Sure! I had an idea how to start but never had made anything quite like that.
Groovy.
Using this formula T
= ((2πR)v)+y+(2πRw) where v equals the number loops you want in your worm, R = the radius of the worm (half the diameter), w equals the radius of the loop you want at the end of the handle, y equals the length of the "handle" portion you want and T equals the total length of the rod before you start, you can calculate the length of the rod you need to form the worm. Because the taper will lengthen the rod slightly, you will end up with a slightly longer rod than you planned, but this is negligible for this purpose... who cares if the rod is six inches longer?
Don't let the math scare you, it looks more difficult than it actually is. I.e: Say you want a 2" diameter worm for a 2 1/2" bore, 3 loops in the worm with a three foot handle that has a 4 inch diameter loop at the end of the handle. This assumes you have a barrel length of about three foot barrel length. If it is longer, you will have to adjust the length of the handle portion. Now plugging in the variables:
(2 x 3.14 x 1 x 3)+(2 x 3.14x2) = 69.1"... the length of the rod you need. I have not checked my math or the formula, so you might want to go over it again. I am many things, but not a math wizard.
Start with a 3/8" mild steel or wrought iron round bar... you can use a square one, but it will be more work because you want the screw to be of round stock. Forge a point, you want that tapered down over maybe a three to four inch length. Now go to the horn of your anvil and start bending the tip into a spiral pattern. The "circles" you will form will run parallel to the rest of the rod you are working with. You want the diameter of the worm to be less than the bore diameter of your cannon... how much less depends upon the bore diameter. For a two-inch bore, you probably want a 1" to 1 1/2" diameter worm. Figure you want your worm to be three to six inches long when it is stretched out. This means that you will need three to six circles.
At this point, your work piece will NOT look at all like a worm. Don't worry, it'll get better. Right now your rod will form a tangent to the last circle you made. You want to bend your rod so that it forms a geometric ray that starts at the last circle and goes through the center point of the circle. Once this is done, you bend that ray so it is perpendicular to the circle from the center point and goes out to form the handle.
Heat up your coils, then clamp the handle in a vice, use tongs to grab the pointy end of the worm and stretch the coils until the worm is the approximate length you want. Make any adjustments you want while it is still hot. Quench it.
Now you plug in the second part of the equation: (2 x 3.14 x 2)=12.56 We'll just make that 12.5". Measure 12 1/2 inches from the end opposite the worm and make a perpendicular bend. This will be the part that gets made into a loop at the end of the worm's handle. You can bend it on the horn or a mandrel if you have one. When finished quench it.
Square up a portion and add decorative twists if you wish, then quench. Wire brush it and coat with wax... or whatever you use for preservative. Most smiths have a favorite secret formula for coatings that they may or may not share with you. One formula I know of involves beeswax and carbon black. I've found that simple paraffin wax works just fine.
If it works out, thank Hephaestus and go on to use your new cannon worm. If it doesn't, tomorrow is another day. I would guess that you will have to read this a few times before you can envision the techniques. Might help to make some drawings, or use a piece of scrap wire to form what you want in miniature. This helps me when I am making something complex.