Quoted: For shamayim's theory to be correct, the nominal rear sight height would have to be higher than the nominal front sight height.
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The nominal rear sight height (as measured over the bore) is higher than the front. That isn't in doubt. You always have to tip the barrel up to give the bullet a positive trajectory to counteract the effects of gravity.*
Quoted: This would make zrxc77's exagerated drawing correct, as well. This explanation also assumes that the over-bore axis nominal height of the A2 rear sight is the same as the A3 CH's sight.
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The drawing was specifically intended to illustrate a possible need for different front sight heights between rifles and carbines even when the rear sights are the same height. Don't confuse the drawing with the fixed/detachable carry handle question. For the sake of clarity and simplicity, assume that both the rifle and carbine pictured in the diagram are both fixed carry handle A2 style uppers.
Quoted: If, OTOH, the rear sights are different heights - that is the only reason for the front sight post to be higher.
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I disagree. Sight geometry (as illustrated) and trajectory differences caused by the change in velocity with barrel length (as scottryan emphasized) are also possible reasons for different front sight heights.
Regarding shamayim's contention and those who dispute it, I think a couple questions need to be answered before one could judge the merits of the conflicting views:
1. How much does the need to raise the carbine's front sight due to simple geometry considerations compare to the need to lower it due to velocity induced trajectory changes? I believe I could figure out a reasonable estimate of the change required by the geometry, but I don't have a ready means to calculate the change required by the trajectory differences.
2. Is the net change in height from question one large enough to warrant a change to the FSB, or would it fall within the normal adjustment range of the front sight post?
Quoted: This is relatively easy to figure out. Who has the correct measurements?
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You would think so, wouldn't you? But in the year and nine months I have been lurking here I have yet to see an unequivocal, absolutely indisputable resolution of this question. I am relatively new to firearms, but I have already seen that there seems to be a distressingly large amount of this type of confusion in the firearms field in general. There is too much speculation and too many people (myself included) with too many opinions, but not enough unassailable fact. I don't know why this is, but it is what I have observed.
* Assuming the nominal case where your target is at the same level as you. In other words, you aren't shooting downhill at a target below you.