There is a science behind judging distances, we will get to that at the end. Seeing as most people like examples first, here is my “delightfully” freaky hand drawing, no art prizes expected!
Put your arm out in front of you as far as possible, then bend your fingers so that they are visible, (a bit like the freaky hand picture)
You are going to see that certain parts of your hand can be used to legitimately gauge distances.
However, there is a wrinkle in the plan!
If you are trying to accurately gauge distances with this method, you need to know what is the size of the Target you are trying to gauge the distance to.
Now this is not so bad, you may (should) become familiar with the target faces you are shooting and how high they are. You may also become familiar with the height of the back stops.
You could use the width of an average tree stump. A bit of practice is needed.
So here is an example, if i look at a standard target butt (42” high).
I put my arm straight out in front of me, pointing at the target, bend my fingers so that they are visible and place the fingers so that they obscure the distant object.
If the distant object is just covered by all 4 fingers (1st Joint) then the object is 10 yards away!
If the distant object is just covered by 3 fingers (2nd Joint) then the object is 15 yards away!
If the distant object is just covered by 2 fingers (1st Joint) then the object is 20 yards away!
If the distant object is just covered by 1 finger (1st Joint) then the object is 40 yards away!
Hang on, where is 30 yards?
I can gauge 30 yards from putting my thumb up. (Tip of thumb to joint)
Mileage may vary! You and I are guaranteed to be different, you may have hands that escaped from Frankenstein’s coffin or little dainty things, you need to do a bit of self discovery.
Ready for the science (and history)?
Thales (c624BC – c547BC) is often considered to be the first mathematician because he was the first person (we know of) who looked for non-supernatural reasons for phenomena. He is also credited with measuring the pyramids in Egypt. His method is interesting because it does not involve a brute force use of measuring instruments, i.e., get out measuring rods and send people up the pyramids with them. His proof is more elegant than that. He measured the height of a slave (I do not condone such practices, unless the participant is willing) and when the sun was such that the length of the shadow of the slave was equal to his height they measured the length of the shadow of the pyramid. From this shadow the height of the pyramid could be found.
Using Thales method, we can find the wanted distance if we know the distance from the dominant eye to a measuring item (i.e. sight ring, scope, arrow rest, etc) placed on the bow (or your hand), called d, which width is called a, and the width of the size of what you see on the target, called A.
The relationship between these elements will give you the distance to the target, called D, by simply applying the relationship :
a / d = A / D
a = the height of your thumb (for example)
d = distance from your eye to the thumb
A = height of Target you are trying to gauge the distance to
D = Distance to target
You need at least 3 of the 4 values to work out the unknown.
Food for much thought!