Technical sight radius question?

[Buckeye 50]

Is there any evidence or research done that at least somewhat quantifies (or attempts to quantify/correlate) scientifically the length of sight radius and accuracy? 

What I mean is something along the lines of like, "For every inch increase (of sight radius -half inch, centimeter, whatever) groups average a .2" increase."

We all know practically and empirically, that the longer the sight radius the more accurate.

Thanks,

P

[sw.sharpe]

Assuming that a short barrel has the same ballistic accuracy as a long barrel - which it does not - I believe that a longer sight radius simply allows the shooter to better gauge the error in the pointing angle. I do not believe that there is an actual formula or equation that relates site radius to accuracy.

The sight radius represents a near-field (visual) projection of where the bullet will impact in the far-field. The error in the impact position is a function of the aiming angle from the true line of fire and takes the form Error=Distance x Tangent(Angle), where

Error = linear displacement from intended point of impact
Distance = distance from rear sight to point of impact
Angle = Deviation in pointing angle from angle required to hit intended target

For example holding 1-degree off of the point of impact will result in an error or displacement of 13-inches at 21 yards. A ¼-degree angle off of the point of impact will result in an error or displacement of 3.3-inches at 21 yards. As you can see, very small changes in the aiming angle will have a large influence on the displacement of where the bullet hits the target. The longer sight radius allows the shooter to better judge the point of impact.

[sqlbullet]

Assuming that a short barrel has the same ballistic accuracy as a long barrel - which it does not -

Just to be clear...All else being equal a stiffer barrel is a more accurate barrel.  And a shorter barrel is usually stiffer.  With a given load a given barrel may benefit from a few more or less inches to reach a specific point of bullet exit in it's harmonic vibration during firing.

The above statement seems to imply that longer barrels are more accurate, which is not true.

http://www.thetruthaboutguns.com/2013/10/daniel-zimmerman/the-truth-about-barrel-length-muzzle-velocity-and-accuracy/

http://www.6mmbr.com/barrelFAQ.html#24642

http://www.fieldandstream.com/blogs/gun-nuts/2014/04/barrel-length-shorter-better

There are numerous valid citations on the subject if you don't like those above.

As sw.sharpe correctly points out the real issue here is the ability of the shooter to align the sites.  The degree to which length will assist the shooter varies from person to person.  You could mathematically quantify the amount of variance in MOA at 100 yards for a given set of sites for a given length, but it would vary from one size of sites to another.