I understand this one
You are thinking of lines that are one or two minutes of angle long. You are correct in that a 100 yard MOA line is twice a 50 yard line. But groups, especially shot with more and more rounds, are not lines, not one dimensional. They have length and width/diameter.
A minute of angle at 50 yards is roughly one half inch. So.....take a pencil and draw a square that is one half inch on a side. A one minute of angle square. A one MOA group shot at 50 yards must fit inside that square.
Now......one MOA at 100 yards is roughly one inch. Draw a square with one inch sides. Compare the two squares. The 100 yard square is four times the size of the 50 yard square.
and thank you for helping me understand I shoot 4 times whorse then I thought I did .
This one just makes my brain hurt
Since groups are often roughly circular when they are shot, another way to look at it is to think of a small circle that is, let's say, two MOA in diameter, and take the area of one for 50 yards and one for 100 yards. Two MOA at 50 yards is one inch. At 100 yards it is two inches.
The formula for the area of a circle is A = 3.14 x r^2. So....the area of the little circle at 50 yards is A = 3.14 (0.5)^2 or 3.14 X .25 = 0.785 sq.in
Do the same for a two MOA circle at 100 yards. It'd be two inches wide. The radius is one inch. One squared is one. So the area of that two inch diameter circle is A = 3.14 X 1 = 3.14 sq.in.
Compare the two areas. The 100 yard circle has four times the area of the 50 yard circle.
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