you dredged up a really, really old post.
Now, for your question. Re-distillation is usually done for a couple of reasons.
1. you are using a simple pot still, and 2 runs are required to get the proof up.
2. you are running a column still to make neutral, and want to make a cleaner neutral.
For both of these, you usually perform the first run, which is often called a stripping run. In this run, you would normally run the still about as fast as you can, take few (if any) cuts, and run it until all of the ethanol has been removed from the boiler (well, until almost all is gone). Now, any run can be 'called' a strip run. If you have run it through a column, but something got messed up, then you can still 'call' it a stripping run (if you got all the ethanol out).
Now, for the first 'kind' (simple pot still), frequently, people will distill about 1/4 to 1/3 the original volume in the strip. Then they will do a couple of these, and combine them all into a 2nd run. So, you start out with 30 gallons of 10%, run 3 stripping runs of 10 gallons each, and end up with 8 to 10 gallons of 30-35% 'low' wines. These low wines are then run again, slower and carefully this time, taking careful cuts. You will end up with about 4 gallons of 65% or so (barrel strength) and a couple gallons of feigns (heads and tails). These would be put into the next stripping run, to reclaim the ethanol.
For a column still, again, the first run is usually a stripping run. However, a column will output a higher proof product, even if running fast and not worrying about cuts. This is the part that you will want to water down. So, say you started with 10 gallons of that same 10%. Run though a column, you would likely end up with 2 gallons of 50% (or even less volume at higher percentage), by the time you exhausted all of the ethanol from the boiler. This will vary greatly, and depend upon how fast you can run, and how little percentage of reflux you can get the still to run at. Some will make a 'semi-normal' 1st run, so may end up with a gallon or so, of 90-95% from their first run.
There are a couple of reasons to water down. Some are safety. Some are economy, and some are helpful for making a cleaner end product.
1. (safety first) you will NEVER want to put anything stronger than 40% into a boiler (some would say even less than this). The reason for this, is that 40% is about the lowest percentage of ethanol/water mix that will burn. This is not entirely true, since when hot (it's boiling in the boiler), a lower percentage WILL burn. Now, why you want to keep the ABV under 40%, is that if you have a problem with the boiler, such as it springs a leak, has a cato failure, the burner stand falls over, etc, you are going to have hot ethanol mix all over the place. Big fire danger. Keeping the ABV lower helps to reduce this. If the ABV is low enough, it will not burn at all, so if there is spillage of any kind, it will not ignite. ADDITIONAL SAFETY NOTE. Keep a bucket (or more) of water right next to the still. If you do have a problem with the boiler, you can kick over that bucket(S) quickly, and retreat back, and if there is any ground fire, the water will lower the ABV of any liquid, and the fire will die out.
2. (economy). It actually takes less power, to distill out the ethanol from a lower concentration, than trying to crack it apart if the ABV is 'too' high. Also, it is much more economical (time and power), to do 4 stripping runs, followed by a slow, careful spirit run, than trying to do 4 slow careful spirit runs from the original wash.
3. (cleaner product). Doing a stripping run, then a careful 2nd run, produces a cleaner end product. That first run, concentrates the ethanol. It removes ANY left over solids (or dead yeast). Also, if you have to water it down (say it was 70% and you drop it to 35%), that water will help to wash out flavors that carried over in the first run. Yes, in the boiler on your first run, there was a LOT of the nasty flavor/smell stuff, but not all of it. When you do the spirit run, you will find that what is left in the boiler will still have a lot of skanky smell to it.
Hillbilly Rebel: Unless you are one of the people on this site who are legalling distilling, keep a low profile, don't tell, don't sell.