Simple Math for Marksmanship

I like shooting with iron sights.  Unfortunately my eyes quickly get tired from trying to focus on small targets in the distance which makes progress difficult.  There are a few things involved:  distance, the size of the target and the color of the target and its background.

The range I usually go to has a 50 and 100 yard line to shoot from.  I want to use the 100 most of the time, but I can work on the 50 yard line longer before my eyes are too worn out.  To help myself I decided that I should change the target from the zeroing targets the range gives out to something easier on my eyes.  The problem is that I don’t want something huge (really easy to hit).  I want a target that will sit on top of my front post and be about as wide, I also want to be able to clearly see it.

So at 100 yards how big does the circle need to be to appear to be the width of my front post on my rifle?  Turns out the answer is about 9 inches.  But how did I get that?

Simple: similar triangles.  First, lets set up the parts we need to know:

The values we are working with are:

• Size
• Distance
• Angle

In the first triangle we will use the rifle so the values are:

• Size=.05 inches for the front sight post (your post might be different – go measure it)
• Distance = 20 inches from the eye to the front post (your rifle might be different – go measure from your cheek weld to the front post)

We need to find the angle.  To get the angle we divide size by distance. So the angle of the triangle is .14 degrees (small).

Now for the bigger triangle we know the Distance and Angle.  To find the size of a target that will sit on top of the front post we multiply the tangent of the angle by the distance (tan(angle)*distance):

• Distance = 3600 inches (100 yards)
• Angle = .14

So a target that is the size of the front post at 100 yards (3600 inches) will be 9 inches in diameter (if it is a circle). 

So if I want it to be roughly half the size of the front post a 4.5 inch circle will work.  I should mention that as you do this for yourself you need to keep your units the same.  So if you want to make a target for 300 yards you’ll have to convert yards to inches (10800).

The next question is what color?  Black on a white background would be great, unfortunately I wouldn’t be able to see where I hit.  Red, green or blue might also work.  I’m not sure about yellow?  I’ll have to experiment to see.

I can probably buy a book of targets that are already the right size.  But what fun would that be?  A program like Publisher or PaintShop will let me make whatever I want.  I can customize it to my heart’s content – grid lines, faces, shapes, different colors, etc.  We’ll give it a try this weekend and see what happens.