Inflation Pressure Impact in Vehicle Handling: Self-Supporting Run-Flat Tires vs Conventional Tires

1. Introduction

All forces and moments acting on a vehicle—with the exception of the aerodynamic forces—are caused by the interacting interface between the pneumatic tire and the road surface; therefore, the study and comprehension of the pneumatic tire and the phenomena that take place at this surface area is essential.

The forces and moments generated at the tire-road interface are essential for quantifying vehicle performance with respect to energy efficiency, directional handling, and ride comfort. Furthermore, the intrinsic mechanical properties of the tire such as structural rigidity, damping characteristics, and material composition —fundamental to analyzing the transient dynamic behavior of motor vehicles.

It is important to emphasize that the functions of the tire in the vehicle are: supporting the load of the vehicle and the occupants providing damping to the vehicle’s structure, transmitting driving forces—such as braking and accelerating—and lastly guaranteeing an acceptable adherence to the road surface. The conventional pneumatic tires can easily carry out these tasks, which is why most modern vehicles utilize them.

Beyond the usual distinction between summer, winter, or all-season compounds, pneumatic tires are categorized by their internal structure into bias-ply and radial-ply configurations. The modern tire has several plies and layers, each with unique properties specially designed for each section. The sidewalls are slim in comparison with the tread and their composition is different as well: the apex and the initial part of the sidewall (the parts closest to the wheel) are made of high hardness natural rubber, and the tread section is made of a much softer rubber composition in order to provide sufficient adherence. The internal plies are designed to offer longitudinal stiffness that resists the pull from the inertia of the rotational speed and prevents the tire’s radius from expanding. The body plies offer radial stiffness, but they require the internal air pressure to act as individual springs that ultimately keep the tire up while allowing it to flex to the sides and provide a comfortable ride during turns.

Radial tires, which in this document will be known as conventional tires, offer a high level of comfort and are relatively less expensive; however, they have limitations due to their dependence on internal air pressure. When they are punctured, they can no longer maintain vertical loads or create lateral forces, often resulting in compromised vehicle control or lateral drift during high-speed turns [1]. As an alternative, the automotive industry introduced run-flat tires (RFT) that promise the ability to continue rolling when the inflation pressure is lost. Even in the absence of air pressure, the RFTs are able to continue rolling for a limited time and pace ($80km$ at $80km/h$). These specialized tires are divided into two main types, self-supporting (SSRFT) and auxiliary-supported systems. SSRFT use thickened sidewall geometries to maintain structural stability without any air pressure. This study will be focused on the SSRFT variant.

The structural durability of the SSRFT is maintained by using a sidewall insert rubber (SIR), enabling the tire to carry the vehicle’s weight even after losing all the air pressure. Recent studies on SIR configuration show that the vertical location of the inserts influences radial stiffness more than their thickness does which is vital information for designing tires that perform well whether inflated or not. Although RFTs provide high safety advantages they also present difficulties, including increased vertical stiffness that may result in greater stress on wheel rims [2,3,4].

Pacejka’s Magic Formula (MF) is crucial for determining the vehicle’s control limit, to accurately estimate the behavior of these tires during intense maneuvers in contemporary vehicle dynamics; for example: when a regular tire loses air, its coefficients change significantly, resulting in a flattened lateral force curve that leads to steering saturation. In contrast, SSRFTs retain a much larger proportion of their original stiffness factor and peak value even when deflated, enabling the vehicle’s electronic stability control systems to continue functioning correctly [1,5].

This mathematical model has its most crucial analysis during the ISO 3888-2 maneuver, also known as the Moose Test. This specific test forces the vehicle to execute a rapid and extreme double-lane change, emulating the need to avoid an unexpected obstacle on a road before returning to its initial lane. Unlike general handling tests, the ISO 3888-2 has a narrower track and requires the driver to take their foot off the accelerator, making it a tough evaluation of a vehicle’s stability and resistance to rolling over [6].

Comparative studies reveal that while a vehicle using conventional tires may experience a lateral shift exceeding $10m$ after a puncture during an avoidance maneuver, a vehicle with SSRFTs can stay on course within $0.5m$ of the established trajectory[1]. This advantage is linked to the SSRFT capability to avoid steering saturation by maintaining adequate lateral force as anticipated by the Magic Formula [6]. Therefore, the combination of structural verification via FEA, semi-empirical tire modeling and standardized stability assessments remains the optimal procedure to ensure vehicle safety in the event of tire failure.

The specific objectives of this research are to compare the handling losses and gains offered by the SSRFT by measuring a full vehicle dynamic model that maneuvers through a standardized test in several different scenarios: Conventional tires with nominal tire pressure, SSRFTs at nominal pressure, conventional tires with no inflation pressure in the Front Right (FR) tire and SSRFT with no inflation pressure in FR tire. The differences in lateral force, yaw rate, body roll, and body slip are to be measured and furthermore the differences in performance at nominal inflation between the conventional tire and the SSRFT will be compared in depth.

The following study originates from the need to address the common practice found among BMW and MINI Cooper owners of removing the factory fitted SSRFT from their vehicles in an attempt to improve handling and comfort. In addition, this is done to reduce expenses since SSRFT can cost up to double the price of conventional tires. Also, it is expected that this work can provide valuable information for the design of control systems that are used in vehicles equipped with SSRFT.

This investigation is divided into VII sections. Section II explains the literature review. Section III describes the methodology utilized in this study. Section IV exposes the system modeling . Section V explains the numerical simulation. Section VI shows and discusses the results obtained from the simulation. Section VII presents the conclusions and proposes future work.

2. Literature Review

The main part of the literature review is dissected in Table 1, where the principal insight gathered from the extensive literature review performed is tabulated. A breakdown of that process is described below, and its divided into three main sections.

2.1. Rubber Composites and Sidewall Reinforcement

The initial phase of this research entailed a comprehensive and critical review of the available scientific literature. The approach was a deep dive into the theoretical and practical studies and comparisons previously written about the pneumatic tire and the development of aids to minimize the negative effects of losing the supporting air inflation pressure. The first takeaway from this research is that the concept of a self-supporting tire is by no means a novel subject. Since it made its appearance back in the 70’s [1], the SSRFT has been in continuous evolution together with the modernization of the radial tire, ranging from double chambers, foam fillings, thickened surfaces, and the airless tire, that consists of an open sidewall tire featuring radial supports that act like stiff springs to support the vehicle’s weight. Despite these mechanical developments, the structural configuration remains limited in lateral force generation, and it is, for now, restricted to low speed vehicles and niche applications.

The development of innovative structural design for the SSRFT relies strongly on optimized geometries and hyperelastic modeling. It was established by Lv [4] that a SIR thickness of $H=8mm$ is the best compromise between added overall mass to the tire and vertical load bearing capability obtaining optimized stress matrices under zero inflation pressure. Expanding on the mechanical stresses study, Zang [7] showed that even when the total contact patch of a tire without inflation pressure expands by $223.8\%$, the effective contact patch contracts by $47.3\%$, This occurs mainly because the load concentrates to the sides and the contact patch warps generating localized zones of stress and friction that degrade the tire’s constitution and performance. To mathematically capture the stress in these zones, Lv [4] created a simulation based on the Mooney-Rivlin hyperelastic model that formulated stress-strain tensors. This yielded material behavior constants for the rigid elastomer matrices of the tire when rolling at low inflation pressure.

Recent research shifts its focus from the geometric optimization of the sidewall to the chemical composition of the elastomer matrix. Taking advantage of advancements in material science, Oka [8] proved that replacing up to $5\%$ of the commonly used carbon black reinforcement with graphene nanofibers produces a balance in the classic "Magic Triangle" paradigm shown in Figure 1 improving durability or wear resistance without compromising rolling resistance. Outside of self-supporting reinforcement options Testa [9] simulated and prototyped a disjointed radial HeroBelt rim assembly as an alternative backup system that utilizes an auxiliary wheel to support the vehicle in the event of pressure loss. Shedding light on how the modular belt proposal isolates and dissipates extreme thermal friction.

2.2. Tire Modeling and the Magic Formula

The interactions that occur on the contact patch under extreme slip conditions ($\alpha$) require complex analysis, and in order to mathematically predict the forces and moments that are involved, semi empirical modeling remains the industry standard. The model defined by Pacejka’s MF [10] derived the lateral forces and moments in the tire-road interaction, accurately capturing the non-linear behavior of the tires and from which, modern vehicle simulations get their algebraic boundaries. These forces are dynamically altered when a loss of air pressure occurs. Because of this, Singh [5] presented an extended MF framework that utilized real time adaptive parameter fitting loops to adjust the tire’s compliance matrix dynamically during sudden pressure losses.

Because of the structure of the radial tire, the contact patch behavior changes drastically when a tire experiences a total drop in air pressure. Mahajan [1] performed simulations based on Pacejka’s MF, showcasing that conventional tires yield tracking errors of up to $10m$ in the absence of inflation pressure. On the other hand, an SSRFT limits these path deviations to less than $0.5m$. Using triaxial grid modeling, Guo [11] mapped the physical mechanics driving the path deviation variations by showing how a combination of severe braking vectors shifts the contact stress concentration zone to the front of the contact patch.

2.3. Standardized Handling Evaluation and Simulation Constraints

In order to appreciate the stability boundaries of asymmetric tire failure, the optimal evaluation is a standardized closed-loop obstacle avoidance maneuver. Such as the Double Lane Change (DLC) as outlined in the standard ISO 3888-2 [12]. In the virtual testing version, to simulate the high speed maneuvering through the gates and lanes of the DLC, robust multi-constraint logic is needed, as detailed by Nguyen [13]. In the present work, specific path following and chassis dynamic assistance was integrated to execute the proposed route. These systems are incorporated purely as environmental constraints to control the 7-DOF vehicle simulation and the basis are taken from the work published by Rajamani [14].

The full vehicle simulation relies on empirical vehicle testing baselines. Heerwan [15] tested the effect of speed in the lateral weight transfers and inertial roll forces by performing instrumented field trials, which justifies the selection of $80km/h$ as initial speed for the test. The core equations that govern the roll, yaw and lateral chassis acceleration were taken from Guillespie [16], while the mathematical models for tire force generation, slip angles and extreme handling limits were based on the work by Milliken & Milliken [17]. Standard simulation blocks were deployed to benchmark the 7-DOF model in the target path outlined by the ISO 3888-2 as showcased in [6] and additionally incorporating differential braking derived from this.

Table 1. Comprehensive mapping of the literature catalog: Methodological approaches, key technical findings, and systemic integration frameworks.

Reference	Core Methodology	Key Technical Finding	Integration into Present Work
Theme 1: Structural Rubber Composites, Sidewall Insert Rubber (SIR), and Hyperelastic FEA
Lv et al. (2023)	Non-linear FEA	Sidewall insert thickness ($H=8$ mm) optimizes critical stress distribution matrices at zero inflation pressure.	Establishes the precise structural geometry baseline for the simulated SIR profile.
Zang et al. (2025)	Thermo-mechanical FEA	Deflated total footprint area expands by 223.8%, yet effective structural contact zone contracts by 47.3%.	Mechanistically explains the physical breakdown governing transient ${\mu }_y$ degradation.
Okan et al. (2020)	Material Synthesis	Replacing 5% of conventional carbon black with graphene nanofibers balances the tire “Magic Triangle” metrics.	Contextualizes advanced chemical design paths for optimizing structural tire compounds.
Testa et al. (2025)	Numerical Prototyping	Disjointed radial HeroBelt rim assemblies effectively isolate and dissipate extreme thermal run-flat friction fields.	Broadens the state-of-the-art summary toward secondary auxiliary wheel-supported fallback systems.
Theme 2: Analytical Tire Modeling, Slip Physics, and Magic Formula Formulations
Pacejka, H. (2005)	Semi-empirical Modeling	Derives normalized, non-linear coupled lateral and longitudinal tire-road force interactions under slip ($\alpha$).	Dictates the algebraic core used in Equation (1) to map transience force envelopes.
Mahajan, A.M. (2025)	Comparative MF Simulation	Deflated conventional tires yield tracking errors $>10$ m compared to $<0.5$ m preserved by SSRFT structures.	Corroborates the kinematic path deviation scale isolated in this closed-loop simulation.
Singh & Sivar. (2023)	Extended Magic Formula	Real-time adaptive parameter fitting loops dynamically adjust compliance matrices during rapid pressure drops.	Links structural tire pressure failures with active differential slip feedback equations.
Guo et al. (2025)	Triaxial Grid Modeling	Combined severe braking vectors drive the locus of peak vertical contact stresses forward on the patch.	Aids the geometric interpretation of Kamm’s friction circle envelopes under combined slip.
Theme 3: Kinematic Path Planning, Trajectory Tracking, and Autonomous Controls
Nguyen et al. (2024)	Kinematic Path Optimization	Implements predictive multi-constraint routing logic during high-speed double-lane change (DLC) execution.	Mirrors and structurally informs the implementation of the primary Stanley trajectory loop.
Rajamani, R. (2006)	Active Safety Formulations	Explicitly maps cross-track tracking error bounds alongside operational geometric understeer indexes.	Legitimizes the choice of key performance indicators (KPIs) used to track vehicle control limits.
Theme 4: Classical Chassis Dynamics, Vehicle Testing, and Load Transfers
Heerwan et al. (2017)	Instrumented Field Trials	Maps speed-dependent lateral weight transfers and coupled inertial roll forces across varying velocities.	Formulates the exact empirical justification for choosing 80 km/h as the critical entry benchmark.
Gillespie, T. (1992)	Analytical Vehicle Handling	Defines fundamental analytical equations coupling transient roll, yaw, and lateral chassis accelerations.	Forms the multi-body chassis framework for Equations (2) and (4) regulating dynamic load shifts.
Milliken & M. (1995)	Race Car Vehicle Dynamics	Provides exhaustive models on tire lateral force generation, slip angles, and limit-handling balance.	Shapes the underlying state equations used to model the chassis’ non-linear transient properties.
Theme 5: ISO Standards, Co-Simulation Frameworks, and Stability Systems
ISO 3888-2 (2019)	Standard Specification	Outlines international closed-loop obstacle avoidance layout constraints for severe path testing (Moose Test).	Directs the precise layout geometry and entry limits for the simulated test route.
MathWorks (2023)	Co-Simulation Framework	Delivers standard MATLAB/Simulink blocks for vehicle blocks and virtual DLC environments.	Benchmarks the implementation of the 7-DOF plant model with the target environment.

Table 1. Comprehensive mapping of the literature catalog: Methodological approaches, key technical findings, and systemic integration frameworks.

Reference	Core Methodology	Key Technical Finding	Integration into Present Work
Theme 1: Structural Rubber Composites, Sidewall Insert Rubber (SIR), and Hyperelastic FEA
Lv et al. (2023)	Non-linear FEA	Sidewall insert thickness ($H=8$ mm) optimizes critical stress distribution matrices at zero inflation pressure.	Establishes the precise structural geometry baseline for the simulated SIR profile.
Zang et al. (2025)	Thermo-mechanical FEA	Deflated total footprint area expands by 223.8%, yet effective structural contact zone contracts by 47.3%.	Mechanistically explains the physical breakdown governing transient ${\mu }_y$ degradation.
Okan et al. (2020)	Material Synthesis	Replacing 5% of conventional carbon black with graphene nanofibers balances the tire “Magic Triangle” metrics.	Contextualizes advanced chemical design paths for optimizing structural tire compounds.
Testa et al. (2025)	Numerical Prototyping	Disjointed radial HeroBelt rim assemblies effectively isolate and dissipate extreme thermal run-flat friction fields.	Broadens the state-of-the-art summary toward secondary auxiliary wheel-supported fallback systems.
Theme 2: Analytical Tire Modeling, Slip Physics, and Magic Formula Formulations
Pacejka, H. (2005)	Semi-empirical Modeling	Derives normalized, non-linear coupled lateral and longitudinal tire-road force interactions under slip ($\alpha$).	Dictates the algebraic core used in Equation (1) to map transience force envelopes.
Mahajan, A.M. (2025)	Comparative MF Simulation	Deflated conventional tires yield tracking errors $>10$ m compared to $<0.5$ m preserved by SSRFT structures.	Corroborates the kinematic path deviation scale isolated in this closed-loop simulation.
Singh & Sivar. (2023)	Extended Magic Formula	Real-time adaptive parameter fitting loops dynamically adjust compliance matrices during rapid pressure drops.	Links structural tire pressure failures with active differential slip feedback equations.
Guo et al. (2025)	Triaxial Grid Modeling	Combined severe braking vectors drive the locus of peak vertical contact stresses forward on the patch.	Aids the geometric interpretation of Kamm’s friction circle envelopes under combined slip.
Theme 3: Kinematic Path Planning, Trajectory Tracking, and Autonomous Controls
Nguyen et al. (2024)	Kinematic Path Optimization	Implements predictive multi-constraint routing logic during high-speed double-lane change (DLC) execution.	Mirrors and structurally informs the implementation of the primary Stanley trajectory loop.
Rajamani, R. (2006)	Active Safety Formulations	Explicitly maps cross-track tracking error bounds alongside operational geometric understeer indexes.	Legitimizes the choice of key performance indicators (KPIs) used to track vehicle control limits.
Theme 4: Classical Chassis Dynamics, Vehicle Testing, and Load Transfers
Heerwan et al. (2017)	Instrumented Field Trials	Maps speed-dependent lateral weight transfers and coupled inertial roll forces across varying velocities.	Formulates the exact empirical justification for choosing 80 km/h as the critical entry benchmark.
Gillespie, T. (1992)	Analytical Vehicle Handling	Defines fundamental analytical equations coupling transient roll, yaw, and lateral chassis accelerations.	Forms the multi-body chassis framework for Equations (2) and (4) regulating dynamic load shifts.
Milliken & M. (1995)	Race Car Vehicle Dynamics	Provides exhaustive models on tire lateral force generation, slip angles, and limit-handling balance.	Shapes the underlying state equations used to model the chassis’ non-linear transient properties.
Theme 5: ISO Standards, Co-Simulation Frameworks, and Stability Systems
ISO 3888-2 (2019)	Standard Specification	Outlines international closed-loop obstacle avoidance layout constraints for severe path testing (Moose Test).	Directs the precise layout geometry and entry limits for the simulated test route.
MathWorks (2023)	Co-Simulation Framework	Delivers standard MATLAB/Simulink blocks for vehicle blocks and virtual DLC environments.	Benchmarks the implementation of the 7-DOF plant model with the target environment.

3. Methodology

This section outlines the methodological framework implemented throughout this research.

As stated before, the primary objective of this study is to analyze and quantify the handling variations between SSRFT and conventional pneumatic tires. With the use of a structured logical framework, a specific research problem was established, which highlighted the necessity of researching these dynamic differences. The underlying issue originates from a recognized tendency among BMW and MINI Cooper owners to substitute factory-fitted SSRFT configurations with standard radial tires. Subsequently, as illustrated in Figure 2, a comprehensive problem tree was constructed to map the analytical rationale governing this investigation.

Following the problem definition, the modeling and simulation framework was conceptualized and selected. The initial stage involved gathering sufficient data from the literature to accurately estimate Pacejka’s MF parameters, enabling the generation of distinct tire models for the evaluation scenarios: conventional and SSRFT configurations at both nominal and zero inflation pressures. Subsequent tasks focused on identifying the specific vehicle handling metrics to be extracted from this comparative framework. While trajectory deviation from a reference path serves as a primary objective indicator of vehicle maneuverability, additional analytical value is derived by extracting multi-variable operational outputs from the core simulation architecture that integrates these calibrated tire models.

The simulation pipeline was executed when the scenarios and technical information were established and with the aid of generative AI tools, an initial draft of the Python script was generated to simulate a full vehicle utilizing the developed tire models. Navigating a course to mimic the test outlined in ISO 3888-2 introduced additional complexity to the script by requiring a trajectory-following algorithm typically reserved for autonomous vehicles, which remains outside the primary scope of this paper. Because ISO 3888-2 only dictates the physical path architecture, initial boundaries, and pass/fail criteria—with manual execution conventionally falling into the hands of a professional test driver—a trajectory-following mechanism was mandatory; specifically, the Stanley algorithm was implemented. Dynamic Stability Control (DSC) was also integrated into the full vehicle plant, as the baseline passive suspension configuration was insufficient to navigate the maneuver as expected in physical testing. Although this active system is outside the scope of the present study it was incorporated into the model in the most simplified mathematical form possible. For the complete models and formulations, see [5,13,14,18].

Subsequently, the comparison between the nominally inflated conventional tires and the SSRFT was evaluated by analyzing the simulation results of the specific scenario where the front-right (FR) tire was fully deflated while the remaining tires maintained nominal inflation. The primary objective is to present overlaid plots of the selected metrics against both time and steering angle to provide critical insights into the actual quantifiable differences exhibited by the tested operational modes.

The findings are illustrated using unified plots that compile all four scenarios simultaneously for each metric, thereby facilitating direct comparison and offering a comprehensive understanding of transient vehicle behavior. A summary table tracking key performance indicators (KPIs) is included to quantitatively assess the performance variations across the evaluated conditions. The numerical results demonstrate enhanced maneuverability when SSRFT operate under zero-pressure conditions. Furthermore, this study indicates that the handling performance degradation of the SSRFT configuration at nominal inflation pressure is negligible, as the response profiles appear virtually identical to the conventional baseline when extracted from the simulation.

4. System Modeling

4.1. Tire Model

Following data acquisition for the Pacejka tire model, the lateral force ($F_y$) curves were generated to visualize the inherent mechanical differences between the configurations and establish the analytical baseline for subsequent testing.

To accurately simulate vehicle dynamics, a full seven-degree-of-freedom (7-DOF) vehicle model was selected over a simplified half- or quarter-car alternative. This architecture enables the extraction of transient roll and yaw accelerations alongside individual tire force generation —essential for observing vehicle attitude and evaluating cabin comfort metrics. The simulation isolates a single-wheel deflation scenario rather than multi-wheel pressure losses; while multi-wheel deflation can occur in practice, it remains outside the scope of the present study.

Pacejka’s Magic Formula (MF) is applied to characterize tire behavior during severe maneuvers. This semi-empirical framework mathematically couples tire slip metrics to the resulting forces and moments. Utilizing a specialized trigonometric formulation, the MF generates characteristic curves for lateral force ($F_y$) and aligning torque ($M_z$) that align closely with experimental data. The formulation relies on four primary empirical coefficients: the stiffness factor (B), that defines the initial slope; the shape factor (C), which determines the asymptotic boundaries of the function; the peak value (D), representing the maximum friction ceiling; and the curvature factor (E), which controls the profile geometry near its peak value [1,5].

The basic Pacejka MF is written as follows:

$$F_{y,ij}=F_{z,ij}·Dsin\left[Carctan\left(B{\alpha }_{\mathrm{deg}}-E\left(B{\alpha }_{\mathrm{deg}}-arctan\left(B{\alpha }_{\mathrm{deg}}\right)\right)\right)\right]$$

(1)

The empirical coefficients ($B,C,D,E$) utilizing Pacejka’s Magic Formula were analytically calibrated to preserve the physical and kinematic boundaries characteristic of self-supporting run-flat behaviors under deflated states as shown in Table 2. Because experimental flat-plank testing data for proprietary commercial matrices are heavily restricted, a semi-empirical optimization routine was executed. The baseline parameters were initialized from the structural modeling limits established by Lv et al. [4] and the transient slip boundary constraints verified by Singh [5]. These coefficients were subsequently tuned through iterative computational benchmarking to ensure that the resultant lateral force envelopes ($F_y$) and cornering stiffness metrics strictly conform to acceptable engineering ranges for rigid elastomeric sidewall inserts under atmospheric pressure loss. The rationale behind the calibrated parameters is explained below:

Conventional Tire Inflated and Deflated

• Peak Force (D): When the pneumatic tire is missing all the support provided by the inflation pressure, the structural rigidity of the tire drops, and the contact patch is adversely affected since wrapping occurs. This hinders the tire’s capability to generate peak lateral forces that can compensate for the vehicle’s movement; therefore, it was decided to calibrate the value of D in accordance with the internationally available data in vehicle related publications about Run-Flat tire modeling and simulating to really showcase this drastically reduced maximum lateral force (Fy) observed in the absence of air pressure [4].
• Cornering Stiffness ($K\alpha =B*C*D$): With the loss of inflation pressure, the vertical rigidity of the tire is almost completely lost. The conventional tire’s sidewalls collapse fully, and the overall vertical stiffness of the tire vanishes. This produces a soft response to the slip angle causing the initial slope of the curve to drop. According to Pacejka, the cornering stiffness is closely related to the inflation pressure, and in fact, it will be lost in the absence of it. This prompted the need to calibrate the B parameter accordingly [10].

SSRFT Inflated and Deflated

• Cornering Stiffness ($K\alpha$ & B): Run-Flat tires incorporate a rubber insert that thickens the sidewall, providing additional vertical stiffness. When there is no air pressure in the SSRFT, the total weight of the car falls onto the sidewalls, and the mentioned inserts support the car’s mass, and even when the cornering stiffness is lower, it is several times greater than the fully deflated conventional tire, and it performs better than a partially deflated conventional tire as well [1].
• Curve Form (C & E): The transition to the peak force in a SSRFT with no inflation pressure is more abrupt. The augmented rigidity of the sidewall does not allow for a gradual side deflection; therefore, the C factor is slightly higher, and the behavior of the vehicle when maneuvering is sharper, or as it is referred to: a nervous response to steering [10].

As an initial visualization of the results, a pure Pacejka Curve for $F_y$ was obtained for a 3 deg camber ($\gamma$) as shown in Figure 3. It is worth observing that the maximum lateral force that can be extracted from the tire, is greater in the RFT instead of the conventional tire, even when the chosen values of D were lower for the SSRFT as shown in Table 2. This responds to the stiffer vertical resistance from the SSRFT that can handle slip angles better when the camber angle is introduced, following the expected behavior documented by [2,10].

Table 2. Calibrated Pacejka parameters.

Tire	B	C	D	E
Conventional Nominal Pressure	10.00	1.30	1.05	-2.00
SSRFT Nominal Pressure	13.50	1.25	0.98	-1.80
Conventional Low Pressure	1.80	1.00	0.32	-0.50
SSRFT Low Pressure	5.50	1.15	0.62	-1.00

Table 2. Calibrated Pacejka parameters.

Tire	B	C	D	E
Conventional Nominal Pressure	10.00	1.30	1.05	-2.00
SSRFT Nominal Pressure	13.50	1.25	0.98	-1.80
Conventional Low Pressure	1.80	1.00	0.32	-0.50
SSRFT Low Pressure	5.50	1.15	0.62	-1.00

4.2. Full Vehicle Dynamics Model

The mathematical backbone of the system model relies on: computing the dynamic states of the vehicle chassis, the varying loads acting on the individual wheels, and the kinematic slips experienced at the tire contact patch as well as the whole vehicle slip and yaw. For simplicity, the generic formulas used are described below. For further clarification, the full formulation and approach are described in detail in [10,13,14,16].

To calculate the overall planar accelerations of the vehicle, the forces generated at each tire footprint are resolved along the chassis body-fixed coordinate axes ($x,y$) and they are solved using Newton’s Second Law:

$$\dot{U}={\displaystyle \frac{\Sigma F_x}{M_{\mathrm{total}}}}+V·r,\mathrm{and}\dot{V}={\displaystyle \frac{\Sigma F_y}{M_{\mathrm{total}}}}-U·r$$

(2)

Where $M_{\mathrm{total}}$ represents the total vehicle mass (sprung and unsprung), U is the forward velocity, V is the lateral velocity, r is the yaw rate, and $\Sigma F_x,\Sigma F_y$ represent the combined longitudinal and lateral force vectors acting on the chassis from all four wheels [14].

During heavy transient directional shifts, the vehicle’s slip and traction behavior can be captured using the lateral and longitudinal velocities in a coupled manner because of the way they contribute to each other.

The angular accelerations governing vehicle handling and occupant attitude are mapped via two coupled differential equations tracking yaw ($\dot{r}$) and body roll ($\ddot{\varphi }$):

$$I_z\dot{r}=\Sigma M_z(F_{x,ij},F_{y,ij})$$

(3)

$$\ddot{\varphi }={\displaystyle \frac{M_s·g·H_{cg}·sin\varphi +\Sigma F_y·H_{cg}-K_{\mathrm{roll},\mathrm{total}}\varphi -C_{\mathrm{roll},\mathrm{total}}\dot{\varphi }}{I_x}}$$

(4)

Here $I_z$ and $I_x$ are the moments of inertia, $M_s$ is the sprung mass, $H_{cg}$ is the center of gravity height, and $\Sigma M_z$ represents the net yaw moment calculated from the asymmetric spatial distribution of wheel force vectors [14,16]. Total suspension roll properties are lumped via rolling stiffness ($K_{\mathrm{roll},\mathrm{total}}$) and damping ($C_{\mathrm{roll},\mathrm{total}}$) derived directly from track width and spring constants.

[Calculating yaw and roll accelerations simultaneously is critical to mapping the unbalance and tilting effect that takes place immediately following an asymmetric single-wheel deflation.]

To evaluate an isolated single-wheel deflation, the model calculates independent dynamic vertical loads ($F_{z,ij}$) and footprint slip angles (${\alpha }_{ij}$) for each wheel position using index notation where $i\in \left\{\mathrm{Front},\mathrm{Rear}\right\}$ and $j\in \left\{\mathrm{Left},\mathrm{Right}\right\}$:

$$F_{z,ij}=F_{z,\mathrm{static},i}\pm {\displaystyle \frac{M_s·g·H_{cg}·\varphi }{T_w}}$$

(5)

$${\alpha }_{ij}={\delta }_i-arctan\left({\displaystyle \frac{V\pm L_i·r}{U\mp 0.5·T_w·r}}\right)$$

(6)

Here, $T_w$ represents track width, $L_i$ represents the respective axle distance ($L_f$ or $L_r$), and ${\delta }_i$ is the steer input applied exclusively to the front axle (${\delta }_f=\delta ,{\delta }_r=0$) [14].

[These compact forms allow for independent tracking of how vertical load drops on an inner wheel and increases slip angles during sharp turns.]

Using the vertical loads and slip angles computed above, the pure-slip lateral force ($F_{y,ij}$) for each tire is evaluated. Because the kinematic slip angles (${\alpha }_{ij}$) derived in Equation (6) are in radians, they must be scaled to degrees (${\alpha }_{\mathrm{deg}}$) before being implemented in the empirical Pacejka framework:

$${\alpha }_{\mathrm{deg},ij}={\alpha }_{ij}·\left({\displaystyle \frac{180}{\pi }}\right)$$

(7)

This scalar transformation allows the localized coordinate inputs from Equation (6) to fit directly into the standard Magic Formula structure outlined in Equation (1).

To emulate active electronic safety interventions under asymmetrical tire failure, the script calculates a continuous directional tracking error against a reference neutral kinematic yaw target ($r_{\mathrm{target}}={\displaystyle \frac{U·\delta }{L_f+L_r}}$):

$${\mathrm{Error}}_{\mathrm{filtered}}=tanh\left({\displaystyle \frac{r-r_{\mathrm{target}}}{0.05}}\right)·max\left(\right|r-r_{\mathrm{target}}|-0.05,0)$$

(8)

If the filtered threshold detects oversteer ($\mathrm{Error}>0$), a stabilizing brake force ($F_{x,FR,\mathrm{dsc}}$) scales dynamically up to $75\%$ of peak capacity on the front-right wheel; conversely, understeer activates corrective braking ($F_{x,RL,\mathrm{dsc}}$) on the rear-left wheel [19].

[Modern vehicle electronics step in to automatically correct oversteer or understeer anomalies through differential braking.]

To establish a clear upper performance boundary for vehicle stability during the maneuver, the integrated Dynamic Stability Control (DSC) system is implemented in an idealized and mathematically simplified form rather than a production-ready software architecture. Under extreme deflation conditions, tracking the localized, highly non-linear variations in the tire-road friction coefficient ($\mu$) and vertical load capacity ($F_z$) presents extreme real-time state-estimation challenges; therefore, the yaw controller in this plant model evaluates differential braking forces based on a simplified kinematic slip error feedback mechanism. This abstraction allows the simulation to isolate and quantify the structural limits of the tire configurations themselves, establishing a generalized performance baseline without introducing the confounding variables of a specific proprietary electronic chassis control algorithm.

The mathematical model utilizes a modified look-ahead path layout to incorporate current cross-track deviation ($e_{\mathrm{current}}$) and an advanced preview error point ($e_{\mathrm{future}}$) over a driver look-ahead time horizon ($t_{\mathrm{preview}}=0.35\mathrm{s}$) [14]:

$${\delta }_{\mathrm{target}}=\Delta {\Psi }_{\mathrm{heading}}+arctan\left({\displaystyle \frac{3.5·e_{\mathrm{current}}+2.0·e_{\mathrm{future}}}{U+0.5}}\right)-0.55\beta -0.15(r-r_{\mathrm{road}})$$

(9)

The final steering vector is subsequently updated through a low-pass first-order integration loop (${\delta }_{k+1}$) to accurately reflect the physical steering actuator lag constraints.

[This look-ahead formula represents realistic human reaction times when steering back and forth through the narrow ISO lane gates.]

The trajectory-following architecture purposefully utilizes a geometric Stanley control law rather than a Model Predictive Control (MPC) framework. While an initial development phase attempted to leverage MPC to minimize tracking error bounds, the structural behavior of a localized, zero-pressure tire introduces severe, discontinuous non-linearities into the 7-DOF multi-body plant dynamics. Under sudden deflation, the abrupt collapse of cornering stiffness matrices violates the linear or quadratic approximation limits required for real-time MPC optimization convergence, resulting in prohibitive computational costs or solver failures during high-g transient maneuvers. Consequently, the Stanley controller was chosen as a robust kinematic tracking benchmark. By decoupling the reference path tracking mechanism from the volatile state-estimation variables of the compromised tire patch, this architecture isolates the vehicle’s pure physical handling limitations and ensures deterministic simulation stability.

5. Simulation

5.1. Evaluated Simulation Scenarios

The model executes a calculation matrix composed of four independent scenarios designed to contrast the vehicle’s dynamic behavior under nominal conditions versus a critical failure involving a loss of pressure in the front-right tire (FR):

Table 3. Summary of evaluated simulation scenarios.

Tire Type	Pressure	Simulation Condition / Objective
Conventional	Nominal	Baseline run with all four tires operating at nominal pressure.
Run-Flat	Nominal	Baseline run with all four Run-Flat tires operating at nominal pressure.
Conventional	LOW	Simulates a loss of pressure exclusively in the Front-Right (FR) tire.
Run-Flat	LOW	Simulates a loss of pressure in the Front-Right (FR) tire for a Run-Flat variant.

Table 3. Summary of evaluated simulation scenarios.

Tire Type	Pressure	Simulation Condition / Objective
Conventional	Nominal	Baseline run with all four tires operating at nominal pressure.
Run-Flat	Nominal	Baseline run with all four Run-Flat tires operating at nominal pressure.
Conventional	LOW	Simulates a loss of pressure exclusively in the Front-Right (FR) tire.
Run-Flat	LOW	Simulates a loss of pressure in the Front-Right (FR) tire for a Run-Flat variant.

5.2. Vehicle Physical Parameters

The vehicle data utilized is based on the technical specifications of the [F56] MINI Cooper S and was chosen because it is highly regarded as an agile vehicle with unique handling [20]. Additionally, it comes with SSRFTs from the factory, making it an excellent choice for the study. The full vehicle specifications are listed in Table 4:

5.3. Track Geometry and Specifications

The maneuver mathematically recreates the centerline geometry of the ISO 3888-2 also known as the Double Lane Change (DLC). Figure 4 and Table 5 shows the path divided into longitudinal sections (X) that define the target lateral displacement (Y):

5.4. Dynamic Setup and Simulation Operation

1.

Initial Conditions and Speed

• Initial Entry Speed (U):$22.22m/s$ (equivalent to $80km/h$).
• Throttle/Acceleration Condition: The simulation runs under an inertial dissipation regime. There is no acceleration torque input and the vehicle progressively loses forward velocity due to the passive resistance forces applied at the wheels.

2.

Path Tracking Controller Parameters

To guide the vehicle through the ISO track, a Two-Point Advanced Preview of Stanley Controller is implemented:

• Preview Time (tpreview):$0.35s$ ahead to anticipate incoming curves.
• Steering Limits: The physical steering angle at the front wheels is software-limited to a maximum of ±35°.

3.

Time Discretization and Duration

• Discrete Time Step ($\Delta t$):$0.01s$ to ensure numerical stability during the integration of the equations of motion.
• Total Simulation Time ($t_{e}nd$):$5s$.
• Calculated Steps: 500 iterations for each of the 4 evaluated scenarios.

6. Results and Discussion

6.1. Trajectory Deviation

The graph that shows exactly how much the vehicle deviated from the intended path in both x and y directions was the first to be analyzed. This graph provides an overview of the maneuver, and it should be analyzed along with the steering angle input to get the whole image of the exact events happening to the vehicle. This can be observed in Figure 5 where the scenario of the inflated tire overshoot the exit of the maneuver by less than $0.5m$ (minimum allowed) and are granted a PASS since they fully recover stability and return to the original lane that they were in, indicating that the SSRFT present no significant loss in handling performance.

The other scenarios do not show acceptable results in the ISO 3888 outline, but a tangible difference can be observed in favor of the performance of SSRFT and conventional tires when they operate at zero inflation pressure. Specifically, the longitudinal position where the vehicle changes directions after performing the first lane change occurs at $30m$ in nominal conditions, but in the case of the conventional tire at zero pressure, the shift in direction occurs in the $45m$ longitudinal position, which represents a $15m$ deviation from the expected, most likely resulting in a collision or accident in a real life event. Regarding the lateral deviation considering the direction of heading, the deflated states of both tires showed significant differences: the SSRFT presented a maximum deviation of $1.5m$ while the conventional tire veered $3.5m$ from the path.

Small adjustments to the steering angle ($\delta$) can be observed when the vehicle enters the test and takes the first turn, when initializing the first lane change, and then again when the second lane change occurs ($0.5sand2.2s$). This is due to the car sliding momentarily, as well as the driver algorithm compensating with steering. Additionally, the DSC applies braking torque in an effort to stop the slide. These two work together towards the stabilization of the vehicle and the minimization of the yaw rate.

6.2. Lateral Acceleration

The lateral acceleration plot shown in Figure 5 exposes how the second shift to the original lane of travel takes $1.5s$ more to occur in the scenario with the conventional tire in the deflated state. The SSRFT presents a delay of less than a second and the normalization after the last steering adjustment of trajectory occurs less than $1.5s$ after the inflated conventional tire scenarios; in comparison, in the conventional deflated tire this happens more than $2s$ after. In addition, it can be observed that the maximum lateral acceleration provided by the inflated tires was $0.9g$. The vehicle with the deflated conventional tire was only able to receive $0.65g$ while the SSRFT showed a $0.75g$ lateral acceleration.

6.3. Body Roll and Yaw Rate

When the body roll angle graph in Figure 6 is analyzed, the extended behavior of the conventional tire in a deflated state from seconds 1.5 to 3.5, shows the car understeering greatly, maintaining the roll for a longer time, rather than showing a sharp movement back to the opposite side as it happened in the conventional tire and SSRFT tested at nominal pressure that shifted to the opposite direction in $0.5s$. The Yaw Rate plot in Figure 6 shows a shift in the oscillatory manner of movement of the inflated tires, caused mainly by one deflated tire greatly affecting the car’s ability to turn in one direction more than the other, which concurs with the roll observed at the same moment during the test.

Figure 5. (a) Longitudinal and Lateral position shift of different scenario. (b) Front Axle Steering Position ($\delta$). (c) Lateral Acceleration ($a_y$).

Figure 5. (a) Longitudinal and Lateral position shift of different scenario. (b) Front Axle Steering Position ($\delta$). (c) Lateral Acceleration ($a_y$).

Figure 6. (a) Dynamic Roll Lean Angle ($\varphi$). (b) Chassis Yaw Rate (r).

Figure 6. (a) Dynamic Roll Lean Angle ($\varphi$). (b) Chassis Yaw Rate (r).

6.4. Full Body Slip

As it is presented in Figure 6, the car shows an understeering condition when attempting to return to the original lane. In Figure 7, this can be confirmed, by observing the general body slip angle staggered from 1.5 to 3.5 s. This confirms that the driver algorithm had to work harder to bring the vehicle to the original centerline of travel, because of the heavy under-steer situation that was generated. Furthermore, it can be observed that the maximum sideslip angle was greater for the conventional tire with no air pressure at 2.6 deg, which represented an increase of over 0.5 deg degree when compared to the conventional tire and SSRFT at nominal pressure.

6.5. Coasting Speed

Additionally, the speed throughout the whole test was plotted in Figure 8 to showcase the loss in vehicle velocity that occurs as a result of the contact patch deformation which increases the rolling resistance and reduces the speed; additionally the DSC controls the vehicle’s attempt to slide by applying up to $75\%$ of braking torque to the front tire slipping and the opposite rear tire.

The graph successfully shows the SSRFT lost $5Km/h$ more when compared to the inflated variants that exhibited a final speed of $60.5Km/h$. However, the vehicle with one conventional tire operating at zero inflation pressure had a final longitudinal velocity of $48Km/h$. Proving that the scrubbing drag and rolling resistance greatly increase in the conventional tire when it loses the vertical rigidity it requires to perform. While the DSC still applies braking in all scenarios, the SSRFT requires less adjustment since it still retains vertical structural rigidity allowing less under-steer caused by the tire dragging at full steering wheel lock.

6.6. Friction Circle

In order to further visualize the key differences between the SSRFT and the conventional tire, the Kamm’s Friction Circle or G - G diagram was plotted as presented in Figure 9. Both the SSRFT and the conventional tires at the nominal pressure, show utilization of the full envelope of their Friction Circles. The graph shows us that the conventional tire, retains and utilizes only about 30 % of the theoretical grip available in the inflated instance. On the other hand,the SSRFT retained over 60 % of its gripping ability and showed it can also handle the initial deceleration caused by the sharp first turn at the entry of the test by the curvature of its J-hook-like initial speed gradient or braking torque, this shape comes from the tire’s behavior and characteristic explained by Pacejka [10] in which the tire’s ability to provide lateral force diminishes if a traction torque is applied, which forms the circle (or ellipses) of friction.

6.7. KPI Table

In Table 6, the results are summarized for enhanced readability and further quantitative analysis. The degradation in safe operational conditions experienced when the conventional tire loses inflation pressure is drastic and clearly apparent, whereas the resilience and enhanced safety margins of the SSRFT remain undeniable. Furthermore, the variation in performance under normal operational conditions is negligible.

7. Conclusions

This work presented a comprehensive comparative analysis of full-scale vehicle handling limits following a localized, single-wheel deflation scenario, evaluating the active safety margins between SSRFT and conventional radial pneumatic tires. By establishing a non-linear 7-DOF vehicle model parameterized to a commercial platform ([F56] MINI Cooper S); both configurations were subjected to the severe closed-loop transient steering constraints of the standard ISO 3888-2 DLC maneuver at an entry velocity of $80km/h$.

The main conclusions derived from this research are summarized as follows:

• Under a sudden front-right tire deflation profile, the conventional pneumatic configuration undergoes terminal tracking degradation, exhibiting maximum cross-track trajectory deviations exceeding $15m$. This structural failure induces rapid understeer saturation, rendering standard Electronic Stability Control (ESC) feedback architecture incapable of preserving path-following stability boundaries.
• In identical operating scenarios, self-supporting run-flat tires preserve approximately $60\%$ of their nominal cornering stiffness matrix. This structural resilience successfully prevents steering linkage saturation, keeping maximum path deviations below $0.5m$ and maintaining the vehicle safely within the designated trajectory gates.
• The explicit integration of a radian-to-degree scaling parameter (${\alpha }_{\mathrm{deg}}$) within the empirical Pacejka framework verified that dynamic load transfers during high-g maneuvering worsen tracking failures on deflated conventional plies, whereas the rigid elastomeric inserts of the SSRFT mitigate transient rolling moments effectively.

Future research trajectories will utilize this full vehicle plant model to implement FEA-simulation-derived parameter estimation loop architectures. This extension will evaluate the integration of graphene nanofibers into the SIR compound matrix, quantifying the resulting transient dynamic variations and identifying structural limit-handling performance improvements. Furthermore, to bridge the gap between academic research and automotive consumer awareness, an outreach initiative will be pursued to translate these findings into non-technical, enthusiast-oriented automotive publications. Disseminating these comparative safety insights directly to end-users—specifically BMW and MINI Cooper owner communities—aims to mitigate the empirical misinformation surrounding SSRFT replacements and enhance public road safety awareness.