A shuttle is the fastest projectile in sport and the quickest to give up

A badminton shuttle leaves a smash faster than any other object struck in sport, and it arrives at the other end of a court that is 13.4 m long having lost most of that speed. Both facts have the same cause, and it is not the shuttle’s shape as such. It is the ratio between how much air the shuttle has to push and how little there is of it.

Sixteen feathers standing in an open cone, on a base 25 to 28 mm across, weighing between 4.74 and 5.50 grams.

Reference The shuttle’s construction — sixteen feathers, a base of 25–28 mm, and a mass of 4.74 to 5.50 g — from Law 2.2 of the Laws of Badminton.

That is a large frontal area attached to almost no mass. Everything below follows from it.

What was measured

A 2013 study set out to construct and validate a motion equation for the flight of a badminton shuttle, and to establish the relationship between air resistance and speed. It applied aerodynamic theory to build a trajectory model under gravity and air resistance, then compared the predicted path with measured flight.

Reference The study’s aim — to construct and validate a motion equation for the shuttle’s flight and establish the relationship between air resistance and speed — and its method of applying aerodynamic theory under gravitational and air-resistance forces, from the paper’s abstract.

Two results matter.

The first is the form of the resistance. The drag force was found to be proportional to the square of the shuttle’s velocity.

Reference That the drag force was found to be proportional to the square of a shuttlecock’s velocity, from the paper’s abstract.

The second is what the trajectory reduces to. The motion equation for the shuttle’s flight path could be constructed by determining the terminal velocity, and the predicted trajectory fitted the measured data fairly well.

Reference That the motion equation of the shuttle’s trajectory could be constructed by determining the terminal velocity, and that the predicted trajectory fitted the measured data fairly well, from the paper’s abstract and key points.

Why a squared law hurts a light object so much

Drag proportional to v² is not unusual — it is the ordinary high-speed regime for a bluff body moving through air, and it applies to a cyclist, a football and a cricket ball alike. What is unusual about the shuttle is the deceleration that force produces, because deceleration is force divided by mass.

Halve the speed and the drag force falls to a quarter. Double it and the force quadruples. A shuttle struck at a very high speed therefore meets an enormous retarding force immediately — and, having five grams to slow down, sheds speed at a rate no heavier projectile experiences.

Terminal velocity is the compact way to express this. It is the speed at which drag balances weight, and the paper’s finding is that once you know it, you know the trajectory. A heavy object with a small drag area has a high terminal velocity and a flight path close to a parabola. A light object with a large drag area has a low one, and its path is a steep arc that flattens on the way up and then falls almost vertically.

That is why a badminton clear looks the way it does, and why the shuttle drops nearly straight down at the back of the court instead of continuing forward. It is not spin, and it is not the feathers steering. It is a projectile that has already reached the speed at which the air can hold it.

The proposal the paper makes

The study’s last suggestion is the one with institutional consequences, and it is worth quoting carefully.

The authors suggest that a scientific approach could be used to measure a shuttlecock’s velocity objectively when testing the quality of shuttlecocks, and that it could replace what they describe as the traditional subjective method of the Badminton World Federation, based on players striking shuttlecocks.

Reference The suggestion that a scientific approach could measure shuttle velocity objectively for quality testing, replacing what the authors describe as the BWF’s traditional subjective method based on players striking shuttlecocks, from the paper’s abstract.

That is a direct challenge to Law 3, which certifies a shuttle by having a player hit one from the back boundary and observing whether it lands between 530 mm and 990 mm short of the far line.

Reference The speed test and its 530–990 mm landing window, from Law 3 of the Laws of Badminton.

The criticism is fair on its own terms: a test whose apparatus is a person is not repeatable in the way an instrument is, and two competent players will not produce identical results.

But the argument cuts both ways, and this article will not pretend otherwise. The virtue of Law 3 is precisely that it is conducted in the hall where the match will be played, in the air that will actually be there. A laboratory velocity measurement is more repeatable and less local; it would certify a shuttle under conditions no rally happens in. The Laws already lean the other way, allowing a Member Association to approve modified shuttles where altitude or climate make the standard one unsuitable — a permission that only makes sense if the test travels with the shuttle.

Which of those matters more is a judgement about what a governing body is for, not a question the physics answers.

What is established, and what is not

Three things can be said with different confidence.

Firm. Drag on a shuttle rises with the square of its speed. This is a measured result in the paper and the expected regime for an object of this shape and speed.

Well-supported. That the shuttle’s trajectory can be reconstructed from its terminal velocity, and that the resulting model fits observed flight — the authors’ own phrasing is that it fitted “fairly well”, which is a claim about adequacy rather than precision.

Outside this evidence. Anything about a specific shuttle model, a specific altitude, or the difference between feathered and synthetic construction in flight. The study builds and validates a general model; it does not compare products, and nothing here should be read as doing so.

The paper also notes, without quantifying it, that the angle and strength of a stroke influence the trajectory.

Reference That the angle and strength of a stroke could influence the trajectory, from the paper’s abstract.

Which is the least surprising sentence in it, and a useful reminder of what a flight model is: a description of what happens to the shuttle after it has been hit, and no account at all of the hit.