# 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

Filed under For All Coaches

### 8 responses to “Margin of Error”

1. Pieter Mogree

Hi Steve,
Very interesting to see how accurate one has to be hitting the 10-ring. But something is wondering me. If I do the calculation, as you describe, I get an answer saying 0,0123 m or 12 mm. If right, it makes hitting the 10 a litle bit more human after all.

Kind regards, Pieter

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• Hi, Pieter, maybe I did the math wrong. I tend to do these things roughly, to get a rough answer, before I pick up a calculator and sometimes this leads me astray. In simple form the tip of the arrow is 0.7 m from the shooting line. The target is 70 m from the shooting line, that is a ratio of 1 to 100. The 12 cm circle at 70 then will appear 100 times smaller at 0.7 m and 1/100 of 12.2 cm is 0.122 cm or 1.2 mm. This corresponds to a comment Rick McKinney made regarding that circle at 90 m in which he said the margin of error was about 1/16 of an inch.

Is this not right? Maybe I typed the numbers wrong in the post. I will check them and correct them if I did something wrong.

Yep, I listed the arrow as being 0.071 m long, when it is 0.71 meters long. And that would have made the calculation 10X too small … if I had used that number, which I hadn’t, it was just a typo. The numbers have been corrected. So, using the correct numbers, am I still making a mistake?

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• Pieter Mogree

Hi Steve,
I better like the way you describe your math calculations in the answer. So then, efter getting the comma at the right place, the calculation is giving me the same value as you statet in the post. Well, no way around, my students have to work on a strong shoulder & bow arm the comming Christmas days!
/Pieter.

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• What I find even as fascinating is that humans can shoot, for short stretches, better than a shooting machine at this task. A lot of people think that if a shooting machine is used, all of the arrows get packed into the 10-ring, if not one long sequence of Robin-Hooded arrows. This is not the case. Anyone with real world experience will tell you that even with a shooting machine, a great deal must be done to match the accuracy and consistency of an elite archer. One of the more difficult aspects is to stabilize the machine itself. There is enough jarring during a shot that the machine will change positions from shot to shot, so sandbags or some such are needed. Careful positioning of the bow from shot to shot is needed. The bow needs to be tuned to the machine, etc. Once set up such a machine shows admirable consistency while humans had more variability day to day. But, when the humans are “on,” they can beat the machines. (John Henry would be proud.)

I am reminded of a compound unlimited shoot-off I saw at a novelty shoot in Oregon. The target was 101 yards away and the max scoring circle was no more than eight inches or so across. A three-way shoot-off was reduced to two but those two kept hitting the central dot. So, A three-inch colored dot was placed in the center of the central dot and a single arrow, closest to the center final decider was made. The first archer shot and just missed that three-inch dot. The second archer hit it dead center. I knew both of those archers (one only by reputation) and yes, they were that good.

From our viewpoint the aperture is never still, but the arrow points hover around the centers of those little circles so that we are not far from perfect.

On Mon, Dec 18, 2017 at 8:39 AM, A Blog for Archery Coaches wrote:

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2. Ian Kershaw

Hi … I know that 1/2 degree out of line at 70m is off the target. I don’t really do very much maths any more!!! I wouldn’t want to burden my archers with any of that, add in a little wind and poor alignment …. poor shot execution … I might be spending more time on motivation and curing target panic than I’d like to be doing!!!

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• This is a blog for coaches, not archers. And I am never in favor of providing archers with information that does not help them. So, for example, I think it is counterproductive to talk to archers about the muscles used to make shots. We do not consciously select the muscles we use for any physical activity, so that information has no value for archers … but it may help coaches when they have to improvise activities to help their archers “use the right muscles.”

Consider this background information for coaches.

On Tue, Dec 19, 2017 at 7:39 PM, A Blog for Archery Coaches wrote:

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3. Ian Kershaw

I agree totally, Steve. Only give them as much information as they need to know and understand it to improve their performance. Too much to think about as they are going through their shot process is not good at all.
Merry Christmas, a Happy and prosperous New Year to all the Coaches out there.

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• And to you my friend!

On Wed, Dec 20, 2017 at 6:07 PM, A Blog for Archery Coaches wrote:

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