Archery robot drawing a bow: Nakamura 2019 study

A conference communication on an archery robot built at Osaka City University, designed for one precise task: to find, within a batch of arrows, the three or six that behave the same way, so that the athlete can take them to a competition without doubts. The paper describes the prototype, reports a shooting test and then calculates what would be needed to reach Olympic conditions, that is, 70 metres and a 52 pound bow.

The shooting test is small: a training bow requiring about 9 kilogram-force, 18 metres of distance, the same arrow shot ten times in a row on a day with no perceptible wind. The ten impacts all fell within a circle of 160 millimetres, that is, the 7-and-up zone of a 50 or 30 metre face, which was the result the authors had set themselves as a target with that equipment. There is spread on both axes all the same, and the authors attribute it to two things outside the robot: vertically to the nock, because the nocking point of the training bow is wider than the nock itself and the arrow sits slightly differently each time, at a different angle; horizontally to crosswind and to the absence of a clicker, which lets the amount of draw vary.

The calculation part is about that wind. Taking the arrow as a cylinder and using the Beaufort scale, the authors note that a person does not feel the wind up to 1.5 metres per second. With a crosswind of 0.3 metres per second, the lowest that scale counts, the training bow's arrow moves 5.11 millimetres over 18 metres; at 1.0 metres per second, 56.8 millimetres; at 1.5, 128. With competition equipment at 70 metres the computed drag drops to about two thirds, because the arrow is thinner and lighter, but the displacement becomes about 3.8 times larger, 19.4 millimetres already at 0.3 metres per second, because the flight time goes from 0.81 to 1.58 seconds.

The other checks are design work: with a 52 pound bow the most loaded joint of the bow-holding arm would reach a stress of 236 megapascals against the 245 of the yield point of the steel used, so it would stay elastic but with no margin; the trapezoidal screw that draws would need a torque of 0.113 kilogram-force metres; the solenoid that opens the fingers would have to go from 1.22 to 3.03 kilogram-force, or have a longer lever.

The prototype is made of four parts: the arm that holds the bow, the arm that draws, an angle adjustment stage and a base. The arm that holds the bow does not grip it; it pushes on the grip through a sheet of silicone rubber, so that the bow can jump forward after the shot as it does in an archer's hand. The drawing arm splits into a drawing mechanism, in which a trapezoidal screw turned by a bar converts rotation into straight-line movement, and a release mechanism with fingers shaped like human ones, onto which a tab can be fitted: the fingers are held closed by a claw hooked on a lever and open when a solenoid pushes the lever and releases the claw. The elevation angle is set with a two-axis stage.

The test was run at the range of the university archery club, on a day when those present felt no wind, with the front foot of the base 18 metres from the target. The same arrow (809 millimetres, 7.5 millimetres in diameter, 26.22 grams) was shot and pulled out ten times; for each impact the horizontal and the vertical distance were measured, and in the graph the origin is the mean position of the impacts, because the robot was not aiming at the centre. The robot vibrates while it draws the string, so each shot was taken only after the vibrations had stopped entirely.

The wind calculations use a simple model: the arrow is a cylinder of 809 by 7.5 millimetres, the drag coefficient is 1.2, the air 1.247 kilograms per cubic metre at 10 degrees, the change in momentum equals the impulse of the crosswind and the displacement is half the transverse velocity acquired times the flight time. For competition conditions the authors redo the calculation with a competition arrow (5.24 millimetres in diameter, 774.7 millimetres, 17.57 grams) and a flight time of 1.58 seconds. The sizing of the structure is a static calculation: 100 kilogram-force of simple tension or compression on the members, the bending stress on the most loaded joint, the efficiency of the trapezoidal screw (0.659) and the force of the solenoid derived from the balance of moments on the lever.

This is a four-page conference communication, without peer review, on a prototype openly described as such: the study is not a measurement of how arrows behave, it is a design check. The shooting test is one arrow shot ten times, at 18 metres, with a training bow the authors themselves call imprecise, and the target was not the centre. No comparison with an archer, no repetition on different days, no measurement of arrow speed or attitude: only the impact points.

The crosswind displacement is a calculation, not a measurement. The model treats the arrow as a cylinder with a constant drag coefficient of 1.2, ignores the vanes, the rotation about the axis, the orientation of the arrow relative to the flow and the fact that wind on a field is not uniform; the wind in the tests was not measured, it was inferred from what the people present could feel. The figures should be read as orders of magnitude, and for competition shooting at 70 metres as an extrapolation, because nothing was shot at that distance.

The structural calculation says something interesting and awkward: with a competition bow the most loaded joint would reach 236 megapascals against the 245 of the yield point, that is, almost at the limit, and the authors conclude that the part needs redesigning with more margin. At the time of publication, then, the 70 metre robot did not exist. The clicker was missing too, which the authors name as a source of variability both in initial speed and in the deformation of the bow arm. The text is in Japanese, with an abstract in English.

What remains is an order of magnitude for the wind nobody feels. A crosswind of 0.3 metres per second, which no one perceives, moves a competition arrow by about 2 centimetres at 70 metres according to this calculation; at 1 metre per second, still within what the Beaufort scale counts as imperceptible, the displacement would be several times larger. The reason is flight time: the same air acts for 1.58 seconds instead of 0.81, and the displacement grows with the square of that time.

From this comes the most useful conclusion: selecting matched arrows outdoors makes no sense, because the spread measured contains wind that cannot be felt and cannot be taken back out of the data. The authors write as much themselves, that the job should be done indoors.

There is a second observation, about equipment rather than about the robot. The vertical spread of the ten shots was attributed to the nocking point being wider than the nock: the arrow sat in a slightly different place each time, and so at a different angle, and that reached the target. It is the authors' hypothesis, not something they measured by changing nocks, and it concerns a training bow; but it is a place to look when vertical spread seems unaccountable.

About the archer's own movement this study says nothing, and measures nothing: the robot exists to take the archer out of the equation, not to describe them.