What is the maximum range?

When the sight pin or the target is obscured by the arrow it is not possible to get an accurate sight mark and this defines the maximum practical range for that combination of arrow, bow and anchor set-up.  By studying the sight calibration equation a relationship is derived which gives the maximum range defined in this way.  For the specific case of an arrow length of 0.75m and an arrow speed of 60m/sec the maximum range was found to be

    200*(sqr(1+9.8q)-1)

where q is the eye to nock separation.  Clearly the larger the q the greater the range achievable.  By anchoring under the chin q = 0.13m approximately and the range is 101m whereas anchoring on the cheekbone q = 0.05m approximately and the maximum range reduces to 44m.