Allen,
Great question.
By the amount of threads left on the housing I think there were three and someone may have add a fourth one?? Would be a good place to start troubleshooting it at.
I tried to keep an eye on the temperature, but after speaking with someone in the business for 20 years. He seemed to think that two drops per minute is a little low and if they doesn’t leak just a little bit sitting in the slip it could damage the packing? I adjusted it to 2 drips per minute at cruise speed heading out to sail and also at ideal sometimes. I am new and know enough to be concerned dangerous.
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Some thoughts on your post (not in any particular order).
I used to own a Catalina 30 with a conventional stuffing box. So I'm very familiar with the boat.
Number of rings: I would say 3 rings of packing is typical. The main thing is, you don't want it to leak excessively, nor do you want the packing nut to be too hot. I use the GoreTex GFO packing. It's a synthetic graphite-impregnated packing. It's pretty well indestructible in my experience.
All forms of packing require some water for lubrication. MaineSail points this out on his very excellent site, and Buck Algonquin tech support confirmed this to me in some email exchanges. As for how much water, see next point.
In gear and rotating: A "perfect" setting is just seeing some water glistening on the interface where the the propshaft exits the packing nut. It need not not actually drip but you should be able to observe the presence of water there. You can also adjust it so it drips a bit more. 2 drops per minute is certainly not too little; what you were told is wrong. (I presume the packing nut is not overheating.) You could just leave it at that and be fine; your bilge pump will remove water from the bilge that will eventually accumulate. You may just want to confirm the temps and call it good.
At the dock, engine off: You may well find that after the boat sits at the dock for a while with the engine off, the drip rate slows down. That's all the better. So, what is a "perfect" setting would be just slightly weeping water while the engine is running in gear, and then not dripping when at the dock, engine off. If you don't get that exact result, then make it slightly looser and you'll be fine.
How hard to adjust the packing nut: The fact that you have to really apply pressure to tighten the packing nuts tells me something is wrong. I found that I had to go just a little beyond hand tight, if that. If you are having to wail on it to get the dripping down that suggest to me something is tweaked with the packing. In that case, I'd pull out the packing and start with new.
Replacing the packing in the water: I noticed in a following post the caution about replacing the packing in the water. That's the only way I've ever done it on three different boats, including my 1987 Catalina 30, essentially the identical boat to yours. I never had a bit of problem doing this. You do need to have a working bilge pump. I found the bilge pump *easily* kept up with the water ingress.
After you replace the packing: It will take several hours (10 or so?) for the packing to "break in" and set. I'd try "sneaking up" on the proper adjustment. Let it be a bit on the loose side to start with, dripping more than ideal, and then progressively tighten it as you put more hours on the packing. Once it's settled, you can get a good adjustment and then it will be fine for a long, long time. I find with the GoreTex, once I've got it dialed in I can leave it alone for literally years.
How hot is too hot? You can use an infrared thermometer to check the temp. You are checking the temperature of the packing nut. The range might be anywhere from around 80 deg. to 120 deg F. If it starts going above 120F then that's more than you want.
Hope this helps.