How Far Apart Are Rifle Barrel Accuracy Nodes
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Nov 14, 2017 A longer barrel would (By my thinking) have a wider accuracy node due to the longer frequency of the vibration compared to a shorter barrel with a higher frequency of the vibration. Just a thought. I did drop out of an Engineering school, so I may not be on the mark with this. Tweaking the NEF and the Ultra H&R rifles for improved accuracy. H&R Ultra 25-06, 26' Barrel, 4-12x40 Bushnell Banner scope, Weaver med Rings on H&R rail base. Here is a list of things you can do with simple tools. There is no way of knowing that they will improve accuracy in all Handi rifles but they did in the 25-06 Ultra I have.
- 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.
- In addition, short, thick barrels have wide(r) nodes so velocity isn't as critical to achieving a sweet spot. Because the velocity of the bullet passing through the barrel affects the way it flexes accurate loads should deliver as consistent a velocity from shot to shot as is possible so that the bullet exits the muzzle at the same point in the.
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
| FEA Model | FEA Model with a Bullet | Mesh Detail | Test Range | Dynamic Movies | Test 1 | Results Test 1 | Test 2 | Results Test 2 | Pressure Curves | N-133 Pressure Curve | Front Rest Placement | Muzzle Projection Curve | Mode Shapes & Frequencies | Bong Test! | Powder Effect | Ladder Test | Tuner Adjustment | 600 Yard Tune | |
Distortions amplified by 500X.
OBJECTIVE.... The objective of this study was to compare the FEAcalculation results using the 3D model of the rifle to Test Data on an accuratebenchrest rife. The dynamic response calculations gives some insight andunderstanding on what a tuner does to the motions of the rifle barrel and how amuzzle tuner might affect the accuracy of a rifle and Point of Impact (POI). Thecalculation loads simulates the gas pressure traveling up a rifle barrel behindthe bullet. The deformations in the rifle and barrel are calculated and then a100 yard projection of the barrel's muzzle is displayed. The FEA results arethen compared to test data for four different loads of N-133 powder and theresulting average muzzle velocities.
SUMMARY.... For the reader who doesn't want to wade through all thediscussion here is a summary of what a tuner can do to correct for smallvariations in muzzle velocity from round to round. The Muzzle Projection Curveshows where the muzzle is pointing at a 100 yard target while the rifle is beingfired. The most important aspect is the curve is where the muzzle is pointing atthe time the bullet exits the muzzle.
Improving accuracy by compensating for small variations in muzzlevelocity.
Smaller Groups Left of the Peak - UPWARD SLOPE:
Higher velocity shots exit early while pointing lower at the target but dropless in reaching the target.
Lower velocity shots exit later while pointing higher at the target but dropmore 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 dropless in reaching the target.
Lower velocity shots exit later while pointing lower at the target and drop morein reaching the target.
Bad additive combination. Bad. This is currently being called 'NegativeCompensation'.
The additional mass of a Muzzle Tuner slows down the muzzle movements and allowsthe bullet exit before the peak of the muzzle projection curve during the upwardslope without resorting to high pressure loads.
POWERFUL TOOL.... This analysis was done with the LS-DYNAFinite Element Code. This software is a very powerful tool for analyzing thedynamic and static loading of structures. It was used here to calculate therifle's response to the high pressure gas that forces the bullet out of a barrelwhen it is fired. For the first calculation, the breach end of the barrel wasfixed in space which treats the barrel as a cantilever beam. The results showedthat a more complex model was required to capture the dynamics of the completerifle. There is a vertical plane of symmetry in the model and only motions inthe vertical direction are calculated. In the movies, the displacements aregreatly amplified so that they can be viewed.
THE BARREL.... The 416 Stainless Steel 5.39 lb barrel in this modelhas a breach diameter of 1.24' for one inches and then a straight taper toa 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 6mmwith no rifling modeled. The 416 Stainless Steel tuner base weighs 7 oz.. The 7oz brass weight is threaded and can be positioned at various locations on thetuner base. The full rifle is in a one G gravitational field to simulate earth'sgravity. The muzzle sag is calculated at the start of each calculation with theImplicit method using dynamic relaxation . Then the dynamic calculation proceedswith the pressure time data using Explicit method. The burning powder's gaspressure is applied to the chamber walls and the bolt face. The barrel's chamberis the size of the 6PPC caliber brass. But for the calculation, I did notinclude the brass case and merely applied the pressure to the bolt face and thechamber walls.
THE ACTION.... The action is 1.25 inches in diameter and is 7.2 incheslong. The weight of the action is 1.5 pounds. The bolt is merged into theaction's cylinder. The gas pressure acts on the bolt face. Since there is nobolt, there is also no bolt handle.
THE SCOPE AND RINGS.... The scope weighs approximately 20 oz and isaluminum with a 0.1 inch wall thickness. There is a simulated lens in both theeyepiece and the objective to stiffen the otherwise open ends. The scope ringsare 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. Theaxis bore is projected to the zero point with zero gravity. Once gravity isapplied, the muzzle sags and the model's scope is also pointing lower by about0.003' more with the tuner base and brass weight than it does with the barebarrel.
THE STOCK.... The stock has the mechanical properties of wood. Theaction is 'glued in' to the stock and the barrel is completely freefloated. The stock is supported at two places, one 2' section near the buttand another 2' section on the forearm. The complete rifle is allowed freerecoil, that is no shooter's shoulder is modeled. The stock in the model ismore bulky that the actual stock. The decrease the rigidity of the model'sstock, the modulus was reduced by 25%.
THE TUNER.... The tuner base is screwed onto the barrel and butts upagainst the muzzle. It weight approximately 7 ounces. The 7 ounce brass weightis threaded so its axial position can be changed. Once positioned, the brassweight is prevented from moving by tightening the clamp screw.
Esten's RifleWeights in the Model
(Actual Rifle Weight + Tuner+ Weight is 12.13 lb)
| 1 5.389 lb 86.227 oz Barrel 2 1.502 lb 24.038 oz Action 3 3.024 lb 48.389 oz Stock 4 1.248 lb 19.966 oz Scope 5 0.053 lb 0.842 oz Scope Mounts 6 0.016 lb 0.249 oz Scope Lens 7 0.431 lb 6.902 oz Tuner Base 8 0.429 lb 6.858 oz Brass Weight -------------------------------- 12.092 lb 193.470 oz Total Weight |
THE 3-D MESH.... This view shows the mesh detail. Only half of themesh is actually in the calculation. There is a vertical plane of symmetry (X-ZPlane) down the bore axis and the center of the stock. The mesh is reflectedacross this plane for the for this 3-D mesh picture. The boundary condition forthe 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-Dmodel without a tuner, there are 17,196 nodes and 12,080 elements. For the modelwith 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 werestored for post-processing to generate the curves. Each shot calculation takesabout an hour to setup and run and the stored data requires about 2.5 Gb of harddisk space. An hour is plenty of time for the FEA barrel model to 'cooldown' in between shots. Then more time is involved in post processing theresults so that the results may be compared to test data.
| CONCLUSION.... Maybe the 'consensus' was that a rifle barrel vibrated in one or more of the mode shapes when fired. That was because the mode shapes and frequencies were easy to calculate and they did seem to answer some of the questions. From these FEA dynamic pressure calculations, it appears that the recoil and forced deformations are much more important than the natural vibration modes in determining where a barrel is pointing when the bullet exits the muzzle. Then after the bullet exits the muzzle, the rifle barrel vibrates in its various natural frequencies and mode shapes. Put another way, consider a guitar string being plucked. One pulls the string into a position (forced position) then releases it and the string vibrates at is natural frequency. The recoil and bullet motions 'pulls' the rifle barrel to a new shape and once the bullet leaves the barrel, then the barrel vibrates. However, the addition of the scope to the model has shown some small high frequency vibrations superimposed on the forced deformations, both of which, slightly alter where the muzzle points before the bullet exits. For lowering the amplitude of the high frequency vibrations, it appears that even an 'out of tune' tuner is better than no tuner at all. |
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 brassweight in the center position. The second view shows a cut-away view so thedetails of the inside of the tuner base can be seen. In the FEA model, the tunerbase and brass weight are not threaded but are bonded to each other by mergingnodes of different materials.
TEST DATA 1.... Here is Esten's Test 1 Data taken at the range. Duringthe test, the scope was NOT adjusted.
Table: Test 1 Data Summary
| Barrel Condition | Average Muzzle Velocity (fps) | Average Measured Point of Impact (in) |
| Bare Barrel | 3287 28.4 gr N-133 | -0.11 |
| Tuner Base | -0.60 | |
| Tuner Base + Weight (rear) | -0.86 | |
| Tuner Base + Weight (center) | -0.95 | |
| Tuner Base + Weight (forward) | -0.86 | |
| Bare Barrel | 3364 29.0 gr N-133 | -0.26 |
| Tuner Base | -0.67 | |
| Tuner Base + Weight (rear) | -0.78 | |
| Tuner Base + Weight (center) | -0.88 | |
| Tuner Base + Weight (forward) | -0.80 |
TEST TARGET 1.... Here is Esten's Test 1 Target and the aim points heused. During the test, the scope was NOT adjusted.
PRESSURE CURVES COMPARED.... The calculations were done with twodifferent pressure curves. I received the N-133 pressure curves after I hadalready done the calculations with the RS curves. Esten was using N-133 riflepowder in the test. The N-133 powder has a much narrower and higher peakpressure than the Recreational Software data with a generic powder that is notspecified. The RS data also starts at zero time with a pressure of about 10000psi. The N-133 data has a zero pressure at zero time.
6PPC PRESSURE CURVES.... I received permission form RecreationalSoftware, Inc to use their 6PPC Pressure vs Time data. I downloaded the FreePressure Trace software in demo mode. Included in the download is the samplefive shot pressure vs time curves for a 6PPC out of a clean cold barrel shootingthe 70 gr Nosler Ballistic Tips (Moly) bullets. I was able to extract the 249points of digital data from the file for each of the five curves. I create 5separate 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 curvesare much different than the pressure curves from N-133 powder data. I am showingthem here to indicate the difference that pressure curve data can make on thecalculations. With the RC pressure curves, one would have to use a tuner orshoot a very high pressure load for the muzzle exit time to occur before thepeak in the muzzle projection curve.
PRESSURE CURVE.... Ralph Stewart got these pressure curves from JohanLoubser, Ballistician at Western/Accurate Powders. Apart from the N-133 Johanalso included Accurate-2015 and the Accurate-2230 Spherical powder as acomparison.
The respective charge mass loading density (%) and velocities were as followsfrom 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 generatemuzzle velocities of 3287 and 3364 fps in a 22 inch barrel to duplicate theaverage muzzle velocities that Esten measured during the Test 1 testing. Laterthe curve was scaled to duplicate the muzzle velocities of each 4 shot group inTest 2.
MUZZLE PROJECTION CURVES.... With the stiff stock the projection to the100 yard target is quite different using the N-133 pressure curve data andscaling it to the average muzzle velocities measured in the test. The firstthing one notices that the muzzle exit time shifts leftward coincides with themuzzle's peak pointing position. The generic pressure curve had the muzzle'sprojection on a downward swing at muzzle exit time. It looks like a highpressure load with N-133 puts the muzzle exit time on or near the left side ofthe curve's peak even without a tuner. The point of impact results did not matchthe test data very well. It was possible to normalize the FEA model and relaxthe stiffness of the stock to improve the calculation's accuracy.
MORE COMPLIANT STOCK.... The 'clubby' rifle stock in the FEAmodel appears to be too rigid compared to Esten's rifle stock. The elasticmodulus of the hard wood stock was reduced by 25% to make it more compliant. Thepoint of impact results with this more compliant stock are a better match to thetest data. The FEA model with the more compliant stock appears to be areasonably good representation of Esten's rifle.
BARE BARREL.... The movie shows the gas pressure traveling down thebarrel at 1/4' increments for the 3365 fps muzzle velocity. The pressurewas applied with 82 separate pressure curves with the arrival time of thepressure calculated from the bullets movement. The deformations are amplified by500X so one can see the movement. The muzzle is at the top it its swing whenprojected to the target but it has a downward velocity that is transmitted tothe bullet as it exits. The still picture is the muzzle just as the bullet isabout to exit. The muzzle sag from gravity was not included in these movies tomore clearly show the movement. Note that the bolt moves aft a few mils from thechamber pressure. See Panda Bolt Page. When the few milsis 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 deformationare shown at 1X.
BARREL WITH TUNER BASE.... The movie shows that with the Tuner Base themuzzle projection is still climbing at bullet exit time.
BARREL WITH TUNER WEIGHT CENTER.... The extra weight slows down themotions and the muzzle projection is still climbing but quite a bit below themaximum upward swing.
Watchthe scope's motion on this 50 caliber on YouTube.
The scope needs to be strong to survive a 50 caliber!
SpringfieldM1A High Speed Video.
Watch the barrel's forced deformations. After the bullet has left, then thebarrel vibrates.
Table: Test 1 Data Summary & CalculationResults
| Barrel Condition | Average Muzzle Velocity (fps) | Average Measured Point of Impact (in) | Test 1 POI Shifted for Average of Zero (+0.677)* | Calculated POI Shifter for Average of Zero (+2.1951)** |
| Bare Barrel | 3287 28.4 gr N-133 | -0.11 | 0.567 | 0.2843 |
| Tuner Base | -0.60 | 0.078 | 0.0750 | |
| Tuner Base + Weight (rear) | -0.86 | -0.183 | -0.1949 | |
| Tuner Base + Weight (center) | -0.95 | -0.273 | -0.2435 | |
| Tuner Base + Weight (forward) | -0.86 | -0.183 | -0.2973 | |
| Bare Barrel | 3364 29.0 gr N-133 | -0.26 | 0.417 | 0.4013 |
| Tuner Base | -0.67 | 0.007 | 0.1187 | |
| Tuner Base + Weight (rear) | -0.78 | -0.103 | -0.1515 | |
| Tuner Base + Weight (center) | -0.88 | -0.203 | -0.1963 | |
| Tuner Base + Weight (forward) | -0.80 | -0.123 | -0.2495 |
How Far Apart Are Rifle Barrel Accuracy Nodes Located
* 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 withthe average Test POI values plotted along with the Calculated POI values. ThePOI values of each set were shifted vertically for an average of zero. This wasdone so one may more easily compare the calculated results against the testdata. In essence, it is the best way I could set the FEA's scope to the same'zero' as that of Esten's rifle.
TEST DATA 2.... The firing order (1, 6, 2, 7,...etc.) on this test was28.7 gr N-133 Bare group then 29.3 gr N-133 Bare group. It was easier to switchloads than to change the tuner setup for each group.
TEST TARGET 2.... Before the test Esten raised the scope setting by1/2'. The scope was NOT adjusted after that. The same aim points were usedas in Test 1.
Table: Test 2 Data POI Summary andComparison to Calculated POI
| Barrel Condition | Average Muzzle Velocity (fps) | Average Measured Point of Impact (in) | Test POI Shifted for Average of Zero (+0.188)* | Calculated POI Shifter for Average of Zero (+2.1951)** |
| Bare Barrel | 3349 28.7 gr N-133 | +0.30 | 0.488 | 0.3502 |
| Tuner Base | -0.25 | -0.062 | 0.1224 | |
| Tuner Base + Weight (rear) | -0.21 | -0.022 | -0.1582 | |
| Tuner Base + Weight (center) | -0.34 | -0.152 | -0.1995 | |
| Tuner Base + Weight (forward) | -0.33 | -0.142 | -0.2354 | |
| Bare Barrel | 3418 29.3 gr N-133 | +0.17 | 0.358 | 0.4431 |
| Tuner Base | -0.28 | -0.092 | 0.1591 | |
| Tuner Base + Weight (rear) | -0.30 | -0.112 | -0.1238 | |
| Tuner Base + Weight (center) | -0.36 | -0.172 | -0.153 | |
| Tuner Base + Weight (forward) | -0.28 | -0.092 | -0.2049 |
* 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 withthe average Test POI values plotted along with the Calculated POI values. ThePOI values of each set were shifted vertically for an average of zero. This wasdone so one may more easily compare the calculated results against the testdata. In essence, it is the best way I could set the FEA's scope to the same'zero' as that of Esten's rifle.
For each calculated shot's Point of Impact (POI), the following wascalculated:
1. Muzzle's projection to the 100 Yd Target
2. Muzzle's vertical velocity transmitted to the bullet at exit
3. Time of Flight (TOF)
4. Drop during the flight to the target (ballistics)
5. Bullet's vertical displacement from 2. during the TOF
6. Pressure curve scaled for the correct Muzzle Velocity
7. Bullet exit time
Note. Not only is the muzzle exit angle changing in time, but the muzzle is alsomoving in the vertical direction while the bullet is traveling down the barrel.When the bullet exits the muzzle the bullet will have the same vertical velocityas the muzzle. This vertical velocity during the TOF will also effect thevertical placement of the impact at the target.
The bullet has the pressure on its base. The deformations are not amplified.
The bullet would be out of the picture in one frame if the deformations wereamplified.
BULLET MESH.... The bullet is a 70 gr 6mm bullet. The ogive is truncatedto simplify the mesh. The bearing surface is correct and the friction betweenthe bullet (static = 0.2 dynamic=0.17). There is a 0.0005 inch clearance aroundthe bullet before it enters the 6mm bore diameter. The barrel is smooth bore.There is no rifling in the barrel. The inclusion of rifling would require a full3-D model which is very complex.
BULLET DISPLACEMENT.... The base of the bullet exits the muzzle at0.0010203 seconds with a velocity of 3338 fps. After the bullet exits the muzzlethe pressure on its base is reduced to zero in 0.000001 second.
BULLET VELOCITY.... The bullet achieves a muzzle velocity of 3338 fps asthe base exits the muzzle. The bullet is in contact with the bore and thecontact surfaces between the bullet and bore constrain it vertical position tothat of the barrel's bore.
MUZZLE PROJECTION CURVES.... The inclusion of the sandbag rests and thebullet only slightly changes the Muzzle Projection Curves from the earliercalculations. Esten's original tuner with the weight forward puts the muzzleexit time near the center of the upward slope. Without the tuner and a barebarrel there is no compensation for small variations in muzzle velocity. Forcomparison, I also included Esten's Rifle model with the ShadeTree tuner withthe weights centered.
LOAD ON THE SAND BAGS.... Here is the calculation of how Esten's Rifle,with the bare barrel, loads the sand bags when it is fired. When gravity isapplied the full weight is on the sand bags. The load on the forearm is morebecause the CG is closer to the forward sand bag. The loads decrease to zero asthe bullet moves and the rifle starts to recoil. Then the buttstock is forceddown on the rear sand bag with about 112 pounds as the rifle rotates around theCG. All this time the forearm is rising and when the bullet exits the muzzle,the rifle is not loading the sand bags at all. The forearm is about 0.0012inches above the front rest at bullet exit time. I have felt my rifles jump whenI fire them, but never thought that it could be completely off the sand bagswhen the bullet exits. The calculation is free recoil. No shooter's shoulderpressure.
DIFFERENT POWDERS.... This chart shows that A-2015 powder with differentburning characteristics causes the bullet to exit earlier, but the MuzzleProjection Curve is increased in amplitude and the muzzle exit time is nearly atthe same location with respect to the peak of the curve.
FRONT REST PLACEMENT.... I ran a number of cases with the FEA model ofEsten's Rifle and the only change for each calculation was the position of thefront rest. The first calculation had the front edge of the rest flush with theend of the forearm. A new calculations was done for each 1/2 inch position asthe front rest was moved aft. The front rest was the width of the forearm andthe longitudinal support length was two inches. The muzzle velocity of eachcalculation was 3326 fps with the N-133 pressure curve and the bullet exit timewas 0.001047 seconds.
CHANGE IN POI.... With perfect bullets, a perfect hold, the same 3326 fpsvelocity, and the same N-133 pressure curve the Point of Impact (POI) at the 100yard target dropped as the front rest was moved closer to the action. At 2inches back from the end of the forearm, a position change of 1/2 inch of thefront rest would result a vertical spread of approximately 0.018 inches. Howevergoing from flush with the front of the forearm to moving the front rest back 5.5inches would result in a vertical spread of about 0.160 inches. The vertical POIwas 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 foreach 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)
Improving accuracy by compensating for small variations in muzzlevelocity.
Smaller Groups Left of the Peak - UPWARD SLOPE:
Higher velocity shots exit early while pointing lower at the target but dropless in reaching the target.
Lower velocity shots exit later while pointing higher at the target but dropmore 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 dropless in reaching the target.
Lower velocity shots exit later while pointing lower at the target and drop morein reaching the target.
Bad additive combination. Bad.
The additional mass of a Muzzle Tuner slows down the muzzle movements and allowsthe bullet exit before the peak of the muzzle projection curve during the upwardslope without resorting to high pressure loads.
Some ways to getthe 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 theexit time earlier
4. Longer barrel to slow down the muzzle movement
LADDER TEST.... It appears that the 'MuzzleProjection Curve' (MPC) plus the Muzzle's Vertical Velocity that is imposedon the bullet at muzzle exit time tends to shed some light on what is going onin the Ladder or 'Audette' test. The Ladder Test uses loading togenerate a series of loads with increasing velocity shot at the same target tosee 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 shoottight groups even with slight velocity variations. The following calculationswere done to find the Point of Impact (POI) at a 100 yard virtual target. In thefield, it is typical to shoot the Ladder Test at long range. One thing the 300yd Ladder Test does it that it amplifies the bullet drop more than where themuzzle is pointing. The muzzle pointing is line-of-sight and therefore linearbut 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 closeto each other, so 100 yards was used.
BARE BARREL.... The Muzzle Projection Curves for Esten's 6PPC Rifle withno tuner show the bullet exit times fall near the left side of the peak formuzzle velocities ranging from 3200 to 3550 fps.
ZOOM ON THE EXIT TIMES.... The intersection points show where the muzzleis pointing at the 100 yard target at the time of bullet exit for each muzzlevelocity. The high frequency superimposed on the MPC's is excited by the highpressure gas traveling up the barrel behind the bullet. I picked out theintersections by hand and then plotted the points to verify that the correctintersections were selected. I used a similar color code for the curves and theintersection points. Note that the higher velocity bullets exit point at the 100yard target about the same place as the lower velocity bullets. But the lowervelocity bullets will drop more on their way to the target.
MUZZLE'S VERTICAL VELOCITY.... The muzzle of the barrel is movingvertical with the velocities shown in the chart. The muzzle imparts thisvertical velocity to the bullet as it exits. This velocity over the Time OfFlight (TOF) can also cause more drop.
ZOOM MUZZLE'S VELOCITY.... The bullet's vertical velocity was picked bythe 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 thatthey were selected correctly.
How Far Apart Are Rifle Barrel Accuracy Nodes Removed
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 is0.5539 inches compared to 0.2097 inches for the case with the tuner and theweight forward. The chart represents where the bullets would strike at a virtual100 yard target for the range of velocities listed. For Esten's Rifle with notuner, there are three groupings near 3475 fps, 3375 fps, and 3275 fps. Thesemuzzle velocities could be loads where the rifle is 'in tune'. Theyellow circle (3475 fps) is under the gray green circle.
However with a tuner and the weight in the forward, thecalculation shows groupings near 3525 fps, and 3300 fps. One thing to note isthat the total vertical spread for all of the velocities with the tuner is lessthan half the vertical spread with the bare barrel. It appears that even with atuner out of tune, one would expect better accuracy than with a bare barrel.
How Far Apart Are Rifle Barrel Accuracy Nodes In Neck
BARREL TUNER.... The smaller vertical spread with the tuner appears tooccur because the bullet's muzzle exit times are on the left side of the MPC. Onthe average, the barrel is point higher on the target for slower velocity roundsthat drop more in reaching the target.
How Far Apart Are Rifle Barrel Accuracy Nodes In One
ZOOM.... This chart zooms in on the bullet's muzzle exit times with thebarrel tuner.
ADJUSTING THE TUNER.... One way to adjustyour tuners to minimize the vertical spread. First, trying to remove thevertical spread, with ammo that is carefully prepared to give consistentvelocity and very little vertical, is difficult. The effects of tuner movementon vertical spread will be difficult to see. It makes it difficult to tune outthe 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 3rounds with your normal load +0.5 gr of powder and 3 rounds with your normalload -0.5 gr of powder. This ammo should exhibit vertical spread. Then adjustyour tuner to minimize the vertical spread. Shoot 6 shot groups alternatingbetween the two loads (one high velocity round then one low velocity round.etc.). This procedure would amplify the vertical and better show the effect ofthe tuner's position on minimizing vertical.
This could be done with the rifle and no tuner to see the magnitude of thevertical and then later with the tuner to show if the tuner does decrease thevertical when adjusted correctly.
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 ofEsten's Rifle. I only show the first 8 Mode of vibration. The addition of thescope and a more realistic rifle stock added a number of lower naturalfrequencies and their mode shapes. The boundary conditions are Free-Free. Thisis as if the rifle were suspended in space with zero gravity.
LONG RANGE TUNE.... Here is an interesting set of trajectory plots. Nomatter how carefully one loads his ammo, there are going to be small differencesin muzzle velocity. Consider a load with an average muzzle velocity of 2915 fpswith a muzzle velocity variation of 15 fps. Then consider this load tuned forzero vertical at 100 yards that overcomes that small difference in muzzlevelocity.
This same load will be out of tune by 73.23-71.50=1.73 inches of vertical at 600yards. However if the load is tuned so that there is 12.21-11.92=0.29 inches ofvertical at 100 yards (with the slower muzzle velocity hitting higher)then there would be zero vertical at 600 yards. This chart is for a 6.5mm 140 grVLD bullet with a 0.64 BC. A similar chart or table can be made for each longrange load. If you are in tune for zero vertical at 100 yards, you will not bein tune for zero vertical at 600 or 1000 yards.
BONG TEST RESULTS.... Esten performed the 'Bong Test!' on his6PPC benchrest rifle and was able to find the node locations for three differentconditions. I used the FEA model of Esten's rifle to calculate the modefrequency and node location for the conditions that Esten tested. Possiblypositive compensation would occur if the node were moved to the muzzle. Thehighest angular variations occur at the node. The anti-nodes are the onlylocations where the barrel stays parallel to the axis and there is no angulardisplacement. The calculated results are compared to the test results and listedbelow. 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
How Far Apart Are Rifle Barrel Accuracy Nodes Destiny 2
The 'Bong Test' convinced Esten that the node could not be moved tothe muzzle on a Standard Taper Centerfire Barrel within the weight constraintsof NBRSA LV or HV. Here is a humorous article about a BongTest. Note: This is from TheWayBackMachine without pictures.
ON A FINAL NOTE.... These guys are building an improved version ofEsten's Tuner. Here is the link: ShadeTreeEngineering & Accuracy Selling the Improved Esten Tuner.
Good Hunting... from Varmint Al
For the serious reader: How to CheckAnother Engineer's Calculation.
How Far Apart Are Rifle Barrel Accuracy Nodes In Adults
Short Rifle Barrel Accuracy
Last Updated: 07/19/2015
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