or 3/32".)
1" I.D. PVC pipe, 3-1/2" long. (The "keeper.")
accurate saw: table saw, chop saw, or backsaw.
rasp or coarse sandpaper.
Measurement gets tricky here. A single cut at 14 degrees will produce two pipe pieces, each with one beveled end. You may not get exactly a 14-degree bevel (which isn't important), but both pieces will have exactly the same bevel (which is).
Start by checking one end for squareness (cut if necessary.) Cut off a piece exactly 1" long, and save it for the pulley. If you have a table saw or a chop saw, it's easy. To cut a pipe evenly with just a handsaw or backsaw, start by wrapping blue tape evenly around the pipe, with the tape located on the measured side of the cut line (not on the scrap piece). Then, rather than sawing through, saw just enough to start a groove alongside the tape edge. Rotate the pipe and saw a bit more, and continue around the pipe until it's done. Finally take a rasp or coarse sandpaper to the new-cut ends, to remove any irregularities.
Measure and cut the other end square at 22-1/8 + kerf.
The next cut is diagonal, at 14 degrees; the longer and shorter sides will differ by about 3/8". Cut to produce a maximum length of about 19-5/8". The short piece that remains will measure about 3" at the longest and 2-5/8" at the shortest.
For a freehand angled cut, place one corner of a scrap of blue tape at 19-5/8", and halfway around place another at 19-1/4". Lay down a length of tape from one tape corner to the other. Clamp the pipe with the tape length facing upward, so your sawing starts at the midpoint. Saw without rotating the pipe, but check often that the saw's going where you want it.
Use a rasp or sandpaper to round down the inner edge of the 2-1/2" pipe's beveled end. Round down the keeper's outer edges at both ends. You now have parts for a drum axle that will be both stable for use and collapsible for storage.