Japanese bow and arrow flight: Kobayashi 1997

The study asks what the twist the left hand applies to the grip of a Japanese bow does to the flight of the arrow. That action is called tsunomi in kyudo, and its purpose is to bring the push of the string into line with the axis of the arrow. The question is the archer's paradox: the string pushes the nock towards the centre of the bow rather than towards the point, so the arrow receives a moment that turns it and in some cases brings it against the wood.

The authors built a model of the bow as three rigid bodies joined by two elastic hinges, and a rig that applies a twist of controlled shape and size to the grip alone, with strain gauges measuring that twist, string tension, the bending moment at the centre of the arrow and the compressive force at the nock. The comparison gives a similar shape over time between calculation and experiment, but not the same magnitudes: the calculated bending moment at the centre of the arrow is about one sixth of the measured one, and the authors name this as the main problem to fix.

They then held everything else fixed, bow and arrow alike, and changed only the shape of the twist over time, using three sinusoidal profiles chosen so that the integral over the 26 milliseconds of the launch was the same. The first profile, taken from earlier work as the one with the best energy transfer from bow to arrow, sends the arrow straightest. The second, with a great deal of twist at the start and then falling away, which the text describes as common among beginners, bends the arrow towards the wood of the bow, contact happens early and the arrow is thrown well to the right. The third, with little twist at the start, bends the arrow the other way and contact becomes unlikely or late. Arrow speed changes by less than one per cent across the three cases, so contact costs accuracy and almost nothing in distance.

The last step is the sharpest. Taking the first profile and changing only the value of the twist at time zero, that is at the aiming position, by plus 50 and minus 50 per cent, the flight comes to resemble the second and the third case respectively. With the same total amount of twist, it is the starting condition that decides where the arrow goes.

The model follows Hickman's 1937 scheme: the bow becomes three rigid bars, the grip and the two limbs, joined by two elastic hinges that return a moment proportional to the angle. To write it this way the bow was made symmetric top and bottom, which a Japanese bow is not, and the motion of the arrow was confined to one plane. The string is a massless linear spring carrying tension only, air resistance is neglected, the cross-section of the bow at the contact point is circular, and the twist acts only on rotation of the grip about the vertical axis.

Arrow bending is treated as the transverse vibration of a simply supported beam, reduced for simplicity to a single degree of freedom, from which the bending moment at the centre is obtained. This is where the relation between bow power and arrow stiffness enters, that is the spine. At each computation step the string tension and the contact force between arrow and bow are found by trial, until two constraints hold: the distance from nock to string loop equal to half the string, and the arrow not passing inside the radius of the grip. The calculation ends when the string stops pulling or the nock passes the string loop, that is when the arrow separates.

The rig is an improved version of one used in earlier work. The bow is held on a bearing that lets it rotate freely about the vertical, with a stop released in step with the shot so that the twist can change sharply around release. A cam fixed to the bearing turns the push of a follower into torque on the grip: changing the cam profile changes the shape of the wave, and adjusting the follower spring changes its size. The bow used is a Western hunting bow reworked to be symmetric, chosen precisely so that it would not produce the vertical forces of the action that accompanies tsunomi in kyudo. A potentiometer on the bearing measures the rotation of the bow.

No archer shot in this study. Everything it says about the action of the hand comes from a rig applying a clean twist to a bow locked on a bearing, and from a calculation that only partly matches that rig. The bending moment at the centre of the arrow, the quantity from which the shape of the flight is deduced, is underestimated by a factor of about six: the authors write that the two curves share a trend but not the same magnitudes, and that improving this is the main task remaining. While that gap stands, the flight figures show a tendency rather than a trajectory.

The simplifications are numerous and pull in different directions. The bow is symmetric, whereas a Japanese bow has its grip set low, and the test bow is not a Japanese bow at all. The motion stays in a horizontal plane, so the vertical component of the hand action, called uwa-oshi in kyudo, is excluded by construction and not on its merits. The arrow vibrates with a single degree of freedom, there is no air, and the string has no mass.

The study measures no accuracy at all. There is no target, no score and no group: the conclusions concern the direction and curvature of the arrow in the first 26 milliseconds, and the link between those and where the arrow lands at twenty-eight metres remains an inference. Three twist profiles are compared, plus two variants of the first, and they are sinusoidal shapes chosen at a desk: the label attaching the second profile to beginners comes from teaching tradition, not from measurements on people. The text is in Japanese, with an English title and abstract.

For a kyudo archer the study puts a number on something usually taught in words: how much the bow hand twists at the start, at the moment of aiming when the arrow has not yet moved, matters more than how it twists afterwards. The same total work by the hand, distributed differently over time, gives opposite flights.

For someone shooting a modern recurve the transfer is partial, and that is worth stating. The same problem exists, because the string pushes the nock off the axis of the arrow, but the equipment handles it differently: through the button, which sets the contact, and through the spine of the arrow, which decides how the shaft bends its way past. What is achieved here by twisting the grip is largely left to tuning on a recurve.

The study does not say what contact between arrow and bow costs in points, since it measured no scores, and it does not say how the hand should twist, since the profiles were imposed by a cam. What it does measure is that contact costs almost no speed, less than one per cent, while clearly changing direction: a fault of this kind does not show in the distance reached, it shows on the target face.