In this article, we will discuss the consistency of our speeds for long distance shooting practice.
Analyzing target groups remains fairly simple, but it gets more complicated when analyzing our speeds. And for good reason? This generally involves notions of statistics and mathematics that most of us are not comfortable with.
In this article, I propose to explain to you what is hidden behind these often misunderstood figures!
Some notions of mathematics:
During a series of shots, a chronograph will collect a series of speeds, this series will be continuously analyzed by the device in order to give us mathematical values such as the standard deviation (in English standard deviation), the maximum deviation (extreme spread), the average of the series, etc.
An example of the FX ballistic radar display from a rather remarkable series.
But what do these values correspond to?
The average (Avg Average in English) is quite simple to understand, the formula is also (sum of all speeds / number of shots). This value is used to configure your ballistic calculator. For the rest of the article and in math, we will use the µ sign to talk about the average.
Standard deviation is a more complex concept whose symbol in math is generally “sigma” σ, English speakers often refer to this value as SD or STD (Standard Deviation) and the simplified definition of standard deviation is as follows:
- In the speed interval [µ - 1σ ;µ + 1σ] are 68.2% of the values of the series
Example on a series of 100 shots whose average is 800 m/s and the standard deviation is 3m/s, then 68 shots have a speed between 797 and 803 m/s therefore in the interval [797; 803]
- In the speed interval [µ - 2σ;µ + 2σ] are 95.4% of the values of the series.
Example on a series of 100 shots whose average is 800 m/s and the standard deviation is 3m/s, then 95 shots have a speed between 794 and 806 m/s therefore in the interval [794; 806]
- In the speed interval [µ - 3σ ;µ + 3σ] are 99.7% of the values of the series
Example on a series of 100 shots whose average is 800 m/s and the standard deviation is 3m/s, then 100 shots have a speed between 791 and 809 m/s therefore in the interval [791; 809]
So the lower the standard deviation, the more "pointy" the curve and the better the regularities.
The extreme spread or maximum deviation is the difference between the highest and lowest speed.
Example on a series the fastest is at 808 m/s, my slowest at 792 m/s so my extreme spread is 16 m/s (808-792)
What level of regularity for what use?
Let's take an example, your goal is 100% hits on a 30cm high target at 800 meters. You shoot a 6.5 CM 140gr ELD M bullet (CB 0.326) speed 840 m/s.
How to determine the minimum standard deviation to achieve this performance?
Just use a ballistic calculator set in centimeters and not mils
The calculator tells us a fall of 538 cm at 800m to be centered on the gong
It now remains to vary the exit speed to reach the edges of the gong which for a gong 30 cm high are respectively 15 cm higher and lower, i.e. a drop of 538 + 15 = 553 cm and 538 - 15 = 523 cm.
By varying the exit speeds, we reach these falls at 800 meters with exit speeds of 830 m/s and 850 m/s.
What should we conclude from this? We return to the definition of the standard deviation.
- In the speed interval [µ - 3σ;µ + 3σ] lie 99.7% of the values of the series.
Since our average speed in the example is 840 m/s and we found our lower bound of the interval to be 830m/s then:
µ - 3σ = 830 m/s
So σ = (840- 830)/3 = 3.33 m/s
So you know where to place the cutter bar. A load with a standard deviation greater than 3.33m/s does not guarantee you 100% plate impact at 800m.
Please note that this is valid for this loading case, 3.33m/s standard deviation in ammunition such as a 308 in 168gr does not absolutely guarantee you 100% hits!
It's up to you to start your calculations! (Strelok and other apps on phones also give the falls in centimeters to do the same exercise)
Be careful, these calculations often give us a shock and we realize that we would have to move to a more efficient caliber to achieve it!
Please feel free to share this article with your loved ones.
Jeremy