Step 4: The Most Important Part.
Once you have built a 4 inch barrel potato gun, you will probably realize that pototoes are too small to touch the sides and you can't build any compression. Rutabegas work, but firing off 2 dozen of those gets expensive. Wads of wet newspaper is labor-intensive and messy. Bigger suddenly isn't better. However, if you take a yogurt or cottage cheese container, and trace around it snugly in the barrel, you get a perfect fit.
When you are done, cut off the excess, and see if it fits tightly.
Now, for a little strength and better compression, wrap the surface that will contact the barrel with some electrical tape.