Proceedings of the Institution of Mechanical Engineers, Part P: Journal of Sports Engineering and Technology

Proceedings of the Institution of Mechanical Engineers, Part P: Journal of Sports Engineering and Technology http://pip.sagepub.com/ Analysis of scores and arrow grouping at major international archery competitions James L Park and James E Larven Proceedings of the Institution of Mechanical Engineers, Part P: Journal of Sports Engineering and Technology published online 28 January 214 DOI: 1.1177/175433711351976 The online version of this article can be found at: http://pip.sagepub.com/content/early/214/1/27/175433711351976 Published by: http://www.sagepublications.com On behalf of: Institution of Mechanical Engineers Additional services and information for Proceedings of the Institution of Mechanical Engineers, Part P: Journal of Sports Engineering and Technology can be found at: Email Alerts: http://pip.sagepub.com/cgi/alerts Subscriptions: http://pip.sagepub.com/subscriptions Reprints: http://www.sagepub.com/journalsreprints.nav Permissions: http://www.sagepub.com/journalspermissions.nav >> OnlineFirst Version of Record - Jan 28, 214 What is This? Downloaded from pip.sagepub.com by Marcel van Apeldoorn on April 6, 214

Original Article Analysis of scores and arrow grouping at major international archery competitions Proc IMechE Part P: J Sports Engineering and Technology 1 9 Ó IMechE 214 Reprints and permissions: sagepub.co.uk/journalspermissions.nav DOI: 1.1177/175433711351976 pip.sagepub.com James L Park 1 and James E Larven 2 Abstract Archers lose score for a variety of reasons. While some of those have been studied, there appears to have been little consideration of their relative importance. Archers scores and arrow groups on the target were analysed at two of the major international tournaments held during 213. It was found that many archers lose score through incorrectly adjusting their sights, which can have a major impact on their final placing in the event. It was also found that as the archer s ability improves, so does the relative importance of factors with regard to their equipment and technique, which result in score loss that increase faster than linearly with distance. Keywords Archery, arrow group, score, wind drift Date received: 1 November 213; accepted: 1 December 213 Introduction Major archery competitions are generally decided by the archers first shooting a ranking round, typically consisting of either 144 arrows shot over four distances or two sets of 36 arrows shot at one distance, followed by ranked one-on-one knockout match play, usually consisting of 9 16 shots at one distance. The format differs a little on a year-by-year basis and depends upon the types of bow (recurve or compound) being used. In both the ranking round and matches, the scores are often close, with the winners being decided by small margins. In these competitions, archers using recurve bows hold the bow string across three fingers of their drawing hand; archers using compound bows hold the bow string using a mechanical release device with trigger. Equipment and competition rules are as defined by World Archery 1 (the international archery federation). Archers lose score through a combination of the various technique errors they make together with various equipment imperfections and choices. While some of those errors and imperfections have been studied in isolation 2 (and primarily in popular magazines rather than in learned journals), there would appear to have been little consideration of their relative importance. With a view to establishing a sound data set against which to test various hypotheses, agreement was sought from World Archery to gather data at several major international events (World Cups and World Championships) during 213. The competition format used for archers using recurve bows in major international competition will be changed for subsequent years, with those archers no longer competing on individual target faces at the shorter distances. Consequently, 213 would appear to have been the last opportunity to capture some of these data at a major competition for the foreseeable future. This article provides an analysis of archers scores and arrow grouping on the target from World Cup 1, 213, conducted in Shanghai, China, and from the World Archery Championships, 213, conducted in Belek, Antalya, Turkey. World Cup 1, 213, was selected with the expectation of low wind drift during the majority of the event as it was conducted in a major stadium providing good shelter from prevailing conditions. The World Archery Championships were selected due to the large number of top-level competitors 1 Department of Mechanical and Aerospace Engineering, Monash University, Clayton, VIC, Australia 2 Archery Australia, Panania, NSW, Australia Corresponding author: James L Park, Department of Mechanical and Aerospace Engineering, Monash University, Wellington Road, Clayton, VIC 38, Australia. Email: jlpark@bigpond.net.au

2 Proc IMechE Part P: J Sports Engineering and Technology expected and since the venue was likely to be windy (especially in the afternoons) due to its proximity to the sea. Results of major international events over many years are available from World Archery, 3 although the prevailing weather conditions are not recorded. Method At both events, archers using recurve bows shot a ranking round of 144 arrows. For the men, that comprised 36 arrows at each of 9, 7, 5 and 3 m. The women shot 36 arrows at each of 7, 6, 5 and 3 m. In both cases, a 122-mm, 1-ring target face was used for the two longer distances and an 8-mm, 1-ring target face for the two shorter distances. The archers were able to have practice shots at their longest distance but at no other distances during the competition. Arrows were shot in sets ( ends ) of six between scoring. Archers using compound bows shot a ranking round of 72 arrows at 5 m at an 8-mm 1-ring target face. The arrows were shot in two sets of 36, with archers able to have practice shots prior to the first set but not prior to the second set. Arrows were shot in ends of six between scoring. When the 8-mm target face is used, only the inner six target rings are included on the target face. That enables the use of multiple target faces on a single target butt, so that each archer is able to have an individual target face. Arrows hitting outside the outer ( five ) ring score zero. When the 122-mm target face is used, there are typically three or four archers using it simultaneously. For both target faces, the inner ring scores 1 points with the score for each subsequent ring reducing by one. There is an additional ring in the centre of the 1 ring, the X ring, which also scores 1 points and is used to break ties during the ranking round and for world records. Wind strength during the ranking rounds and most matches at World Cup 1 was estimated to be less than 1 m/s. The medal matches were conducted at a different venue, and the wind strength was higher. At the World Archery Championships, there was a moderate quartering wind from the rear right in the afternoons, with the wind strength estimated to be up to 5 m/s. During the one-on-one matches, there was, unusually, very strong wind indeed, with gusts measured at over 2 m/s. Following the ranking rounds, the archers had ranked one-on-one knockout matches: for archers using recurve bows, the matches were at 7 m and for archers using compound bows, the matches were at 5 m. Archers of different genders and bow types compete in separate divisions. The top eight ranked archers in each division have the advantage of not entering into the knockout matches until the field in their division has been reduced to 32 archers, that is, they are protected for the first one or two matches, depending upon the total number of archers in their division (although that is not done for the Olympic Games). Consequently, it is a very real advantage to rank in the top eight. Depending upon the total number of archers, in the first round of matches, the archer ranked 9th competes against the archer ranked 14th, and in the second round of matches, the archer ranked 9th (assuming that he won the first match) competes against the archer ranked 56th (also assuming that he won the first match). The top 8 ranked archers then enter the matches giving a remaining total of 32 archers for the third round, the 1st ranked archer competes against the 32nd ranked archer, and so on until only a single archer remains. Depending upon the total number of archers, some higher-ranked archers might have byes in the early matches. Archers ranked lower than 14th do not participate in the matches, with their final placings being their ranking places. World Cup events are major world-level tournaments, ranking only behind the Olympic Games and World Championships. Consequently, the archers are usually the world s best, although the numbers do vary from event to event. The majority of the world s best archers (including many who have been successful at the Olympic Games and World Championships and who have held or hold world records) competed in these events in 213. A greater number of archers competed in the World Archery Championships than in the World Cup events. Analysis of many previous events has shown that the medal winners after the matches are highly likely to come from those placed in the top 2 in the ranking round. Consequently, that analysis was conducted for both World Cup 1, 213, and the World Archery Championships, 213. In addition, scores from the ranking event were studied in order to ascertain competitive score levels and the relation (for those archers using recurve bows) of scores at one distance to those at other distances. For those archers using recurve bows, each individual target face was photographed following the 5 m distance. At World Cup 1, the target faces were then changed and again photographed following the 3-m distance. At World Cup 1 for those archers using compound bows, each individual target face was photographed following the practice shots (typically 12 3 shots) and then after the first 36 shots at the 5 m distance. Some of the target faces were then changed, and all target faces were photographed following the second set of 36 shots at 5 m. Data were not gathered for the archers using compound bows at the World Archery Championships other than for the practice shots for the women. Each of the arrow groups was then digitised and statistically analysed. The digitisation was cross-checked using the total scores recorded by the archers for the relevant shots. In total, approximately 2, arrow holes were analysed for World Cup 1 and about 1, for the World Archery Championships. While the analysis was partially automated, the challenges of overlapping arrow holes and arrows very close to target ring

Park and Larven 3 ing score 14 135 13 125 12 115 11 15 1 lines meant that most arrow positions needed to be evaluated manually. Results Men's Recurve WC1 213: total score 2 4 6 8 1 Figure 1. Men s Recurve ranking round scores for 144 arrows. ing round scores for the Men s Recurve division at World Cup 1 are shown in Figure 1. The maximum possible score for the 144 arrows was 144. The world record at the time of writing was 1387. The highest score achieved at this event was 1371, which was relatively close to the world record in accord with the minimal wind strength during the event. ing round scores for the other three divisions at World Cup 1 showed the same features as those in Figure 1, as did the scores from the World Archery Championships. Figure 1 is typical of those for these events over many years. Usually, there are several outstanding scores for archers in the top 1 3 ranking positions, followed by an approximately linear decline in scores with ranking position. At some point, the scores fall off very quickly in the tail where the archers are simply not competitive at this level of event (or where they have had some unexpected problem during the event, such as an equipment failure or illness). Excluding the tail in each case, each ranking place was worth about 1.4 points in the total score for the archers using recurve bows and about.7 points for archers using compound bows, that is, in both cases, approximately.1% of the possible score per ranking place. Scores obtained in the Men s Recurve division at each of the four distances for World Cup 1 are shown in Figure 2. As is usually the case, the scores obtained at 7 m using the 122-mm target face were very similar to those obtained at 5 m using the 8-mm target face. The scores for the Women s Recurve division show a similar match between scores at those distances. Note that if the archer s group size increased linearly with distance, an archer s score at 5 m on an 8-mm target face would be expected to be similar to that obtained at a distance of 76 m on a 122-mm target face, that is, the archer s group size increases faster than linearly with distance (given similar weather conditions at both distances). Least squares lines of best fit for the Men s Recurve scores at 7 and 5 m at World Cup 1 are shown in Figure 3 for those archers in the linear portion of ing score 36 34 32 3 28 26 Men's Recurve WC1 213: distance scores 24 2 4 6 8 1 Figure 2. Men s Recurve distance scores. The lowest line is for 9 m, the highest line is for 3 m and the two centre lines are for 7 and 5 m. Score Men's Recurve WC1 213: 7 m & 5 m comparison 345 34 335 33 325 32 315 31 2 4 6 8 7 m 5 m Figure 3. Least-square lines of best fit for the Men s Recurve 7 and s. Figure 1 (with the y-axis scale changed). Note that while the scores at those two distances were similar, there was a small and increasing difference as the archer s ability increased. This strongly suggests that as the archer s ability increases, the relative importance of those factors, which degrade the archer s score more quickly than linearly with distance, increases. Factors such as wind drift 2 or variation in the bow s lateral angle (variable bow cant ) are hence potentially of significant interest. Analysis of the scores for the Women s Recurve division showed a similar trend, as do those from other similar events, such as the World Cups from 25 to 213, the World Archery Championships from 1995 to 213 and the Olympic Games from 1996 to 212. Assuming that an archer loses score through the combined impact of a number of independent causes and using the central limit theorem, it can be expected that the radial distance of the archer s arrows from the centre of the target will be normally distributed. Assuming, for simplicity, that archers score similarly at 7 and 5 m, the standard deviation of the archer s group on the target, W, can then be modelled as W = D expð A I + B + C DÞ ð1þ where D is the distance to the target in metres, I is the archer s skill level, A =.27, B = 2.37 and C =.4.

4 Proc IMechE Part P: J Sports Engineering and Technology Place 6 5 4 3 2 1 Men's Recurve WC1 213: final place 2 4 6 8 1 Place 35 3 25 2 15 1 5 Women's compound WC1 213: final place 1 2 3 4 5 6 Figure 4. Placing following the one-on-one matches for the Men s Recurve division. The solid line shows the expected placing if the higher-ranked archers win each match. The dots show the actual results. Figure 5. Placing following the one-on-one matches for the Women s Compound division. The solid line shows the expected placing if the higher-ranked archers win each match. The dots show the actual results. Those coefficient values correspond to the modelling used for many years by Archery Australia 4 (developed by Kay, Bysouth and Park, although not previously published in the learned literature). Coefficients A and B were selected such that the skill level index encompassed a useful range and C allowed for the non-linear effect of the target distance. Coefficients A and B were selected such that the World Record at the time (mid 197s) corresponded to a skill level index of approximately 1 and a skill level of 3 corresponded approximately to a beginner archer. Coefficient C was selected, so that an archer s score at a distance of 7 m on a 122-mm target face was approximately the same as for 5 m on an 8-mm target face. The score for a particular ranking round can then be calculated from overlaying a normal probability density function with that standard deviation on the relevant target face at each distance. Since an arrow touching a scoring line is allocated the higher score, allowance does need to be made for the diameter of the arrows used and Archery Australia assumes a typical diameter of 5. mm, representing the small diameter carbon fibre composite arrows used by most archers for target archery competitions. Using an archer skill level of I = 1 gives expected scores for 36 arrows of 31 at 9 m, 33 at 7 m, 33 at 5 m and 352 at 3 m, for a total of 1322 for the 144 arrow ranking round, corresponding to a ranking position of about 17th in the Men s Recurve division at World Cup 1. The relation between ranking position and placing after the one-on-one matches for the Men s Recurve and Women s Compound divisions at World Cup 1 is shown in Figures 4 and 5, respectively. Results for the other divisions show the same features. If the higher ranked archers win every match, those archers ranked higher than 56th will be allocated 57th place after the matches. Those ranked from 33rd to 56th will be allocated 33rd place. Those ranked from 17th to 32nd will be allocated 17th place. Those ranked from 9th to 16th will be allocated 9th place. Archers finishing in the top eight will be placed 1st to 8th depending upon their scores in their final matches. It can be seen from Figures 4 and 5 that in most cases the higher ranked archers do win the matches, although there are some upsets. Upsets can be expected because of the limited number of arrows shot in matches compared to the ranking round and particularly where the ranking results in archers of similar abilities competing against each other. Consequently, upsets are most likely to happen around ranking places 32 and 56, and that can be seen in Figures 4 and 5. In almost all cases, only those archers ranking in about the top 2 in the ranking round win sufficient consecutive matches to advance to the medal matches. That is, a high score and placing in the ranking round are vital if the objective is to win a medal. Lower ranked archers may win an occasional match, and are hence very dangerous competitors for the top archers, but almost never win sufficient consecutive matches to feature in the medal matches. Given a ranking of about 2, the required ranking scores for World Cup 1 were as follows: 132 for Men s Recurve and 1325 for Women s Recurve, both for the 144 arrow ranking round over 4 distances, and 695 for Men s Compound and 675 for Women s Compound, both for the 72 arrow ranking round at 5 m. The corresponding archer skill level indices using the Archery Australia model were as follows: 1 for Men s Recurve, 95 for Women s Recurve, 116 for Men s Compound and 16 for Women s Compound. Were the archers shooting recurve bows to use a 72 arrow ranking round at a distance of 7 m, as is done for the Olympic Games, then those archer skill level indices would result in a required score of 66 for the men and 646 for the women. Photographs of typical arrow group patterns from World Cup 1 are shown in Figures 6 1. Each group was for 36 scoring arrows, with those for the archers using compound bows also including a number of practice arrows. In each case, the diameter of the yellow area on the target face (the X ring, 1 ring and 9 ring) is 16 mm. The diameter of the X ring (the innermost ring) is 4 mm. The subtended angle of the 1 ring at a distance of 5 m is 5.5 min of arc. At a typical arrow

Park and Larven 5 Figure 6. Women s Recurve 3 m. Figure 8. Men s Compound 5 m. Figure 7. Men s Recurve 5 m. length of.7 m, keeping the bow s sight within the 1 ring corresponds to the archer holding the bow position to within a tolerance of approximately 6.5 mm. Figure 6 shows the arrow group at 3 m for one of the top archers in the Women s Recurve division. The group is obviously to the left. The archer s score was 347 of a possible 36 points. If the same group was moved a little to the right and down, the score could have been 353. Figure 7 shows the arrow group at 5 m for one of the top archers in the Men s Recurve division. The group is obviously to the low left. The archer s score was 335. If the same group was moved a little higher and to the right, the score could have been 341. Figure 8 shows the arrow group for one of the top archers in the Men s Compound division at 5 m. The two high arrows were practice shots and not counted in Figure 9. Women s Compound 5 m. the score. The archer scored 358, and the group was optimally placed for the highest score. Figure 9 shows the arrow group for one of the higher placed archers in the Women s Compound division at 5 m. The group is obviously too low, and the score was 341. Had the group been a little higher and to the left, the archer could have scored 346. Figure 1 shows the arrow group at 5 m for one of the top archers in the Men s Compound division. Two of the high arrows were practice shots and not counted in the score. The archer s score was 353, and the group was positioned for the optimum score. In this case, the majority of the archer s arrows were very close to the centre of the target (primarily in the X ring), with points mainly lost through Wilde [sic] shots. The digitised arrow group for every archer was moved to obtain the maximum score that the archer

6 Proc IMechE Part P: J Sports Engineering and Technology Score loss Men's Recurve: score loss at 5 m due to group posi on 25 2 15 1 5 24 26 28 3 32 34 36 Figure 11. Men s Recurve potential score loss. Figure 1. Men s Compound 5 m. could have obtained if it was optimally positioned on the target face. The coordinates of the centre of the group were calculated, and the group was moved so that it was centred on the target face. The score for the group in that position was then calculated and if it was higher than the actual score obtained by the archer, that difference was recorded as the potential score loss. If the score of the moved group was lower, the original score was retained. In a small number of cases, the group was moved slightly off-centre to obtain a higher score. The results for the 5 m distance for the archers using recurve bows and for the first 5 m set for the archers using compound bows are shown in Figures 11 14. In each case, the potential score loss has been plotted against the score obtained by the archer. Note that some archers did obtain the same scores for the distance (and hence the number of points plotted is fewer than the total number of archers), for example, 16 archers in the Men s Compound division scored 35 or higher. Observations from the pictures of the arrow groups and from the above analysis include Score loss 12 1 8 6 4 2 Women's Recurve: score loss at 5 m due to group posi on 24 26 28 3 32 34 36 Figure 12. Women s Recurve potential score loss. Score loss 12 1 8 6 4 2 Men's Compound: score loss at 5 m due to group posi on 3 31 32 33 34 35 36 Figure 13. Men s Compound potential score loss. Remembering that a score loss of 1 point represents approximately one ranking place and that the ranking place is critical in relation to the archer s final result following the one-on-one matches, some of the score losses were very severe indeed. The potential loss of score is not confined to only the less capable archers, except for the Men s Compound division. In that division, the top 22 ranked archers gave away just six points between them, and three of those points were for a single archer. Possibly, because the top archers in the Men s Compound division have smaller arrow groups than those for other archers, it is easier for them to ensure that their groups are optimally placed. A higher proportion of the women archers did not have their arrow groups optimally placed. The archers may have been changing their sight settings during the 36 shots at that distance. As that was not captured in the analysis (it would be impractical and intrusive to do so), the size of the archer s group shown on the target is greater than the archer s inherent skill level would indicate, and hence, the estimated potential gain from moving the archer s group on the target underestimates the potential score change. While the above figures do not show the results for archers using recurve bows at 3 m, the results were similar, as was the case for the second set for the archers using compound bows at 5 m.

Park and Larven 7 Score loss 9 8 7 6 5 4 3 2 1 Women's Compound: score loss at 5 m due to group posi on 3 31 32 33 34 35 36 Figure 14. Women s Compound potential score loss. SDx/SDy 3. 2.5 2. 1.5 1..5 Men's Compound: group shape at 5 m. 3 31 32 33 34 35 36 Figure 17. Group shape at 5 m for the Men s Compound division. SDx/SDy 3. 2.5 2. 1.5 1..5 Men's Recurve: group shape at 5 m. 24 26 28 3 32 34 36 Figure 15. Group shape at 5 m for the Men s Recurve division. SDx/SDy 3. 2.5 2. 1.5 1..5 Women's Compound: group shape at 5 m. 3 31 32 33 34 35 36 Figure 18. Group shape at 5 m for the Women s Compound division. SDx/SDy 3. 2.5 2. 1.5 1..5 Women's Recurve: group shape at 5 m. 24 26 28 3 32 34 36 Figure 16. Group shape at 5 m for the Women s Recurve division. The shapes of the archers arrow groups were examined by comparing the sample standard deviation horizontally with the sample standard deviation vertically. Figures 15 18 show the ratio of those for each division. If the ratio is 1, then the group was round. If the ratio is greater than 1, then the group was elongated laterally, or less than 1, then elongated vertically. While some archers had groups elongated vertically, the majority had groups elongated laterally, with the average ratio for archers using either recurve bows or compound bows being 1.15. The results for archers using recurve bows at 3 m were similar. If there was a gusty wind, it could be expected that the archer s Correla on Men's Recurve: correla on at 5 m.5.4.3.2.1. -.124 26 28 3 32 34 36 -.2 -.3 -.4 -.5 Figure 19. Correlation between the lateral and vertical arrow position for the Men s Recurve division. groups would be elongated laterally, but for this event, the wind strength was very low. Hence, it is likely to be the result of other factors. Lateral and vertical arrow positions showed a small positive correlation (an average correlation of.1) for the archers using recurve bows (a small tilt in group shape from upper right to lower left). The majority of the archers shot right-handed. Those archers using compound bows showed minimal correlation between lateral and vertical arrow positions (an average correlation of 2.3). Figure 19 shows the correlation for the Men s Recurve division.

8 Proc IMechE Part P: J Sports Engineering and Technology Place 6 5 4 3 2 1 Men's Recurve WAC 213: final place 2 4 6 8 1 12 Figure 2. Placing following the one-on-one matches for the Men s Recurve division. The solid line shows the expected placing if the higher-ranked archers win each match. The dots show the actual results. Place 6 5 4 3 2 1 Women's Compound WAC 213: final place 1 2 3 4 5 6 7 8 Figure 21. Placing following the one-on-one matches for the Women s Compound division. The solid line shows the expected placing if the higher-ranked archers win each match. The dots show the actual results. While the ranking round scores obtained at the World Archery Championships were a little lower than those for World Cup 1 due to the windier conditions, the same trends were apparent. The relation between ranking position and placing after the one-on-one matches for the Men s Recurve division at the World Archery Championships is shown in Figure 2 and for the Women s Compound division in Figure 21. The final placings following the one-on-one matches for the archers using recurve bows showed the same features as for World Cup 1, that is, despite the very strong winds, archers ranked in approximately the top 2 places dominated the final placings the strong wind did not materially impact the nature of the results, even though the scores were generally lower. The situation for those archers using compound bows was, however, quite different, with many more lower ranked archers featuring in the higher places following the oneon-one matches. This difference between the two bow types seems likely to arise through those archers using recurve bows, using basically similar techniques (although some more expertly than others), while there are significant differences in the manner in which archers using compound bows initiate operation of their mechanical release devices. It was quite apparent that those archers reaching the final stages of the competition with compound bows in this event were those who operated their release devices very quickly following their sight reaching the centre of the target rather than those who squeezed the trigger slowly while trying to hold their sight on the centre of the target. Potential score loss due to arrow group position at the World Archery Championships was of a similar magnitude to that for World Cup 1. However, following World Cup 1, the Australian archers were shown pictures of the arrow groups at that event together with the potential score loss, and various methods for optimally setting their sights were demonstrated. At World Cup 4, 213, a number of Australian archers were given direct feedback on an end-by-end basis of the required sight setting changes to optimally position their arrow groups (calculated by modelling their arrow groups and their equipment and expertise level in real time). Cumulatively, for the six Australian archers competing in the recurve divisions at the World Archery Championships, the potential score loss due to arrow group position was just 3 points compared to an average of 3 points per archer across the whole field of competitors and to a total of 17 points for the six Australian recurve archers in World Cup 1, that is, simply raising awareness of the issue was in itself very useful and effective. Nevertheless, the optimum strategy for archers to adjust their sight settings in real time remains a matter of ongoing research it is a matter of estimating the mean of an arrow group with very few data points and in a manner manageable by the archer while competing. The shapes of the archers arrow groups on the target at the World Archery Championships were affected by the wind, with the average ratio of the width of the group to its height increasing to 1.25, compared to 1.15 for World Cup 1. Summary The analysis of arrow groups showed that besides those archers competing at the highest levels in the Men s Compound division, many archers could potentially gain score and hence ranking places at major archery competitions simply by paying greater attention to the arrow group position on the target. That potential improvement in ranking position is then likely to translate directly into a more favourable final position after the one-on-one knockout phase of competition. Of the various factors that degrade an archer s score, it seems likely that those affecting the arrow s lateral position on the target are of greater importance than those affecting the vertical position. In particular, those factors that impact an archer s score more severely than linearly with distance are of importance, especially as the archer s ability increases.

Park and Larven 9 While the very strong wind during the one-on-one matches during the World Archery Championships, 213, had little impact on final placings for those archers using recurve bows, it significantly impacted those archers using compound bows and highlighted differences in technique. Acknowledgements The authors are grateful to World Archery for allowing them time during World Cup 1, 213, and the World Archery Championships, 213; permitting them to gather the data necessary for this article and for the kind assistance of the event officials during its collection. Declaration of conflicting interests The authors declare that there is no conflict of interest. Funding This research received no specific grant from any funding agency in the public, commercial or not-for-profit sectors. References 1. World Archery. Equipment rules, http://www.worldarchery. org/en-us/home/rules/constitutionrules.aspx (accessed 1 November 213). 2. Park JL.Minimising wind drift of an arrow. Proc IMechE, Part P: J Sports Engineering and Technology 212; 226(1): 52 6. 3. World Archery. Tournament results, http://www.world archery.org/en-us/results/results/bracketsandsummary.aspx (accessed 1 November 213). 4. Archery Australia. Score index, http://www.archery.org. au/faqs/records-awards-classifications/how-to-deter mine-rating-handicap (accessed 1 November 213).