How do you calibrate a sight?  

The most straightforward way to calibrate a sight is to go to each range and shoot arrows, moving the sight until the arrows group in the middle. By noting the sight setting at each range it can be reproduced as required. This procedure is time consuming and requires still conditions for the settings to be reproducible.   

Some years ago somebody produced a sight chart which allowed all sight marks to be derived from just two accurately measured settings. How and why this chart worked was not explained but it seemed to. The attached note explains the theory behind the sight chart and gives an alternative way of performing the calibration process. For those more interested in fast results, the chart is shown below. As can be seen all the lines are straight and may be reproduced by calculating one point for each range and drawing a line from the origin to that point and beyond. By lining up the actual sight marks achieved by experiment with the corresponding range values, all the other marks can be read off from the chart.

Note that in this chart the measurements are made from the top of the sight. Although the sight markings are indicated in mm, since the lines are straight, any scaling may be used. For those who want to draw their own version the equation is

s = A*(80/R + R*(1 + 0.0025*R))