Gun sighting equation and trigonometry

Factual Questions
1

There is an equation for aligning the rear sight of a firearm. The rear sights can be moved left or right.

The movement = (error/distance)x(sight radius)

Error=the distance between the point of aim and the actual place bullets go.

Distance=length to target.

Sight radius=distance between the front and rear sights.

I can see that a right triangle is created by the muzzle to the gun, the bulls eye and the place where bullets actually hit. Given opposite/adjacent, the equation gives the tangent of the angle between bulls eye and actual place where bullets go.

Why the sight radius? I see that it preserves units, and presumably gives us a sine to change the tangent into an x coordinate, but it is along the the distance to the target.

I hope someone better at trig than I can explain it.

2

Don’t see what’s puzzling you. The rear sight moves in a straight line, perpendicular to the muzzle? If so, two similar triangles: front sight to bullseye to where the bullet hits, and front sight rearward along the barrel centerline, then right-angle to the rear sight.

3

Eureka!

Thanks, Timz.

I love the ‘Dope.

4

I should have thought a little more. We’re assuming the bullet goes where the riflebarrel is pointed, so the above similar triangles aren’t right.

5

I think our error is the way the barrel is situated in relation to the rest of the gun. The barrel forms an arm of the triangle, we must adjust the sight to follow the same (similar) arm.

6

Think of it as correction = error x ( sight radius/distance ).

There are two similar triangles,

  1. the triangle to target, with error at the far end.

  2. the triangle with the sights and the sight radius, with correction in the place of error.

If the error is 1 metre ( = 1000mm) out at the target, but the sight radius is a 1000th the distance to target, the adjustment of this sight is a 1000th the error, ie, 1 mm.

7

Known as “windage.” The rear sight can also be moved up or down, known as “elevation.” At least, that’s how things were on my competition rifle, with iron sights.

Does elevation affect your formula? If so, how?

(I know nothing about trigonometry, and very little about equations, so my question might seem dumb, but I do know how to sight in a rifle. Maybe I knew both of those without realizing it.)