Hi Papa Smurf
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There are a couple diffrent ways you could go with this. My suggestion is if you are all ready and itching to get some painting done NOW, then a temporary set up is the way to go. All you need is a nice sized cardboard box, a length of dryer vent tube, a small fan, and some duct tape. You can get small venilation fans designed for bathrooms at most hardware stores for pretty cheap prices. And the dryer vent tube is also very very cheap, and available from the same hardware store. And duct tape should be just about everywhere that also has the fan and tube. Then just put it all together.
I also would suggest that you make sure that the fan moves enough air to be effective. If you get a measurement of how many cubic feet/meters your box is, you would want a fan that moves that many cubic feet/meters of air per second. Also while not necessary, a filter of some type would be a good idea so that you don't paint the side of the house what ever color you are running throught the airbrush, and also to cut down on the fumes you are pumping outside for your neighbors to get to deal with
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And one thing that I missed on my litte art work above is to make a piece of wood or heavy cardboard with a round hole that the dryer vent tube fits through, that also blocks off the entire area of open window. That way the vented fumes will not come right back in the house through the opened window that the vent tube is sticking out of.
This will work fairly well as a temporary paint booth. And then if you like the idea, you can search the internet for airbrush paint booths to get some good plans to make a better, sturdier, more permanent one.
Gary B)