i want to make a battery powered shop vac
First you find a shop vac with a DC motor, and see how many volts and amps it requires. Then you find enough batteries to produce that much power. Lead acid batteries are heavy. Lithium ion batteries are lightweight but expensive.
Start by finding a motor that gives you the suction required. Try to find one with a DC motor (that may be very difficult). It's very likely that you'll need to find yourself a brushless DC motor and couple it with an air pump that provides the suction you require. Once you know the power requirements of the motor you can figure how many batteries (combined in series to provide voltage and parallel to provide duration) you'll need and what size they'll be. Watch the discharge rates. Batteries get hot when they charge or discharge. If it goes too fast in either direction they may catch fire or melt the housing you pack them in. For example, a couple of 12v automobile or marine batteries will fit quite nicely into a milk crate and the open-air nature of them will help cooling and venting as well. Start with the requirements, then work with the logistics and appearance. Good luck.
