HOW IT WORKS, PRINCIPLE BEHIND THE TANGENT SIGHT OF THE AKM

 

HOW IT WORKS, PRINCIPLE BEHIND THE TANGENT SIGHT OF THE AKM

You know there is a match behind the working of the tangent sight of the AKM. Let us dive into it, there are three parts of the trajectory of the any rifle projectile. They are called as First Zero, The Apex, Second Zero.

Because the sight sit above to the axis of the bore and the barrel is rifle is slightly angled upward, the bullet travels in an arc twice.

·       First Zero: The short-range point (usually between 25 and 50 yards), depending on the caliber and scope height) where the bullet first crosses the line of sight while travelling upward.

·       The Apex: The highest point of the bullet’s arc, which occurs roughly halfway between the first and second zeros.

·       Second Zero: The longer-range point (often 100 to 200 yards) where the bullet drops back down through the line of sight.

To determine exactly where your first zero falls based on your specific ammunition, bullet weight, and ballistics, use a trajectory calculator like the one provided by shooter’s calculator to estimate your near and far zeros.

The Tangent Math Behind It:

            To hit a target further away, the barrel must be angled upward so the bullet flies in an arc (parabolic trajectory) and intersects the target. The math governing this relies on a right-angled triangle formed by the rifle’s geometry.

Let’s breakdown the geometry:

·       Opposite side (OPP): The required rise of the rear sight notch.

·       Adjacent side (Adj): The fixed sight radius (distance between front and rear sights).

·       Angle (Theta): The angle of the elevation needed to hit a specific distance.

The trigonometric equation applied is: tan (theta) = Opposite side / Adjacent side.

To adjust the rear sight so the bullet hits a target at distance D, the sight slider must be moved to raise the notch by Opp. By rearranging the formula, the exact height required is:

OPP= Adj / tan (theta)

Why a “Curved” Ramp?

If bullet drop were perfectly linear, the sight ramp could be a simple straight wedge. However, because gravity accelerates the bullet in a parabolic curve, the relationship between the distance (D) and the required elevation angle (theta) is non-linear.

The curve cam underneath the sight leaf is precisely shaped to mirror the tan(theta) curve. As the shooter slides the sight forward for greater distances, the curvature physically elevates the notch at an increasing rate to perfectly account for the bullet’s drop over the specific range.

Here is the step-by-step mathematical calculation to find the target distance based on the physical elevation of an AKM rear sight.

For this example, let us assume the rear sight slider is raised to a physical height of h = 3.3 mm (0.0033 m).

1.     Identify Given Values:

First, we list the fixed physical constraints of standard AKM firing a 7.62 x 39mm round:

 

·       Sight Height (h): 3.3 mm = 0.0033 m

·       Sight Radius (r): 378mm = 0.378 m (The distance between front and rear sights)

·       Muzzle Velocity (V₀): 715 m/s

·       Gravity (g): 9.81 m/s²

 

2.     Calculate Sight Angle:

We use the inverse tangent function (arctan) to find the mechanical elevation angle (theta) created by raising the rear sight.

 

Theta = arctan (h / r)

 

Substitute the numbers into the equation:

 Theta = arctan (0.0033m / 0.378 m)

 Theta = arctan (0.008730)

 Theta Approx. 0.00873 radians (Approx. 0.50 degree)

Calculate Ideal Distance:

Next, we plug the barrel angle (theta) into the standard physics range formula. This calculates how far the bullet travels before gravity pulls it back down to earth in an ideal vacuum.

4.     Adjust for Air Drag:

In the real world, air resistance drastically slows down the bullet. A standard 7.62 x 39mm bullet loses speed quickly, causing it to drop much shorter than the ideal vacuum distance. To get the actual distance, we apply a ballistic drag coefficient reduction factor (f _drag), which reduces the ideal distances by roughly 67% at this range.

 

The total calculated target distance for a rear sight elevated by 3.3 mm on an AKM is 300 meters.

 How the Tangent sight works?

The AKM tangent sight works by adjusting the height of the rear sight, which causes you to tilt the rifle upward when aiming, even though the barrel itself does not move. You are correct that the sight is placed above the bore axis about 2 inches higher. The rear sight consists of a pivoting leaf with a sliding adjustment bar that moves along grooved graduations marked 100-1000 meters. When you press the slide catch and move the adjustment slider forward along the leaf, you are raising the rear sight notch higher. Since your eye must align the front sight post with this higher rear notch to aim properly, you naturally have to point the entire rifle including the barrel slightly upward. This upward tilt changes the barrel’s angle of elevation relative to your line of sight, which compensates for bullet drop over longer distances.

The term “tangent sight” comes from the mathematical relationship: the sight graduations are calculated using the tangent function from trigonometry, where tangent = opposite / adjacent (the height you raise the rear sight divided by the sight radius between front and rear sights), which corresponds to the elevation angle needed for each specific range.

When you set the AKM’s rear tangent sight to 700 meters, you are raising the rear sight notch significantly higher than its normal position. Because the rear sight is now so much higher, your front sight post will appear lower in your field of view, and you would not be able to align them properly unless you tilt the entire rifle upward. After shouldering the rifle, you naturally need to raise it slightly so that your eye can see through the elevated rear notch and align it with the front sight post. This upward tilt of the rifle is what actually changes the barrel’s angle of elevation. Pointing it higher so the bullet can travel the longer distance to 800 meters before dropping back to your line of aim. The slider is positioned so that the left side of the cylinder aligns with the 800 line for that setting, and once aligned, you aim dead center of your target at that distance. This is the fundamental principle behind how all tangent sight work: raising the rear sight forces you to raise the barrel to maintain sight alignment.