My own favourite version of "compost tea" is to take worm castings from my worm farm, put them into a watering can, and then part fill with a firm spray from the hose in order to "liquify" them. To this I sometimes add urine, fish emulsion, seaweed solution, or even blood and bone. I'd suggest you could do the same with compost, though I do believe that the boost of additives (especially nitrogen) would be of benefit.
A more traditional version is the old drum with a lid to which you add a bag (such as hessian or shade cloth, tied and tethered at one end) full of weeds, compost, manure, etc, a dash of urine, and water, seal the lid and leave to ferment for a few weeks and then apply diluted (1prt tea to 9prts water is generally a safe bet, though use the colour of the resulting brew as a guide, better to always be on the cautious side initially till you find the brew your plants prefer). Be warned, the smell can be a little...nasty.
Your compost or worm tea should not smell bad, that is a sign that it is anaerobic. The main benefits of compost/worm tea comes from the aerobic microorganisms that are reproducing at an astronomical rate. Doubling every seven minutes is what I've heard. Get a cheap aquarium pump and an airstone and some aquarium tubing to fit the pump and airstone. Put your compost into a paint strainer bag and tie up the top. Fill your water container to near the top, I use a five gallon bucket. Pour in an ounce or two of blackstrap molasses. (Food for the microoganisms.) Toss in the airstone and plug in the pump. The worm leachate tea that I make with this method never stinks. If you were using raw manure or minimally composted manure it might stink. If I can't get to the tea in 24 hours I just add a bit more molasses and use it the next day. I think you can likely find a used aquarium pump for cheap at a second hand store. I think that the pump, airstone and tubing cost me about $14 at walmart.
Interestingly, I've done both aerobic and anaerobic versions of compost tea. Last year I filled a trashcan with weeds, a bit of compost, manure, urine... and then lots of water, and let it steep. After a few days the smell was incredible. I dipped my watering can into that and fed all the plants in my greenhouse for months, topping off the trashcan when the level got low. It worked wonderfully. I had rich, lush plant growth.
Alternately, I bubbled compost tea and used that. It worked fine as well, but the results weren't as amazing as that anaerobic stuff. I'm not sure why.
I did an article for Mother Earth News a week or two ago on "fertilizing organically on the cheap:"
I should have gone further into compost tea. Basically, the organic tank mix I make sits in my sprayer for a day or two before I use it. I do this to let it all steep, though I don't know if it's necessary.
1) Scrape up the droppings in the chicken tractor and put them in a gallon bucket, fill it to the top with water, let it sit overnight.
2) Day 2: Dump the one-gallon bucket into a five gallon bucket, fill 3/4 full with water. Put it on to aerate (cheap little air pump for a 10 gal aquarium).
3) Go scrape up half a gallon of well rotted leaf litter from the woods behind the house. Sprinkle it over top of the aerating manure tea. After a couple hours of aerating, the offensive smell is gone.
4) Day 3: Blend up a half cup of biochar in a quart of water and add it to the aeration bucket. Let this aerate a couple more hours, giving time for the bacteria to move into their biochar condominiums.
I use this full strength on everything in the garden. I only have 3 chickens in the chicken tractor, so I am only starting out with at most 100 g of droppings.
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