There are a large variety of variables that can result in misaligned sights on an AR, making diagnosis and detection a difficult process.

EDITED TO ADD:  Pictures
Please note:  These pictures are do not represent defective or misaligned product, they are just meant to be helpful illustrations of the specific parts of the rifle.

The front sights are mounted working off aligning the index pin that is installed into the barrel extension.  This index pin will represent the Top Dead Center (TDC).  The center threaded bore of the front sight base (where the front sight post is installed), is lined up with the index pin to properly install the front sight base.  Provided the bore is perfectly straight and the threads for the barrel extension are perfectly square, you will have a perfectly lined up barrel assembly.



Here is where it can get messy:
Looking at a upper receiver, if the index slot for the index pin is not machined perfectly on the center to hold the index pin at center, your front sight will be canted to one side.




For a flat top upper receiver, if the 1913-Pic rails that will hold your iron sight (at the position your iron sight is mounted) are not lined up parallel to a perfectly aligned index slot your front and rear sight alignment can appear canted.

Because rail mounted iron sights actually index off the right side of the flat top 1913-Pic rail, if that side of the rail is machined to thick or thin or the geometry is off, that will result in misalignment of the sights.




If the hole drilled to hold the rear sight aperture assembly (on a A2 or various BUISs) is not drilled on perfect center, that will result in misalignment of the sights.



If the hole in the rear sight aperture itself is not machined on perfect center, that will result in misalignment of sights.



So there are really a lot of variables to look at.  Some will affect the sights more than others and some are easier to identify and isolate.  

Originally Posted By Tweak: One thing I would like to make clear (you asked Paul ) is that even if all parts are correct your sights can still end up misalined. The slop between the index pin and its slot is enough to effect the windage, the error gets larger as the sight radius gets shorter. This is why Sam recommends boresighting WHILE tightening.

Originally Posted By Tweak: the amount of torque has nothing to do with the barrel alinement. you can boresight while installing the barrel or correct the alinement on the range with a no mar mallet but lucking into a acceptable alinement is rare except with the best parts.

Ok, with a set of assumptions could the Mil-Spec information be extrapolated to give us a guide line for the allowable adjustment that is “with-in spec” ?

For the 20” M16 (Rifle length gas and sight radius), using  M16A2 – MIL-R63997B
Assuming a 2” group
Assuming 1 click = ½ MOA
You get the initial +/- 5 clicks
Plus the 9.6 clicks to adjust a shot that is on the width of the target (as defined in D from the table -11.6”W), left or right to adjust the POI to POA.

That would leave you with approximately 14.6 clicks of adjustment for zero



For the M4 (Carbine length gas and sight radius), using  M4A1 – MIL-C-71186
Assuming a 2” group
Assuming 1 click = .68 MOA
You get the initial +/- 12 clicks
Plus the 10.3 clicks to adjust a shot that is on the width of the target (as defined in D from the table -14”W), left or right to adjust the POI to POA.

That would leave you with approximately 22.3 clicks of adjustment for zero

.

Do you have a picture of this?  I'm not sure how to line a stubby pin on one end of the barrel with an elevated hole at the other.
ETA: Are you using a hollow rod over the pin and a solid rod in the front sight base and then aligning the two?

With the m16 or ar15 you have a battle sight zero and then a true zero.  with the m16 the trajectory of the bullet is the same at 36 yards and 300 yards.  With this you can set your sights to your true zero.  you have a elevation adjustment on your front sight and a left and right  "windage adjustment" on the rear sights.  as you sight in your weapon adjust your front sight for up and down and rear sight for left and right by using the knob on the right. don't worry about the tick marks on the back of the rear sight until you are done sighting in your weapon. afterward use it for windage.  With the windage knob you can get your battle sight zero which is what your weapon zeros at taking wind and distance into account.

Hope this helps.  My recruits usually took an entire week to understand this concept.

I agree with you exempt for the above statement.

The holes for the apertures are not both drilled centered, but off set from each other/center for a reason.  When you flip between the small and large apertures, they entire sight  aperture piece will rotate either left or right on the windage threads due to the threads, and if the offsets between the holes are correct, you will not lose zero.

And agreed, hand tighten the barrel nut only and confirm that you have bore sight zero that same as a barrel sight zero from the start before tightening the barrel nut farther.  At that stage, you can either Pepsi can made shim the trunion pin in tight to the upper receiver barrel socket slot for a solid fit between them (less likely that the barrel will slip in the upper socket when the barrel nut is tightened correctly), or if corrections are needed (as in the case with the upper socket slot not centered), enlarge the slot, and again, Pepsi can shim the pin tight into the slot.

But will add, before installing any barrel, confirm that the barrel extension pin and FSB/Gas port are all set TDS together. If they are not, then you are fighting a losing battle.  You may be able to shim/set the barrel for the FSB to be correctly indexed, but this will cause the barrel extension feed ramps to be canted, and if bad enough, will not allow the bolt lugs to enter and exit the barrel extension with binding.

If theres any paly at all I always shim it and im always able to zero in 3 to 5 clicks.

Great info!

Does anyone have a link for a how to do the "Pepsi can shim" for me? I have a BCM upper flat top and a FN manufactured barrel assembly. There is just a bit of play from left to right when inserting the barrel extension/index pin inside the receiver slot. Under torque, for tightening the barrel nut I can easily see the barrel rotating toward the right, giving a slight cant, when looking from the bore to the receiver. When I hold the barrel at it's left most position inside the receiver slot wall, again looking from the bore toward the receiver, then hand tighten the barrel nut, the FSB is then aligned perfectly. I need to make sure the index pin and barrel assembly cannot rotate to the far right wall slot under torque. Thanks for the help!

Small sliver shim between the side of the barrel extension pin to the upper receiver barrel socket U slot side wall.


But have said this, it easier to just slip the entire barrel in the upper barrel socket after the barrel nut is tighten correctly to rotate the barrel with FSB attached back to the needed index instead.