L*, Characteristic Chamber Length, Day 2

One of the first things you need to do for sizing your rocket chamber is to find the characteristic chamber length (L*) for the propellant combination you've chosen. A list of values can be found here: http://www.braeunig.us/space/propuls.htm#engine
Excluding hydrogen peroxide (which needs a catalyst bed) combinations, the longest L* is 127 cm (typical values are between 50 and 100 cm, or so I've heard). Based on anecdotal searching around the internet, I get the impression that using gaseous propellants means your necessary L* is lower. I've heard values of L* around 80 cm (~31.5") being used for propane/air (though I think that's conservative), so let's go with that as a minimum.

Given a certain throat area and chamber cross section area, L* (L star) helps you find how long your chamber needs to be:
http://www.braeunig.us/space/propuls.htm#engine

L* is characteristic length
V_c is chamber volume
A_t is throat area.
So, we can re-write. that as:
L*=A_c·L_c/A_t
where: A_c is chamber cross-section area, which is fixed for us at ~pi·(18mm/2)^2 = ~2.545cm^2 = ~.3944 in^2
and
L_c is chamber length, which cannot be more than travel length of our drill press at 2.5 inches minus length of the spark plug into the chamber which is .75 inches or so, giving a max of about 1.75". Ideally, we'd want a little less than that so we can drill the nozzle straight through with the drill press, so ideally we'd want about 1.25" for L_c, though that's a little too short, as we will find out. (I still assume L_c is 1.75" in the rest of the section, here.)

We can rearrange the above to get:
A_t=A_c · L_c/L* = .3944 in^2·1.75 in/31.5 in = ~.02191 in^2
pi·r^2=area, thus 2·sqrt(area/pi)=diameter, so: 2·sqrt(.02191 in^2/pi)=.1670 inches, or a little less than 11/64" (but more than 5/32") for the throat diameter. This fits in with my previous Back-of-the-Envelope calculations, which gave me a throat diameter of about 1/8" (the older BotE calculations were based on conservative assumptions on the steady-state capability of the air compressor I have access to, which is something like 5 SCFM at 90psi).

So, I want to make my nozzle throat no wider than 11/64" diameter and use the full travel-length for my drill press. I think I'll go with 1/8" throat for a nearly 100% margin in the throat area (I can always bore it out larger). That's a pretty small rocket, but as long as it's flamey and makes mach diamonds and doesn't leave me broke or dead, I'm happy. :)