Hello, I already have diameter calculations for a small parachute: It is about 34 cm (13.38 inches). My only question is, how do you determine the number of gores a parachute must have? Is it more empirical?
On a 13" chute, I would probably do six gores, maybe 8 if it was 3/4 oz nylon. For 18" - 30" I usually do 8 gores, I made a 60" with 12. My 9 ft. chute had 24 gores.
The more gores, the more shaped the chute will be, but the more seams and shroud lines you end up with. I don't know how much the Cd is affected by increasing the gores. You can probably find out in the Recovery System Design Guide here from the Defense Technical Information Center. Just click the View the full text of this report link and save the .pdf if you want a copy. The Canopy Geometry part starts on page 78.
I prefer a couple extra gores vs too few. I typically sew even my 12" drogues with 12 gores (both for aesthetic and extra strength in case of a very late deployment). However, 6-8 should work just fine. As Handeman said, the more gores, the more round and even your canopy skirt will be, more closely approximating the ideal shape. I've done as many as 24 gores in a 24" (Apollo orange and white), 36 gores in an 8' (my avatar) and as few as 16 in an 18'. The 18' recovered a 130-lb airframe just fine.