The Purdy Prescription
Thank You for giving my idea a try. Together we will work thru what I believe will be an effective, if not best, tune for your rifle.
My tuning is based on the harmonics that develop in a closed end tube when excited, and putting the muzzle at the even quarter wave in the series. Only odd numbered harmonics develop in a closed end tube, so all our calculations will be based off of that. It just a matter of figuring out which harmonic you want to tune to, or in some cases, have to tune to. If you would like to know more about how I came about this idea, just drop me a line and I will be glad to explain the story behind this.
Listed below are a few of the terms we will be using:
Acoustic Length (AL) – This will be the overall total length of the tuned barrel that includes that little distance the waves travel before reflecting back into the barrel
Physical Length (PL) – The actual physical length you will be setting with your tuner to get the correct overall length from the breach face to the end of the tuner
End Correction (EC) – This, I think, is the real key to the success of the tune. The End Correction is the distance the waves travel past the muzzle before reflecting back into the barrel. This is what we subtract from the Acoustic Length to get out Physical Length. The End Correction is based on the diameter of the opening of the tuner. As it stands now, based on the research I have done, 0.3 is the factor I have chosen to use. We multiply the opening at the tuner by 0.3, and subtract that form the AL to get our PL
Quarter Wave Length (QW) – We need to know what the QW length is for a given harmonic. To find the QW length we need to divide the barrel length by the harmonic we want to tune, to minus 1. IE – The 9th Harmonic requires us to divide the barrel by 8 to determine the QW length we need.
A couple of things you will need:
A calculator
Paper and pencil. Or you can print this out and use it to keep a record
A tape measure
Optional is a set of calipers, if you are really into getting down to the 0.000
You will need to know the length of your barrel from the breach face to the tip of the muzzle. An easy way to do this is to slide your cleaning rod into the barrel from the muzzle (carefully, we don’t want to mess up the crown), with the bolt installed and closed. Take a piece or tape and wrap it around the rod even with the muzzle. Then remove the rod and measure it. Most tape measures will be marked by 1/16th’s of an inch. Each 1/16th is equal to .0625”. If it is between the marks you can use your judgment to add or subtract an additional .03 or so. If you have an 11 degree crown, or one that is recessed, you will need to account for that as well. Bottom line is we need to know the length from the breach to the point where the bullet actually leaves the barrels rifling.
The depth of your crown at the muzzle. (Or you can use .010 for an 11 degree crown)
So, lets give this a try shall we:
We’ll start with tuning for just the Tuner alone (No weight ring, no slide). This will work best for barrels that are between 22” and 25” long. I believe that the 9th Harmonic works best for these length barrels.
Take your barrel length and divide it by 8: (Remember, 9th Harmonic – 1)
__________ / 8 =______________ QW
Now we multiply the QW by the harmonic we have chosen (9th):
__________ X 9 = ___________ Acoustic Length(AL)
Now we have to remove the EC. This is where some different components start to come into play. There are technically two openings in the tuner. The inner tube and the outer shell. Each can influence the EC depending on how far out the tuner shell is adjusted.
We’ll start with the inner tube, which has an opening of about 0.62. To get the EC for this we need to multiply .62 by .3 and we get .186. This gets removed from the AL
__________AL - .186 = __________Physical Length (PL)
What we now have is the new length the barrel and tuner need to be, for our tune.
If your cleaning rod is long enough, you can transfer this measurement to it and mark it with a piece of tape, insert it into the muzzle and bottom it out on the face of the bolt and turn the tuner in/out, until it matches up.
If after you have done this, the outer shell is more than a ¼” farther out than the inner tube, you will need to refigure the PL by using the EC for the outer shell. The outer shell is about 1.34” inside diameter. So you need to multiply 1.34 by .3 and you get .402. This is the new EC you need to remove from the AL to get your new PL.
The rest of the process is the same.
_________AL - .402 (EC) = ________PL
For barrels a little longer than 25”, you will probably need one of the screw-in weight rings to make the length you will need for a proper tune.
I also believe that everything works best when you can have the barrel of the tuner somewhere close to mid range of its travel. So if your tune brings the naked tuner out toward the end of its adjustment, just screw in a weight and back the tuner barrel up until you get the proper length. I took this advice from a friend who said he has seen some different things happen when the tuner is out towards it max adjustment. Shooters who have tested the difference seem to think the tuner & weight combination, shoots a tiny bit better as well.
Using the weight does require a different EC be used. The opening of the weight is right at .92, so your EC is now .92 X .3 = .276. (AL - .275 = PL)
How about the long slide
The process is near identical. Only difference is we are looking at a lower harmonic. The 3rd Harmonic is as low as you can go. Nice thing about the slides, is that there is just one EC to contend with. The opening is a consistent 1.50 (per Mr Pappas). So we have an EC of 1.5 X .3 = .45
_________________BL / 2 (Remember 3rd Harmonic – 1) = __________________QW
_________________QW X 3 = ______________AL
_________________AL – .45 EC = ___________PL
This where the tape measure sure does come in handy since you’ll be out 33” to 40” or so.
More than likely you will need the link and the washers as well to make length
The short slide requires a little thinking outside the box. Up to now, we have trying to put the muzzle at the last even numbered quarter wave.
With the short slide, we are going to back that up some, to the second to last quarter wave. For this, lets use the 11th harmonic. Since we are now moving back to the next even QW, we need to subtract 3 from the harmonic, instead of 1.
______________________BL / 8 (11th Harmonic – 3) = ________________QW
_____________________QW X 11 = ___________________AL
_____________________AL - .45 (EC) = __________________PL
Again the link and blue washer will be probably be needed to get the proper length
I know this has been a lot of info all at once, but once you run thru it a couple of times, it begins to make sense.
This paper also is not meant to be the complete answer. Some barrels may require a little “special” attention. And some barrels may not respond to this at all
Please let me know what questions you have, and how I can help.
I’m also working on the story behind the idea and how I got to this point
Thanks
Tony Purdy
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