Consider a “normal” arrow shot at an 122 cm archery target set 70 meters away. What is the margin of error in aiming to hit the ten-ring?
The 10-ring is 12.2 centimeters wide. A “normal” arrow we will define to be 71 cm long (28˝) and viewed from the shooting line it protrudes from roughly the shooting line 71 cm in the direction of the target. Wherever the rear of the arrow is held, there is a circle at the tip of the arrow, which if the arrow tip is there when the arrow is launched, the result will be a hit in the 10-ring. So, how big is this circle?
This is a simple calculation. the 71 cm (0.71 m) distance the arrow point is from the shooting line will have a diameter of 0.71 m / 70 m times the 12.3 cm diameter of the 10-ring at its tip. This circle turns out, when the calculation is done, to be 0.00122 m or 1.22 mm (0.05˝) at the point of the arrow. If the archer is holding in the exact center of that circle, he/she has just half that distance to the edge, or 0.61 mm (0.024˝ … that’s 24 thousandths of an inch), to an aim point that will be in the 9-ring.
This is an incredibly tiny margin of error and shows the accuracy of Olympic and World Champions to be truly outstanding.