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Circular error probable/R50

Davo308

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Full Member
Minuteman
Feb 18, 2019
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I came across this passage while reading up on the K31 rifle...

Karabiner Model 1931s are noted for their excellent accuracy and quality for a service rifle. The Swiss armed forces considered individual marksmanship to be of utmost importance. Therefore, the K31 was made with tight tolerances and excellent overall craftsmanship. According to the Swiss Military manual for the Karabiner Model 1931 using standard issue 7.5×55mm Swiss GP 11 ball ammunition in a fixed mounting the expected accuracy of fire at a range of 300 m (328 yd) is 4 cm (2 in) (R50) in the horizontal (windage) axis and 6 cm (2.4 in) (R50) in the vertical (elevation) axis. Accuracy of fire at a range of 1,000 m (1,094 yd) is 21 cm (8 in) (R50) in the horizontal axis and 43 cm (16.9 in) (R50) in the vertical axis. R50 at a range means the closest 50% of the shot group will all be within a circle of the mentioned diameter at that distance.[3] The employed circular error probable method cannot be converted and is not comparable to US military methods for determining rifle accuracy. For reference a 1 minute of arc (MOA) circle at 300 m (328 yd) has a diameter of 8.72 cm (3.4 in) and at 1,000 m (1,094 yd) has a diameter of 29.08 cm (11.4 in). When the R50 results are doubled the hit probability increases to 93.7%.

That led me to CEP... https://en.wikipedia.org/wiki/Circular_error_probable

I think Im grasping the basics of the idea, its also covered in Brian Litz's books, and have seen it in ballistic simulators but I still have a few questions.

Why use R50 (50% of shots within x distance from center)? What about R97, etc? What value would be most useful for long range shooters?

And how does one go from CEP to calculate "hit probability"?

Thanks in advance, Im just trying to wrap my head around this.

Also found this site... http://ballistipedia.com/index.php?title=Describing_Precision