Tag Archives: archery physics

Margin of Error

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.

Outside Ring Diameters on FITA Targets

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Q&A How does arrow length affect the point on distance? Will a longer arrow increase the point on?

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I got this question from “Ken” on the blog.

First Some Background
The “point-on-target distance” or “point on” for a barebow setup is an indicator of the power or “cast” of the bow-arrow combination. Powerful bows have longer point ons than weaker ones and heavier arrows result in closer point ons than lighter ones. Beware! There are a whole host of other factors that are involved. I give you the example of a compound archer who cranked his draw weight down by one whole turn on each limb and got an increase in point on! The reason was that the adjustment in draw weight, while making a less powerful bow, created a better spine match with the arrow, resulting in better energy transfer from bow to arrow (a greater % of the energy stored in the bow ended up in the arrow), offsetting the lower draw weight to create more cast and a farther point on.

So, point-on-target distance is determined by a great many factors: the question is about the effect of arrow length. Any such discussion has to occur assuming all of the other factors stay roughly the same, otherwise we will end up talking about those effects and not just the length of the arrows, so point weight, fletching, spine match with bow, all must be ceteris paribus. (How’s that for classy language? So, you don’t have to look it up, it means “all other things being equal or the same.”)

So, Now the Question
How does arrow length affect the point on distance? Will a longer arrow increase the point on?

Actually the reverse is true; a longer arrow will decrease point on. Here’s the reasoning: since the arrow is slanting upward (arrow nock is near the anchor point which is below the eye line, arrow point is on the eye line, (also called the line of sight), the longer the arrow, the lower one must hold the bow to get the arrow point onto the sight line (the eye is looking at the point of aim). Think about being at full draw with a normal arrow, lined up with a point of aim (POA), and then magically the arrow grows three inches. Since the arrow is slanted upward, the point goes outward from the bow and upward above the line of sight (since the behavior of the arrow is being held constant so it will fly in the same arc as the shorter one, you must lower the bow to bring the point down onto the line of sight. If the bow is held at a lower angle, the distance of trravel is reduced.

So, for an indoor setup, in which most bows have too much cast, one is left with either a POA on the floor or a large crawl if stringwalking. Many archers switch to a much longer, much stiffer arrow (about one spine group stiffer per extra inch of arrow). This gives a shootable arrow (with roughly the same dynamic spine as the shorter one) with a much higher POA (hopefully on the target or very near it) or smaller crawl. Some are so adept at this that they can create a point on equal to the target distance.

Outdoors the situation is the reverse; there is no such thing as “too much cast/bow power.” Since the targets mostly are farther away, you want a shorter arrow, correctly spined, and as light as possible to give a POA down near the target and not up in the trees.

The Short Answer
So, longer arrow, closer point on; shorter arrow, farther point on.

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