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Question: Determining the curvature of the bore.

Physics is physics. All barrels will have a slight curvature. Sure, some will be very hard to detect.

How to you determine the curvature?
Measure the "crown" of the curvature (using wood working vernacular).
If there is more than one curve?

Last: Should the curve be up or down?
 
I think it's beyond the capability of a 'smith with a lathe and indicator to measure the runout of a bore (if there is any at all) over a distance of 26 inches I don't care how many rods you have. Whether the bore is in the center of the turned O.D. on the end of the barrel or not doesn't indicate bore runout. If you want to find out where the "rainbow" is put the barrel between centers and indicate the barrel in the middle as you rotate it by hand. You'll find a lot more rainbow there than you ever will in a bore.
 
Ok if the barrel blank is dialed in perfect for the deep hole drilling and reaming,rifling.
the bore isn't going to be parallel to the outside of the blank it will have a curve or helix through the bore.
So if you want to know the high point of the bore at the muzzle because you dialed in the first 3-4 inches of the breach and chambered it. A gauge pin or indicator rod with bushing in the muzzle and the indicator on your pin or rod will tell you just how far off your muzzle bore is and the high point to work with.

Myself I indicate each end muzzle and projected throat.
 
I have seen three or four barrels which were almost visibly straight and one which was so straight that any movement was imperceptible; this out of many hundreds I have set up for fitting and chambering. The rest varied from very slightly curved to damned crooked. If I buy a match grade barrel which is excessively crooked, I just send it back. Crooked barrels are more work to set up and chamber so they cost me money and the results may not be what I want to see. Life's too short. WH
 
I have seen three or four barrels which were almost visibly straight and one which was so straight that any movement was imperceptible; this out of many hundreds I have set up for fitting and chambering. The rest varied from very slightly curved to damned crooked. If I buy a match grade barrel which is excessively crooked, I just send it back. Crooked barrels are more work to set up and chamber so they cost me money and the results may not be what I want to see. Life's too short. WH


Crooked on the ID or OD?
 
I'm not measuring anything. You will note that I said "visibly straight". One can see very small deviations in a barrel mounted in the lathe and spinning. So, when I say "visibly straight" I mean I could see no apparent curvature whatsoever.
On the single barrel I have seen which appeared to be perfect, I chambered the blank left full length then had to cut off four inches to achieve the requested length. I dialled the muzzle in to zero runout and when the barrel was cut, TIR was .0003. That's .00015 of offset so that barrel wasn't perfectly straight either but was close enough to be called so. On a barrel which showed a slight wobble, the bore was running out just over .002 TIR at that point so it was eccentric by only .001 yet this was immediately apparent. I bought one barrel on which the drill had obviously wandered a bit and the bore was offset by nearly .030 at the muzzle (relative to the OD). After I contoured this barrel, I set it up in the headstock for chambering and, not too surprisingly, it looked pretty grotesque but I suspect the actual curvature was no more than .010 or so. It looked like the deflection occurred fairly early in the drilling so the bore just angled off. This actually shot pretty good; better than I expected given the cost (cheap). As for the very straight barrel; it was a decent performer but not exceptional by any measure.
I am sure that optical measuring equipment exists with which one could accurately measure the curve in a barrel but I doubt that I'll ever see it. Using rods and dial gauge, I think it's pretty difficult to accurately measure runout any further than about four inches down the barrel due to deflection of the rod and error in the set-up.
By mounting a barrel in a tube with four screws at muzzle, four at the breech end, and four in the middle, one can see how little it takes to change the curvature of the bore to the point that it can be seen. WH
 
I have seen other Douglas barrels and have a Douglas .22LR barrel that has a bore that is not concentric with the outside surface. This can been easily seen. The barrel is 18 inches long and was from a 26 inch long blank. I would not be surprised to observe a more concentric bore at the end of the 26 inch long blank.
 
FWIW, in another discussion of barrel curvature and how to deal with it, Rod Hendricks made the suggestion to clamp one end of a barrel in a steady rest and the other in the lathe chuck and use the tool rest to push on the outside of the barrel, all the while observing the calibrated deflection on the inside. Set up like this, I was not able to see less than about .008” inside the bore. .010” was noticable and anything more was readily apparent.
 
Rod was speaking about a stationary barrel and it is difficult to see minute curvature through a stationary barrel; not so much if the barrel is rotating. WH
 
You will find bores have an ellipse, not a straight curve. I don't think you could machine a curve that is flat on one plane.
I'm sure you are correct in this and it is useful so I'll come back to it. I didn't mean the roundness of the bore, I meant the arc of the barrel.

Now how does the ellipse of the bore plus the arc of the barrel interplay?
 
Why would you need to know the answer?

What difference would it make to building an accurate rifle?
The arc of the barrel will affect everything about how the barrel shoots.

A simple example is if the arc of the barrel is pointed to the right side if the gun, excessive "left" will be needed in sighting.

@butchlambert , @Stan Taylor Please tell me if I have that correct. It could be the other way around.

As @Kurtz points out, I want the arc/curve/bullet direction to be "up" not left, right, down or off in any way from up.
 
Your quote: "@butchlambert , @Stan Taylor Please tell me if I have that correct. It could be the other way around".
What does it matter. I think you are talking about a barrel that would have been scrapped. I believe I made the wrong comment, "ellipse" should have been an irregular helix.
 

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