Barrel Tuner Analysis
Esten's 6PPC Rifle With and Without a Muzzle Tuner
FEA (Finite Element Analysis) compared to Test Data
Rifle Barrel Dynamic Pressure Analysis

Esten's Tuner

OBJECTIVE.... The objective of this study was to compare the FEA calculation results using the 3D model of the rifle to Test Data on an accurate benchrest rife.  The dynamic response calculations gives some insight and understanding on what a tuner does to the motions of the rifle barrel and how a muzzle tuner might affect the accuracy of a rifle and Point of Impact (POI). The calculation loads simulates the gas pressure traveling up a rifle barrel behind the bullet. The deformations in the rifle and barrel are calculated and then a 100 yard projection of the barrel's muzzle is displayed. The FEA results are then compared to test data for four different loads of N-133 powder and the resulting average muzzle velocities.

SUMMARY.... For the reader who doesn't want to wade through all the discussion here is a summary of what a tuner can do to correct for small variations in muzzle velocity from round to round. The Muzzle Projection Curve shows where the muzzle is pointing at a 100 yard target while the rifle is being fired. The most important aspect is the curve is where the muzzle is pointing at the time the bullet exits the muzzle.

Improving accuracy by compensating for small variations in muzzle velocity.

Smaller Groups Left of the Peak - UPWARD SLOPE:
Higher velocity shots exit early while pointing lower at the target but drop less in reaching the target.
Lower velocity shots exit later while pointing higher at the target but drop more in reaching the target.
Counteracting combination. Good.

Larger Groups Right of the Peak - DOWNWARD SLOPE:
Higher velocity shots exit early while pointing higher at the target and drop less in reaching the target.
Lower velocity shots exit later while pointing lower at the target and drop more in reaching the target.
Bad additive combination. Bad.

The additional mass of a Muzzle Tuner slows down the muzzle movements and allows the bullet exit before the peak of the muzzle projection curve during the upward slope without resorting to high pressure loads.

POWERFUL TOOL.... This analysis was done with the LS-DYNA Finite Element Code. This software is a very powerful tool for analyzing the dynamic and static loading of structures. It was used here to calculate the rifle's response to the high pressure gas that forces the bullet out of a barrel when it is fired. For the first calculation, the breach end of the barrel was fixed in space which treats the barrel as a cantilever beam. The results showed that a more complex model was required to capture the dynamics of the complete rifle. There is a vertical plane of symmetry in the model and only motions in the vertical direction are calculated. In the movies, the displacements are greatly amplified so that they can be viewed.

THE BARREL.... The 416 Stainless Steel 5.39 lb barrel in this model has a breach diameter of 1.24" for one inches and then a straight taper to a diameter of 0.935" at a distance of 21". The diameter is 0.935" x 32 tpi from there to the end of the barrel at 22". The caliber is 6mm with no rifling modeled. The 416 Stainless Steel tuner base weighs 7 oz.. The 7 oz brass weight is threaded and can be positioned at various locations on the tuner base. The full rifle is in a one G gravitational field to simulate earth's gravity. The muzzle sag is calculated at the start of each calculation with the Implicit method using dynamic relaxation . Then the dynamic calculation proceeds with the pressure time data using Explicit method. The burning powder's gas pressure is applied to the chamber walls and the bolt face. The barrel's chamber is the size of the 6PPC caliber brass. But for the calculation, I did not include the brass case and merely applied the pressure to the bolt face and the chamber walls.

THE ACTION.... The action is 1.25 inches in diameter and is 7.2 inches long. The weight of the action is 1.5 pounds. The bolt is merged into the action's cylinder. The gas pressure acts on the bolt face. Since there is no bolt, there is also no bolt handle.

THE SCOPE AND RINGS.... The scope weighs approximately 20 oz and is aluminum with a 0.1 inch wall thickness. There is a simulated lens in both the eyepiece and the objective to stiffen the otherwise open ends. The scope rings are also aluminum and are bonded to the action and scope. For the calculations, the scope is only for adding the additional mass in the correct location. The axis bore is projected to the zero point with zero gravity. Once gravity is applied, the muzzle sags and the model's scope is also pointing lower by about 0.003" more with the tuner base and brass weight than it does with the bare barrel.

THE STOCK.... The stock has the mechanical properties of wood. The action is "glued in" to the stock and the barrel is completely free floated. The stock is supported at two places, one 2" section near the butt and another 2" section on the forearm. The complete rifle is allowed free recoil, that is no shooter's shoulder is modeled. The stock in the model is more bulky that the actual stock. The decrease the rigidity of the model's stock, the modulus was reduced by 25%.

THE TUNER.... The tuner base is screwed onto the barrel and butts up against the muzzle. It weight approximately 7 ounces. The 7 ounce brass weight is threaded so its axial position can be changed. Once positioned, the brass weight is prevented from moving by tightening the clamp screw.

Esten's Rifle Weights in the Model
(Actual Rifle Weight + Tuner + Weight  is 12.13 lb)

THE 3-D MESH.... This view shows the mesh detail. Only half of the mesh is actually in the calculation. There is a vertical plane of symmetry (X-Z Plane) down the bore axis and the center of the stock. The mesh is reflected across this plane for the for this 3-D mesh picture. The boundary condition for the calculation forces all nodes on the symmetry plane to remain on the plane, but the nodes are allowed to move while remaining on the plane. For the 3-D model without a tuner, there are 17,196 nodes and 12,080 elements. For the model with the tuner base and weight, there are 19,404 nodes and 13,592 elements. Every microsecond of pressure vs time data, the conditions of the model were stored for post-processing to generate the curves. Each shot calculation takes about an hour to setup and run and the stored data requires about 2.5 Gb of hard disk space. An hour is plenty of time for the FEA barrel model to "cool down" in between shots. Then more time is involved in post processing the results so that the results may be compared to test data.

ESTEN'S TEST SETUP.... The chronograph is 4 ft in front of the muzzle. Beautiful place to shoot groups!

Tuner Weight in the forward position.

Tuner Weight in the rearward position.

FEA MODEL OF THE TUNER.... Here is a view of the FEA model with the brass weight in the center position. The second view shows a cut-away view so the details of the inside of the tuner base can be seen. In the FEA model, the tuner base and brass weight are not threaded but are bonded to each other by merging nodes of different materials.

Esten's Test 1 Data

TEST DATA 1.... Here is Esten's Test 1 Data taken at the range. During the test, the scope was NOT adjusted.

Table: Test 1 Data Summary

TEST TARGET 1.... Here is Esten's Test 1 Target and the aim points he used. During the test, the scope was NOT adjusted.

Comparison of Pressure vs Time Data

PRESSURE CURVES COMPARED.... The calculations were done with two different pressure curves. I received the N-133 pressure curves after I had already done the calculations with the RS curves. Esten was using N-133 rifle powder in the test. The N-133 powder has a much narrower and higher peak pressure than the Recreational Software data with a generic powder that is not specified. The RS data also starts at zero time with a pressure of about 10000 psi. The N-133 data has a zero pressure at zero time.

6PPC PRESSURE CURVES.... I received permission form Recreational Software, Inc to use their 6PPC Pressure vs Time data. I downloaded the Free Pressure Trace software in demo mode. Included in the download is the sample five shot pressure vs time curves for a 6PPC out of a clean cold barrel shooting the 70 gr Nosler Ballistic Tips (Moly) bullets. I was able to extract the 249 points of digital data from the file for each of the five curves. I create 5 separate pressure loading curves for the Finite Element model of the full rifle. The T4 curve was scaled to give a muzzle velocity of 3287 and 3364 fps.

RECREATIONAL SOFTWARE CURVES.... The results with these pressure curves are much different than the pressure curves from N-133 powder data. I am showing them here to indicate the difference that pressure curve data can make on the calculations. With the RC pressure curves, one would have to use a tuner or shoot a very high pressure load for the muzzle exit time to occur before the peak in the muzzle projection curve.

PRESSURE CURVE.... Ralph Stewart got these pressure curves from Johan Loubser, Ballistician at Western/Accurate Powders. Apart from the N-133 Johan also included Accurate-2015 and the Accurate-2230 Spherical powder as a comparison.
The respective charge mass loading density (%) and velocities were as follows from a 24” barrel:

N-133   27.7 grains  99.7% MV = 3179 fps.
A-2015  28.0 grains 100.1% MV = 3130 fps
A-2230  30.5 grains  98.2% MV = 3304 fps

N-133 PRESSURE CURVES.... The N-133 curve was scaled to generate muzzle velocities of 3287 and 3364 fps in a 22 inch barrel to duplicate the average muzzle velocities that Esten measured during the Test 1 testing. Later the curve was scaled to duplicate the muzzle velocities of each 4 shot group in Test 2.

MUZZLE PROJECTION CURVES.... With the stiff stock the projection to the 100 yard target is quite different using the N-133 pressure curve data and scaling it to the average muzzle velocities measured in the test. The first thing one notices that the muzzle exit time shifts leftward coincides with the muzzle's peak pointing position. The generic pressure curve had the muzzle's projection on a downward swing at muzzle exit time. It looks like a high pressure load with N-133 puts the muzzle exit time on or near the left side of the curve's peak even without a tuner. The point of impact results did not match the test data very well. It was possible to normalize the FEA model and relax the stiffness of the stock to improve the calculation's accuracy.

MORE COMPLIANT STOCK.... The "clubby" rifle stock in the FEA model appears to be too rigid compared to Esten's rifle stock. The elastic modulus of the hard wood stock was reduced by 25% to make it more compliant. The point of impact results with this more compliant stock are a better match to the test data. The FEA model with the more compliant stock appears to be a reasonably good representation of Esten's rifle.

For each calculated shot's POI, the following was calculated:
1. Pressure curve scaled for the correct Muzzle Velocity
2. Bullet exit time
3. Drop during the flight to the target
4. Muzzle vertical velocity transmitted to the bullet at exit
5. Time of Flight (TOF)
6. Bullet vertical displacement from 4. during the TOF
7. Muzzle's projection to the 100 Yd Target

Dynamic Movies of Deformations Amplified 500X

BARE BARREL.... The movie shows the gas pressure traveling down the barrel at 1/4" increments for the 3365 fps muzzle velocity. The pressure was applied with 82 separate pressure curves with the arrival time of the pressure calculated from the bullets movement. The deformations are amplified by 500X so one can see the movement. The muzzle is at the top it its swing when projected to the target but it has a downward velocity that is transmitted to the bullet as it exits. The still picture is the muzzle just as the bullet is about to exit. The muzzle sag from gravity was not included in these movies to more clearly show the movement. Note that the bolt moves aft a few mils from the chamber pressure. See Panda Bolt Page. When the few mils is amplified by 500X, it looks like a big hole in the receiver.

SAME MOVIE AT 1X.... This is the same movie as above, but the deformation are shown at 1X.

BARREL WITH TUNER BASE.... The movie shows that with the Tuner Base the muzzle projection is still climbing at bullet exit time.

BARREL WITH TUNER WEIGHT CENTER.... The extra weight slows down the motions and the muzzle projection is still climbing but quite a bit below the maximum upward swing.

Watch the scope's motion on this 50 caliber on YouTube.
The scope needs to be strong to survive a 50 caliber!

Springfield M1A High Speed Video. 
Watch the barrel's forced deformations. After the bullet has left, then the barrel vibrates.

Results Test 1:

Table: Test 1 Data Summary & Calculation Results

* Each Test POI has 0.677 added to make the average POI = 0.0
**Each calculated POI has 2.1951 added to make the average POI = 0.0

GRAPHICAL COMPARISON.... This is the same data as the above Table with the average Test POI values plotted along with the Calculated POI values. The POI values of each set were shifted vertically for an average of zero. This was done so one may more easily compare the calculated results against the test data. In essence, it is the best way I could set the FEA's scope to the same "zero" as that of Esten's rifle.

Esten's Test 2 Data 

TEST DATA 2.... The firing order (1, 6, 2, 7,...etc.) on this test was 28.7 gr N-133 Bare group then 29.3 gr N-133 Bare group. It was easier to switch loads than to change the tuner setup for each group.

TEST TARGET 2.... Before the test Esten raised the scope setting by 1/2". The scope was NOT adjusted after that. The same aim points were used as in Test 1.

Results Test 2:

Table: Test 2 Data POI Summary and Comparison to Calculated POI

* Each Test POI has 0.188 added to make the average POI = 0.0
**Each calculated POI has 2.1951 added to make the average POI = 0.0

GRAPHICAL COMPARISON.... This is the same data as the Table above with the average Test POI values plotted along with the Calculated POI values. The POI values of each set were shifted vertically for an average of zero. This was done so one may more easily compare the calculated results against the test data. In essence, it is the best way I could set the FEA's scope to the same "zero" as that of Esten's rifle.

Effect of Powder Selection on Barrel Motion

DIFFERENT POWDERS.... This chart shows that A-2015 powder with different burning characteristics causes the bullet to exit earlier, but the Muzzle Projection Curve is increased in amplitude and the muzzle exit time is nearly at the same location with respect to the peak of the curve.

Front Rest Placement and POI Change

FRONT REST PLACEMENT.... I ran a number of cases with the FEA model of Esten's Rifle and the only change for each calculation was the position of the front rest. The first calculation had the front edge of the rest flush with the end of the forearm. A new calculations was done for each 1/2 inch position as the front rest was moved aft. The front rest was the width of the forearm and the longitudinal support length was two inches. The muzzle velocity of each calculation was 3326 fps with the N-133 pressure curve and the bullet exit time was 0.001047 seconds.

CHANGE IN POI.... With perfect bullets, a perfect hold, the same 3326 fps velocity, and the same N-133 pressure curve the Point of Impact (POI) at the 100 yard target dropped as the front rest was moved closer to the action. At 2 inches back from the end of the forearm, a position change of 1/2 inch of the front rest would result a vertical spread of approximately 0.018 inches. However going from flush with the front of the forearm to moving the front rest back 5.5 inches would result in a vertical spread of about 0.160 inches. The vertical POI was zeroed with the front rest flush with the front of the forearm.

For the POI of each front rest placement the following was calculated:
1. Pressure curve scaled for the correct Muzzle Velocity (N-133 MV=3326 same for each shot)
2. Bullet exit time (0.001047 seconds same for each shot)
3. Drop during the flight to the target (1.6487 inches same for each shot)
4. Muzzle vertical velocity transmitted to the bullet at exit (Ranged from -0.79673 to -0.97325 in/sec)
5. Time of Flight (TOF) (0.09496 seconds same for each shot)
6. Bullet vertical displacement from 4. during the TOF Ranged from -1.0745 to -1.2352 inches)
7. Muzzle's Projection to the 100 Yard Target vs time (See the chart)

Muzzle Projection Curve and Muzzle Exit Time

Improving accuracy by compensating for small variations in muzzle velocity.

Smaller Groups Left of the Peak - UPWARD SLOPE:
Higher velocity shots exit early while pointing lower at the target but drop less in reaching the target.
Lower velocity shots exit later while pointing higher at the target but drop more in reaching the target.
Counteracting combination. Good.

Larger Groups Right of the Peak - DOWNWARD SLOPE:
Higher velocity shots exit early while pointing higher at the target and drop less in reaching the target.
Lower velocity shots exit later while pointing lower at the target and drop more in reaching the target.
Bad additive combination. Bad.

The additional mass of a Muzzle Tuner slows down the muzzle movements and allows the bullet exit before the peak of the muzzle projection curve during the upward slope without resorting to high pressure loads.

Some ways to get the muzzle exit time on the Left Side of the Peak

1. Add weight to the muzzle to slow down the muzzle movement
2. High pressure/high velocity load to make the muzzle exit time earlier
3. Faster burning powder to have the bullet gain velocity early and make the exit time earlier
4. Longer barrel to slow down the muzzle movement

Ladder Test with Esten's 6PPC Rifle FEA Model

LADDER TEST.... It appears that the "Muzzle Projection Curve" (MPC) plus the Muzzle's Vertical Velocity that is imposed on the bullet at muzzle exit time tends to shed some light on what is going on in the Ladder or "Audette" test. The Ladder Test uses loading to generate a series of loads with increasing velocity shot at the same target to see if some of the rounds print at the same POI even with different velocities. If a convergence is found, then loading in that range of velocity should shoot tight groups even with slight velocity variations. The following calculations were done to find the Point of Impact (POI) at a 100 yard virtual target. In the field, it is typical to shoot the Ladder Test at long range. One thing the 300 yd Ladder Test does it that it amplifies the bullet drop more than where the muzzle is pointing. The muzzle pointing is line-of-sight and therefore linear but the bullet drop during the Time Of Flight (TOF) is not linear with distance. With the calculation it is possible to calculate the POI even if they are close to each other, so 100 yards was used.

BARE BARREL.... The Muzzle Projection Curves for Esten's 6PPC Rifle with no tuner show the bullet exit times fall near the left side of the peak for muzzle velocities ranging from 3200 to 3550 fps. 

ZOOM ON THE EXIT TIMES.... The intersection points show where the muzzle is pointing at the 100 yard target at the time of bullet exit for each muzzle velocity. The high frequency superimposed on the MPC's is excited by the high pressure gas traveling up the barrel behind the bullet. I picked out the intersections by hand and then plotted the points to verify that the correct intersections were selected. I used a similar color code for the curves and the intersection points. Note that the higher velocity bullets exit point at the 100 yard target about the same place as the lower velocity bullets. But the lower velocity bullets will drop more on their way to the target.

MUZZLE'S VERTICAL VELOCITY.... The muzzle of the barrel is moving vertical with the velocities shown in the chart. The muzzle imparts this vertical velocity to the bullet as it exits. This velocity over the Time Of Flight (TOF) can also cause more drop.

ZOOM MUZZLE'S VELOCITY.... The bullet's vertical velocity was picked by the intersection of the muzzle's vertical velocity at bullet exit time. Again, these values were picked by hand and then the points plotted here to verify that they were selected correctly.

For each calculated shot's POI, the following is calculated:
1. Pressure curve scaled for the correct Muzzle Velocity
2. Bullet exit time
3. Drop during the flight to the target
4. Muzzle vertical velocity transmitted to the bullet at exit
5. Time of Flight (TOF)
6. Bullet vertical displacement from 4. during the TOF
7. Muzzle's projection to the 100 Yd Target at bullet exit time

 
LADDER TEST RESULTS.... The total vertical spread with the bare barrel is 0.5539 inches compared to 0.2097 inches for the case with the tuner and the weight forward. The chart represents where the bullets would strike at a virtual 100 yard target for the range of velocities listed. For Esten's Rifle with no tuner, there are three groupings near 3475 fps, 3375 fps, and 3275 fps. These muzzle velocities could be loads where the rifle is "in tune". The yellow circle (3475 fps) is under the gray green circle.

However with a tuner and the weight in the forward, the calculation shows groupings near 3525 fps, and 3300 fps. One thing to note is that the total vertical spread for all of the velocities with the tuner is less than half the vertical spread with the bare barrel. It appears that even with a tuner out of tune, one would expect better accuracy than with a bare barrel.

BARREL TUNER.... The smaller vertical spread with the tuner appears to occur because the bullet's muzzle exit times are on the left side of the MPC. On the average, the barrel is point higher on the target for slower velocity rounds that drop more in reaching the target.

ZOOM.... This chart zooms in on the bullet's muzzle exit times with the barrel tuner. 

Tune Adjustment Procedure

 ADJUSTING THE TUNER....  One way to adjust your tuners to minimize the vertical spread. First, trying to remove the vertical spread, with ammo that is carefully prepared to give consistent velocity and very little vertical, is difficult. The effects of tuner movement on vertical spread will be difficult to see. It makes it difficult to tune out the vertical if there is none.

PREPARE AMMO WITH VERTICAL.... Load ammo WITH a vertical spread built in. Here is a possible test procedure. Test with 6 shot groups. For example, load 3 rounds with your normal load +0.5 gr of powder and 3 rounds with your normal load -0.5 gr of powder. This ammo should exhibit vertical spread. Then adjust your tuner to minimize the vertical spread. Shoot 6 shot groups alternating between the two loads (one high velocity round then one low velocity round. etc.). This procedure would amplify the vertical and better show the effect of the tuner's position on minimizing vertical.
This could be done with the rifle and no tuner to see the magnitude of the vertical and then later with the tuner to show if the tuner does decrease the vertical when adjusted correctly.

Mode Shapes and Natural Frequencies

Mode 1 @ 134.5 Hz	Mode 2 @ 299.0 Hz
Mode 3 @ 383.6 Hz	Mode 4 @ 400.5 Hz
Mode 5 @ 691.3 Hz	Mode 6 @ 1024 Hz
Mode 7 @ 1204 Hz	Mode 8 @ 1629 Hz

FIRST 8 MODES.... Here are the mode shapes and natural frequencies of Esten's Rifle. I only show the first 8 Mode of vibration. The addition of the scope and a more realistic rifle stock added a number of lower natural frequencies and their mode shapes. The boundary conditions are Free-Free. This is as if the rifle were suspended in space with zero gravity.

"Bong Test!" Tapping a barrel to fine a node.

BONG TEST RESULTS.... Esten performed the "Bong Test!" on his 6PPC benchrest rifle and was able to find the node locations for three different conditions. I used the FEA model of Esten's rifle to calculate the mode frequency and node location for the conditions that Esten tested. I personally don't know the significance of trying to position the node at the muzzle. The highest angular variations occur at the node. That would indicate to me that is should not be located at the muzzle. The anti-nodes are the only locations where the barrel stays parallel to the axis and there is no angular displacement. The calculated results are compared to the test results and listed below. For the modal analysis the FEA model boundary condition was free-free. That is as if the rifle were suspended in zero gravity.

THE CONDITIONS....

Bare Barrel. Calculated/Test
Node location back from the muzzle (in): 5.28/5.75
Mode Frequency (Hz): 383.5/Not Recorded

Barrel with only the Tuner Base attached. Calculated/Test
Node location back from the muzzle (in): 3.45/4.75
Mode Frequency (Hz): 344.5/Not Recorded

Barrel with the Tuner Base and the Weight in the forward position. Calculated/Test
Node location back from the muzzle (in): 2.20/3.62
Mode Frequency (Hz): 326.6/315.0

The "Bong Test" convinced Esten that the node could not be moved to the muzzle on a Standard Taper Centerfire Barrel within the weight constraints of NBRSA LV or HV. Here is a humorous article about a Bong Test.

ON A FINAL NOTE.... These guys are building an improved version of Esten's Tuner. Here is the link: ShadeTree Engineering & Accuracy Selling the Improved Esten Tuner.

Good Hunting... from Varmint Al
For the serious reader: How to Check Another Engineer's Calculation.

Last Updated: 05/09/2008
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