NathanA wrote:
1) Are the air-hole and chamber at a perfect 90 degrees or is there a slight tilt between the two?
The bowl should be canted slightly away from the shank. I don't measure, I just go by what looks good. It's a couple of degrees past 90 I would guess.
2) Are there any guidelines as far as dimensions and proportions (bowl height vs. diameter, shank length vs. stem length, overall height vs. length, etc) that I should be aware of? I have looked at so many different ones, all slightly different, I didn't know if there were any hard and fast rules or just rough guidelines (or if it is just a matter of preference).
Yes. Shank length roughly equal to height of bowl. Stem slightly longer than shank. That is not a hard and fast rule, but it will help in figuring out your first few and how to compose them. Beyond that you can start considering the golden ratio as a way to help you understand the whys and wherefores of pleasing design - but even that isn't a hard and fast rule. Frankly, there are no rules, only interpretations of form.
3) I have noticed that the bowls of many billiards have a slight inwards taper from the base of the bowl to the rim (or maybe better stated as a slight bulge towards the bottom of the bowl), but that the amount of taper (or bulge) varies greatly. Is there any formula for this; and if the walls are more or less straight (but not flat-bottomed like a poker) does this make it something other than a billiard?
There is no formula (with apologies to Todd). One thing you do want to avoid is a barrel shape. Make the billiard more bottom heavy. Make it even more bottom heavy, and you end up with a brandy. Really it boils down to what you find attractive.
For your billiard, you'll have a hell of a lot more fun if you find an example that you would buy without really being concerned about price, and attempting to copy it. Before beginning your work, find the facets that you think really "make" the pipe, and focus on those as you're making your copy. Feel free to use a ruler to find ratios, composition, etc to help you kind of understand why things are working together the way they are. While I wouldn't necessarily advocate pipe design by way of ruler, it can help if you're still trying to figure out composition and design.