Effects of Wheel-Ground Conditions on Racing Car Aerodynamics Under Ride-Height-Related Attitude Variations

Featured Application

Racecars’ aerodynamics are highly sensitive to ride-height-related attitudes due to unique downforce sources, which cannot be overlooked in wheel-ground condition studies.

Abstract

In racing cars, a low ride height is crucial for inverted wings and ground-effect systems to function effectively, significantly enhancing aerodynamic performance but also increasing sensitivity to pitch and roll variations. However, the specific impact of wheel-ground conditions on racing cars under ride-height-related attitude variations has not received attention. This study employed numerical simulations (compared with wind tunnel test data) to investigate these effects on racecar aerodynamic characteristics, analyzing three specific wheel-ground combinations: moving ground with rotating wheels (MR), moving ground with stationary wheels (MS), and stationary ground with stationary wheels (SS). A systematic analysis was conducted on aerodynamic changes associated with wheel-plane total pressure coefficient differences, upper-lower surface pressure coefficient variations, and front-rear axle aerodynamic force distributions, elucidating individual component contributions to overall performance changes induced by wheel-ground alterations. Results indicate that wheel conditions, especially rear wheels and their localized interactions with the diffuser-equipped body predominantly influence drag. In contrast, ground conditions primarily affect the body and front wing to alter downforce, with induced drag variations further amplifying total drag differences. Moreover, ground conditions’ impact on the front wing is modulated by vehicle attitude, resulting in either increased or decreased front wing downforce and thus altering aerodynamic balance. These insights highlight that ride-height related attitudes are critical variables when evaluating combined wheel-ground effects, and while wheel rotation is significant, the aerodynamic force and balance changes induced by ground conditions (as modulated by attitude) warrant greater attention. This understanding provides valuable guidance for racecar aerodynamic design.

1. Introduction

Motorsport, as an integration of technology and engineering, is a critical platform for applying and validating new automotive technologies, thereby advancing the industry. Aerodynamics plays a pivotal role in racing car performance [1]. A review of motorsport aerodynamic design shows that inverted wings [2,3,4,5,6,7,8,9] and ground effect techniques [10] effectively generate downforce, counteracting the lift of early low-drag designs [11,12]. This enhances tire adhesion, allowing racing cars to handle complex tracks with greater efficiency and consistency, ultimately reducing lap times [13,14,15].

As the sole vehicle component in contact with the ground, the wheel directly affects both driving and braking forces. Aerodynamically, the wheel is commonly idealized as a short-aspect-ratio cylinder, with its initial flow understanding rooted in the classical principles of two- and three-dimensional cylinder flows [16,17]. However, this model deviates significantly from reality due to two paramount physical effects: rotation and interaction with the ground. To bridge this gap, extensive experimental studies have investigated these coupled effects on short cylinders. The pioneering work provided the first indirect force measurements validating the drag and positive lift on a rotating and grounded tire, underscoring the complexity of this physical system [18]. Due to the complexity of the surrounding flow structures, research on isolated wheels remains ongoing. While debate persists regarding the presence of hub vortices in the lower wake and the interaction between lower and upper vortex strengths, there is broad consensus on the pressure distribution and upper wake structure of isolated tires [19,20,21,22,23,24,25,26,27]. Compared to stationary wheels, the flow separation point on the top of a rotating wheel occurs earlier, resulting in the upper wake simultaneously exhibiting lateral arching vortices and a pair of counter-rotating vortices; this flow modification ultimately reduces both the drag and lift of rotating wheels relative to their stationary counterparts.

As a complex multi-scale geometry, the vehicle exhibits significant interactions among various flow regions. Regarding the interaction between the wheel and the vehicle body, research has primarily focused on how the wheel and its states affect the overall aerodynamic performance of the vehicle. To systematically deconstruct these interactions, current research frequently employs simplified reference models with appropriate bluffness [28,29,30,31,32,33,34,35]. These canonical models serve to isolate key flow separation and wake behaviors behind road vehicles. They have been instrumental in identifying the origins of aerodynamic drag and, more specifically, in highlighting the localized influence of wheels in the near-wake region, as well as the effect of wheel design and ground condition variations on the overall wake structure. Moving beyond these fundamental studies, research has expanded in the more geometrically detailed DrivAer model to explore the impact of wheels and ground conditions [36,37,38]. In contrast, research focusing on the influence of wheel conditions on the aerodynamics of racing cars remains relatively limited [2,39], with the few existing studies noting that wheel configurations are not merely a drag concern but also pivotal in determining downforce characteristics.

The generation of downforce in racing cars is primarily attributed to complex pressure gradients and vortex structures produced by inverted wings and ground effects. As the first aerodynamic element encountered by the incoming flow, the front wing plays a key role in modulating downstream wheel flow, with both components being subject to ground effects. The aerodynamic performance of the front wing is closely associated with the state of its tip vortices, where vortex breakdown at the endplate generally occurs near the ride height corresponding to maximum downforce [40]. In wing–wheel interactions, the wheels alter the trajectory and structure of front wing tip vortices [6], while the wake from the front wing influences the surface pressure distribution on the wheels. Research has shown that the extent of wing–wheel overlap significantly affects the ride height at which vortex breakdown occurs [3,4,7,41]. Additionally, the circulation induced by the front wing over the wheel delays flow separation on the wheels, a phenomenon modulated by the wing’s angle of attack [5,42,43].

Under real-world racing conditions, the ride height of a race car is affected by vehicle attitude, mainly manifested as pitch and roll. Recent years have seen a growing research focus on the aerodynamic behavior of race cars under such attitude changes [8,44,45,46,47], with studies primarily quantifying the resultant changes in overall downforce and aerodynamic balance. However, while the critical roles of ground effects and wheel configurations have been established in static settings, their specific influence on, and interaction with, the vehicle’s aerodynamics under ride-height-related attitudes have not yet been systematically investigated. This gap in the literature forms the central motivation for the present work.

Therefore, this study focused on investigating the evolutionary characteristics of a racecar’s aerodynamic performance under pitch and roll attitude changes with different wheel–ground combinations. By analyzing the aerodynamic forces acting on individual components of the racecar across three operating conditions with attitude angles as variables, coupled with the evolution of total pressure distributions, surface pressure distributions, and aerodynamic balance dominated by front and rear axle lift distributions, this work aims to reveal the underlying mechanisms by which wheel and ground conditions modulate the racecar’s aerodynamic performance under ride-height-related attitude changes.

2. Digital Aerodynamic Model

2.1. Vehicle Model

The racing car geometric model utilized in this study has been shown before [47]. A brief overview of this model is provided below. The racing car consists of four primary systems: the body system, chassis system, powertrain system, and electrical system, each containing multiple distinct components. To facilitate digital simulations of the overall vehicle aerodynamics, it is essential to enclose the exposed elements of each system while preserving as much detail as possible regarding components that significantly influence the aerodynamic characteristics of the racing car.

The geometric model of the racing car used for digital simulations includes not only the major aerodynamic components such as the front wing, rear wing, and diffuser but also incorporates the wheels and body. In open-wheel racing cars, the influence of the wheels cannot be overlooked. Typically, in numerical simulations, the wheel modeling treats the contact patch with the ground as a small convex feature, primarily aimed at reducing the abrupt connection of the tire’s contact area mesh [4]. Additionally, considering the assembly relationship between the diffuser and the body, this paper collectively refers to all structures of the vehicle, excluding the front/rear wheels and front/rear wing, as the “CAR”. In the geometric model of the racing car presented in this study, the body section retains intricate details such as the headrest, main hoop, and driver while also accounting for crucial components like the engine air intake and cooling radiator. However, geometries such as the suspension and rear wing support struts, which do not significantly impact the aerodynamic coefficients, are disregarded. The geometric details of the entire vehicle are depicted in Figure 1a.

2.2. Equations for Controlling

In high-Reynolds-number applications of automotive aerodynamics, Large Eddy Simulation (LES) is often limited by its high computational cost. In contrast, the Reynolds-Averaged Navier–Stokes (RANS) approach, though less accurate in simulating turbulent noise [48,49] and unsteady wake details (particularly for square-back vehicle configurations) [50,51,52,53], can effectively capture the overall trends of aerodynamic performance under complex flows [49] and varying attitude angles [3,5,45,46,47], making it a valuable complement to wind tunnel testing. This makes it especially suitable for analyzing complex geometries and supporting design iterations in industrial applications. Accordingly, the RANS method was employed in this work.

The Realizable k-ε turbulence model is one of the most commonly used turbulence models in RANS simulations. It is one of the most widely used two-equation models, commonly applied to model the Reynolds stress tensor in the closure of the RANS equations. In motorsport, the Realizable k-ε turbulence model has also been proven to effectively characterize the complexity of the wake in wheel and wing combinations [3,5], and has been successfully applied to studies on the impact of wheel conditions on the overall aerodynamic performance of racing cars [2].

As an improved form of the Standard k-ε model, the Realizable k-ε model was employed in this study. Normally, turbulent viscosity is obtained through deriving a series of partial differential transport equations. Two additional transport equations are introduced in this turbulence model to describe the properties of turbulent flow and reflect the convective as well as diffusive effects of turbulent kinetic energy. Specifically, these transport equations contain two key variables: turbulent kinetic energy ($k$) and turbulent dissipation ($\epsilon$).

$$\left\{\begin{array}{l}{u}_j{\displaystyle \frac{\partial k}{\partial x_j}}={\tau }_{ij}{\displaystyle \frac{\partial u_i}{\partial x_j}}-\epsilon +{\displaystyle \frac{\partial }{\partial x_j}}[(v+{\displaystyle \frac{v_t}{{\sigma }_k}}){\displaystyle \frac{\partial k}{\partial x_j}}]\\ u_j{\displaystyle \frac{\partial \epsilon }{\partial x_j}}=C_1{\displaystyle \frac{\epsilon }{k}}{\tau }_{ij}{\displaystyle \frac{\partial u_i}{\partial x_j}}-C_2{\displaystyle \frac{{\epsilon }^2}{k+\sqrt{v\epsilon }}}+{\displaystyle \frac{\partial }{\partial x_j}}[(v+{\displaystyle \frac{v_t}{{\sigma }_{\epsilon }}}){\displaystyle \frac{\partial \epsilon }{\partial x_j}}],\end{array}\right.$$

(1)

The symbols $C_1$ and $C_2$ can be expressed as:

$$\left\{\begin{array}{ll}{C}_1=\max (0.43,{\displaystyle \frac{\eta }{5+\eta }})& \\ \eta =\sqrt{2s_{ij}{s}_{ij}}{\displaystyle \frac{k}{\epsilon }}& \\ C_2=1.9& ,\end{array}\right.$$

(2)

The strain rate tensor $s_{ij}$ and the Reynolds stress ${\tau }_{ij}$ can be expressed as:

$$\left\{\begin{array}{l}{s}_{ij}={\displaystyle \frac{1}{2}}({\displaystyle \frac{\partial u_i}{\partial x_j}}+{\displaystyle \frac{\partial u_j}{\partial x_i}})\\ {\tau }_{ij}=-{\displaystyle \frac{2}{3}}{\delta }_{ij}+2v_t{s}_{ij}\\ v_t=c_{\mu }{\displaystyle \frac{k^2}{\epsilon }}\end{array}\right.,$$

(3)

The closure coefficient $c_{\mu }$ of the Standard k-ε model is a constant. When the mean strain rate is high, standard eddy viscosity models with constant coefficients face the risk of failure, manifesting in possible unphysical negative normal stresses and violation of the Schwarz inequality for shear stresses. The fundamental reason lies in the fact that the assumption of constant coefficients fails to capture turbulent characteristics under strong strain. Therefore, to ensure the generality of the formulation, the model coefficients must be revised from constants to variables related to the mean strain rate. This is precisely the improvement introduced in the Realizable k-ε model, whose closure coefficients are specifically expressed as:

$$\left\{\begin{array}{l}{c}_{\mu }={\displaystyle \frac{1}{A_0+A_s\frac{k}{\epsilon }U}}\\ A_0=4.04,A_s=\sqrt{6}\cos \varphi \\ \varphi ={\displaystyle \frac{1}{3}}\arccos (\sqrt{6}W)\\ W={\displaystyle \frac{s_{ij}{s}_{jk}{s}_{kj}}{\sqrt{s_{ij}{s}_{ij}}}}& ,\end{array}\right.$$

(4)

The internal energy $U$ can be expressed as:

$$\left\{\begin{array}{l}U=\sqrt{s_{ij}{s}_{ij}+{\tilde{\Omega }}_{ij}{\tilde{\Omega }}_{ij}}\\ {\tilde{\Omega }}_{ij}={\Omega }_{ij}-2{\epsilon }_{ijk}{\omega }_k\\ {\Omega }_{ij}={\overline{\Omega }}_{ij}-{\epsilon }_{ijk}{\omega }_k& ,\end{array}\right.$$

(5)

2.3. Computational Domain and Meshing

A rectangular computational domain, resembling a wind tunnel test section, was established. The domain dimensions were 10, 6, and 5 times the vehicle’s length, width, and height, respectively. This yielded a blockage ratio of 3.33%, which fell below the commonly accepted threshold of 5% for aerodynamic simulations [2]. Boundary conditions comprising inlet, outlet, walls, and ground were applied as shown in Figure 1b.

In terms of geometry, the computational model was discretized into five independent components, namely the front wheels, front wing, rear wing, vehicle body and rear wheels, to standardize the mesh generation and boundary condition definition procedures. To strike a balance between numerical calculation accuracy and computational resource consumption, the node distribution density and mesh scale of each component were adjusted. This approach ensured the solution resolution of key regions while effectively controlling the total number of mesh elements. Specifically, high-quality surface meshes were generated for regions with high curvature or critical aerodynamic characteristics, including the airfoil leading edges, endplates, the diffuser, and main hoop.

Considering the turbulence model used in conjunction with the wall function, the target (y+) values were set to 50 [2,54]. The octree method was employed to construct the volumetric mesh, which was configured to be denser near the vehicle surfaces while becoming progressively sparser toward the boundaries of the domain. Following mesh generation, a thorough quality check and improvement process was conducted to ensure that the mesh met the specified quality standard prior to the solving phase.

After ensuring a sufficiently fine mesh in the near-field region, to simplify the determination of the location and size of the body wake refinement zone, the mesh independence was verified by refining the volume mesh following the same steps as has been shown before [47]. The results were then compared with wind tunnel test data from a baseline case. Figure 2 and Figure 3 illustrate the detailed mesh structure and the race car positioned in the wind tunnel, respectively.

2.4. Boundary Conditions and Solver Setting

Figure 1b outlines the boundary conditions implemented in the simulations. The inlet for the incompressible flow is designated as a velocity inlet, while the outlet boundary is specified as a pressure outlet. To minimize the influence of wall viscosity on the computational results, the side and top boundaries are defined as no-slip walls with specified wall shear stress.

To investigate the effects of wheel–ground interaction, this study considered three different conditions regarding the ground and wheel combinations: (1) moving ground with rotating wheels (MR), (2) moving ground with stationary wheels (MS), and (3) stationary ground with stationary wheels (SS). The details of the three combinations of wheels and ground conditions can be observed in Figure 1c. In these scenarios, the bottom surface representing road conditions is designated as either a stationary wall or a moving wall. Aside from the tire model, the surfaces of the vehicle model are set as fixed no-slip walls. For the case of stationary tires, the tire model is also defined as a fixed no-slip wall. In contrast, for the rotating tire condition, the simplified tire model is defined as a rotating wall that incorporates tangential airflow components, with the corresponding angular velocity calculated based on the vehicle speed and tire radius.

This study utilized ANSYS Fluent 19.0 for computation and solving. A pressure-based segregated solver was employed, with the pressure–velocity coupling achieved using the SIMPLIC algorithm. Second-order upwind discretization was applied to compute flow variables. To ensure convergence of the calculations, relaxation factors were adjusted according to the computational progress, and multiple key variables were monitored, including residuals, aerodynamic drag, lift, and moments. The criterion for convergence was defined as requiring residuals to be less than 10⁻³. Additionally, stability or periodic variation in the values of multiple variables during the iteration process indicates that the desired convergence accuracy had been achieved [9].

3. Results

3.1. Pitch Cases

3.1.1. Drag

The aerodynamic drag characteristics for the three wheel-ground combinations are presented in Figure 4a as a function of pitch angle. A common trend is evident, with drag initially rising and then falling over the nose-down to nose-up pitch range, albeit with notable inflections at −0.25° and 0.75°. The data reveal that stationary tires (MS condition) universally increase drag relative to the rotating benchmark (MR). In contrast, the SS condition, which employs both stationary tires and ground, produces a lower drag profile.

To isolate the effect of wheel and ground conditions, the differences in the vehicle’s overall aerodynamic drag ($D$), lift ($L$), and pitching moment ($M$) for the MS and SS conditions were computed with respect to the MR baseline. The specific calculation method is shown in Equation (6).

$$\Delta F_{i,X-MR}=F_{i,X}-F_{i,MR},$$

(6)

where the subscript $i$ denotes the aerodynamic component ($D$, $L$, $M$), and $X$ signifies the test condition (MS or SS).

The influence of pitch attitude on drag differentials is shaped by the wheel and ground states, as evidenced by the data in Figure 5a. In the former case (MS vs. MR), the differential is significant and grows with increasing nose-down angle but becomes smaller and stable under nose-up conditions. In the latter case (SS vs. MR), the trend is inverted, with a larger, more persistent differential manifesting during nose-up attitudes.

The component-wise drag distributions, presented in Figure 5a, were analyzed to attribute the total drag variation to the different wheel–ground conditions. A zero-value region is marked to clarify the sign of the component differences. The analysis reveals that the front wheels’ drag differential remains relatively constant in nose-down attitudes but increases progressively with the pitch angle in nose-up attitudes. In contrast, the rear wheels contribute significantly only under pronounced nose-down conditions. Consequently, the net vehicle drag differential under the MS condition is attributed to this interplay: it exhibits a marked increase only in strong nose-down attitudes, where the rear wheel contribution is substantial, while remaining largely unchanged in nose-up attitudes, where the front wheel trend dominates.

From a physical perspective, aerodynamic drag arises from the dissipation of mechanical energy in the fluid, with total pressure ($C_{pT}$) loss serving as the most direct measure of this dissipation. To clearly delineate the differences in energy loss mechanisms and their evolution under varying wheel and ground conditions, the disparity in total pressure coefficient ($\Delta C_{pT}$) at the plane 35 mm above the ground was employed to identify the sources of drag variation. This difference is quantified using Equation (7).

$$\Delta C_{pT,X-MR}=C_{pT,X}-C_{pT,MR},$$

(7)

The left side of Figure 5b presents the distribution of the $\Delta C_{pT}$, providing clear flow-field evidence of wake behavior under the MS and MR conditions. Distinct flow structures were observed around the front and rear wheels. In the front wheel region, the wake pattern indicates that with the high angle of attack and outwash-oriented endplate design of the front wing effectively organizes, guides, and confines the broad wake and rotational vortex structures generated by the front tire.

In the rear wheel region, the wake exhibits a structure of a central positive core flanked by negative lobes. The presence of the positive core indicates that the total pressure in the near-wake of the rotating wheel is significantly lower than that of the stationary wheel. This is attributed to the rotating wheel transferring rotational momentum to the surrounding fluid, generating an active pumping effect that accelerates the discharge of wake flow and prevents stagnation and accumulation. Concurrently, the adjacent negative lobes highlight regions where total pressure loss is substantially greater under the MS condition. This further confirms that the rotating wheel suppresses the large-scale stagnant separation bubble typical of a stationary tire, constraining the wake into a narrower and more concentrated structure. This shift in the role of the wheel from a passive flow obstacle when stationary to an active flow organizer when rotating leads to the resulting variation in wheel drag.

Moreover, the structural characteristics of the rear wheel wake directly determine the aerodynamic efficiency of the diffuser. A compact and well-organized wake is essential for enhancing diffuser performance. Although the low-energy flow in the wheel region may adversely affect the adjacent rear diffuser by inducing flow separation, the associated reduction in induced drag contributes to a slight decrease in the overall vehicle resistance. Pitch variation analysis reveals that the front wheel wake remains largely unchanged across different attitudes, whereas the rear wheel wake strengthens as the vehicle pitches nose-down and weakens as it pitches nose-up. Consequently, an expanding wheel wake intensifies the total pressure loss around the vehicle body, while a contracting wake alleviates such losses. This behavioral pattern explains the origin of the drag difference depicted in Figure 5a, indicating that the net drag difference between the MS and MR conditions stems from an aerodynamic trade-off between the wheel and the vehicle body.

Under the SS condition, while the primary contributors to the drag differential remain the rear wheels and the body, the net effect is reversed compared to the MS condition: the reduction in body drag now outweighs the increase in wheel drag, resulting in a net decrease in total vehicle drag. Furthermore, the component-wise drag differentials are both sensitive to the pitch angle. The body drag differential decreases in nose-down attitudes but increases in nose-up attitudes, while the rear wheel differential remains constant in nose-down attitudes and grows in nose-up attitudes. This results in the overall vehicle drag differential under the SS condition being smaller in nose-down attitudes and larger in nose-up attitudes, as previously noted in Figure 4a.

On the right side of Figure 5b, the distribution of the $\Delta C_{pT}$ under the SS condition is illustrated. In addition to the changes in the wake flow near the wheels, the introduction of the stationary ground leads to significant deceleration of the underbody airflow over a large area due to strong ground shear. This is directly reflected by the extensive negative $\Delta C_{pT}$ in the underbody region—consistent with the mechanism that strong shear induces flow turbulence and enhanced viscous losses, thereby reducing the local total pressure relative to the MS condition. Furthermore, the $\Delta C_{pT}$ beneath the front wing exhibits a sign reversal with varying pitch attitudes. This phenomenon likely stems from a fundamental shift in the dominant flow mechanism within the “front wing-ground” coupled system, driven by changes in ride height associated with different pitch angles.

From the perspective of trends associated with pitch attitude changes, the wheel wake differences, particularly those of the rear wheels, exhibit a consistent pattern: they gradually increase with the nose-down angle and decrease with the nose-up angle. In contrast, the wake region differences of the vehicle body (including the diffuser) display an opposite trend, decreasing with an increasing nose-down angle and increasing with an increasing nose-up angle. This observation effectively explains the competitive relationship between vehicle body drag and wheel drag presented in Figure 5a, as the opposing trends in pitch-driven flow losses directly govern the net drag trade-off.

3.1.2. Lift

The aerodynamic lift of the entire vehicle under pitch attitudes for the three wheel-ground combinations is illustrated in Figure 4b. A systematic loss of downforce is observed in both the MS and SS conditions relative to the MR baseline, with the loss being more pronounced in the SS condition. While the overall trend of downforce variation with pitch angle is consistent across all configurations, initially increasing and then decreasing as the vehicle transitions from a nose-down to a nose-up attitude, a key difference emerges in the critical pitch angle for peak downforce. This angle shifts from 0° for the MR condition to 0.25° for both the MS and SS conditions.

Figure 4b further compares the downforce differentials for the MS and SS conditions against the MR baseline. In the former (MS), the differential is pronounced and progressively increases with pitch angle in nose-down attitudes, but becomes smaller and constant in nose-up attitudes. In the latter (SS), the trend is distinctly different, as the downforce differential is larger under nose-up attitudes than under nose-down ones.

The aerodynamic downforce differences for each component are illustrated in Figure 6a. The introduction of the MS condition primarily increases the lift generated by the front and rear wheels, while also causing a slight reduction in the downforce produced by the vehicle body and its diffuser. The combined effect of these changes is a net reduction in the vehicle’s overall downforce. Analysis of the pitch variation reveals that the front wheel lift difference remains stable in nose-down attitudes but increases in pronounced nose-up attitudes, whereas the rear wheel and body contributions show minimal variation. Consequently, the overall vehicle lift difference under the MS condition exhibits only a slight increase in significant nose-down attitudes and remains largely constant elsewhere.

Aerodynamic downforce is directly determined by the static pressure distribution ($C_p$) acting on the vehicle’s surface. It results from the net vertical force obtained by integrating the static pressure over the upper and lower surfaces. While flow acceleration over the upper surface of the wheels generates lift, the inverted wings and diffuser underside produce strong suction (i.e., low-pressure zones), which constitutes the primary source of downforce. To clearly identify the key regions responsible for downforce variation under different wheel and ground configurations, the differential in pressure coefficient ($\Delta C_p$) was analyzed. This difference was quantified using Equation (8).

$$\Delta C_{p,X-MR}=C_{p,X}-C_{p,MR},$$

(8)

In vehicle aerodynamics, the physical implications of $\Delta C_p$ are defined by regional aerodynamic functions and underlying flow mechanisms: a positive $\Delta C_p$ over downforce-generating surfaces (e.g., the wing or diffuser) signifies degraded aerodynamic performance, attributed to intensified viscous losses induced by strong ground shear or flow separation. These effects disrupt orderly flow acceleration, weaken the pressure differential across the surfaces, and thus compromise downforce generation. Conversely, a negative $\Delta C_p$ over lift-generating components (e.g., the upper wheel surfaces) indicates increased lift, stemming from weakened adverse pressure gradients or diminished flow stagnation due to altered viscous dissipation. This reduces the downward pressure acting on the wheel surfaces, thereby enhancing the net lift force.

The left side of Figure 6b presents the $\Delta C_p$ distribution, which elucidates the physical mechanism behind the force differences under the MS condition. The pressure field confirms that the lift increase is primarily driven by a positive $\Delta C_p$ on the upper surfaces of the wheels. The stronger pressure differential on the rear wheel quantitatively accounts for its larger lift increment compared to the front wheel. Conversely, the downforce-generating surfaces (underbody and front wing) exhibit only weak negative values (indicating minor suction loss) at extreme pitch angles, underscoring their limited influence on the net aerodynamic change.

Under the SS condition, the primary sources of the vehicle’s downforce variation are the body and the front wing. The stationary ground induces a profound downforce loss on the vehicle body. The front wing’s behavior, however, is pitch-dependent: it partially compensates for this loss by generating increased downforce in most nose-down attitudes, but contributes to the deficit in most nose-up attitudes. Despite the compensatory effect from the front wing in nose-down stances, the more severe downforce loss from the body ultimately dictates a net reduction in the vehicle’s overall downforce.

The right side of Figure 6b illustrates the $\Delta C_p$, between the SS and MR conditions. The most pronounced differences, beyond those at the wheels, occur on the negative-pressure surfaces of the primary downforce-generating components: the vehicle body (with diffuser) and the front wing. Under the SS condition, the vehicle body exhibits a significant loss of suction (weaker negative pressure), which consequently accounts for the substantial downforce reduction from this component. In contrast, the front wing’s behavior is pitch-dependent; its suction is enhanced in nose-down attitudes but diminished in nose-up attitudes, directly explaining its opposing downforce trends. Although the stationary wheels also contribute to the overall downforce loss through increased lift, their influence is secondary to that of the body and front wing. The rear wing, being distant from the ground, experiences a negligible change.

3.1.3. Pitch Moment and Aerodynamic Balance

Figure 4c illustrates the aerodynamic pitching moment about the center of gravity. While the MS and MR conditions yielded nearly identical moments, the SS condition caused a noticeable deviation: it increased the moment in nose-down attitudes and decreased it in nose-up attitudes relative to MR. Furthermore, the pitch angle corresponding to the maximum moment shifted from 0° under MR and MS to 0.25° nose-down under SS, despite all configurations sharing a common trend of initial increase followed by a decrease.

Figure 7a illustrates the pitching moment differences at the center of mass for various components under the MS and SS conditions, relative to the MR baseline. Under the MS condition, the introduction of stationary tires induces a positive pitching moment from lift components ahead of the center of mass and a negative moment from those behind it, creating a counterbalancing effect. The influence of the rear wheels is more pronounced in this balance. Meanwhile, the vehicle body (equipped with the diffuser) experiences only a slight pitching moment increase due to its aerodynamic center’s proximity to the vehicle’s center of mass. Consequently, the net change in the overall vehicle pitching moment under the MS condition was a slight increase over the MR condition, though the values remained very close.

The pitching moment difference under the SS condition primarily stems from the vehicle body and front wing. The body contributes a positive moment difference that strengthens with pitch angle, while the front wing provides a positive moment in nose-down attitudes that becomes negative in nose-up attitudes. This opposition creates a balancing effect in nose-up attitudes. Although the body suffers a greater downforce loss, its aerodynamic center’s proximity to the vehicle’s center of mass limits its moment contribution. Therefore, the front wing, benefiting from a longer lever arm, exerts a dominant influence. The variation of the front wing’s moment thus predominantly determines the overall vehicle pitching moment trend, accounting for its opposing behaviors across the pitch range.

The aerodynamic balance of a vehicle, defined as the proportion of total downforce borne by the front axle, characterizes the longitudinal distribution of aerodynamic load. Under the assumption that aerodynamic drag acts proximate to the center of mass, the balance is predominantly governed by the total downforce and the pitching moment. This relationship is quantified as Equation (9):

$$F\mathrm{r}\mathrm{o}\mathrm{n}\mathrm{t}\%={\displaystyle \frac{L_f}{L}}={\displaystyle \frac{M_{pr}}{a+b}},$$

(9)

where $L_f$ is the front axle downforce, $M_{pr}$ is the pitching moment relative to the rear axle position, and $a+b$ is the wheelbase of the race car.

As illustrated in Figure 7b, a common trend was observed across all three boundary conditions: increasing pitch angle from nose-down to nose-up shifted downforce from the front to the rear axle, thereby reducing the vehicle’s overall aerodynamic balance. Under the MS condition, the introduction of stationary wheels caused a slight downforce loss on both axles. The loss was more pronounced at the rear, which resulted in a marginal improvement in aerodynamic balance. In contrast, the SS condition induced more complex changes: the downforce loss at the rear axle remained relatively constant with pitch angle, while the loss at the front axle was minimal in nose-down attitudes but substantial in nose-up attitudes. Consequently, the vehicle’s aerodynamic balance increased notably in nose-down attitudes but remained largely unchanged in nose-up attitudes.

3.2. Roll Case

3.2.1. Drag

The aerodynamic drag of the entire vehicle under roll attitudes for the three wheel-ground combinations is illustrated in Figure 8a. Consistent with the pitch condition observations, the MS condition increased the drag relative to the MR baseline, while the SS condition reduced it. In comparison to the MR condition, the MS condition exhibited a comparable trend with roll angle, whereas the SS condition showed a markedly different response. Specifically, for both MS and MR conditions, the total drag remained stable at low roll angles, peaked at 1.5°, and then decreased at 2°. In contrast, the vehicle under the SS condition displayed a more complex sequence, with drag initially increasing, then decreasing, and finally stabilizing.

The differences in component-level aerodynamic drag under the MS and SS conditions, relative to the MR baseline, are illustrated in Figure 9a. Similar to the pitch condition, the drag differential under the MS condition stems from a trade-off between the wheels and the vehicle body: an increase in wheel drag is partially offset by a decrease in body drag, with the former slightly dominating to yield a marginal net increase in total vehicle drag. Analysis of the roll angle variation revealed that the front wheel drag differential remained largely constant, whereas the rear wheel differential and the negative body differential initially increased before slightly decreasing with increasing roll angle. Consequently, these opposing trends balance out, resulting in a nearly constant net drag differential for the entire vehicle under the MS condition across the roll angle range.

From the $\Delta C_{pT}$ distribution shown on the left side of Figure 9b, it is evident that under the roll attitude, the $\Delta C_{pT}$ distribution in the MS condition differs significantly from that in the MR condition, primarily in the wake region of the wheels and the vehicle body near the wheels (equipped with a diffuser). Notably, the changes in the wake region at the rear wheels are more pronounced than those at the front wheels, and the magnitude of $\Delta C_{pT}$ in the vehicle body is closely related to that of the rear wheels. Under the roll attitude, the wake changes at the rear wheels become asymmetric on the sides closer to and farther from the ground, with the wake variation farther from the ground being significantly larger, while the change in the wake region closer to the ground is noticeably smaller. In contrast, the wake differences at the front wheels do not exhibit a clear asymmetry. The variations in the wake region of the rear wheels also induce a similar trend in the influence area of the vehicle body. This explains the trend observed in the drag differential at the rear wheels and vehicle body with respect to changes in roll angle.

With further introduction of stationary ground, the drag of the vehicle body is further reduced. This reduction in drag exceeds the increase in drag from the wheels, resulting in an overall decrease in the total vehicle drag. Furthermore, the trend of the drag differentials of various components with respect to the attitude angle indicates that the drag differentials at the front wheels, rear wheels, and vehicle body continue to follow the pattern observed in the MS condition. However, at a roll angle of 1.5°, the front wing exhibits a negative drag differential, which alters the distribution trend of the total vehicle drag differential.

From the $\Delta C_{pT}$ diagram on the right side of Figure 9b, it is evident that the distribution of total pressure coefficient differentials under the SS condition still reveals significant differences in the wheel wake, as well as an asymmetry in the wake differences on the sides that are closer to and farther from the ground during the roll attitude. Additionally, significant differences in total pressure distribution have been observed in the underbody and the wake region of the entire vehicle. Similar to the pitch attitude case, the airflow velocity over the underbody is lower under the SS condition, and the wake differences of the entire vehicle also exhibit asymmetry. However, this asymmetry is opposite to that observed in the wheel wake. This highlights the balancing relationship between the drag variations of the vehicle body (equipped with a diffuser) and the wheel.

3.2.2. Lift

Figure 8b illustrates the variation of total vehicle lift with roll angle. The downforce hierarchy established under pitch conditions was preserved under roll: the MR condition provided the highest downforce, followed by MS, with SS producing the least.

From the trend of overall vehicle downforce variation with roll angle, it can be observed that the downforce under MR and MS conditions is relatively similar, while significant changes occur under the SS condition. Specifically, as the roll angle increases, the overall downforce under the MS and MR conditions initially exhibits a slight increase, followed by a noticeable loss of downforce at larger roll angles (2°). In contrast, under the SS condition, the overall downforce at a 2° roll angle does not show a loss; instead, it increases.

Figure 10a illustrates the differences in component-level aerodynamic downforce under the MS and SS conditions relative to the MR baseline during roll attitudes. Consistent with the pitch condition observations, the introduction of stationary tires (MS) increases the lift generated by both the front and rear wheels, while the downforce produced by the vehicle body experiences a slight decrease. The net effect of these changes is a minor reduction in the vehicle’s overall downforce. Furthermore, the drag differences of these components exhibit minimal variation with changes in roll attitude, which explains the generally consistent overall drag trend observed between the MS and MR conditions.

The left side of Figure 10b illustrates the $\Delta C_p$ distribution under roll attitudes for the MS condition relative to the MR baseline. Consistent with the pitch condition, significant $\Delta C_p$ is observed on the upper surfaces of both front and rear wheels. The diffuser’s lower surface also shows distinct positive and negative pressure differential regions. As the roll angle increases, the pressure distribution beneath the diffuser becomes increasingly asymmetric. Specifically, the region of enhanced suction (negative $\Delta C_p$) expands on the ground-adjacent side, while the area of suction loss (positive $\Delta C_p$) grows on the ground-opposed side. However, this established trend is disrupted at the largest roll angle of 2°.

It is evident that under the SS condition (with the further introduction of a stationary ground), the loss of downforce on the vehicle body intensified. Combined with the increased lift at the front and rear wheels, a greater overall loss of downforce for the entire vehicle was generated. Furthermore, significant changes in downforce were also observed at the front wing under larger roll angles.

From the trend of lift differential changes with respect to the attitude angle across various components, the lift differentials at the front and rear wheels remained relatively constant as the roll angle varies, while the lift differential of the vehicle body decreased only at larger roll angles. However, at roll angles of 1.5° and 2°, the front wing exhibited a reduction and increase in downforce, respectively. This alteration modified the trend of overall vehicle downforce changes with roll angle under SS conditions.

The right side of Figure 10b illustrates the $\Delta C_p$ distribution for the SS condition under roll attitude. The most significant differences, beyond those at the tires, were located on the key suction surfaces: the front wing and the diffuser. A negative $\Delta C_p$ on the wheel upper surfaces indicates a loss of suction, correlating with the observed increase in wheel lift. Conversely, a positive $\Delta C_p$ on the body and diffuser signifies a loss of negative pressure, accounting for the reduction in downforce. This pressure field evolves with roll angle: the diffuser’s $\Delta C_p$ distribution becomes increasingly asymmetric, characterized by a substantial decrease in the negative pressure differential on the ground-far side, while the ground-near side remains relatively stable. This trend is, however, disrupted at a 2° roll angle, where the negative pressure differential on the ground-near side also exhibits a notable reduction.

3.2.3. Pitch Moment and Aerodynamic Balance

Figure 8c presents the pitching moment about the vehicle’s center of mass as a function of roll angle for the three configurations. Relative to the MR condition, the pitching moment under the MS condition is slightly elevated and exhibits a consistent, gradual decrease with increasing roll angle. In contrast, the SS condition induces a marked deviation in the trend, characterized by a sharp decrease in pitching moment at a roll angle of 1.5°, followed by an equally sharp recovery at 2°.

Figure 11a illustrates the differences in aerodynamic pitching moment among various components under the MS and SS conditions compared to the MR condition during roll attitudes. It is evident that under the MS condition, both the front and rear wheels, acting as lift-generating components, produced opposing pitching moment differentials. Notably, the increase in pitching moment at the rear wheel was greater, and the increase at the vehicle body further ensured an overall increase in the vehicle’s pitching moment under the MS condition.

Pitching moment differentials exist between the rear wheel, the vehicle body, and the front wing under the SS condition. The pitching moment differential between the rear wheel and the vehicle body remained consistently positive. In contrast, the pitching moment differential at the front wing exhibited a stable negative value at small roll angles but showed a sharp decrease and subsequent increase at roll angles of 1.5° and 2°, respectively. These variations collectively define the overall trend of the pitching moment under the SS condition.

As illustrated in Figure 11b, a consistent baseline trend was observed under the MR condition: increasing roll angle shifts aerodynamic load rearward, reducing the front aerodynamic balance. The introduction of stationary wheels (MS condition) moderated this trend by inducing a downforce loss on both axles that was more pronounced at the rear, resulting in a marginal net gain in front balance. In contrast, the SS condition fundamentally altered the system’s response. While it also caused downforce losses on both axles, the vehicle’s balance was critically modulated by the front wing’s performance at specific roll angles (1.5° and 2°). This front-wing-induced perturbation is a major contributor to the front axle loss and drives the longitudinal shift in the vehicle’s center of pressure.

4. Conclusions

This study systematically investigated the evolutionary characteristics of a racecar’s aerodynamic performance under ride-height-related pitch and roll attitude changes, focusing on the regulatory effects of different wheel–ground combinations. By quantifying the aerodynamic forces (drag, lift, and pitching moment) acting on individual vehicle components across three operating conditions (MR: moving ground with rotating wheels, MS: moving ground with stationary wheels, SS: stationary ground with stationary wheels) with varying attitude angles, and combining analyses of total pressure distributions, surface pressure distributions, and aerodynamic balance dominated by front and rear axle lift distributions, the underlying mechanisms of wheel and ground condition modulation on racecar aerodynamics were clarified.

Wheel condition variations (from rotating to stationary) primarily act through the wheels themselves and their localized interactions with the diffuser-equipped body, with distinct impacts on drag, downforce, and aerodynamic moment. The wheels and their body interactions exhibit a counterbalancing relationship, limiting the magnitude of net drag variation. Specifically, the MS condition results in higher total drag compared to the MR condition. Unlike the counterbalance in drag, wheels and their body interactions collectively reduce the overall downforce in the MS condition relative to MR. The trend of aerodynamic moments remains essentially unchanged despite drag and downforce variations, as the local force compensation between the wheels and the body mitigates net impacts on moment distribution.

The overall aerodynamic effects of wheel condition variations are closely associated with the flow structures around the front and rear wheels and their impacts on the diffuser. Among these effects, the more pronounced force differences at the rear wheels are primarily attributed to the front wing guiding and confining the broad wake and rotational vortex structures generated by the front wheels. The rotating wheel suppresses the large-scale stagnant separation bubble typical of a stationary tire, constraining the wake into a narrower and more concentrated structure. This shift in the role of the wheel from a passive flow obstacle when stationary to an active flow organizer when rotating directly leads to variations in wheel drag. Furthermore, the structural characteristics of the rear wheel wake directly determine the aerodynamic efficiency of the diffuser, and the induced drag resulting therefrom also affects changes in the vehicle’s overall drag—this relationship is influenced by attitude angles.

Ground condition variations (from moving to stationary) reshape the global pressure field of the vehicle, exerting more significant regulatory effects on aerodynamic performance, with impacts differing across force and moment parameters: Drag variation stems from the balance between the body and wheels (especially rear wheels), with the body’s influence dominating—leading to lower total drag in the SS condition compared to MS.

The body and front wing are the primary contributors, with the SS condition further reducing the total downforce relative to MS. Critically, the sign of the front wing’s downforce difference is sensitive to ride-height-related attitude changes. The peak value of the moment-downforce correlation shifts in the SS condition, and the coupled effect of ground conditions and attitude angles drives adjustments in moment trends, ultimately altering the vehicle’s aerodynamic balance. The pressure field elucidates that SS causes significant body suction loss (major downforce reduction), while the front wing suction varies with pitch (enhanced nose-down, diminished nose-up, explaining opposing downforce trends). Stationary wheels contribute secondarily to downforce loss via increased lift, and the rear wing (distant from the ground) has negligible impact.

Racecars’ unique downforce sources render their aerodynamics highly sensitive to ride-height-related attitudes, which must not be overlooked in wheel and ground condition studies. The SS model exhibits dynamic, nonlinear errors that change sign with attitude, leading to both quantitative inaccuracies and qualitative misguidance for balance trend judgments. Prioritizing realistic ground simulation is essential for accurate performance prediction.