It happens to everyone, at every level: at 18 metres your group fits in a fist, then you move back to 50 or 70 and it looks as if somebody else had been shooting. The instinctive reaction is to think you have two techniques, a good one for short range and a poor one for long, but much of the time the technique is the same, and it is the distance that puts it under magnification.
Geometry sets the baseline for how much the group should grow: an error in direction grows with the metres, so at double the distance the group should be double the size. Scores from international competitions, though, suggest that the group grows a little faster than the distance even in light wind, and according to the author of those analyses two causes grow faster than the metres: the wind, and a bow tilted sideways by a different amount from one arrow to the next. Comparing your group at two distances tells you which of the two parts weighs more in your shooting, and all it takes is a tape measure.
The error starts as an angle, not as centimetres
The starting point is easily forgotten: an error in direction is an angle, and the ten centimetres you then measure on the target are merely the consequence. The arrow leaves in a direction slightly different from the one you intended and, if nothing else disturbs it, keeps that angle for the whole flight, so it is the metres that turn it into centimetres: the farther the arrow travels, the wider the miss it leaves on the target.
This leads to a rule of elementary geometry: for the same angular error, the miss on the target grows in proportion to the distance. A tenth of a degree of deviation amounts to about 3 centimetres at 18 metres and about 12 at 70. So you did not get four times worse between the two distances: the error in direction is the same, and you are seeing it from farther away.
At the sight, a tenth of a degree is tiny: over one metre it comes to 1.74 millimetres. The same ratio appears in an engineering paper on bow tremor, which opens its argument with an example: a sight that moves 1.74 millimetres at a distance of one metre sends the arrow 122 millimetres off at 70 metres. A similar calculation, done on the 10 ring of the 80 cm face at 50 metres, concludes that keeping the sight inside it with a 70 cm arrow means holding the bow still to within about half a millimetre. These sums are geometry and they hold up, but they are still sums, which is why the claim that while aiming, a movement of a fraction of a millimetre becomes centimetres of error on the target is transferred in the registry.
On archers there is only the scale of the effect. In fifteen national-team archers shooting at 18 metres, the aiming point moves about 8 centimetres on the target in the last three tenths of a second before the release, and that amplitude is linked to the score in only two of the four conditions tested: those who move more while aiming do not always score less, and nobody has measured how much of that movement ends up in the arrow.
Errors in direction come from everything to do with the shot and the aim: a release that is not quite the same each time, an anchor that shifts by a millimetre, an aim that settles in a slightly different spot, a bow hand that puts a different torque on the grip from one arrow to the next. On torque the models give striking figures: on a 166 newton recurve, a difference of thirteen hundredths of a degree from one shot to the next moves the arrow by more than one ring at 70 metres, and corresponds to less than two millimetres of offset between the arrow point and the front stabiliser, seen at full draw.
High-speed footage of sixteen recurve archers from national teams shows, however, that the bow does not rotate measurably before the arrow has left, and that seven of them were probably holding it twisted already while aiming: what matters is the torque the hand sets, and above all how much it changes from one arrow to the next. On a mechanical launcher with a Japanese bow, changing the torque alone moves the point of impact at 28 metres from one side of the target to the other, but nobody has measured torque and point of impact on the same shots by a recurve archer, so the claim that twisting the bow with the hand moves the arrow on the target is reported. All these errors, in any case, grow with distance in proportion, doubling when the distance doubles.
The official target sizes
The official target sizes are also best read as angles. The face a recurve archer shoots at 70 metres is 122 centimetres across, the indoor face at 18 metres is 40: seen from the shooting line, the first subtends about one degree and the second about 1.27 degrees. The 10 ring of the 122 face is 12.2 centimetres across, which at 70 metres is about a tenth of a degree, the same angle as in the earlier example; the recurve indoor 10 is 4 centimetres, about 0.13 degrees at 18 metres, so in angular terms it is a little larger than the outdoor one.
It is, after all, how large the target looks from the shooting line that drives the score. At a fixed distance, in nine young Korean competitive archers at 50 metres, the average per arrow rises with the diameter of the face, from 7.7 points on the 60 cm face to 8.93 on the 100 cm; and in eighteen experienced archers who shot thirty arrows at each distance, from twenty distances for the men and eighteen for the women, the thirty-arrow total falls almost in a straight line, by about 1.34 points per metre for the men and 0.60 for the women, with no jumps at the competition distances. The claim that scores fall as shooting distance increases is reported in the registry: the fall is there, but its shape changes with level, and in beginners it is concentrated in the first few metres of moving back.
So if you shoot excellent scores indoors and then lose more than you expected at 70 metres, your long-range technique is not the first thing to blame: the outdoor 10 is a little smaller in angle, and at that distance causes come into play that carry little weight at 18 metres. The author of the competition analyses described below suggests that archers who do much better indoors may carry a larger share of errors that grow with the square of distance, possibly a bow cant that changes from arrow to arrow, and he leaves the question to future research.
How much the group grows in competition
If error in direction were the only cause at work, the group would grow exactly with distance, and the 122 cm face would give the same score as the 80 cm face at 50 metres only at 76 metres. An analysis of the scores at two major international competitions in 2013 finds the match at 70 metres instead, the recurve competition distance, which for the author means that at 70 metres the group is already wider than geometry alone would predict. The same paper finds that the gap between the two distances grows with the archer's level, the opposite of what you would expect if the angular error always stayed the same.
The same researcher finds the match again at five world-level competitions with little wind, between 2007 and 2009, and turns it into a model: at 70 metres about three quarters of the points lost come from errors that grow in step with distance and about a quarter, 24.1%, from errors that grow with its square. In his classification there are only two causes of the second kind, wind and a bow cant that varies from one arrow to the next, while all the others, anchor, aim and grip torque included, grow in step with distance.
On that basis the claim that arrow groups widen more than in proportion to distance is reported in the registry, and no more than that. Both papers come from the same author and both go through scores, which mix up how wide the group is with where its centre sits, and the share that grows with the square is fixed by a calibration the author chose. The one study that measured group width at several distances, on eight experienced archers between 18 and 90 metres, sees the group widen but describes the relationship as not significant.
How to read the doubling
This gives you a tool to take to the range, with one correction to pure geometry: when you double the distance, a group that ends up a little more than double is normal, even in light wind and even for archers who shoot very well. When it grows far beyond the ratio of the distances, something has joined in along the flight that carried little weight at short range, such as wind, a bow canted differently from one arrow to the next, or an arrow that leaves misaligned and drifts more as a result.
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Grows roughly in proportion
Double the distance and the group roughly doubles, or a little more: errors in direction carry most of the weight (aim, release, anchor, bow hand), and you can work on them at short range, where repetitions cost less.
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Grows far out of proportion
At double the distance the group is well over double, a sign that something is acting along the flight. Before blaming your technique, look at the wind, the cant of your bow and your tuning.
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Changes shape
If the group goes from round to a horizontal oval, suspect wind, spine, release and bow hand; if it becomes a vertical oval, suspect draw length consistency, launch speed and arrow weight, or, in field and 3D, distance estimation.
The third reading connects this article to reading impact patterns, with one caveat: even in almost still air an experienced archer's group tends to be slightly wider than it is tall. At the 2013 World Cup stage in Shanghai, with almost no wind, the elite archers' groups at 50 metres had on average a horizontal spread 1.15 times the vertical, in both recurve and compound, and at the windy World Championships the same year the ratio rose to 1.25. The claim that arrow groups are wider horizontally than vertically is therefore reported, and a slight oval is the shape to start from: what matters is how much it stretches as you move back.
What the air adds
The arrow slows down along its flight, and the loss has been measured since 2007 in several independent laboratories, with different methods. An inertial sensor inside the shaft recorded about 8% of the speed lost over 55 metres indoors, and the same authors note that on a 70 metre range the loss is around 15%; that is why the claim that along its flight the arrow loses an appreciable part of its launch speed is corroborated. The arrow therefore flies the last stretch of a long shot more slowly than the first, and the wind has more time to push it.
Ballistic models calculate that in a side wind the drift grows roughly with the square of distance: for a compound arrow, at 90 metres it is 62% larger than at 70. Where the wind comes from matters too. For the recurve, two independent simulations calculate that at 70 metres a crosswind of three metres per second moves the point of impact by 26 or 36 centimetres, while the same wind from in front or behind moves it by 8 to 10 centimetres. The claim that at 70 m a crosswind moves the arrow far more than a head or tail wind is transferred in the registry, because it rests on physics rather than on measurements with archers on the range; in practice a crosswind widens the group mainly sideways, and does so faster than the distance grows.
Launch speed and vertical spread
The model underneath all this reasoning is a simple one: gravity and air drag are enough to say where the arrow lands. With a compound bow mounted on a shooting machine, a physicist found at several distances the sight mark that put the arrow in the centre and converted it into a launch angle, and the points fell on the curve of a calculation that contains only gravity and drag, with no need to add lift. It is the only test that compares the calculation with the point of impact, with one bow and one arrow, no archers and no wind, which is why the claim that gravity and air drag are enough to say where the arrow lands is reported.
The same calculation quantifies a source of error that is not an angle: two arrows that leave in the same direction but at different speeds stay in the air for different times, and gravity pulls them down by different amounts. At 70 metres, with a compound arrow launched at 74.5 metres per second, a one metre error in distance moves the impact by about 7 centimetres, while one metre per second of extra launch speed raises it by about 13. In archers the speed changes little from one arrow to the next: in three Malaysian national-team archers measured at 70 metres it varied by one or two kilometres per hour around averages between 198 and 220. In the classification used in the competition analyses above, variations in draw length and arrow mass, which change the launch speed, also count among the errors that grow in step with distance.
On a shooting machine, with fifty-nine arrows of the same model characterised one by one, mass and mean spine account for 46.7% of the vertical spread, and the heavier arrows land lower. The same study finds, however, that the ballistic calculation inflates the size of the effect, since it predicted over 14 centimetres of vertical spread at 70 metres and the measurement gave 8.8; and in seven German national-team archers neither average arrow speed nor its consistency entered the score model. The claim that small differences in launch speed account for much of the vertical spread is therefore reported: the direction holds, the size needs revising. If your group stretches vertically at long range, the first things to check are the consistency of your draw length and the weight of the arrows in your set.
Tuning at long range
That leaves the equipment. Every model that has studied it says that spine has to be matched to draw weight and arrow length, and on a shooting machine with a right-handed bow the stiffer shafts end up on the left. Nobody, however, has measured the groups of archers shooting matched and mismatched spine, so the claim that arrow spine has to be matched to draw weight and arrow length is reported in the registry.
What it costs at 70 metres when an arrow does not leave aligned with its path is something the models calculate mainly with the wind. In a computational fluid dynamics simulation of an X10 shot at 57 metres per second towards a target at 70 metres, with a crosswind of three metres per second, the arrow that leaves aligned with its path moves at most 12.5 centimetres, while the one that leaves with three degrees of angle of attack reaches 27. An earlier model that lets the shaft flex gives the arrow's attitude little weight, about ten millimetres per degree on a drift of around 245, and adds that a poorly tuned bow changes the arrow's launch angle very little and mainly gives it an initial rotation. That is why the claim that an arrow that leaves the bow aligned with its path drifts less in a crosswind is transferred, and it says little about what imperfect tuning costs. It is still one more reason not to judge tuning at short range alone, and to shoot the group test at competition distance.
On the range, the sign that points to tuning is a group that holds together at short range but opens horizontally at long range more than proportion would justify, sometimes with the odd arrow that always strays to the same side. Before you rework your technique, spend half an hour comparing fletched arrows with a bare shaft, because if that is where the problem lies, no amount of work on the shot will make it go away.
The two-distance test, in practice
The procedure is simple, and it pays to do it properly once rather than judging by eye for months. Pick two distances with a convenient ratio, say 20 and 40 metres, or 30 and 60, and shoot at least a dozen arrows at the first, measuring the width of the group on both axes, horizontal and vertical, and leaving out at most one arrow you clearly called as a bad shot. Then repeat at the second distance with the same number of arrows and the same tape.
Then compare the numbers. If at double the distance the group is roughly double, or a little more, the work to be done is on the shot itself, and you can do it at short range; if it is far more than double, or clearly changes shape, look at your tuning, the cant of your bow and how you read the wind before touching your technique. In both cases the rule for reading impact patterns applies: change one thing at a time, then measure again.
The test is there to guide you, not to pass judgement, not least because scores become more variable as you move back, at least relative to the average. In the beginners of a 1966 study, over 24 arrows, the standard deviation of the score was between 12 and 15 points at 10 yards, on averages between 177 and 190, and between 20.6 and 23.2 at 40 yards, on averages between 50 and 62. The claim that the longer the distance, the more variable the score becomes is reported in the registry, and for experienced archers at competition distances the question remains open; the practical warning still stands that one set of twelve arrows is not a verdict and that a windy day muddies any comparison. If the result looks strange, repeat the test on a calm day before drawing conclusions.
As for the distance to train at, the studies do not point to a right one. In eighteen experienced archers the competition distances do not sit above the score line any more than expected, the one exception being 70 metres for the men, and the claim that training at competition distances gives a specific advantage at those distances is contested. I go into it in detail in the article on what distance to train at.