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Long Range Shots and first round hit probability

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From Brown Dog


The Error Budget’

Grouping ability at a given range is just one element of the issues to consider when attempting to guarantee first round hits . What's actually critical is realistic quantification of the distance between the POA and the probable POI of your first bullet. That distance is determined by a raft of variables known as the error budget.

The error budget in gunnery is extensive. Each element will affect the shooters capability to place his first shot near his POA:

Crosswind error
Rangewind error
Ranging error
Weapon cant
Weapon pointing error
MV variance
Round dispersion
Air Temp Change
Air Density variation
Angle of fire
Horizontal zeroing error
Vertical zeroing error
Sight resolution
Optical Path Bending

I shan’t consider each in detail, but it's worth observing that changing light conditions alone (ie Optical Path Bending or refraction) can move the POI vertically 0.5MOA (or left or right for a low sun).

Hit Probability and Error Discs’

Many sporting shooters fail to understand the error budget at play in hit probability and are unable to distinguish their hit probability from their ability to group.

Be clear: In shots at sporting quarry we are not talking about grouping theory or ability; we must concern ourselves with the theory of hit probability’.

As soon as you've fired your first "adjusting round" at a target you've directly measured the environmental effects; and can adjust subsequent shots accordingly…but we're not in that business with shots at game animals; the first round must have an acceptably high probability of killing humanely …- and thus first round hit probability has to be assessed realistically.

Lets say a 0.5MOA grouper at 100yds (many people mistakenly believe the group size-range relationship is linear, it is not.) prints his 0.5moa group half an inch off dead-nuts centre of his POA. His outermost round could be 0.75MOA from his POA. That's an error radius of 0.75MOA. His circular error actually subtends twice that: 1.5MOA. So, in hit probability terms, this 0.5MOA shooter actually has a circular hit probability that subtends 1.5 MOA -doesn't sound quite so cool does it?

At game animals we're in the business of guarantee; so let's round that 1.5moa to 2 moa to give ourselves an additional 0.25moa fudge factor around the tgt to allow for those 0.75moa group days

Thus, at a range the shooter can achieve 0.5MOA groups, his unadjusted hit probability actually spans a 2MOA disc over any given POA -before we consider wind!

Taking this eg to an A4 size kill zone at 400yds; firstly the disc only just fits, and secondly; you can't move it much laterally until it comes off the sheets: about 3.5"”

…..so you'd have to know your wind call is accurate to better than 3.5" of deflection to take that shot.

My Rifle Groups to 0.5MOA at 400yds, So I'm Good-to-Go with stalking shots at 400yds. Right?

You should now realise that considering your first round capability to be 0.25 MOA around your POA; because you can usually group to 0.5MOA is unrealistic in 'guarantee' terms.

Grouping ability is a measure of the rifle, not the shooter-rifle system's”ability to make first round hits under field conditions.

Once you consider the 'system' it is rarely realistic to guarantee field accuracy better than within 1 MOA of POA (ie a 2 MOA circle); and, at deer, we're talking 'guarantee'

….. and remember, 2 MOA is a guarantee level of within 1 MOA of POA, not "sometimes I can do 0.5MOA with my rifle at 400m on a no-wind range day".

How far is Too Far’?

As outlined earlier, a clever way of applying hit probability theory quickly is to visualise the killzone (as say, a piece of A4 in Landscape) and place your POA 1MOA in from the windward edge (ie even if the wind ceases, you still guarantee a kill-hit within your 2MOA system guarantee -in effect you are visualising drawing your 2MOA guarantee as a circle disc and fitting it inside the leading edge of the A4 sheet). Then determine go/no go by calculating how much wind will take any part of your 2moa 'guarantee disc' out of the leeward edge of the A4 sheet -and deciding whether you have the wind more accurately than that all the way to the target.

Pretty soon you'll realise that it's not a 'strong gust' that'll mess things up; hunting at long range it's as little as being out by a few mph on your wind call; or not noticing a wind change of only a few mph.

In order to quantify this, think of wind in terms of "inches of deflection per 1 mph change".

For example; a 308 at 400yds:

A 10mph wind will push the bullet around 14” at 400yds.

This means every 1mph change pushes the bullet 1.4 inches at 400yds.


Even if you are capable of grouping with a 308 to 0.0001MOA at 400 yds (and you won't be),

for every 1 mph you misjudge the wind, you will miss your POA by 1.4 inches .

Miss a 5mph wind change and your bullet goes 7 inches wide of the aiming point. Miss a 10mph change and you’re 14 inches wide.

...and that's forgetting the natural dispersion of your group compounding the error.

In Closing:

If an individual considers their deflection-per-mph-wind-change at a distance they're considering; add that to their error disc at that range and then compare that to the size of the animal's kill zone, they should quickly get an idea of what their max range should be, based on their wind reading capability.

And if anyone is claiming first round wind reading guaranteed better than to the nearest 5-10mph over unknown and broken ground they're ...err.... kidding themself.

It doesn't take much to get blown out of an animal's kill zone.

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