Maximum range of pellets fired from a shotgun

A mathematical model to determine the maximum range of pellets fired from a shotgun has been suggested. It has been assumed that the air resistance experienced by a pellet is proportional to the square of its velocity (?μV²) where $\text{μ =}\text{A}\text{C}$ with

$\text{C=0.061}\text{86}\text{N}{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}$

and

$\text{A=}\text{1}\text{[17 696+2N+10 000(0.2?d)]}$

N is the number of pellets/ounce and d is the diameter of the pellets in inches. A method for calculating the maximum range has been suggested, and the values obtained for Buck 00, size 8 and size 9 American pellets are very close to the reported experimental observations. The maximum ranges for other sizes of pellets have also been calculated. The angle of projection decreases with increase in velocity and increases with increase in the weight of the pellet. It varies between 26° to 32° for common sizes of pellets and standard shotgun velocity. The maximum range in air is only 1 – 3% of the range attained by a pellet in vacuum.