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If you know the proof and weight (or volume) of the rum and the target sugar loading then you can calculate the quantities of sugar and dilution water required to achieve 80 proof using the calculator downloadable from www.katmarsoftware.com/alcodenslq.htm But the final proof must be verified as described by bluefish_dist

Yeah, mixers can be useful to bring cooler liquid down to the bottom. Bigger the delta T, the better the heat transfer and efficiency. We used to run direct fire, without agitation and it was slow. At least in the brandy world, it is believed that the high heat and copper contact in a slow warm up contributes positively to flavor. Not sure if that is the same for rum or not. We switched to direct steam coils, still no agitation on that still and warm-up is faster, but still slow, agitation would help with that, but it is fast enough, and the flavor profile seems unaffected. We used to pre-heat our wine for the still to 120 to shorten warm-up. Might be an option for you if you have an insulated tank, drain the still through a coil in an insulated tank (or use another heat exchanger of your choice) to save the heat for the next day. My understanding is LP is typically much more expensive than NG, (although I'm sure that varies depending on location), so that could be another reason to try to save/reclaim heat.

A few constants I've used, and confirmed: You yield 11% of your kettle volume in finished whiskey. This is double pot stilling with minimal reflux. A column with proper deph control will yield you about 16-17% kettle volume in finished whiskey in one run. Assuming 9-10% distillers beer. variability to the above comes from your actual ferment ABV. For every 100 G of still volume you can expect (roughly) around 500 bottles of white dog/unaged at 80 proof per week (5 days). This is assuming you're running a single run through column. I've found this to be spot on. To predict finished whiskey bottles at 80 proof take the above bottles-per-run and account for 10% loss the first year then 3% annually beyond that. This varies depending on climate. Those 500 bottles per 100 G kettle volume look like 410 bottles in 4 years. To change any of those numbers (like bottle proof) use the equation [concentration 1][volume 1] = [concentration 2][volume 2]. So those 410 aged bottles at 100 proof would be: [80p][410btls] = [100p][x] which is: 328btls of 4 year old whiskey at 100 proof per 100 G of still volume. If you have a 450G still, divide by 100 and multiply by the 328 btls we figured out above and you can produce 1476 bottles of 4 year old whiskey per week...which you can sell in 4 years. The equation i used does NOT account for volume loss when you blend water with ethanol. It is significant, and it will cause these numbers to be lower. Tons of variables to account for. ROUGH numbers we're working with here. As your example of a 450G still you're looking at ~72 proof gallons per run. You would produce around 2200 bottles at 80 proof per week on a 5 day single run schedule. We average about 58 proof gallons per 53G barrel so you're looking at 6.8 barrels per week if you batch 5 runs then barrel at 115. 120 puts you at 5.7 barrels per week (roughly). In terms of stripping runs, 20% of kettle volume is about what we yield pretty consistently. We kill it at a TP of below 15 at the parrot. Not worth my time beyond that.