Outdoor archery, especially in long-range disciplines such as Bhutanese archery, is influenced by environmental factors, including air density, which affects arrow trajectory through aerodynamic drag. Although the effects of air density on projectile motion have been studied in ballistics, they have not been empirically examined in archery. In this study, we conducted online surveys with Bhutanese players and developed iterative arrow-trajectory models for four equipment setups to investigate how diurnal changes in air density affect arrow range. To validate these models, we conducted an experiment using a shooting machine alongside real-time weather data to quantify how air-density variations affected arrow range at a 145 m Bhutanese archery field in Thimphu, Bhutan. Archers' subjective estimates of air-density effects on arrow range averaged 0.69 m, while the iterative models predicted range changes of 0.11-0.25 m for a 0.05 kg/m3 air-density shift across the examined equipment setups. The range change observed during the shooting-machine trial (0.19 m) closely matched the predicted range change from the corresponding equipment setup in the iterative model (0.17 m). Overall, the findings suggest that archers can enhance accuracy by adjusting their aim according to expected air-density fluctuations throughout the day, with temperature serving as a practical on-field proxy for air-density changes. The study offers a framework for integrating air-density effects into archery performance, reducing reliance on mid-play trial-and-error.

Compound archery bows have an eccentric cam at the end of each bow limb. These cams are used to shape the bow’s force-draw characteristic. If the cams are not timed correctly, the archer will have arrows hit high or low on the target, depending on how firmly they pull into the bow when at full draw. The various commonly used methods to adjust cam timing are either indirect, imprecise or require elite archer expertise. This paper provides a new method that directly measures any rotation of the bow as the draw length is varied about the full draw position and is independent of the archer’s skill level. Only simple equipment is required.

Results from major international target archery competitions from 1995 to 2023 have been used to show the score trends and the probability of winning either a podium position or the event versus the archer's position in a ranking round. The probabilities versus ranking position fall approximately exponentially. Subjectively, archers need to rank at least in the top 16 to have a reasonable probability of winning a medal. Ideally, a team selection process should select those archers with the highest probabilities of winning at least a podium position at the international competition. That can be achieved by using the arrow value scores over the entire selection process, providing bonuses for exceeding given scores in ranking rounds or matches and by not including elimination matches in the selection process.

During an archery competition, archers frequently fail to correctly adjust their bow's sight so that their arrow groups are centred on the target. Arrows are shot in ends of three or six, depending on the phase of the competition, and consequently each end provides very limited data on which to make sight adjustments, although at the conclusion of the competition it is usually obvious if an archer has succeeded in the task or not. This paper considers three sight optimisation processes with a view to minimise score loss both in ranking rounds and in matches. It is shown that archers should take a more aggressive rather than a less aggressive approach to sight movements, especially for the first end. Each sight adjustment process can be implemented using a simple look-up table.

Results from major international target archery competitions from 1995 to 2024 have been used to show the score trends and the estimated probability of winning either a podium position or winning the event versus the three-archer team’s position in a ranking round. The probabilities fall approximately exponentially versus ranking position. Subjectively, teams need to rank at least in the top 7 to have a reasonable probability of winning a medal. The corresponding average ranking position of each of the three team members needing to be in the mid-20s. The unique impact of the Republic of Korea’s participation in recurve team events has also been considered.

Variation of the bow’s lateral angle (‘bow cant’ angle) affects the lateral position of arrows on the target, thus impacting an archer’s score. The displacement of arrows on the target depends approximately on the target distance squared and is hence of greatest impact at longer distances. A total of eight archers participated in this study, ranging in skill level from three who have performed at the highest levels internationally through to competent club-level archers, plus the author. The bow cant variation was measured and the impact on archers’ scores was calculated, assuming no other score loss mechanisms. The results show that the score loss associated with bow cant angle can be a substantial portion of an archer’s total score loss, particularly for elite archers using recurve bows.

One method used by archers and coaches to optimise archery equipment is to measure the size of arrow groups on the target prior to and following an adjustment. The group sizes are then used to determine if an equipment change assisted or detracted from the archer's performance. A model based on a Monte Carlo method and group size measurements from seven elite archers were used to test the validity of this process. The results showed that this method was neither an effective method nor useful process because the probability of false positives or false negatives was too great. A better approach to optimise archery equipment is to monitor the archer's skill level or average score over an extended time following any change.

Field archery is conducted on an archery course similar in layout to a golf course. Archers shoot at targets placed one after another, usually involving the archers shooting up, down and across slopes. Archers need accurate sight settings if they are to obtain high scores. However, the required sight settings for slopes differ from those on flat ground. One method used by archers is to set the sight to the horizontal distance to the target (the 'rifleman's rule'). It has been shown that method does not provide the required precision. It has also been shown that a simple 'percentage distance cut' is not viable. An alternative method is provided.

A Monte Carlo technique was used to study the arrow mass and stiffness tolerances necessary to minimise the degradation of an archer’s likely score at normal competition distances. The archer’s arrow groups on the target were modelled using a half-normal distribution, where the standard deviation of the arrow’s distance from the centre depends upon the archer’s skill level and target distance. Equipment tolerances were modelled by varying the arrow positions on the target in either or both the vertical and lateral axes. This study showed that score loss due to arrow tolerance can be reduced well below score losses resulting from other sources by matching arrow mass to ±0.5 grains and arrow stiffness to ±1%.

This work examines the distribution of shots in target archery. In previous work, based on a small sample size, it was concluded that the radial distance [Formula: see text] from the centre of the target to the point of impact had a half-normal distribution. In this work, with a very large sample size, we find that [Formula: see text] follows a Rayleigh distribution very closely, and that only varying the scale, this holds for subpopulations of interest: compound, recurve, male, female, indoors, outdoors and from intermediate to elite skill level. The importance and utility of an accurate statistical model of shot distribution is demonstrated by developing a model of the expected increase in qualification score due to arrow diameter, and the probability of winning head-to-head matches, conducted under World Archery rules. It is concluded that the choice of shot distribution has a significant impact on the accuracy of predictive models of archery performance and that shot distribution is accurately characterized by the Rayleigh distribution. It is found that there are substantial benefits in selecting the maximum permitted arrows shaft diameter, for indoor archery. The benefits vary with archer skill level but are not confined to elite archers.

Major target archery competitions are conducted outdoors and rarely pause due to inclement weather. The impact of the atmosphere on both the equipment and the archer is a very important consideration, affecting the arrow in free flight and the archer’s aim. This article provides a survey of research covering the arrow’s initial conditions as it enters its free flight phase, its behaviour during free flight including wind drift and the effects of wind on the archer’s aim. Potential areas for further investigation are highlighted.

Archers frequently lose score by having their sights set incorrectly, resulting in off-centre groups on the target and lower scores than would otherwise have been possible. The archer's group on the target has been modelled using a normal distribution where the size of the archer's group depends upon the archer's skill level and target distance. Off-centred groups were modelled by varying the arrow positions on the vertical axis and the score loss at the usual competition distances using a Monte Carlo technique. A method of using the centroid of each three or six-arrow end is used to optimise the sight setting and minimise score loss, realising that this is done using data from a very limited number of shots. It is best to correct for only a portion of the error for each end, rather than for the full error.

Major international target archery competitions include World Cups, World Championships and the Olympic Games. Those events include both a 72-arrow ranking round and then one-on-one ranked knock-out matches, until one archer or team remains. Previous modelling of the probabilities of winning podium positions at these events has assumed that the distance of an archer’s arrows from the centre of the target is normally distributed and that an archer’s performance levels in ranking rounds and matches are the same. This paper considers those two assumptions. For the top level of men’s recurve archers, this study determined that those assumptions are reasonable.

Target archery competitions are conducted outdoors, exposed to the prevailing weather conditions. Competition takes place over long target distances and wind drift of the arrows is a significant cause of score loss. In this article, the dynamic behaviour of an arrow in free flight and wind drift are modelled, allowing for both the arrow initially aligning itself with the resultant airflow and the arrow flexing. The arrow has been modelled as an inextensible flexible beam, and the resulting partial differential equations solved using a finite difference method. Lift and drag for the various arrow components have been calculated using the local angle of attack for those components. It is shown that archers should use small diameter arrow shafts with a high density in order to minimise wind drift. Even for the best arrows, the drift for a 3-m/s side wind is greater than four score rings for a recurve bow at a target distance of 70 m with a 1220-mm diameter target face and nearly two score rings for a compound bow at a target distance of 50 m with an 800-mm diameter target face.

During competitions, archers lose points due to errors that vary linearly or quadratically according to the distance to a target. Minimizing the quadratic variables, such as bow cant variation, should result in improvements in an archer’s performance at longer distances in major competitions. Theoretically, a bow cant angle variation of 0.1° from shot to shot can significantly affect an individual’s score. However, this error factor has not been directly measured or observed. Thus, a wireless sensor suite was developed to measure the bow’s movements and confirm that such variations exist. This unit can measure up to 0.05° in multiple orientations and record additional information, such as acceleration at 200 Hz sampling rate. Based on results from experiments with six state-level archers, the wireless sensor system successfully recorded more than 200 shots. From the acquired data, variations were reported from shot to shot. Therefore, it is predicted that an archer may lose up to 23 points per 36 arrows shot using a recurve bow due to this lateral bow angle variation.

The World Archery shooting rules provide some latitude in relation to an archer's position on the shooting line. This means that the archer could stand at different distances from the target, while still meeting competition regulations. One would think that standing closer to the target should be an advantage; however, most archers do not take this approach. This article considers the score increase that may be attributable to standing in the optimum position, which can lead to a potential higher ranking place at major international indoor and outdoor archery competitions.

Major international target archery competitions usually include a 72-arrow ranking round, followed by one-on-one knockout matches conducted over a small number of arrows, until one archer or team remains. This article considers the mixed pair team event that includes teams consisting of one male and one female archer, both using the same bow type. The relation between a team's place in the ranking round and the likelihood of that team finishing in a top position following the one-on-one knockout matches has been modelled and compared to the results from competitions from 2010 to 2017 inclusive. The team's ranking round score has been used to indicate the ability of each archer in the matches and to calculate the probability of the team winning sufficient matches in succession to succeed in the competition. The study found that the probability of the team winning the competition decreases exponentially with ranking place. Due to the importance of the ranking round, a team must finish in or near the top seven places in the ranking round for the team to have a reasonable chance at winning a medal.

Major international target archery competitions include World Cups, World Championships and the Olympic Games. These events include both a 72-arrow ranking round and then one-on-one ranked knockout matches, until one archer or a team remains. To win either an event or at least a podium position, it is necessary for the archer or team to do very well in the ranking round. This article considers the individual, three-archer team and mixed team events over the period 2010–2017 and provides score objectives for each of them for future years and for the World Championships in 2019.

Arrows are available in various straightness grades. Their grouping ability as the straightness varied was assessed using a compound bow and shooting machine. The research showed that archers would benefit from selecting arrows with the highest straightness grades (as might be expected). In addition, nock selection was determined to significantly impact group size. The fletches needed to be set at an angle to the longitudinal axis of the arrow shaft in order to have the arrows spin while in free flight, as that further reduced the group size.

Major international target archery competitions usually include a 72-arrow ranking round and then one-on-one knockout matches conducted over a small number of arrows until one archer remains. This article considers the relation between an archer's placing in the ranking round and the likelihood of that archer finishing with a high place following the one-on-one matches. The archer's ranking round score has been used as an indication of the archer's ability in the matches and used to calculate the probability of the archer winning sufficient matches in succession to succeed in the competition. It has been found that the probability of the archer winning the competition decreases exponentially with ranking place. This has been compared with the results from all major international target archery competitions between 2000 and 2014 inclusive and provides a good match. Given the importance of the ranking round, it is suggested that an archer needs to finish in about the top 8 places in the ranking round if the archer is to have good prospects of winning a medal. The score trend for eighth place provides an indication of the likely score required in future competitions, such as the 2016 Olympic Games.