Do you you mean that you are putting the coil into a 5 gallon cooler, filled with cool water, then siphoning your hot wort (or water, in your test) through the cooler and into your fermenter?
Yep that's what I did thank you for your input, shouldn't you account for the already chilled wort in the fermentor, ie when you start the wort is chilled to 50 degrees say you have a gallon of that then your output comes up to 60 so roughly you would have 2 gallons of 55 degree wort then a gallon of 70 to the two of 55 you should have 3 gallons of 60 degree wort and so on, I know the numbers aren't quite right, but shouldn't this let me get away wo changing the water in the cooler
Well, the math here is pretty simple. You are right in your idea that the wort coming out of your chiller is going to be cooler, initially, than the wort that comes out later on, but it should work out in the end.
Basically, the most efficient heat transfer you could have, from 5 gallons of hot wort to 5 gallons of cool water, would be what you would get if you simply mixed them together, and that's the temperature halfway between the two. If you have less wort, you just need to figure the volume in.
((Gallons of cooling water * temperature) + (gallons of hot wort * temperature))/ total gallons.
So if you had 5 gallons of 50 water in your cooler, and you poured 1 gallon of 212 water through the chiller, that first gallon should be around 80 F, and the chiller is probably going to 75 or so. (100% efficiency would have them both at 77, but you won't get that. And as the water in the cooler warms up, the efficiency is going to drop, so by the end your cooler is probably going to be 135-140 and the 5th gallon of wort would be coming out at like 170-180).
The math here is all rough, and it doesn't include the heat energy of any of the containers, heat lost to the air, etc. In the real world, you're not going to get 100% efficiency through your cooler, because nothing is a perfect conductor of heat and wort will spend only a limited time in contact with your copper chiller. Also, there's the thermal mass of the copper chiller, which in your case, should work to your favor (since it will start it cool). But that should be a fairly small effect (for example, you could try dumping a gallon of boiling water through the chiller, with the chiller sitting in an empty cooler, and see how much the water cools down. Some of the temperature drop will be from heating up the copper, and some will be what the copper loses to the air).
If you aren't doing full boils, you could certainly get away without changing the water in your cooler. If you are cooling 3 gallons, put some ice in your cooler, so you start out with, lets just say 40 F water in the cooler. If you stir your wort for a bit before you start running it through the cooler, lets say you do that until it cools down to 200 F. Run your 3 gallons of wort through the chiller and into your fermenter, it should be around 100 F. Now top off with 2 gallons of 50 water, you'd be at 80. If you cool your top-off water in the fridge, you could be in the 70s.
To answer your other question, you do see other designs (this basic idea here is the same as a counterflow chiller, but with no 'flow' and a limited volume on your cooling water). The reason you don't hear a lot about it is because the standard immersion chiller is simple and works great for those who are willing to pump-and-dump the necessary amount of water. Counterflow and plate chillers are usually the 'step up' from immersion, because they are more efficient (more surface area in contact with the wort and the cooling water), and they don't have a hard capacity limit (the limit is how long you are willing to wait for your wort to drain, and how much water you are willing to run through the chiller).
