V
Vibe
Guest
This the 2nd draft of a test I think will answer this debated question once and for all.
If good data can be obtained, I think the statistics will provide the proof - one way or the other.
A Statistical Design of Experiments for Rimfire Accuracy
Material Needed – 3 lots of consistent ammunition of differing speeds. High, low and median.
1 Barrel with enough bore curve to be measurable
4 target cards – marked for X-Y measurement
1 Scoring plug
Return to Battery action set up with continuous barrel indexing capability
Calm conditions or tunnel
Method
This particular test is geared toward finding the effect of barrel bore curve in relation to it's position relative to gravity on the overall accuracy potential of that barrel. To define, in quantifiable terms, if it is of any importance and if so, how much.
The proposed method for measuring shot position involves drawing reference lines on the target card before the card is shot. Draw lines through the center of the bulls both vertically and horizontally. Then draw lines to either side a fixed distance from the first lines – a 1” offset should be sufficient, but any consistent value will work. We will then measure each shot location from these lines using a digital caliper and the scoring plug, as hopefully many of the target centers will be shot away. Measure the diameter of the scoring plug, divide by 2, and subtract this value from the distance found when measuring from a reference line to the other side of the plug. Shots above center will be considered as positive, those below as negative. Likewise, shots right of center will be considered as positive, and those to the left as negative.
Shoot the first 25 bull target card for score, one shot per bull. This will be the baseline Capability Study. Each shot will have to be measured for X and Y position from the center of the bull and each shot chronographed for speed. Record these results in a table.
Next we have to determine the direction and degree of bore curvature. A shadow line technique can be used to eyeball this for the first check, or continue to the first firing. This check should also be done with the median speed ammo.
Mount the barrel into the test action and mark the 0° rotation. Without changing the zero aiming point, fire one shot, rotate 90° fire another, rotate to 180° fire a third, rotate to 270° and fire a 4th. If there is sufficient bore curvature these 4 shots will have landed in 4 distinct locations. Rotate the barrel and repeat this test so that the 6:00 and 12:00 shots are aligned vertically – mark the barrel at the 4 clock positions of this alignment. For convenience sake we will define 0° as the 12:00 position, the rightmost shot as 90°, the bottom shot as the 180° position and the remaining position which fired the left most shot as 270°.
The DOE (Design of Experiments) itself will be a set of experiments where we will set the various combinations of these factors as the 8 corners of our “solution box” - with the optimum setting hopefully contained within. If that solution exists, and is inside of our box, a statistical analysis will find it. In order to set this exercise up we will need to segregate our data by 3 factors, each with two levels. Velocity – high and low, Horizontal Barrel curve – left and right, Vertical barrel curve - up and down. Then arrange the tests to represent the 8 different possibilities. Sighting in for scope zero for each of the following should be done with the baseline mid-velocity ammo as this is what we are comparing the test against.
1) Barrel at 0° - shots hitting 12:00 high, with the fast lot of ammo
2) Barrel at 0° , with the slow lot of ammo
3) Barrel at 180°, fast ammo
4) Barrel at 180 , slow ammo
5) Barrel at 90°, fast ammo
6) Barrel at 90°, slow ammo
7) Barrel at 270°, fast ammo
8) Barrel at 270°, slow ammo
Row 5 and the sighter row of both DOE target cards may be used for scope adjustments and fouling shots
Test Target Card #1 – row 1 – Test Condition 1)
After setting zero with mid velocity ammo with barrel at 0°– clean barrel, shoot 4 or 5 foulers with fast ammo and begin shooting for record. Shoot only the 5 targets on that row.
Test Target Card #1 – row 2 – Test Condition 2)
Do not reset scope zero. Clean barrel, shoot 4 or 5 foulers with the slower ammo and begin shooting for record. Shoot only the 5 targets in the 2nd row.
Test Target Card #1 – row 3 – Test Condition 3)
Rotate barrel to 180°, clean barrel, shoot foulers with mid velocity ammo, zero scope with mid velocity ammo. Clean barrel, foul with fast ammo and begin shooting for score on the 3rd row.
Test Target Card #1 – row 4 – Test Condition 4)
Do not reset scope zero. Clean barrel, shoot 4 or 5 foulers with the slower ammo and begin shooting for record. Shoot only the 5 targets in the 4th row.
This will define the end of our box that is concerned with only the dispersion of velocity and vertical bore curve
Test Target Card #2 – row 1 – Test Condition 5)
Rotate barrel to 90°, clean barrel, shoot foulers with mid velocity ammo, zero scope with mid velocity ammo. Clean barrel, foul with fast ammo and begin shooting for score on the 1st row.
Test Target Card #2 – row 2 – Test Condition 6)
Do not reset scope zero. Clean barrel, shoot 4 or 5 foulers with the slower ammo and begin shooting for record. Shoot only the 5 targets in the 2nd row.
Test Target Card #2 – row 3 – Test Condition 7)
Rotate barrel to 270°, clean barrel, shoot foulers with mid velocity ammo, zero scope with mid velocity ammo. Clean barrel, foul with fast ammo and begin shooting for score on the 3rd row.
Test Target Card #2 – row 4 – Test Condition 8)
Do not reset scope zero. Clean barrel, shoot 4 or 5 foulers with the slower ammo and begin shooting for record. Shoot only the 5 targets in the 4th row.
This will define the end of our solution box that is only concerned with horizontal dispersion with respect to velocity.
This data can now be run though several Statistical Analysis tests to check for the various conditions and inter-relationships between these factors. Once the optimum setting is determined, we will set the barrel into the position predicted to be optimum, and using a lot of ammo nearest to the velocity also predicted to be optimum, we will repeat the first Capability Study and see what the results really are.
If we run this test on 4 or 5 barrels, it will become readily apparent if this is a generally preferred orientation for all barrels or if there is a barrel to barrel preference. If the preference is general – then a default orientation has been found and no other testing for this will be required. If it is a per-barrel preference then it may very well require this test be done on each barrel installation and may indeed be more trouble for most barrels than the gain in accuracy is worth. I would suspect that this may vary with the degree of bore curvature. At any rate it should answer the question once and for all.
If good data can be obtained, I think the statistics will provide the proof - one way or the other.
A Statistical Design of Experiments for Rimfire Accuracy
Material Needed – 3 lots of consistent ammunition of differing speeds. High, low and median.
1 Barrel with enough bore curve to be measurable
4 target cards – marked for X-Y measurement
1 Scoring plug
Return to Battery action set up with continuous barrel indexing capability
Calm conditions or tunnel
Method
This particular test is geared toward finding the effect of barrel bore curve in relation to it's position relative to gravity on the overall accuracy potential of that barrel. To define, in quantifiable terms, if it is of any importance and if so, how much.
The proposed method for measuring shot position involves drawing reference lines on the target card before the card is shot. Draw lines through the center of the bulls both vertically and horizontally. Then draw lines to either side a fixed distance from the first lines – a 1” offset should be sufficient, but any consistent value will work. We will then measure each shot location from these lines using a digital caliper and the scoring plug, as hopefully many of the target centers will be shot away. Measure the diameter of the scoring plug, divide by 2, and subtract this value from the distance found when measuring from a reference line to the other side of the plug. Shots above center will be considered as positive, those below as negative. Likewise, shots right of center will be considered as positive, and those to the left as negative.
Shoot the first 25 bull target card for score, one shot per bull. This will be the baseline Capability Study. Each shot will have to be measured for X and Y position from the center of the bull and each shot chronographed for speed. Record these results in a table.
Next we have to determine the direction and degree of bore curvature. A shadow line technique can be used to eyeball this for the first check, or continue to the first firing. This check should also be done with the median speed ammo.
Mount the barrel into the test action and mark the 0° rotation. Without changing the zero aiming point, fire one shot, rotate 90° fire another, rotate to 180° fire a third, rotate to 270° and fire a 4th. If there is sufficient bore curvature these 4 shots will have landed in 4 distinct locations. Rotate the barrel and repeat this test so that the 6:00 and 12:00 shots are aligned vertically – mark the barrel at the 4 clock positions of this alignment. For convenience sake we will define 0° as the 12:00 position, the rightmost shot as 90°, the bottom shot as the 180° position and the remaining position which fired the left most shot as 270°.
The DOE (Design of Experiments) itself will be a set of experiments where we will set the various combinations of these factors as the 8 corners of our “solution box” - with the optimum setting hopefully contained within. If that solution exists, and is inside of our box, a statistical analysis will find it. In order to set this exercise up we will need to segregate our data by 3 factors, each with two levels. Velocity – high and low, Horizontal Barrel curve – left and right, Vertical barrel curve - up and down. Then arrange the tests to represent the 8 different possibilities. Sighting in for scope zero for each of the following should be done with the baseline mid-velocity ammo as this is what we are comparing the test against.
1) Barrel at 0° - shots hitting 12:00 high, with the fast lot of ammo
2) Barrel at 0° , with the slow lot of ammo
3) Barrel at 180°, fast ammo
4) Barrel at 180 , slow ammo
5) Barrel at 90°, fast ammo
6) Barrel at 90°, slow ammo
7) Barrel at 270°, fast ammo
8) Barrel at 270°, slow ammo
Row 5 and the sighter row of both DOE target cards may be used for scope adjustments and fouling shots
Test Target Card #1 – row 1 – Test Condition 1)
After setting zero with mid velocity ammo with barrel at 0°– clean barrel, shoot 4 or 5 foulers with fast ammo and begin shooting for record. Shoot only the 5 targets on that row.
Test Target Card #1 – row 2 – Test Condition 2)
Do not reset scope zero. Clean barrel, shoot 4 or 5 foulers with the slower ammo and begin shooting for record. Shoot only the 5 targets in the 2nd row.
Test Target Card #1 – row 3 – Test Condition 3)
Rotate barrel to 180°, clean barrel, shoot foulers with mid velocity ammo, zero scope with mid velocity ammo. Clean barrel, foul with fast ammo and begin shooting for score on the 3rd row.
Test Target Card #1 – row 4 – Test Condition 4)
Do not reset scope zero. Clean barrel, shoot 4 or 5 foulers with the slower ammo and begin shooting for record. Shoot only the 5 targets in the 4th row.
This will define the end of our box that is concerned with only the dispersion of velocity and vertical bore curve
Test Target Card #2 – row 1 – Test Condition 5)
Rotate barrel to 90°, clean barrel, shoot foulers with mid velocity ammo, zero scope with mid velocity ammo. Clean barrel, foul with fast ammo and begin shooting for score on the 1st row.
Test Target Card #2 – row 2 – Test Condition 6)
Do not reset scope zero. Clean barrel, shoot 4 or 5 foulers with the slower ammo and begin shooting for record. Shoot only the 5 targets in the 2nd row.
Test Target Card #2 – row 3 – Test Condition 7)
Rotate barrel to 270°, clean barrel, shoot foulers with mid velocity ammo, zero scope with mid velocity ammo. Clean barrel, foul with fast ammo and begin shooting for score on the 3rd row.
Test Target Card #2 – row 4 – Test Condition 8)
Do not reset scope zero. Clean barrel, shoot 4 or 5 foulers with the slower ammo and begin shooting for record. Shoot only the 5 targets in the 4th row.
This will define the end of our solution box that is only concerned with horizontal dispersion with respect to velocity.
This data can now be run though several Statistical Analysis tests to check for the various conditions and inter-relationships between these factors. Once the optimum setting is determined, we will set the barrel into the position predicted to be optimum, and using a lot of ammo nearest to the velocity also predicted to be optimum, we will repeat the first Capability Study and see what the results really are.
If we run this test on 4 or 5 barrels, it will become readily apparent if this is a generally preferred orientation for all barrels or if there is a barrel to barrel preference. If the preference is general – then a default orientation has been found and no other testing for this will be required. If it is a per-barrel preference then it may very well require this test be done on each barrel installation and may indeed be more trouble for most barrels than the gain in accuracy is worth. I would suspect that this may vary with the degree of bore curvature. At any rate it should answer the question once and for all.
(possibly irrelevant to this discussion but so be it!)