Thanks for the thoughtful response. Much appreciated. I just read through this reply - didn't mean to make it so long. I keyboard really fast.
The written language is a crude form of communication, but I'll try to give you my answer as I see it.
The two perpendicular vectors you refer to, one the bullet, the other is the bore. The goal is to machine a chamber that is orthoganal to the bore axis, in the area of the throat. Lets all agree on that.
Uh, yes, I think. I agree with what I think you intended to say.
In the name of precision (yes, language is a tough way to communicate
) I'd like the bullet path and bore to be coaxial vectors, the same, at the pont of entry (throat) and exit (muzzle).
With that in mind, I could agree that the goal is to machine a chamber that is aligned with the bore axis at and for at least a bullet length beyond the start of the lands in the throat, and a muzzle crown the plane of which is orthogonal (at all points perpendicular) to the last bullet length of the bore axis at the muzzle.
That makes
my head hurt, but I think it is correct.
Your rationale cannot be argued with mathmatically...you are correct.
But, in practical terms, you are wrong...because we are forced to live in a world of relatively crude tooling....in the home shop especially.
There are lots of terms for it....some call it stacked tolerance, some call it dilution, it's all the same basic problem a machinist faces. We can only indicate a workpiece within the abilities of the instruments. What we lose in minute angular alignment, we gain in some multiple of accuracy in radial alignment, by DIRECT indication of the throat area, with a .0001" indicator. .
I understand what you are saying, I'm not sure I agree with it in general but let me think for a minute ... OK ... lets do s thought experiment. Same barrel in both cases. The assumption is that the bore and the average centerline between throat radial location and muzzle radial location don't align where the chamber throat and crown will be located. I think we both agree that misalignment is more likely than not and only a matter of degree as a function of the barrel makers triumph over the variety of variables involved.
Suppose you can absolutely perfectly, with zero error, center the measured point at that selected location along the barrel in bore radially right on the spindle axis. If you do, you will still have the angular error between the spindle axis and the local bore axis that occurrs by chance. What ever reduction in group size occurrs as a result of the angular error can't be reduced even by unachievably perfect centering.
If, on the other hand, you could align the chamber centerline with the bore center line for a short distance, say a bullet length, past the throat, that will probably result in the most favorable bullet entry into the bore.
Your reply is based on our being able to do the first measurement more accurately than we can do the second, and for that reason the first measurement will result in the most accurate barrels averaged over time, and thus represents the best approach.
Could be. Can't rule it out with the data in hand, though Gordy thinks he has a different answer. See discussion after the next quote for more on this.
The down side to it is there is no chance to get better using the first approach. The best it can be will always be short of the best the barrel can be other than by chance.
Using the second approach, there is the chance to develop tools and instrumentation approaches that will result in improvement which will at least have the chance of improving shooting performance to what ever extent it can be improved by aligning things correctly. There is real appeal to following an approach that will respond to improvements as we get better.
In simple terms, the range rod is a long sloppy tool, on which assumptions are made. A 10ths indicator is a precise tool, with a lot less chance for error. i.e. it is more repeatable.
Also, if a bore has a shift, bend, whatever in it, of .001" over 6 inches...what is the angle? Yes you can calculate it, but there will be several decimal places. Its a tiny gain.
That would be ~0.57 MOA if I did the math right.
You bring up an interesting point. I wonder about sources of error. Using Gordy's method, with fitted pilots (in increments of .0002") on the end of the 12" Grizzly rod, and the indicator located very close to the breech (or muzzle as the case may be), he is measuring, being conservative, 1" and 3" from the indicator. The bushing will move more than the rod will at the indicator's location. But not much.
How much? would be a reasonable question at this point. Let's see if we can estimate it making reasonable assumptions.
In simple terms, neglecting the force of the indicator trying to bend the Grizzly rod, and the distortion (curvature) that obtains from bushing displacements on the order of 0.001" to 0.002" (they will be displacements more on the order of .0002 at the end of the centering process) at the end of a 12" rod, the movement at the indicator is 11/12 of the bushing movement when the bushing is at the breech end, and 9/12 of the bushing movement when the indicator is moved 2" into the bore as he says in the video. If one is using an indicator with a resolution of 0.000100" at the indicator tip, that says the real resolution is actually .000109" when the bushing is close to the breech and something like 0.000133" with the bushing pushed 2" into the bore.
Thinking about it, I'm not sure an indicator with a 2" tip is that accurate. Actually, if one puts a 2" tip on a 0.0001" indicator that originally had a 1" tip, the resolution is .0002", which is worse with out position and land jumping errors than the Grizzley rod.
But that may not matter. What one is doing is to locate the measurement point on the lathe spindle axis and have no movement at all, or as little as possible. I will be interested to see, but I think getting to that point is easier with out the "noise" of the tip bouncing over the lands.
I need to think about this a bit more, but I'd think if one dipped the bushing on the end of the Grizzley rod in oil before inserting it in the bore, it would provide a very nice smooth motion that would lend itself to easy interpretation. I.e. it would be easy to see when the motion stopped and was smooth. Slop could be eliminated as a source of error buy insuring there was a bit of tension in the rod by it being a tiny bit off center in the tail stock chuck so it would follow the ID of the bore on one side. The bore's deviation from round ought to be way less than the other errors or it isn't a very good bore.
It wouldn't pick up the variation in land height, but I wouldn't expect an indicator with a long tip will do that reliably either with all the bounding around.
I hadn't thought through that part of the process before. Interesting. I think it may be that Gordy's measurement method has less error than the long tip indicator, but I haven't tried it yet.
[/QUOTE]Gordy has a hypothesis, not a theory. Until it can be quantified through analysis of variance, or some other practical means, I would say he cannot correlate his increased amount of accurate rifles to the assumed angular alignment of the bore to chamber
Try this.....
Take a benchrest grade barrel and indicate it in the lathe 5 times using both methods. 10 times total. Remove the barrel from the lathe completely each time.
Check muzzle runout at the spider, and record it all 5 times using Gordy's methods. also mark the index point on the muzzle with a sharpie.
Let us know which method is more repeatable. Repeatability is the cornerstone of accuracy.
Ben[/QUOTE]
That's an interesting experiment. I may do exactly that. But the results may not tell you the same thing they tell me. What I may learn from the experiment is a way to do the measurement better, or at least to become better at using the instrumentation to achieve consistancy.
That said, just as we learn more from our failures than our successes, the most useful experiments are the ones that give an unexpected result.
We can agree to disagree on this, but to me, building on the instrumentation error discussion above, getting something exactly wrong in the same amount every time, while it is repeatable, is not the same thing as getting it approximately correct every time. In the latter case there is the opportunity for systematic improvement as tooling, instrumentation, and skill improve and the error reduces. In the former, there is only being even more precisely wrong by the same repeatable amount on a given barrel, with no opportunity to make it better than the average of the bores wandering around in the run of barrels chambered.
I'll probably use Gordy's approach, though I can understand why folks would choose to use the other. It has resulted in some pretty good barrels. There may not be much difference in outcome in some, or even most cases given the current available tools and instrumentation. But using Gordy's approach there is at least the chance for getting closer and closer to the best that a barrel/action/shooter can be as one's skill, instrumentation, and tooling improve with time and experience. That is not the case with the two point breech/muzzle approach. In any event, the difference in outcome is only knowable as a time average of barrel performance out of the same shop. And such an average may be really hard to track in any objective fashion. Gordy thinks that trend shows an improvement in his case.
For me, maybe not for everyone, I think trying to do my best with theoretically correct approach, within the limits of tooling and measurement errors, my skill level, and other considerations, will yield better results over time than doing as good a job as I could with an approach that basically averages the bore error regardless of measurement accuracy or perfection of implementation.
It will make me feel good, and that's worth something.
I see Gordy's approach as requiring a bit more skill, and the added task of managing the muzzle intercept, but I've got all day and nothing else to do, so I'll give it a go.
I do appreciate your taking the time to answer me. It was a good answer that stimulated the sort of dialog that promotes learning. (Dialog is a much more constructive form of communication than arguement IMO.) I learned something thinking through my reply. I have lot more to learn. But I think I'm gaining on it. I've spent decades working on a variety of problems where the right answer wasn't known, or even correctly guessed at, but had to be recognized when it showed up because we were betting the astronauts lives on the outcome, as it nearly always did.
I can't escape the though that Gordy's approach, because it's theoretical correctness holds out the chance for continued improvement, is on the right track.
Thanks
Fitch