Summary of this posting.
The 22 Long Rifle at long range has a problem that other types of cartridges, such as a modern long range cartridge such as the 308 or the black powder era 45-70 do not have.
That problem is at long range for the 22 LR variations in the ballistics coefficient from shot to shot become the major factor in vertical spread.
This is only a factor at ranges above 200 to 300 yards and beyond 400 yards is quite extreme.
Manufacturers of 22 LR cartridges designed for long range should provide the shooting public with specific data for their 22 LR cartridges. The muzzle velocity and its standard deviation and the ballistics coefficient with its standard deviation.
This will help shooters make choices as to which rounds to spend the money and time on to determine which ones work best for them.
End of summary. For detailed information continue with the posting.
****
A number of 22 Long Rifle ammunition manufacturers have recently come out with offerings they say are specifically designed for better performance at long range.
I have degrees in math and physics, so I like to measure performance from that perspective.
To hit a target at several hundred yards the ammunition needs to be able to maintain a group size somewhat larger than the size of the target to be able to assure a good number of the bullets will hit the target.
I’m talking about the group size the ammunition itself is capable of producing and not considering the skill of the shooter and/or the quality of the firearm. In other words for this discussion they are perfect.
There is both a horizontal and vertical component to a group size. Horizontal spread is mainly due to variation in the speed and direction of the wind. Changes in these from shot to shot will cause horizontal spread.
The main factors producing vertical spread are the variation in the muzzle velocity (MV) and ballistics coefficient (BC) from shot to shot. Only these two factors control the trajectory of the bullet. Two bullets with the same MV and BC will have the same trajectory regardless of their weight, diameter and shape.
Both of these factors vary from shot to shot, this variation is measured with what in Statistics is called the Standard Deviation (SD). The SD measures how much individual shots vary around the average (mean) of each factor.
For most situations about 67% will vary one SD above and below the mean, about 95% two SDs above and below the mean and 99.7% will vary three SDs above and below the mean. It’s common to look at two SDs above and below the mean.
I won’t go into how the SD is calculated here; it is not complicated but is tedious. Most chronographs calculate the SD of MV for a number of shots for us. BC values are hard for the shooter to obtain themselves although there are ways to come up with some pretty good estimates. So we mainly rely on information from the manufacturer for BC values.
Variations in MV result in a variation in the time it takes the bullet to reach the target and therefore results in vertical stringing with a lower MV resulting in a lower impact point.
Variations in BC do the same thing. A lower BC results in the bullet slowing down faster therefore a longer time of flight and a lower impact point.
So variations in both MV and BC contribute to vertical stringing.
If we know the SD of the MV and BC we can use a ballistics solver to get a value for the total vertical spread.
What we do is take the mean MV and BC for whatever round we are interested in and using the ballistics solver enter that data and then leave one of the two factors constant while we vary the other from it’s high to low values (two SD above and below the mean) and see how the impact point changes.
Then set that factor to its mean and vary the other factor the same way again recording the variation in impact points for a two SD spread above and below the mean.
Let’s assume that we have done this and found the vertical spread due to variations in MV is 12 inches and the vertical spread for BC is 5 inches. To get an accurate measurement of the total vertical spread at the 95% level we don’t just add the two spreads together but rather use a Statistical method called Root Sum Square (RSS). We square each number, add the results together and take the square root of that value.
In this case 12 squared is 144 and 5 squared is 25. Adding 144 and 25 results in 169. The square root of 169 is 13. In this case 95% of our shots will fall in a 13 inch vertical spread with the other 5% outside that range either high or low.
Now to measuring the performance of a particular manufacturer’s “long range” offering.
We need to know the MV and BC along with the SD of each of these. I few months ago I corresponded with a representative of a major manufacturer of quality 2 LR ammunition by email. I asked him if they measured the standard deviation of both MV and BC. He said they did. When I asked him to provide that data to me, he refused.
The only place I have been able to get this data is from testing Bryan Litz did in 2015 of 84 different “types” of 22 Long Rifle ammunition. Eley Tenex and Eley Match were considered to be two different types. He measured the standard deviation of both the MV and BC for 50 rounds of each type and published the results in his book “Modern Advancements in Long Range Shooting – Volume II”.
The chart below shows the total vertical spread for the data from Litz’s testing for a type that was ranked 8th out of 84. The mean MV is 1108 with an SD of MV of 5.2 and a mean BC of .155 with an SD of BC of .005. The two SD variations above and below the MV’s mean varied from 1097.6 to 1118.4 and the BC from .145 to .165. Temperature at 75 degrees and atmospheric pressure at 27.00.
Below is a chart that shows the spread due to variations in MV and BC and then the total vertical spread for each range in yards.
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This chart illustrates that as the range increases the variation of BC becomes the significant factor in vertical spread. The skill of the shooter and rifle performance are a major factor in the overall vertical spread at 100 yards. If the shooter/rifle combination is capable of 1 MOA at 100 yards the total vertical spread due to MV and BC along with shooter/rifle 1 MOA is 1.12 inches. At 600 yards the overall vertical spread, when the shooter/rifle is capable of 1 MOA is also considered, the vertical spread only increases to 44.92 inches.
The variation in BC being the major factor at long range is only true for the 22 LR and not nearly as significant for the black powder era cartridges where the vertical spread due to variation in BC is not nearly as much of a factor. This is because they have a much higher BC than the small bullet for the 22 LR.
It would help those of us considering purchasing their products for 22 LR manufacturers to provide us with these four pieces of information discussed above so we could make comparisons based upon actual testing they have done.
The way to see if a new “long range” 22 actually performs better than another round at long range is to test each at long range. To do that we need to see how much of a vertical spread is produced when we fire a number of shots at long range. Shooting groups at short ranges tells us nothing about how the round will perform at long range. At short ranges, like 100 yards, the variations in MV and especially BC haven’t had time to do their thing. If the SD of the BC is large, there will be a lot of vertical spread at long range. Even a round that does not group well at short range may do well at long range if the SD of the BC is small.
The way to do this long range testing is to set up a target that is tall enough to catch all the rounds fired and fire at least 25 rounds to get a good look at the vertical spread. Keep in mind that the numbers in the chart above for total vertical spread are a 95% spread, that means 95% of the 25 rounds, 23.75 rounds, will be inside the two SD range and 1.25 rounds, on the average will be outside that range. Also, this chart does not include the capabilities of the rifle/shooter. So don’t be afraid to throw out one flier.
From Litz’s testing of 22 LR types he tested I can evaluate the data as discussed above and decide which ones I want to spend time and money on to do some field testing. Why should I purchase some rounds for testing when the manufacturer has the data I need which they should be happy to provide if their new round is as good as they say.
The 22 Long Rifle at long range has a problem that other types of cartridges, such as a modern long range cartridge such as the 308 or the black powder era 45-70 do not have.
That problem is at long range for the 22 LR variations in the ballistics coefficient from shot to shot become the major factor in vertical spread.
This is only a factor at ranges above 200 to 300 yards and beyond 400 yards is quite extreme.
Manufacturers of 22 LR cartridges designed for long range should provide the shooting public with specific data for their 22 LR cartridges. The muzzle velocity and its standard deviation and the ballistics coefficient with its standard deviation.
This will help shooters make choices as to which rounds to spend the money and time on to determine which ones work best for them.
End of summary. For detailed information continue with the posting.
****
A number of 22 Long Rifle ammunition manufacturers have recently come out with offerings they say are specifically designed for better performance at long range.
I have degrees in math and physics, so I like to measure performance from that perspective.
To hit a target at several hundred yards the ammunition needs to be able to maintain a group size somewhat larger than the size of the target to be able to assure a good number of the bullets will hit the target.
I’m talking about the group size the ammunition itself is capable of producing and not considering the skill of the shooter and/or the quality of the firearm. In other words for this discussion they are perfect.
There is both a horizontal and vertical component to a group size. Horizontal spread is mainly due to variation in the speed and direction of the wind. Changes in these from shot to shot will cause horizontal spread.
The main factors producing vertical spread are the variation in the muzzle velocity (MV) and ballistics coefficient (BC) from shot to shot. Only these two factors control the trajectory of the bullet. Two bullets with the same MV and BC will have the same trajectory regardless of their weight, diameter and shape.
Both of these factors vary from shot to shot, this variation is measured with what in Statistics is called the Standard Deviation (SD). The SD measures how much individual shots vary around the average (mean) of each factor.
For most situations about 67% will vary one SD above and below the mean, about 95% two SDs above and below the mean and 99.7% will vary three SDs above and below the mean. It’s common to look at two SDs above and below the mean.
I won’t go into how the SD is calculated here; it is not complicated but is tedious. Most chronographs calculate the SD of MV for a number of shots for us. BC values are hard for the shooter to obtain themselves although there are ways to come up with some pretty good estimates. So we mainly rely on information from the manufacturer for BC values.
Variations in MV result in a variation in the time it takes the bullet to reach the target and therefore results in vertical stringing with a lower MV resulting in a lower impact point.
Variations in BC do the same thing. A lower BC results in the bullet slowing down faster therefore a longer time of flight and a lower impact point.
So variations in both MV and BC contribute to vertical stringing.
If we know the SD of the MV and BC we can use a ballistics solver to get a value for the total vertical spread.
What we do is take the mean MV and BC for whatever round we are interested in and using the ballistics solver enter that data and then leave one of the two factors constant while we vary the other from it’s high to low values (two SD above and below the mean) and see how the impact point changes.
Then set that factor to its mean and vary the other factor the same way again recording the variation in impact points for a two SD spread above and below the mean.
Let’s assume that we have done this and found the vertical spread due to variations in MV is 12 inches and the vertical spread for BC is 5 inches. To get an accurate measurement of the total vertical spread at the 95% level we don’t just add the two spreads together but rather use a Statistical method called Root Sum Square (RSS). We square each number, add the results together and take the square root of that value.
In this case 12 squared is 144 and 5 squared is 25. Adding 144 and 25 results in 169. The square root of 169 is 13. In this case 95% of our shots will fall in a 13 inch vertical spread with the other 5% outside that range either high or low.
Now to measuring the performance of a particular manufacturer’s “long range” offering.
We need to know the MV and BC along with the SD of each of these. I few months ago I corresponded with a representative of a major manufacturer of quality 2 LR ammunition by email. I asked him if they measured the standard deviation of both MV and BC. He said they did. When I asked him to provide that data to me, he refused.
The only place I have been able to get this data is from testing Bryan Litz did in 2015 of 84 different “types” of 22 Long Rifle ammunition. Eley Tenex and Eley Match were considered to be two different types. He measured the standard deviation of both the MV and BC for 50 rounds of each type and published the results in his book “Modern Advancements in Long Range Shooting – Volume II”.
The chart below shows the total vertical spread for the data from Litz’s testing for a type that was ranked 8th out of 84. The mean MV is 1108 with an SD of MV of 5.2 and a mean BC of .155 with an SD of BC of .005. The two SD variations above and below the MV’s mean varied from 1097.6 to 1118.4 and the BC from .145 to .165. Temperature at 75 degrees and atmospheric pressure at 27.00.
Below is a chart that shows the spread due to variations in MV and BC and then the total vertical spread for each range in yards.
This chart illustrates that as the range increases the variation of BC becomes the significant factor in vertical spread. The skill of the shooter and rifle performance are a major factor in the overall vertical spread at 100 yards. If the shooter/rifle combination is capable of 1 MOA at 100 yards the total vertical spread due to MV and BC along with shooter/rifle 1 MOA is 1.12 inches. At 600 yards the overall vertical spread, when the shooter/rifle is capable of 1 MOA is also considered, the vertical spread only increases to 44.92 inches.
The variation in BC being the major factor at long range is only true for the 22 LR and not nearly as significant for the black powder era cartridges where the vertical spread due to variation in BC is not nearly as much of a factor. This is because they have a much higher BC than the small bullet for the 22 LR.
It would help those of us considering purchasing their products for 22 LR manufacturers to provide us with these four pieces of information discussed above so we could make comparisons based upon actual testing they have done.
The way to see if a new “long range” 22 actually performs better than another round at long range is to test each at long range. To do that we need to see how much of a vertical spread is produced when we fire a number of shots at long range. Shooting groups at short ranges tells us nothing about how the round will perform at long range. At short ranges, like 100 yards, the variations in MV and especially BC haven’t had time to do their thing. If the SD of the BC is large, there will be a lot of vertical spread at long range. Even a round that does not group well at short range may do well at long range if the SD of the BC is small.
The way to do this long range testing is to set up a target that is tall enough to catch all the rounds fired and fire at least 25 rounds to get a good look at the vertical spread. Keep in mind that the numbers in the chart above for total vertical spread are a 95% spread, that means 95% of the 25 rounds, 23.75 rounds, will be inside the two SD range and 1.25 rounds, on the average will be outside that range. Also, this chart does not include the capabilities of the rifle/shooter. So don’t be afraid to throw out one flier.
From Litz’s testing of 22 LR types he tested I can evaluate the data as discussed above and decide which ones I want to spend time and money on to do some field testing. Why should I purchase some rounds for testing when the manufacturer has the data I need which they should be happy to provide if their new round is as good as they say.
