Effects of diurnal air-density variation on arrow range in Bhutanese archery

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.