Burbank_jung,
You might consider one of the target cameras that talk to your smartphone or tablet or laptop by Bluetooth. You set it down near the target and aimed at it and it sends the image to your device in real-time.
Regarding the different ranges, the main reason Randolf Constantine recommended 300 yards was to get adequate bullet drop difference between load increments. For example, a 30 cal 168-grain Sierra MatchKing fired from a perfectly rigid barrel at 2500 fps and again at 2550 fps will have a drop difference of e 0.11 moa at 100, 0.24 moa at 200, and 0.39 moa at 300. That means your ability to hold has to be that good to be sure you see the 50-fps velocity difference as a vertical separation on the target.
Bart
The OBT theory considers an analog to the same problem with harmonics: you get accuracy as long as the muzzle you shoot through is symmetrical and is in the same position or has the same shape at the moment of every bullet’s departure. But if you have the bullet exit during rapid transitions in any of those factors, small variations in barrel time can produce different POIs on the target.
But as far as the diameter change, it depends how thick the muzzle is, but it is not a lot. It would be proportional to multiplying the outside change by the outer circumference divided by the circumference at the groove diameter. I have also looked at the pressure waves on Pressure Trace plots and on some old piezo transducer plots, and they present as the equivalent to one or two thousand psi. I did hoop stress analysis for a thick wall cylinder on that equivalent pressure, and it agrees the diameter changes are on the order of a millionth of an inch.
One problem in attempting to arrive at a measurement of this is both the piezo transducer and strain gauge measuring systems have response speed limitations that reduce the apparent magnitude of the waves on the display. So, the pressure equivalent deformation is likely larger than appears on the readout. Nonetheless, I am, as I am sure you are, highly skeptical that millionths of an inch, even changing during bullet exit, would produce measurable dispersion on the target.
That said, the OBT and velocity flat spots you can map out with a chronograph do seem to have some correspondence. I think the more likely mechanism is suggested by
some of Varmint Al’s analysis. I note the frequency of a pressure wave traveling up and down the barrel is about twice that of Al’s mode 6 harmonic vibration. It also has two lumps in it, so even if it were at Al’s mode 6 frequency, you would see two occurrences in each cycle. The barrel extending and retreating like that under the influence of the pressure wave would alternately add-to and subtract from bullet velocity via the friction between the bullet and the barrel surface. Another possible mechanism is the pressure wave attempting to straighten the barrel, thereby messing with the timing of muzzle swing. These are just ideas on my part and not known to be a fact, nor I have I identified an experiment to prove one or the other. My point is mainly just that other mechanisms than Chris’s muzzle distortion idea are possible. So his timing predictions could be right even if the mechanism he offers Is not.
One last thing to note is different steel alloys have a little difference in the speeds of sound in them. Stainless and chrome-moly won’t be the same. I think this is why Chris Long suggested the nodes predicted were within about 2% when measured. That’s right about what the sound speed range is going from stainless to mild steel.
I don’t know what to make of chronometer vs. chronograph. The first word is literally “time measurer” and was first used in 1676. The latter literally means “time writer” which distinguishes it from a chronometer by making a record of the time it measured, even if only a temporary record, as with a stopwatch. The term first appeared in 1851. However, the dictionary also describes
chronometer and
chronograph both as synonymous with
timer. I’d always assumed a ballistic chronometer was a bullet stopwatch that gave you the bullet transit time between two points rather than a velocity reading, leaving you to work out velocity for yourself from the time difference. But it seems the dictionary leaves that a shaky difference, as
chronograph can be applied to both.