Over 55 metres indoors, a competition arrow fired at 56.4 metres per second from a compressed-air launcher stayed in the air for 1.04 seconds and arrived about 8% slower than it set off. An inertial sensor mounted inside the shaft recorded it, and the same researchers note that over a seventy-metre field the loss is around 15%. The first half of the question, how much speed the air takes away, therefore has a rough answer; the second, what actually changes that loss, has narrower answers than the ones that go round on the range.
Nearly all of it comes from tools a long way from the shooting line: a Japanese wind tunnel in which the arrow is held up by magnets, compressed-air launchers, shooting machines and a few calculations. I explain how they work on the page about the wind tunnel method; here I look at the results.
How much speed is lost in flight
That the arrow slows appreciably along its flight is one of the few equipment points the registry rates as corroborated: different laboratories, using different methods, all find a steady slowdown that depends on the arrow. An electronic point screwed onto a compound arrow, shot by a machine, left at about 82.1 metres per second and arrived at 78.19 on a target 13.94 metres away, just under 5% lost in fourteen metres. Another compound arrow, launched at 74.5 metres per second and timed at seven distances between 27 and 82 metres, lost speed at a constant rate of 2.31 thousandths per metre.
The force involved is of the same order as the arrow's weight: on an Easton Protour 470 just leaving a compound at 78.6 metres per second it came to 0.94 times the weight, and for the recurve the same author puts it between 0.5 and 1.2 times. Even so, it is small next to launch and arrival. The electronic point, with a range of ±16 g, went outside it only at launch, estimated from video at about 1,100 g, and at impact in a bag target, about 3,700 g; in flight it stayed inside. On that measurement, taken with a compound and a light arrow, the registry rates as reported that the arrow is stressed hardest only at the start and at the end of its journey.
One limit weighs on everything that follows. For the Olympic recurve shot by an archer there is a single measurement of the slowdown, 36 arrows from an expert member of the Japanese national team on a 60-metre indoor range, and it produced a drag coefficient, not the percentage of speed lost. The other figures come from compounds, machines, traditional bows and launchers.
Where the drag comes from
The Protour 470 study also split the drag between the parts of the arrow, with a model that adds them up and follows the speeds measured out to 90 metres. The result greatly reduces the share usually credited to the vanes.
Nearly three quarters comes from the shaft, because its surface is far larger than that of today's small vanes. The author adds that the vanes, while they contribute little to drag, are what governs the correction of the arrow's attitude, and I come back to that below.
If the shaft matters, its cross-section ought to matter too. In the tunnel two competition shafts without vanes, the barrelled A/C/E and the thinner X10, gave the same drag coefficient, and if the coefficient is the same the force grows with the cross-section. That is a deduction, though, and the registry lists the claim that a thinner shaft meets less air resistance as not studied: nobody has measured the force on shafts of different diameters, and those two had no vanes and were slower than a competition shot.
The layer of air around the shaft
The same arrow can be slowed a lot or a little depending on the thin layer of air running along it, the boundary layer. While it stays orderly, or laminar, friction is low; when it mixes and turns turbulent, drag rises. On the Easton A/C/E arrows of the Tokyo group, which carried out almost all of these measurements, the coefficient is about 1.5 in the first case and about 2.6 in the second, nearly double, and in a simulation over 70 metres the ratio of drag to the arrow's weight goes from 0.45 to 0.80.
Very little is needed to switch regime: as soon as the arrow tilts four to six tenths of a degree against the airflow the layer turns turbulent, and in the tunnel three quarters of a degree took the coefficient from about 1.6 to about 3.1. The jump was measured in the tunnel, found again in free flight and reproduced by two calculations, so the registry rates as reported that an arrow flying at an angle to the airflow suffers far more drag. There are two limits: the jump only exists while the flow is still laminar, and in a 2022 test, at almost identical angles, it was the shape of the point that decided the regime.
This has an odd consequence. In a band of speeds below that of the Japanese archer's arrows, the same arrow launched in the same way can fly in two regimes: fired many times by compressed air, its coefficients split into two families, about 1.5 to 1.6 and about 2.6, and within a single flight a sensor in the shaft saw the deceleration drop from 0.65 to 0.30 g as the layer turned laminar again. The authors calculate that the two regimes would shift the point of impact by about 15 centimetres in height at 60 metres, but nobody has counted the impacts of an end to see it: the claim about the two drag regimes is reported, with every measurement from one group.
The same group also calculated how the disturbance arises on a bare shaft: only non-symmetric disturbances grow, and they always travel towards the nock. It is a calculation on a shaft without vanes, and the claim about instability of the layer along the shaft stays transferred; an Australian water channel experiment actually suggests that with the standard bullet point, on an arrow travelling at 85 metres per second, the flow turns turbulent as early as about 81 millimetres along the shaft.
When an archer does the shooting
For a recurve archer this is the part that matters most. Arrows shot by an expert archer at 57 to 58 metres per second always ended up in the turbulent regime, with coefficients between 2.6 and 2.7. The Japanese group puts this down to the flexing of the shaft, which just after leaving the bow oscillates by 6.9 millimetres at the point at 87 hertz and gives the point an angle of attack that swings by about 3.7 degrees.
Whether flexing raises drag, however, is contested by the studies themselves. Below competition speeds flexing can decide the regime, although it is not the only route: an arrow that does not flex needs a tilt of only just over half a degree. At recurve arrow speeds, though, the layer turns turbulent even without flexing, with a coefficient of around 2.5 for every launch method, compressed air included, and in the only experiment that measures flexing and drag together the flexing amplitude bears no relation to mean drag. At competition speeds the regime may therefore already be settled; the jump described above matters mainly where the layer can still stay laminar, at lower speeds or when the launch barely flexes the shaft, as with the mechanical release fitted to the robot in that experiment.
The same experiment found that, at the archers' speed, mean drag did not change with the launch method, but its spread did: it was smaller with the archers than with the mechanical fingers, the mechanical release and above all the launcher, whose standard deviation was almost four times the archers'. It is a single experiment with few launches per condition, and that an arrow shot by an archer has more consistent drag is reported; nobody has checked whether it shows up as a tighter group.
The vanes
On fletching the measurements point the same way, with large effects when the fletchings really differ. In the tunnel the vanes roughly double the drag of the bare shaft, from about 0.75 to about 1.5. Between two straight vanes from the same maker, the Easton Diamond 175 and 280, the coefficient goes from 1.56 to 2.05. With a wooden bow, four-inch natural feathers lost 1.93% of the arrow's energy over the first five metres, two-and-a-half-inch ones 7.51% and flu-flu fletchings over 12%.
Between two similar competition vanes, on the other hand, the difference can vanish. Shot by the archer from her own recurve, the same arrows with Spin Wings and with Gas Pro vanes, which have three quarters of the Spin Wing's area, gave 2.68 and 2.63, the same coefficient. The claim that point and vane change drag a great deal is reported, with the only test on an archer and nearly all the others from the same tunnels: it holds for vanes when the differences are large, much less for the point or between similar competition vanes.
Vanes matter more for something else, the way the arrow straightens: the centre of lift falls about three centimetres ahead of the fletching, which provides nearly all of the restoring force. Going from small to large Diamonds, lift grows by about 60% and the moment that realigns the arrow by about 80%, and the maximum angle falls from 0.36 to 0.27 degrees; on a model released from 45 degrees, the most widely used vane in the world brought it back to zero in 0.934 seconds against 1.283 for an average vane. That vane type changes how quickly the arrow settles is reported, but on few test rigs and with some disagreement, and in that test the tunnel ran at 20 metres per second, about a third of real arrow speed.
A detail for anyone reading the technical papers: set oscillating in the tunnel, the arrow showed an aerodynamic damping term of the order of one millionth, so small that the authors leave it out of their calculations, and yet in their own flight calculation the oscillation dies away all the same. The negligible aerodynamic damping has to be read narrowly: what is negligible is the term measured in the tunnel, not the effect of the air, which works through the lift of the vanes.
Finally, the vanes make the arrow spin, and an archery arrow turns about sixty times a second. The ratio between the speed of the spinning surface and the flight speed stays between 0.028 and 0.033, so spin rises with speed, and point shape did not change it: this link between spin and speed is reported too, with all the direct measurements from a single group.
The point
On the point the picture is narrower than the way it is told on the range. With the arrow aligned with the airflow, bullet and streamlined points give the same drag. The difference appears when the point creates a step or a taper behind its widest part, because that is where the layer of air separates: the standard bullet point used in those tests reached 5.83 millimetres, more than the front of the shaft, while the streamlined one reached its maximum of 5.30 exactly where the shaft begins. With the step the arrow slows down faster, and in 2022 high-speed footage showed it in the speed itself.
The calculated effect, though, stays small. On a compound arrow at 84.1 metres per second, with three metres per second of crosswind, the drift at 70 metres goes from 156 millimetres with a bullet point to 161 with a short bulge point. Nobody has taken the comparison to the target.
From drag to the point of impact
At the target, all of this arrives as the height of the impact. Using a compound on a shooting machine, a physicist found the sight setting that put the arrow in the centre at a range of distances: converted into launch angles, the settings fall on the curve of a calculation that contains only gravity and air drag. On this test the registry rates as reported that gravity and drag are enough to say where the arrow lands, with two obvious limits: no archer and no wind.
The same calculation puts a price on small errors. At 70 metres, one metre per second more launch speed raises the impact by about 13 centimetres, and a 20% change in drag moves it by about 7. Between two competition vanes shot by the same archer the drag was practically the same, a long way from that 20%, whereas the switch from laminar to turbulent, where it happens, nearly doubles it. Crosswind is a subject of its own, covered in the article on wind and weather, and the way the air adds to the other errors is in the one on why groups open up with distance.
What I take from it for the range
No study in the bibliography has compared archers' scores or groups with different points and vanes, so air resistance does not yield a rule for scoring more. It does yield three things worth knowing when you change your equipment.
The first is that big changes can be measured and small ones, as far as we know, much less so. Going from feathers to vanes, changing the size of the fletching a lot or fitting a point with an obvious step against the shaft are differences the measurements pick up; between two competition vanes of similar size the only test with an archer found none. Where there is a difference, the place to see it is your sight marks at the long distances.
The second concerns the point: the join with the shaft matters more than the trade name of the shape. The calculated effect is small, and has to be weighed alongside point weight and spine, which matter to the arrow for other reasons.
The third concerns clean flight. An arrow that leaves aligned has a better chance of staying in the low-drag regime, but arrows shot by recurve archers have always come out in the turbulent regime, and in the same measurements their drag was the most repeatable, which the authors put down to the flexing taken from the bow. Tuning the arrow matters for reasons I cover in the article on arrow flight; on air resistance, what is known today does not allow any further promise.
What is missing
The step from the wind tunnel to the target is missing: nobody has compared points and vanes on the scores or groups of archers shooting, or counted the impacts of many identical arrows to see whether the two regimes fall at two heights. A measurement on the recurve shot by archers is missing, outdoors and at competition distances, with launch and arrival speed on the same shot. And a second laboratory is missing, because almost everything known about the layer of air round the arrow comes from the same magnetic suspension tunnel and the same Tokyo group.