# Influences of an Arrow's Aerodynamic Pressure Center on Recurve Bow Shooting
## 3 Results
### Arrow Behaviors Under Uniform Background Winds
#### 3.2.2 Changes in the Offset  
Figure 18 shows the offset of the arrow on the target and the radial offset in the flight process with time. As shown in Figure 18a, when the initial velocity is 57 m/s, the U\({}_{y}\) is 3 m/s, and the initial angular velocity is zero, the offset reaches the maximum of \(\delta_{\rm r}=0.27\) m, while \(\delta_{\rm r}\) is 0.125 m when the initial \(\gamma\) is zero. This implies that \(\gamma\) significantly affects the offset in the presence of background winds. This is probably because, when the initial angular velocity is zero, the initial \(\gamma\) is 3\({}^{\circ}\), and the boundary layer of the arrow becomes turbulent, which applies more drag, thus increasing the lateral displacement. Therefore, controlling the initial attack angle is a crucial strategy to help athletes improve their scores. When the crosswind speed (U\({}_{y}\)) is 2 m/s, the maximum deviation is 0.16 m, which is 0.1 m less than the deviation observed at 3 m/s. This finding indicates that the magnitude of the crosswind has a significant effect on the arrow's trajectory, confirming that, under crosswind conditions, the deviation is caused by the lateral component of the drag force, FD. The magnitude of wind velocity also affects the boundary-layer state of the arrow: the larger the wind velocity, the greater the drag on the arrow. When U\({}_{x}\) = 3 m/s, the maximum deviation is 0.077 m, which is 0.2 m less than the deviation caused by crosswind at the same wind speed. However, when the wind changes to a headwind, the deviation increases by approximately 0.007 m. This increase is attributable to the headwind's enhancement of the arrow's air resistance, leading to a slightly larger deviation than under tailwind conditions. However, because the largest \(\gamma\) is 0.49\({}^{\circ}\) under headwind conditions, \(C_{\rm p}\) remains stable in flight, and boundary-layer transition does not occur. The drag is low so that the offset is much smaller than that under crosswind. This also demonstrates that the crosswind affects the arrow more than headwind and tailwind. To illustrate the unique characteristic of the pressure center continuously varying with the arrow's motion, this study also examined the deviation of the arrow when the pressure center is fixed. As shown in Figure 18b, the variation in the arrow's deviation is shown with the pressure center fixed at 0.484 m, and a comparison with varying pressure center conditions is presented in Figure 18c. When the crosswind velocities are 3 and 2 m/s and the initial \(\gamma\) is not zero, the offsets of the arrow are separately 0.306 and 0.185 m, which separately increase by 0.04 and 0.02 m compared with those when \(C_{\rm p}\) is not fixed. This greatly influences the scores in archery competitions. In the case of headwind, the deviation is increased by 0.008 m compared to when the pressure center varies with arrow movement. This difference is significant and cannot be ignored. It further implies that the small variation in the pressure center in flight benefits the overall force on the arrow, thus improving accuracy. With an initial angular velocity of zero, the deviations are quantified in Table 5. This table presents the specific deviation values for both models across different wind conditions. In the context of archery, the mental fortitude and release stability of top athletes are undeniable. If these factors are excluded, an accurate assessment of the background wind and the corresponding scientific adjustments to the archer's posture are key determinants of performance. In contrast to previous research, and according to our new, more precise computational model, the adjustment strategies for athletes are as follows: Under crosswind conditions, the accuracy of the non-\(C_{\text{p}}\)-fixed model improves by approximately 15% relative  
Figure 18: Changes in the offset. (**a**) Changes in the offset with time; (**b**) changes in the offset with time under the fixed \(C_{\text{p}}\) position; (**c**) comparison of the offsets.