I got this idea from a mortar somebody built on Instrucables. I hope you enjoy it. For clarity sake, the igniter side of the pipe is the side with the igniter. :~) The firing side is the side with the bottle.
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Step 1: What You Need.
Tape measure, electric tape, wire stripper, hot glue gun (or epoxy), pop bottles, igniter (found on grills), 2-17 inch wires (stripped at both ends), 13 inch pipe (pipe is 13 in only because that is the throat of my bandsaw. Feel free to change it, just make sure the wire is two inches longer.), hairspray, and some paper.
Step 2: The Pipe.
3/4 inch PVC pipe. It will require some sanding and shaping to fit the bottle. On my pipe, the igniter slipped in easily, though you may need to shape the insides for your pipe. You may want to spray paint your pipe. If so, now is the time to do it.
Step 3: Connect the Wires.
Connect the two wires to the igniter. If you have the 2 wires that come with the grill igniter, just use those. Otherwise, you will have to tape or solder the wires to the igniter. Make sure that there are one or two inches of wire at the firing end.
Step 4: Hot Glue the Wires.
Now, put the wadded piece of paper into the firing end, between the two wires. Push it in about 1/2 inch. Cover the paper with glue until level with the top of the PVC pipe. Make sure there are no leaks. You need it to be air tight. Cut the wires about 1/4 inch above the pipe, and bend them until you get the best spark (maybe about 1/4 inch or so) when pushing the trigger of the igniter.
Step 5: Firing the Rocket.
Take your bottle and hairspray (or spray deodorant) and spray for 1-2 seconds into the bottle. Put the bottle onto the firing end and point it in a safe direction.
Disclaimer: This is where it could be dangerous. Make sure you have eye protection, body armor, a helmet, ear plugs, face shield, and any other protective gear to make you resemble a S.W.A.T. team member. :~) Seriously, make sure you are being careful with the projectile. No matter how you slice it, when objects fly through the air, it can be dangerous. Be smart about it.
Pull the trigger and enjoy. Make sure you watch the video!