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I've put a derivation of my equations on my website at cant
if anybody is interested.
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Well, I am...
A question, though. On that page, your unit vectors v (=no cant) and v'(=with cant) both start in the origin of your X,Y,Z coordinate system, right?
But when canting, i.e. rotating the bore around the sight line, the muzzle of the rifle (=the origin of your XYZ coordinate system) moves as well.
Going to extremes to show what I mean: if you have 2" between the bore and the scope, and rotate 180 degr, the bullet starts 2" ABOVE the sight line, not below.
So, yes, the Az and El angles change, but so does the location of the muzzle.
Or do you take this into account in another way?
[my wife just caught me looking at your pages and started complaining that I spend too much time on my work. No, Dear, I read this sinus / cosinus / vector dot product stuff for fun... ]