Aiming with a traditional bow: Jihad 2023 study

The paper, by a physicist at Gadjah Mada University in Indonesia, proposes a way of aiming a traditional bow without a sight: marking a series of horizontal lines on the limb, one for each distance, to be lined up with the target. The author calls them h-lines. The position of each is calculated from the arrow's trajectory, with air resistance proportional to the square of speed, and from the archer's geometry: the height of the eye above the arrow and the draw length.

With a launch speed of 74.5 m/s and a velocity decay coefficient of 0.002 per metre, the curve of launch angle against distance agrees, according to the author, with the calculations and measurements of a 2015 work on the physics of archery. The most informative part is the sensitivity analysis at 70 metres, with 60 m/s and the same drag, where the correct line sits at 20 mm. If the coefficient is estimated at 0.001, the line ends up at 24 mm and the arrow lands 35 cm below the centre; at 0.003 the line moves to 16 mm and the arrow lands 38 cm above. An error of 3 m/s in speed matters more: 80 cm above the centre if speed is underestimated at 57 m/s, 69 cm below if it is overestimated at 63. A nock 140 cm off the ground instead of level with the centre at 130 cm raises the impact by 10 cm, and the line has to move by 1 mm; for a youngster with the nock at 100 cm the shift is 3 mm the other way.

The work is purely theoretical. The author starts from projectile motion without air, then adds drag and, assuming that the path length along the trajectory equals the horizontal distance, derives a closed formula for the launch angle. The velocity decay coefficient depends on the arrow's drag coefficient (from 1.5 to 4 according to the literature cited), air density, shaft radius and mass; according to the author it can be measured by recording the sound of the arrow at launch and at impact, using an acoustic method proposed in earlier work.

The h-line is where the line from the eye to the target crosses the line perpendicular to the arrow at the point where it rests on the bow. The calculations were done in the Maxima programme, assuming the eye 10 cm above the arrow, a 75 cm draw length and g of 9.8 m/s². Left-right aim is not addressed: the author leaves it to the archer's training.

The method has not been tried with any archer or any bow: no arrows were shot, so there is no evidence of whether or how much it improves accuracy, as the abstract claims it does. The model treats the arrow as a point, with no archer's paradox, shaft oscillation or wind, and assumes the archer repeats the same draw length, head position and launch speed on every arrow. The sensitivity analysis itself shows that at 70 metres a difference of 3 m/s is enough to take the arrow off a 122 cm face, whose radius is 61 cm.

The lines have to be recalculated for each archer, bow and arrow, and the author does not say how precisely speed and velocity decay can be measured with simple means. Finally, the paper takes it for granted that lines on the bow are allowed in traditional competitions, without discussing rules that forbid accessories or marks that could help with aiming.

Barebow and traditional archers who aim with reference points on the bow or on the target already do empirically what the paper calculates: they find a different reference at each distance. The formula shows which quantities move it, namely launch speed, air resistance, the height of the eye above the arrow and draw length, and the most instructive number is the sensitivity figure: at 70 metres, a 3 m/s difference in launch speed moves the impact by 69 to 80 cm. It is a useful order of magnitude for anyone who changes arrows, points or draw weight and wonders why their old reference points no longer work.

There is no evidence that calculated lines work better than those found by shooting, and a reference found on the field already carries the quirks of the archer's own technique, which the calculation ignores.