Experimental investigation on the aerodynamic drag of basketballs: Effects of surface characteristics, inflation pressure and yaw angle

Summary

Currently, only a limited number of studies have conducted basic measurements and evaluations of the aerodynamic drag coefficient (C_D) of basketballs. Through wind tunnel experiments, this study investigates the variations in aerodynamic drag and drag coefficients of basketballs across different degrees of surface wear, inflation pressures, yaw angles, and surface roughness characteristics. The results indicate that the C_D of a basketball gradually decreases with increasing flight speed and tends to stabilize (C_D decreased from 0.5–0.55 to 0.3–0.4). Basketballs with lower inflation pressure experience slightly higher aerodynamic drag. A yaw angle of 0° results in the minimum C_D. Furthermore, different surface textures exert varying influences on the C_D at different flight speeds; basketballs with rougher surfaces exhibit higher C_D at low flight speeds but lower C_D at high flight speeds compared with basketballs with smoother surfaces. A mild “drag crisis” was observed across all tested scenarios.

Graphical abstract

Highlights

• •Surface wear and rough textures significantly alter basketball aerodynamics
• •Reveals for the first time how inflation pressure affects basketball drag
• •Yaw angle changes affect channel-flow interactions, altering basketball aerodynamics

Applied sciences; Engineering

Introduction

Basketball is a highly competitive sport. In competitive basketball, the ball’s trajectory during passing and shooting sequences—phases of free flight—is the primary determinant of gameplay outcomes. According to the analysis by Tran and Silverberg,¹ the optimal release velocity for a free throw is 7.2 m/s. Building upon these kinematic constraints, the release velocity for a three-point shot typically ranges from 8.5 m/s to 9.5 m/s, whereas the initial velocity for passing is significantly higher. During flight, the trajectory of the basketball undergoes corresponding changes due to the influence of initial conditions, aerodynamic drag, lift, the Magnus force, and gravity.² In competition, precise shooting and passing are critical factors for victory. Therefore, investigating the aerodynamic characteristics of basketballs is essential for establishing accurate trajectory models, providing supplementary guidance for player training, and optimizing match equipment.

In the realm of ball sports, aerodynamic research is progressively advancing. Goff³ summarized the progress of aerodynamic research on 18 types of flying ball and projectile sports, pointing out that such studies not only assist in improving training but also apply to the optimization of match equipment, which is essential in highly competitive sports. As vital tools for aerodynamic research, wind tunnel testing and computational fluid dynamics (CFD) simulations are irreplaceable methods. Relevant wind tunnel studies already exist for badminton,⁴ American football,⁵ cricket,⁶ soccer,⁷ table tennis,⁸ and volleyball.^9,10 By fixing the research object within a wind tunnel and utilizing a high-precision force balance, aerodynamic forces can be directly obtained to establish comprehensive aerodynamic databases. Asai et al.⁹ conducted aerodynamic tests based on wind tunnel experiments on two types of new and old volleyballs with different surface structures and analyzed the potential aerodynamic differences between them. CFD simulations can explain differences and changes in aerodynamic forces from the perspective of fluid mechanisms and play an important guiding role in the aerodynamic optimization of ball surfaces. In the case of soccer, CFD analysis¹¹ was utilized to simulate the surrounding flow field, visualizing how panels and seams influence both boundary layer separation and the global turbulent structure. Numerical simulation results for badminton indicate¹² that the shuttlecock’s structural construction is crucial to the aerodynamic drag encountered during flight. Comparatively, there is less research related to the aerodynamics of basketballs, and there remains a lack of detailed aerodynamic databases and elucidations of aerodynamic mechanisms. While some studies have employed video analysis to quantify drag,¹³ the precision of such optical methods limits the accuracy of drag quantification, necessitating further high-fidelity investigation.

In elite basketball leagues, long-range and even ultra-long-range shooting have become essential offensive strategies. During such long-distance shots, the basketball remains airborne for several seconds, making aerodynamic drag a critical factor governing the flight trajectory after release. Quantifying the aerodynamic drag experienced during flight is a fundamental parameter for accurately predicting and reconstructing the basketball’s trajectory. Furthermore, this quantification facilitates in-depth analysis of optimal release parameters and offers constructive recommendations for player training. The China University Basketball League (CUBAL) serves as a vital platform for developing high-level basketball talent. Beyond training in basketball skills and physical fitness, a comprehensive understanding of the aerodynamic characteristics of the basketball during flight plays a pivotal role in assisting players to further master their shooting techniques. With the aim of providing auxiliary guidance for CUBAL player training and filling the gap in basketball aerodynamic data, this article is based on wind tunnel experiments and considers the effects of degree of wear, inflation pressure, yaw angle, and surface roughness characteristics on the aerodynamic characteristics of basketballs. Existing literature⁹ suggests that the roughness of a sphere is a significant factor affecting aerodynamic drag. However, almost no literature has considered the influence of the ball’s inflation pressure on its aerodynamic characteristics. Variations in inflation pressure alter the structural stiffness of the carcass. It is hypothesized that reduced pressure induces static aeroelastic deformation, modifying the effective frontal area. The surface texture of the basketball also exerts a certain influence on aerodynamic drag during flight, particularly when the yaw angle changes, which may significantly impact aerodynamic characteristics. This study employs a custom-designed model support system to fix the basketball in the wind tunnel for testing. As the rotation of the ball is not currently considered, the lift coefficient during the basketball’s flight is outside the scope of this paper; therefore, only the drag coefficient (C_D) during flight is considered for the time being. The structure of the article is shown in Figure 1.

Figure 1.

The structure of the article

Results

In this study, two types of size 7 basketballs featuring distinct surface textures (CUBAL and Li-Ning) were employed for aerodynamic testing; the surface textures of the basketballs are illustrated in Figure 2. For analyzing the CUBAL basketball, one brand new and two used balls were utilized, while a brand new ball was employed for the Li-Ning basketball analysis. The aerodynamic characteristics of the different basketballs were evaluated under various flight speeds, surface wear levels, inflation pressures, yaw angles, and surface roughness characteristics, with all experimental configurations listed in Table 1. The design of the test apparatus was adapted from literature.¹⁴ For specific details regarding the experimental setup and data processing methods, please refer to the method details and quantification and statistical analysis sections within the STAR Methods.

Figure 2.

Surface texture of basketball

(A) Surface texture of CUBAL basketball.

(B) Surface texture of Li-Ning basketball.

Table 1.

Setup of test configurations

Factor	CUBAL			Li-Ning
	New ball	Old ball 1	Old ball 2
Speed (m/s)	2.6–17.2	2.6–17.2	2.6–17.2	2.6–17.2
Surface wear	brand new	used ball	used ball	brand new
Inflation pressures (bar)	0.3, 0.4, 0.5, and 0.6	0.3, 0.4, 0.5, and 0.6	0.3, 0.4, 0.5, and 0.6	0.5
Yaw angle	0°, 45°, and 90°	0°	0°	0°
Surface roughness characteristics	pebbled texture	pebbled texture	pebbled texture	ribbed texture

Effect of surface wear on basketball drag

Figure 3 presents the variations in aerodynamic drag force (F_D) and C_D for the CUBAL new ball and old balls under different flight speeds, with the inflation pressure maintained at 0.5 bar. As the flight speed increases, the F_D experienced by the basketball gradually increases, while the C_D generally exhibits a downward trend; however, a precipitous reduction in the C_D is observed near a flight speed of 5 m/s. The right side of Figure 3 displays the curve of the C_D versus Reynolds number for a smooth sphere.¹⁵ It can be observed that the overall trend of the basketball’s C_D under different Reynolds numbers is consistent with that of a classic smooth sphere (highlighted in the red circle). Surface roughness promotes premature boundary layer transition, shifting the drag crisis to a lower Reynolds number. This trend suggests that within the tested speed range, the basketball undergoes a “drag crisis”—a transition characterizing the shift from subcritical to supercritical flow regimes.

Figure 3.

The variation of F_D and C_D of the new and old CUBAL balls at different flight speeds

From the curve of F_D versus flight speed, when the flight speed is less than 5 m/s, the F_D on the CUBAL new ball is slightly greater than that on the two old balls. As the flight speed increases, the F_D of the new ball gradually becomes smaller than that of the old balls. This results in the C_D of the new ball being lower than that of the old balls when the flight speed exceeds 5 m/s (the maximum C_D observed for the old ball was 116.7% of the new ball’s value), making the flight of the new ball more aerodynamically efficient at high speeds. A reasonable explanation for this phenomenon is that at lower flight speeds or Reynolds numbers, the airflow over the basketball surface remains laminar. Although the rougher surface of the new ball may induce greater skin friction drag, the total drag is still primarily dominated by pressure drag. As the Reynolds number increases, the rougher surface of the new ball promotes an earlier transition of the boundary layer from laminar to turbulent. This roughness effectively acts as a turbulator (or vortex generator), energizing the boundary layer. This transition delays flow separation, thereby reducing the pressure drag experienced by the new ball. Since the total aerodynamic drag in this regime is dominated by pressure drag, the F_D and C_D of the new ball become significantly lower than those of the old ball at high speeds, a trend that is particularly evident when the flight speed exceeds 10 m/s.

Okubo and Hubbard¹³ estimated the C_D of a basketball to be 0.54 by using cameras to track free-fall and rebound trajectories. The literature results align closely with the measurements of the new ball in this paper at flight speeds less than 4 m/s. It is worth noting that obtaining the C_D of basketballs at higher flight speeds via the free-fall method is difficult. Based on the wind tunnel test results, this article suggests that the C_D of the basketball stabilizes between 0.3 and 0.4 when the flight speed exceeds 6 m/s; this aligns well with the basketball speed when taking free throws and three-pointers.¹

Effect of different inflation pressures on basketball drag

Tests were conducted on the CUBAL new and old balls under different inflation pressures, with test flight speeds selected at 4, 6.2, 8.1, 10, 11.1, and 14.1 m/s. Figure 4 shows the variation curves of F_D and C_D for CUBAL new and old balls under different flight speeds and inflation pressures. From the F_D curves, it can be found that for basketballs with different degrees of wear and varying inflation pressures, the trend of F_D variation with flight speed is generally consistent, especially at high flight speeds. For the new ball, the F_D is the highest when the inflation pressure is 0.3 bar; as the inflation pressure increases, the F_D decreases slightly. For the old ball, there is a consistent trend where, at higher flight speeds, the F_D of the ball with lower inflation pressure is slightly greater than that of the ball with higher inflation pressure. Overall, the influence of the basketball’s inflation pressure on the F_D experienced during flight is not as significant as the influence of flight speed.

Figure 4.

The variation of F_D and C_D of the new and old CUBAL balls with flight speed under different inflation pressures

From the C_D curves, the differences in F_D due to different inflation pressures are more distinct. When the flight speed is less than 10 m/s, basketballs with lower inflation pressure exhibit larger C_D, and the C_D decreases as the inflation pressure increases. Using 0.3 bar as a baseline, the maximum difference in C_D compared with other pressure conditions reaches 15.4%. As the flight speed increases, the C_D of basketballs with different inflation pressures gradually converge after the flight speed exceeds 10 m/s, eventually maintaining a range between 0.35 and 0.4, with the CUBAL new ball showing the lowest C_D. Considering the most common velocity range of basketballs in matches, insufficient air pressure not only affects the player’s feedback for dribbling and shooting but also influences the flight trajectory to a certain extent. Therefore, it is necessary to ensure that the basketball pressure remains within a reasonable range during games.

The precise mechanism linking inflation pressure to F_D is not fully elucidated in existing literature. However, surface micro deformation during flight caused by insufficient pressure cannot be ignored. Deformation of the sphere may compromise its streamlined geometry, inducing premature flow separation. This separation expands the wake region, thereby increasing pressure drag. Further investigation into this mechanism requires additional research support.

Effect of different yaw angles on basketball drag

The presence of specific stitching direction on the basketball surface may influence F_D during flight. Considering that the channels on the basketball surface account for a relatively large proportion of the total projected area, the angle between the channels and the incoming flow differs at various yaw angles, which may cause changes in the airflow over the basketball surface. This study tested the CUBAL new ball at three yaw angles: 0°, 45°, and 90°, with measurements taken at an inflation pressure of 0.5 bar.

Figure 5 presents the variation curves for F_D and C_D under the three yaw angle conditions. It is evident that the F_D and C_D experienced by the basketball at yaw angles of 45° and 90° are significantly greater than at 0°. At all tested flight speeds, the difference in F_D between the 45°/90° yaw angles and the 0° yaw angle exhibits a trend of initially decreasing and then expanding. When the flight speed is less than 10 m/s, the F_D on the basketball at a 90° yaw angle is significantly greater than in other conditions (the C_D can reach up to 176.5% of that at the 0° yaw angle). When the flight speed exceeds 10 m/s, the F_D and C_D on the basketballs at 45° and 90° yaw angles tend to converge, with both consistently remaining higher than that at 0° yaw angle (the C_D can reach up to 139.3% of that at the 0° yaw angle).

Figure 5.

The variation of F_D and C_D of the new CUBAL ball with flight speed at different basketball yaw angles

It can be concluded that the angle between the channels on the basketball surface and the incoming flow—namely, the yaw angle—has a significant impact on the magnitude of drag during flight. In basketball games, players typically adjust the yaw angle to 0° when shooting or passing; this is beneficial for flight as the C_D is minimized, helping the ball travel faster and farther. During shooting, players usually add backspin to ensure flight stability; however, backspin applied at 45° and 90° yaw angles might lead to flight instability. Further research on the effect of basketball rotation on aerodynamic drag needs to be advanced.

Effect of different surface roughness characteristics on basketball drag

Generally, the basketball surface is characterized by a pebbled texture (as shown in Figure 1A). Depending on different usage requirements (such as outdoor balls) or aesthetic design needs, basketball surfaces may adopt different textures. This study measured the F_D and C_D of two commercially available size 7 basketballs with different surface textures; both were brand new, and the inflation pressure was maintained at 0.5 bar.

Figure 6 shows the variation curves of F_D and C_D for the CUBAL new ball and the Li-Ning new ball under different flight speeds. Viewed holistically, the F_D of both basketballs increases with increasing flight speed, while the C_D gradually decreases with increasing flight speed. Notably, when the flight speed is less than 8 m/s or greater than 16 m/s, the F_D and C_D of the Li-Ning basketball are both greater than those of the CUBAL basketball; however, when the flight speed is between 8 m/s and 16 m/s, the F_D and C_D of the CUBAL basketball are significantly greater than those of the Li-Ning basketball. This is a very interesting phenomenon, indicating that the surface roughness characteristics have a substantial impact on the aerodynamic characteristics during flight. Surface roughness characteristics significantly influence the flow characteristics or flow separation around an object,¹⁶ and the texture of a basketball similarly creates different disturbances to the airflow near the surface. As observed in the C_D curves in Figure 6, both basketballs exhibit a decrease in C_D, followed by a relatively stable phase. The stabilization phase for the CUBAL basketball occurs at flight speeds exceeding 5.2 m/s, whereas for the Li-Ning basketball, it occurs only after 11.1 m/s. This implies that the surface material employed by the Li-Ning basketball may delay the onset of the potential “drag crisis”, thereby increasing the critical Reynolds number interval.

Figure 6.

The variation of F_D and C_D of basketballs with flight speed under different surface roughness characteristics

Regarding the flight speed characteristics of basketballs in matches, considering scenarios where the flight speed is less than 10 m/s, the CUBAL basketball is evidently superior, as a smaller C_D helps the ball travel farther and faster. Regarding the influence of surface roughness characteristics on the flow characteristics around a basketball, further analysis using numerical simulation could be conducted. In the design of basketball surface textures, in addition to considering aerodynamic characteristics, the tactile feel of the ball must also be considered, as this is crucial for player usage.

Discussion

Factors influencing the aerodynamic characteristics of basketballs

Based on wind tunnel experiments, this study provides an in-depth investigation into the effects of flight speed, degree of wear, inflation pressure, yaw angle, and surface roughness characteristics on the aerodynamic drag of basketballs. The experimental results indicate that the magnitude of aerodynamic drag experienced by a basketball during flight is determined by the combined action of multiple factors, representing a complex aerodynamic phenomenon.

In exploring the influence of these factors on aerodynamic drag, it is undeniable that flight speed exerts the most significant impact. For a smooth sphere flying at low speeds—specifically in the low Reynolds number range—the boundary layer on the surface remains laminar. The fluid momentum within a laminar boundary layer is low and insufficient to overcome the adverse pressure gradient on the rear half of the sphere, leading to premature flow separation. This results in the formation of a wide, low-pressure turbulent wake region behind the sphere. The pressure difference between the front and rear causes a high C_D. As speed increases, the Reynolds number reaches a critical value. At this point, the boundary layer undergoes transition before separation, changing from laminar to turbulent. A turbulent boundary layer possesses a stronger fluid mixing effect, capable of transporting high-momentum fluid from the outer layer into the inner layer, thereby possessing higher energy to resist the adverse pressure gradient. The downstream movement of the separation point drastically contracts the wake region, leading to a rapid decrease in pressure drag and a sharp reduction in the C_D.¹⁷ For the CUBAL basketball tested in this study, the “pebbled” texture on the surface likely acts as an efficient turbulator; the rough surface introduces sufficient disturbance at lower speeds to promote the transition of the boundary layer from laminar to turbulent, causing the C_D to decrease earlier at lower Reynolds numbers compared with a smooth sphere. In contrast to the CUBAL basketball, the “ribbed” surface texture of the Li-Ning basketball exerts a starkly different influence on aerodynamic drag (Figure 6). This indicates that the distinct surface textures play significantly different roles in the development of the boundary layer.

Secondly, this study observed that the C_D of the CUBAL basketball at a 0° yaw angle drops rapidly near a Reynolds number of Re = 8.9 × 10⁴ (corresponding to a speed of approximately 5.2 m/s), falling from a range of 0.5–0.55 to 0.3–0.35. This phenomenon likely indicates a potential “drag crisis”, the physical essence of which is a fundamental change in the flow state of the boundary layer.¹⁸ Kensurd and Smith¹⁹ noted that rough sports balls, such as baseballs, exhibit a milder drag crisis compared with smooth spheres. The critical Reynolds number (Re_crit) for a smooth sphere is approximately 3.5 × 10⁵, while for a golf ball with dimples, it is approximately 4 × 10⁴–8 × 10⁴.²⁰ Based on the test results in this study, the Re_crit for the basketball is approximately 6.9 × 10⁴–8.9 × 10⁴, falling exactly between the two, which corroborates the possibility that basketballs experience a “drag crisis” within the tested Reynolds number range. A similar “drag crisis” phenomenon was also observed in wind tunnel tests of other basketballs. In reality, the occurrence of the “drag crisis” enables the basketball to travel faster and farther. Consequently, understanding the specific velocity range in which this crisis occurs is beneficial for helping players determine the optimal release conditions for their shots.

It is important to note that, compared with a new ball, the microscopic particles on the surface of an old ball are smoothed due to wear, resulting in a reduction in effective relative roughness (k/D). A decrease in relative roughness theoretically delays the onset of the drag crisis, implying that an old ball requires a higher speed to trigger the turbulent transition. However, this phenomenon was not distinct in the experimental results across basketballs with different degrees of wear, suggesting that more dense Reynolds number test conditions may be required. Analysis of the test results regarding different yaw angles and surface roughness characteristics reveals that a mild “drag crisis” occurred in all test conditions. Furthermore, compared with the CUBAL basketball at a 0° yaw angle, the onset of this “drag crisis” was consistently delayed in all other cases, which indicates that the surface roughness and its characteristics exert a profound influence on the aerodynamic properties of the sphere. A comparison of the experimental results for the CUBAL and Li-Ning basketballs reveals that the two balls exhibit distinct aerodynamic behaviors across different velocity ranges (Figure 6). This indicates that the surface roughness characteristics and microstructures exert a pronounced influence on the aerodynamic characteristics. Ward et al.²¹ investigated the influence of various surface texture characteristics on aerodynamic drag using 3D-printed soccer balls. Their study indicated that increasing surface roughness by introducing textures—especially those that are larger and more prominent—can effectively reduce Re_crit. This finding bears a strong resemblance to the characteristics of the CUBAL basketball analyzed in this work. In contrast, the Li-Ning basketball features a relatively smaller texture volume. This distinction corroborates our experimental results. Although there are existing studies concerning the fluid mechanisms of surface microstructures,^22,23 research specifically addressing the impact of complex spherical surface structures on fluid dynamics remains limited, and the underlying mechanisms warrant further investigation.

Existing literature²⁴ largely focuses on the effect of inflation pressure on rebound characteristics, ignoring its aerodynamic effects. This study quantifies the influence of inflation pressure on basketball aerodynamic drag in a wind tunnel environment for the first time. The results show that low pressure leads to increased drag at flight speeds below 10 m/s. We propose two possible coupling mechanisms to explain this phenomenon: (1) Static aeroelastic deformation²⁵: a basketball is not a rigid body but a pre-tensioned flexible membrane structure. During flight, the stagnation point at the front of the sphere bears the maximum dynamic pressure. For a low-pressure basketball, the shell stiffness is insufficient to maintain a perfect spherical shape, and the frontal area may undergo slight flattening deformation under aerodynamic forces. This geometric change increases the effective frontal area or alters the surface curvature distribution, promoting earlier flow separation. (2) Dynamic flow-induced vibration²⁶: in the wake region behind the sphere, vortex shedding generates periodic pulsating pressure. When the inflation pressure of the basketball is insufficient, the natural frequency of the shell decreases, making it more susceptible to excitation by pressure pulsations in the wake, resulting in surface vibration. This structural vibration extracts energy from the flow field, macroscopically manifesting as increased drag. Pan²⁷ conducted CFD numerical simulations of a basketball in flight, incorporating fluid-structure interaction (FSI) effects. By establishing monitoring points on the windward surface, Pan observed that as the flight velocity varied between 2 m/s and 8 m/s, the windward surface exhibited deformations ranging from 0.019 to 0.046 cm. This finding confirms that basketballs indeed undergo deformation during flight. Pan’s observations provide indirect support for our “static aeroelastic deformation” hypothesis. Although the study did not explicitly address the influence of inflation pressure on surface deformation, it is reasonable to hypothesize that basketballs with lower inflation pressure exhibit more pronounced deformation at low wind speeds. However, as the wind speed increases, the magnitude of surface deformation tends to converge. This finding has practical implications for competitive sports: maintaining standard inflation pressure is necessary not only to ensure the tactile feel of the rebound but also to guarantee the aerodynamic consistency of the shooting trajectory. Insufficient pressure causes the ball to decelerate faster in the air, leading to “short” shots in long-distance attempts.

Unlike an ideal sphere, the surface of a basketball features prominent channels. This study found that non-zero yaw angles lead to a significant increase in aerodynamic drag. This phenomenon can be explained by a variant of the “seam-shifted wake” effect,²⁸ which has recently gained attention in baseball aerodynamics. Issakhanian²⁹ noted that baseball seams can also serve as boundary layer trips, capable of creating independent flow separation points under specific conditions. In our study, when the basketball is positioned at a 0° yaw angle, the influence of the channels on the boundary layer is symmetric, and the flow field structure is relatively stable. However, when the yaw angle changes, a channel on one side may move precisely into a sensitive region of the laminar boundary layer. If the channel acts as a large roughness element triggering a local transition while the smooth region on the other side remains laminar, this leads to asymmetric flow separation. Although this asymmetry primarily generates lateral force, it simultaneously disrupts the symmetry of the wake, increasing induced drag. More importantly, if the channel is located near the separation point, it may act to “fix” the separation point, preventing it from moving sufficiently downstream as it would on a purely rough surface, thereby causing the wake region to widen and pressure drag to increase. In actual games, players typically impart strong backspin to the ball when shooting. An important aerodynamic function of rotation is to “average out” this yaw angle effect. High-speed rotation renders the surface features (pebbles and channels) effectively uniform relative to the incoming flow, thereby mitigating the extreme drag fluctuations observed in static tests. This also explains why shooting trajectories with stable rotation are more stable and predictable than non-rotating shots.

The high-speed C_D measured in this study (0.3–0.4) is significantly lower than the value of 0.54 derived by Okubo and Hubbard¹³ via video trajectory analysis. This discrepancy primarily stems from differences in experimental methodology: Okubo’s data were derived from free-fall and rebound experiments, where the average speed was likely lower, keeping the ball in the subcritical regime for a longer duration. In contrast, this wind tunnel experiment covered the complete supercritical regime. Additionally, the basketball in video analysis is in a deceleration process, involving unsteady forces and added mass forces, whereas wind tunnel testing involves steady flow.

Aerodynamic parameters are indispensable for the dynamic modeling of basketball flight trajectories. Utilizing the aerodynamic database established in this study, flight trajectories can be described and modeled with greater precision, facilitating the analysis of how different release parameters affect shooting outcomes. Previous studies, such as those by Huston and Grau,³⁰ Silverberg et al.,³¹ and Inaba et al.,³² have employed equations of motion to simulate basketball trajectories; however, due to the absence of experimentally measured aerodynamic coefficients, the accuracy of these models remains limited. In recent years, auxiliary basketball training tools have proliferated, particularly those utilizing virtual reality (VR) for athlete development.³³ A critical success factor for VR training is the provision of realistic feedback regarding the shooting trajectory; indeed, the fidelity of this feedback directly determines the efficacy of the training. In summary, the aerodynamic database established in this study aims to facilitate the construction of more precise flight trajectory models. Furthermore, it serves to help players gain a deeper understanding of the flight characteristics of different basketballs and provides a scientific basis to assist basketball leagues in the selection of suitable match balls.

Main findings

Basketball is a highly popular and competitive sport where the ball remains in an airborne phase for the majority of a match. While aerodynamic characteristics govern flight behavior, comprehensive research specifically targeting basketball aerodynamics—particularly regarding pressure and texture—has remained limited. Focusing on the official CUBAL match ball and utilizing another model (Li-Ning basketball) for comparison, this study investigates the key factors influencing the aerodynamic characteristics of basketballs. Based on wind tunnel experiments, this study conducted aerodynamic drag tests on size 7 basketballs, considering the effects of flight speed (Reynolds number), degree of surface wear, inflation pressure, flight yaw angle, and surface roughness characteristics on aerodynamic drag during flight. The main conclusions are as follows.

• (1)The C_D of a basketball during flight decreases as the flight speed increases and gradually stabilizes between 0.3 and 0.4. Regarding surface wear, basketballs with rougher surfaces exhibit higher C_D at low flight speeds and lower C_D at high flight speeds, with an old ball exhibiting a C_D up to 116.7% higher than that of a new ball at high flight speed.
• (2)Inflation pressure exerts a measurable influence on drag, particularly at lower speeds. Suboptimal pressure results in increased drag due to aeroelastic deformation and flow-induced vibration. Compared to the 0.3 bar case, the variation in C_D under other pressure settings can be as high as 15.4%. As flight speed increases, the coefficient curves tend to converge. Basketballs with lower inflation pressure exhibit slightly higher C_D. Optimal and adequate inflation pressure not only provides players with superior rebound tactile feel but also enhances the aerodynamic stability of the basketball’s flight.
• (3)The yaw angle has a significant effect on the C_D during flight. The C_D is minimized at a 0° yaw angle, which is most favorable for flight. At 45° and 90° yaw angles, the C_D can reach up to 176.5% of that at the 0° yaw angle. This indicates that the channels on the surface have a significant impact on the basketball’s aerodynamic characteristics during flight, and that an optimal flight angle is conducive to faster and farther flight.
• (4)Surface roughness characteristics influence the C_D significantly. Different surface textures alter the roughness and flow characteristics of the basketball, causing changes in the C_D at different flight speeds. A mild “drag crisis” phenomenon was observed in all test conditions. Notably, relative to the CUBAL basketball at a 0° yaw angle, the onset of the drag crisis was delayed for both the CUBAL basketball at 45° and 90° yaw angles and the Li-Ning basketball at a 0° yaw angle. This indicates that the surface texture and microstructural features have a crucial impact on the aerodynamic characteristics of the basketball during flight.

Limitations of the study

This study investigated the influences of surface wear, inflation pressure, yaw angle, and surface roughness characteristics on the aerodynamic drag of CUBAL and Li-Ning basketballs. However, the findings are subject to certain limitations. First, regarding surface wear, this study did not establish a specific definition or standard for the degree of wear. Consequently, the wear level could not be precisely quantified, precluding a detailed analysis of the quantitative relationship between the degree of wear and aerodynamic drag. Second, the experimental apparatus utilized in this study did not account for the rotation of the basketball. Given that introducing rotation could potentially compromise the stability of data acquisition and the testing rig, this research was provisionally limited to the aerodynamic analysis of basketballs in a non-rotating state. In reality, C_D in existing literature may also implicitly include induced drag caused by the Magnus effect or different effects of rotation on the boundary layer. Nikhilesh and Kulkarni³⁴ pointed out that incorporating the Magnus effect and lift forces results in a 5–15 cm increase in the basketball’s vertical displacement during flight. This study only considered the static condition, which is its main limitation. Future work should focus on constructing a “rotating basketball wind tunnel test system” to decouple the combined effects of rotational speed and translational velocity on drag and lift, thereby establishing a more comprehensive basketball flight dynamics model.

Resource availability

Lead contact

Further information and requests for resources and reagents should be directed to and will be fulfilled by the lead contact, Weijian Zhu (24110324@bjtu.edu.cn).

Materials availability

This study did not generate unique reagents.

Data and code availability

• •All data reported in this paper will be shared by the lead contact upon request.
• •This paper does not report original code.
• •Any additional information required to reanalyze the data reported in this paper is available from the lead contact upon request.

Acknowledgments

We sincerely acknowledge the China Basketball College of Beijing Sport University for generously providing the basketballs utilized in the wind tunnel experiments in this study.

Author contributions

C.Y.Z.: conceptualization, methodology, investigation, writing – original draft. W.J.Z.: methodology, investigation,writing – review and editing. B.L.: methodology, resources, supervision. P.H.: supervision.

Declaration of interests

The authors declare no competing interests.

STAR★Methods

Key resources table

REAGENT or RESOURCE	SOURCE	IDENTIFIER
Deposited data
Raw and analyzed data	This paper	N/A
Software and algorithms
MATLAB R2023a	MathWorks	Version 2023a
Origin Pro 2025	OriginLab Corporation	Version 2025
WPS Office	Kingsoft Office Software	Version 12.1.0.24657
ATI-DAQFT data acquisition program	ATI Industrial Automation	Version 2.1
Other
CUBAL basketball	Beijing Sport University	Size 7
Li-Ning basketball	Commercial purchases	Size 7
Closed-circuit wind tunnel	Beijing Jiaotong University	N/A
ATI-Delta 6-component balance	Beijing Jiaotong University	Delta

Experimental model and study participant details

Omitted as our study does not involve biological models.

Method details

Testing equipments

The wind tunnel tests were conducted in the high-speed test section of the BJ-1 wind tunnel laboratory at Beijing Jiaotong University. This wind tunnel is a large-scale, multifunctional, closed-circuit boundary layer wind tunnel with dual test sections. The high-speed test section measures 3.0 m × 2.0 m × 15.0 m (Figure S1). The flow field in the inner section meets the standards of an excellent boundary layer wind tunnel, with wind speeds adjustable between 0 and 40 m/s.

To mitigate interference from the wind tunnel floor boundary layer, a custom-fabricated sting adapter was utilized to mount the basketball to an ATI 6-component internal balance. The connection setup and the basketball are illustrated in Figure S2. The setting of the sting adapter is similar to that mentioned in the literature.¹⁴

Setup of basketball aerodynamic tests

Two types of size 7 basketballs were utilized in the experiment: a CUBAL basketball and a commercially available Li-Ning basketball. For the CUBAL basketball, three balls were selected to represent different stages of surface degradation: one brand new ball and two used balls (designated as Old Ball 1 and Old Ball 2, both having undergone prolonged service lives). The inclusion of two distinct used balls enhances the robustness of our findings regarding surface wear. Furthermore, a brand new Li-Ning basketball was introduced to compare surface roughness characteristics. Unlike the CUBAL basketball’s traditional pebbled surface texture, the Li-Ning basketball features a distinctly ribbed or grooved surface texture (Figure 2). Note that the subsequent tests evaluating the effects of surface wear, inflation pressure, and yaw angle variations were conducted exclusively on the CUBAL basketballs.

The test configurations developed for this study comprehensively encompasses the key variables that dictate a basketball’s aerodynamic behavior. All test configurations are listed in Table 1. The specific setting of these parameters was driven by a rigorous combination of standard sports regulations, practical training or match scenarios, and established aerodynamic theories. The detailed rationale for each parameter setting is summarized as follows.

• 1.Basketball size (Size 7): Selected because it is the universally designated official game ball for major international and regional competitions, including FIBA, the NBA, and CUBAL.
• 2.Test wind speed (2.6–17.1 m/s): Chosen to account for common flight speeds observed in actual basketball games (from passing to shooting),¹ while covering a sufficient spectrum of Reynolds numbers (detailed in Table S1) to successfully capture the ‘drag crisis’.
• 3.Surface wear (New ball and Used ball): Included to evaluate how realistic surface degradation, naturally occurring during prolonged use, fundamentally alters aerodynamic drag.
• 4.Inflation pressures (0.3–0.6 bar): Designed to establish official baseline conditions (0.5–0.6 bar represents the standard operating pressure) and evaluate the aerodynamic penalties of natural deflation (0.3–0.4 bar), while excluding unrealistically over-inflated scenarios to control experimental costs.
• 5.Yaw angle (0°, 45°, 90°): Selected as representative discrete cases to systematically verify the influence of the basketball’s channel orientation on aerodynamic drag during dynamic flight.
• 6.Surface roughness characteristics (CUBAL basketball and Li-Ning basketball): Employed as a comparative model to determine how distinctly different surface textures dictate the ball’s overall aerodynamic profile.

Data acquisition

Experimental data were collected using the ATI-DAQFT data acquisition program accompanying the ATI-Delta 6-component balance. The sampling frequency, sensing range and resolution are 1000 Hz, 165 N and 1/32 N respectively, and the sampling duration was 30 s after the wind speed stabilized. Using the generalized stationarity test criterion, an effective data interval of no less than 20 s was determined.

Quantification and statistical analysis

Data analysis and processing

The aerodynamic drag measurement data of the basketballs were exported in real-time as CSV files via the ATI-DAQFT data acquisition program. By developing a dedicated MATLAB data processing code, the aerodynamic drag (F_D) experienced by the basketball under various experimental configurations was batch-calculated based on these CSV data files. The calculated drag force represents the time-averaged value over the testing duration. It is important to note that all reported F_D values were corrected by subtracting the aerodynamic force on the support strut from the total force measured during testing. This paper uses the drag coefficient, C_D, to compare the aerodynamic drag characteristics of different basketballs:

$$C_D=\frac{F_D}{\frac{1}{2}\rho V^{2}A}$$ (Equation 1)

Where: C_D is the drag coefficient, F_D is the aerodynamic drag force, A is the frontal projected area of the basketball (m²), ρ is the air density (kg·m⁻³), and V is the test wind speed (m·s⁻¹).

Data validation and experimental errors

The experimental errors of gathered data in this study primarily stem from two sources: the intrinsic measurement errors of the ATI force balance and the fluctuations caused by airflow turbulence and device vibration during testing. As previously stated, the resolution of the ATI balance is 1/32 N, representing less than 0.01% of its full-scale range. Prior to the experiments, the balance was calibrated using the manufacturer-supplied calibration file to minimize potential data acquisition errors stemming from the instrument itself. To verify the reliability and repeatability of the measurement data, 7 independent repetitions were conducted for the CUBAL New Ball (at 0.5 bar and 0° yaw angle) across all wind speed conditions. Figure S3 illustrates the 95% confidence interval curve and the corresponding error bars for the F_D of CUBAL New Ball. The results demonstrate excellent repeatability, with a maximum measurement uncertainty of approximately ±0.1 N, indicating that the experimental results are highly reliable and acceptable.

Software

The collection of experimental data was executed using the ATI-DAQFT data acquisition program. Subsequent data processing and analytical procedures were conducted utilizing WPS Office and MATLAB R2023a. Finally, the experimental results were visualized using Origin Pro 2025 and presented in the form of line graphs.