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Dispersion of Arrows

In 1943 Dr. Hickman became interested in comparing the dispersion of arrows with that of rockets and shells. He requested Mr. C. J. Weese to shoot a number of arrows at 40 and 60 yards and to tabulate the arrow deflections, right and left, up and down, in inches so that he could express the dispersion in ballistic terminology.

There are several ways of expressing the dispersion of projectiles. One method is to give the Mean Deviation. The lateral deviation is obtained by adding all the deviations, right and left, and dividing by the number of shots. The vertical deviation is obtained by adding all the deviations, up and down, and dividing by the number of shots. The army usually expresses the deviations of projectiles in terms of Standard Deviation, The lateral standard deviation is obtained by adding the squares of all the deviations, right and left, taking the square root of this value and then dividing by one less than the number of shots. The standard vertical deviation is obtained in like manner. Others prefer to express the deviation as the probable error. The probable error deviation is equal to .674 times the standard deviation. The meaning of probable error is that half of the rounds shot will He in a band which has a width equal to double the probable error. This applies to both the lateral and vertical dispersions.

The dispersion may be expressed in linear units of length or it may be expressed in terms of a ratio of the dispersion in linear units to the distance to the target. The latter method is the one unusually used. The unit used is the mil. This ratio is 1/1000. It means that the deflection is 1/1000 of the range, i.e. one foot for 1000 feet or one inch for 1000 inches range. Ranges are usually given in yards for projectiles so that in this case one mil of dispersion means a deflection of 1 yard for each 1000 yards of range.

The table gives the data as recorded by Mr. Weese and tabulated by Dr. Hickman. Twelve shots were made at both 40 and 60 yards.

DEFLECTION OF ARROWS
Shot by Mr. C. J. Weese.

 40 Yards 120 Ft. 1440 In. 60 Yards 180 Ft. 2160 In. Lateral, in. Vertical, in. Lateral, in. Vertical, in. Shot Right Left Up Down Right Left Up Down 1 4.2 . . . . . . 3.0 . . . 1.5 .9 . . . 2 2.0 . . . 2.0 .5 . . . .9 . . . .5 3 2.9 . . . . . . . . . . . . 5.9 2.9 . . . 4 1.9 . . . .5 . . . . . . 8.0 . . . 3.0 5 .0 . . . .5 . . . 7.0 . . . .7 . . . 6 .5 . . . 2.0 . . . 6.2 . . . 5.7 . . . 7 1.5 . . . 1.0 . . . 5.7 . . . 2.4 . . . 8 1.2 . . . 2.0 . . . 4.2 . . . 3.0 . . . 9 1.5 . . . 3.0 . . . 2.2 . . . 2.2 . . . 10 4.2 . . . .7 . . . . . . 1.0 . . . 5.5 11 1.7 . . . . . . 1.0 . . . 1.5 1.0 . . . 12 . . . 3.0 . . . 4.5 . . . 3.7 3.7 . . . Prob. Error, in. 1.32" 1.47" . . . 2.84" . . . 2.03" Prob. Error, mils .93 1.02 . . . 1.33 . . . .96 Center ofImpact, in. } Rt. 1.6" Up .2" Rt. .2" Up 1.1"

The low value of dispersion is most interesting. The dispersion of the army 105mm. howitzer is about one mil. This is also the dispersion of the Chemical Warfare 4.2 inch mortar. The later unlike most mortars has a rifled barrel. Large navy guns have a dispersion of about one mil. It is only the small guns such as the 30 caliber rifle that has a lower dispersion, it being about ¼ mil.

It should be remembered that the dispersion error of the archer is included in the values given. Mr. Weese is an ex-cellent archer, having won the Eastern Championship for many years, but he has not won the National. The values of dispersion given for guns do not include the error of the gunner. The dispersion of rockets vary from one mil to as much as 100 mils. The dispersion is low for such rockets as the bazooka where the propellant charge is all burned before the rocket leaves the launcher. It is high for those rockets where the burning time is long and the launching tube is short. For example the army 4½ inch aircraft rocket had a dispersion of about 17 mils when fired from a 7 foot tube but it was only 1½ mils when fired from an 80 foot experimental tube. When fired from a plane in flight the dispersion was much less than when fired from a ground launcher of the same length because the velocity of the plane increases the initial drag on the fins and thereby gives the rocket better stability during the burning period.

Many archers think that the dispersion of an arrow could be improved by stabilizing it with spin. In the first place such a long projectile can not be stabilized by spin and in the next place fin stabilized projectiles are just as accurate as those stabilized by spin. In many cases they are more accurate. A slow spin will improve the dispersion caused by wind for fin stabilized projectiles.