What do I need to make this thread?

This question is another example of why the South Bend Lathe Works book, 'How to Run a Lathe', is so valuable. All the info referred to in the above posts is in this handy little book. ISBN number is 1-55918-115-X. Mine is a reprint from Linsey Publications Inc.
 
Well, it doesn’t seem to have any angle to it, and I like the sound of a “seat of the pants” approach. I have a has parting tool that is about the same width I was thinking of working with as a starting point, and have lots of 4140 5/8”stock to practice with (outside diameter). Probably not purchasing an optical comparator, the magnifying glass seems a bit more practical for my level. Thanks for the great explanation
David
The parting tool would not be so great, you would not be able to grind the leading edge clearance on it very easily unless you greatly reduced it's depth at the working end, and sometimes parting tools are not so very stable in their holders so far as sideways movement is concerned.
 
I am no expert here, just to help me remember this, I imagine rolling the rod 360 degree on paper. That means diameter * pi for one side of the square triangle. The other square side is the thread pitch.

So the leading angle is inverse tangent of thread pitch divides the diameter * pi.

Angle = inverse tangent ( pi * Diameter / pitch)

Making the relieve a degree or two smaller as other said. However, depending on how "tall" the cutting bit end, it may need to have more than a few degrees smaller, or bevel at the bottom a little.

For the cutting shape, since this is a "forming" tool, it must have the exact shape as that of the thread.

For advance, only advance on the leading edge on any thread types, which is 0 degree for square thread. For standard thread, instead of 30 degree, they do it 29.5. I read on it and some explains it's for some "pressure" produced from the trailing side. I don't know if that is true.
It's definitely not good to accidentally go above 30, so 29.5 would be on a safe side.
 
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The 1st thing you would need is an optical comparator to check the thread and grind your tool.
An inexpensive microscope from Banggood works also. That's what I use.
 
I’ve got microscopes, job tool! Saw that Brownelll’s has 10 tpi tool for older rifle barrels. I think I got the general idea on the dimensions I need to grind I may have been making the task more difficult than it should be. When I read the texts on how to cut square threads, it gets pretty much in the weeds. I like the forum because the collective experiences of tricks, tips and what works real-world is easier to understand.
 
Exactly, gotta love the forum for the collective experiences we all bring to the table. Sometimes I cant grasp a written document but a couple pics and an explanation written out that even a toddler can understand helps a lot!!
 
I recently used the Brownell’s tool to cut threads for an M1917. The tool is nominally made for that exact pitch and diameter. I first cut threads on a piece of scrap, they would not go. Measurements vs. the original barrel showed that the .050” wide tool was cutting a slightly too narrow groove, to mate with the receiver.
When I threaded the new barrel, I set the compound parallel to the ways, and threaded straight in, using the cross slide. When I reached full depth, I then retracted the cross slide to the starting point, advanced the compound .003”, and cut the threads again, same process. This produced a perfect thread fit.
 
I ...advanced the compound .003”, and cut the threads again, same process. This produced a perfect thread fit.

I was about to suggest making the tool slightly undersize to prevent the cut from being oversized by accident. The above works well, too.
 
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