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.
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.
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.
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
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 Women
Last Updated: 07/19/2015
End of Page
