We've built air catapults successfully before using a round electromagnet from mcmaster.com,
http://www.mcmaster.com/#5698k116/=10s4olc
fast valves aren't that important in my experience. What is important is that you must not retract the piston all of the way. Leave a 'chamber' of air about 2 -4 inches in the bottom of the air cylinder when your mechanism is retracted and position your mechanism so that it doesn't have much leverage against the catapult when it starts.
Fill the cylinder(s) while holding the magnet. when the cylinder is up to 60psi, release the magnet. The 'chamber' of air will 'explode' the catapult forward.
The neat thing about regionals, is that they ARE big robot parties! - MrForbes [more] 
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