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Barrel Harmonics, Pressures and Timing (expanded 12/24/04)

This article is our attempt to explain in simple terms how barrel movement, pressures and timing are related so reloaders can more easily find their "optimal" rifle load. It has been long understood that a rifle's barrel changes shape and moves in multiple directions every time it is fired. These barrel motions coupled with shot to shot pressure variations greatly affect how well a particular barrel and load combination will shoot.

Much has been written about these subjects over the years but the theories often left reloaders with more questions then answers. We will try to reduce the various theories to something that fits what you are likely to see with proper instrumentation. Let's start with barrel motion; sometimes described as "ringing", "harmonics" or "whip".

Builders of accurate rifles agree if the barrel's movement can't be eliminated, the next best thing is that it move consistently with each shot. That's why good shooting rifles have stiff barrels and their actions are firmly bedded in the stock with nothing touching the barrel in front of the receiver (free floating). Experienced shooters learn loads must be "tuned" to each barrel and barrels often seem to have their own personality. Those with chronographs often describe an "optimal" load according to the velocity a barrel seems to prefer, or as a "sweet spot".

Barrel Whip

First lets look at the traditional "barrel whip" theories. Whip, while hardly a technical term, is understood to be movement around the barrel's "static" state caused as the bullet is accelerated into a rapid spin or when the stock has significant drop so there is muzzle rise when the rifle is fired.

If a barrel had no rifling and the stock was directly in line with the bore so recoil energy was dissipated straight to the rear (to eliminate muzzle rise) then barrel "whip" should be minimal.

Sine Wave

The "whip" theory suggests a barrel's thickness and length impacts how much it moves with each shot. Indeed, a short thick barrel mounted nearly in-line with the stock butt (as used on bench rest rifles) should produce far less "whip" then a field profile long hunting barrel with a high cheek piece.

Another variation of this theory suggests the tensile strength of steel (or its ability to resist further bending) increases as it moves away from its static state. Think of it as if the barrel gets stiffer when it is forced to the extremity of its movement. At the point of maximum movement, slight velocity variations change the muzzle location less with each shot; resulting in lower shot dispersion and smaller group size.

We now know this is not the sole explanation for "sweet spots" or optimal barrel performance. Even if whip is a contributing factor there is no easy way to predict how a barrel will whip, or for that matter, how much the whip will affect group size. We also know while long thin barrels rarely perform as well as a short stiff barrels, reloaders may still achieve acceptable accuracy through careful load development.

Chris Long's Traveling Wave Theory
(Where it all starts coming together....)

Shooters often talk about another form of barrel movement sometimes referred to as "ringing". There is no doubt a short stout bench rest barrel whips less then those of a typical hunting rifle. Unlike hunting rifles; bench rest barrels seem more forgiving with extremely wide "sweet spots". Indeed, a good bench rest barrel may have only a few narrow velocity zones where it does not shoot well. We believe Chris Long, engineering consultant and avid shooter, is the first to properly analyze the cause and affect of this phenomenon so that it can be predicted with software and instrumentation.

When each shot is fired the chamber swells and produces an "annular wave" or "pressure pulse" which then bounces back and forth between the muzzle and receiver. This "P" wave is like a "doughnut" traveling up and down the barrel and opens the bore diameter slightly so if the bullet exits the barrel coincidentally with the wave at the muzzle, the barrel will behave as if it has a bad crown. Others have espoused a similar theory but Long is the first to develop a way to predict when the wave(s) are at the end of the barrel so the theory can be applied. For more information about Chris' epiphany, click here.

We have heard reports that a European defense contractor has photographed this phenomenon with high speed film cameras. Not only did they capture the P wave at the muzzle as a bullet exited, but also slight shifting of the muzzle relative to the base of the bullet caused by whip. If anyone would like to share the images, please forward them so we can post them for others to see. This would suggest and resulting rotational movement (whip caused by accelerating a bullet into a rapid spin) is the reason Long's equations work. If the bullet exits the barrel coincidentally with the P wave; and the muzzle is moving off axis, exhausting gases would immediately push the bullet into a yaw as if the barrel had a bad crown.

Our PressureTrace system already accurately captured the time of peak pressure and when the bullet exited the barrel. Long's formulae have been added to the software so PressureTrace now shows when the bullet SHOULD exit the barrel to avoid the annular waves. Reloaders can now "tweak" their loads so the bullet avoids the P wave. We call this "Optimum Barrel Timing".

Optimum Barrel Timing

The above pressures captured with PressureTrace show where the bullet SHOULD have exited the barrel to avoid annular P waves (OBT Diamond markers) and where the bullet actually exited the muzzle for each shot. Timing variations were artificially introduced by slightly varying neck tension. Everything else was the same for each shot. Timing will also change with variations to powder charge, seating depth and component selection. As might be expected the group shot with these loads were entirely unacceptable.

Preliminary results from people using PressureTrace with Chris Long's analysis is quite promising. We have received reports from several who successfully found optimal loads after just 5 or 6 shots by adjusting the powder charge until the bullet exit point was over an OBT marker. Of course these results came from people shooting relatively stiff target barrels and the loads were well crafted to produce minimal pressure variations. Both ringing and whip may exist for long thin barrels and would explain why velocity "Sweet Spots" often do not seem evenly spaced. More research and reports from our customers should help determine to what extent whip is also a factor.

We are hopeful our PressureTrace system with Chris Long's algorithms will prove to be the first new shortcut toward optimal load development since introduction of the chronograph.

Secondary Pressures

Secondary PressuresPressureTrace collects more data then competitive products previously used by shooters. Our output is also not filtered or "smoothed" so "what you see is what occurred". Other strain gage systems either do not collect sufficient data to see anomalous secondary pressures or they are filtering it out as noise.

A short-lived debate occurred when shooters could first see the severity of some secondary pressure spikes. Understandably, some shooters did not want to accept how often it occurs or the severity; especially when the subject has been largely ignored by shooting magazines.

A conclusion by some was that PressureTrace picked up barrel harmonics. In an attempt to prove this theory one shooter even hung a bowling ball off the end of his barrel, but of course there was no change.

Strain gages change resistance when stretched in one direction. A strain gage glued "around" the chamber can only detect radial expansion of the steel under the gage. Only if a gage were attached longitudinally on a barrel would it be able to detect barrel "whip". Even then, movement at the thickest part of the barrel shows only minor current changes that appear as slight "squiggles" in a trace. Public debate over whether these secondary spikes are real was finally put to bed when Charley Sisk at Sisk Rifles blew the end off two barrels. We have also verified changes to the rate of acceleration just prior to, and after these events. Case Closed, it is real!

Indeed powder formulators and powder manufacturers have known about this phenomenon for some time. I first heard about it more than 20 years ago, before good instrumentation was readily available, and in reference to ball powders. A friend who worked at one of the powder companies once told me, "If consistency of performance where the only issue in powder design, ball powders would not exist. Ball powders are simply less expensive to manufacture and make it easier to produce ammo with consistent charges." He then went on to explain, " The three primary formulation features of powder is nitrocellulose content (or base material composition), granule shape and granule coatings. If the granule shape is spherical, then coatings become far more important to maintain a desired burn rate. Unfortunately coatings can burn off and are not the most reliable way to maintain a burn rate for every circumstance."

Power companies have no control over how a particular powder will be used. They must rely on ammo manufacturers and those who produce load manuals to keep things safe. Ammo manufacturers and compilers of load manuals do a tremendous job, but there is no way they can anticipate every possible combination that will cause secondary pressures. Given the litigious nature of our society, this is a real touchy subject, and most in the industry would prefer shooters remain ignorant of the phenomenon.

The above chart is typical of what can be seen in some hand loads and factory ammo. The following is a more severe example of secondary pressures provided by a member of a Midwest Highpower club. It is the club's "reference" ammo tested in a commercial lab to around 63,000 PSI but actually produced nearly 120,000 PSI in his old competition AR!

Serious Chamber Pressure

SAAMI test protocols were established so the highest "primary" pressure that should be expected can be measured in any lab. Test barrel chamber dimensions and bore conditions are strictly controlled at "tighter" tolerances then those of commercial rifles, custom barrels cut with a standard reamer or a rifle that has several thousand rounds through it. SAAMI primary pressure results are nearly always higher then when the same ammo is shot in a standard barrel.

In the case of this rifle, the shooter admits the throat is washed out and at least 3,500 rounds of hot loads have been fired through the barrel. The load probably did originally lab test to 63,000 PSI without secondary pressures in a short tight test barrel. But it is certainly not a load to shoot in a worn gas operated semi-auto barrel. I am surprised it was not tearing off the case rim on extraction. This can happen is any rifle or caliber!

Barrel rack

Note: Customers who send ammo to commercial labs rarely become aware of severe secondary pressure spikes for two reasons. Test barrels are typically only 20 inches long. The above examples of severe secondary pressures should not occur in a 20 inch long tight bore.

At least two major commercial testing labs do not capture the entire pressure curve unless specifically requested by a customer. For convenience they use an electronic meter to capture a peak pressure value. Unfortunately these devices only capture the initial peak event. Any secondary pressures after the first peak is often entirely missed by the instrumentation.

The "Catch Up Theory"
We do not know if the above load suffered from an accelerated burn rate (problematic with some ball powders), but agree with ballistic engineers about the probable cause.

The area under the pressure curve directly relates to the energy imparted to the bullet. The rise to peak pressure engraves the bullet into the rifling and establishes its initial acceleration down the barrel. The highest rate of acceleration occurs just past the point of maximum pressure. As the bullet travels toward the muzzle, lower pressure coupled with bore friction allows the rate of acceleration (not speed) to fall.

If there is insufficient gas produced by the powder (burn rate too slow), pressure behind the bullet will drop excessively. Then, as the bullet's rate of acceleration falls due to bore friction, gases may "catch up" to the bullet before it exits the barrel and produce a secondary pressure event. In the above load we believe the heat generated from initial ignition coupled with a secondary pressure event increased the burn rate of residual ball powder to near detonation.

Note: Secondary pressures readings taken at the chamber are lower and of longer duration then the actual event due to compression of gasses behind the bullet and the time required for expansion and contraction of barrel steel. The above event may have spanned only .1 milliseconds of time but could have reached 150,000 PSI!

Ball powders do not create the phenomenon of secondary pressures but the resultant pressures can be more severe. Indeed, secondary pressures can even occur when using large extruded powder. When using ball powders it is simply more critical that a powder with the proper burn rate be used to avoid secondary pressures entirely.

In every instance when secondary pressures are detected they can be eliminated by using a faster power, heavier bullet or a bullet with more bore contact area. Normal "tweaking" of loads may change the peak of secondary pressures but will not eliminate the problem. Below is the list of factors we now know can cause secondary pressures.

  1. Powder burn rate too slow for the bullet.
  2. Bullet weight too light for the powder's burn rate.
  3. Bullet bore contact area less then normal for the bullet weight
  4. Barrel longer then normal
  5. Bore severely worn or incorrectly lapped (loose/worn toward the muzzle)
  6. Moly in bore or moly coated bullets that reduce bore friction

We are often asked when secondary pressures are too high. Obviously secondary pressures more than 25,000 or 30,000 PSI at the weakest part of a barrel represent a safety issue. On a more practical note, loads that exhibit secondary pressures often show significant variation in barrel timing (when the bullet exits at the muzzle). Even if the timing does not vary shot to shot, it certainly will when the temperature changes so these loads rarely shoot well. Our advice is simply to avoid all loads that produce secondary pressures and keep peak pressures where they are supposed to be, in the chamber. If you shoot factory ammo, try a different brand. If you reload, use a slightly faster powder or heavier bullet.

I recently had the occasion to work with a friend's .223 Douglas barrel that had shot perhaps 6,000 rounds of an off brand ball powder sold as "Data 2200". My understanding is the powder was actually reject 2230, a powder we know produces secondary pressures in small calibers. The owner shot around 2,000 rounds of the load through the barrel each season, then re chamber his good ol' shooter as the throat washed out. When I looked down the barrel with a bore scope I could see rings just down from the muzzle spaced exactly the amount that was removed from the chamber end each time the barrel was re chambered. This convinced me secondary pressures will eventually damage a good barrel.

No doubt there are shooters who will debate our conclusions. We welcome anyone to pose other possible explanations. The "catch up" theory is the only one we have found both fits the evidence and can be used to eliminate these problems. To date, only shooters who do not have access to pressure testing equipment argue adamantly against the "catch up" theory. Professional ballisticians we have talked to whose job it is to formulate powder seem to be in full agreement. Even if the theory is not the "entire" explanation, it is certainly useful.

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