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Polyester is currently the main material used for the manufacture of safety belts used in car transport for the protection of passengers and the driver. The seat belt is the main passive safety element used in vehicle engineering. In this work, the behavior of two safety belts, one with three-point fastening and the other with four-point fastening, which equip the seat of a racing car used in Formula Student for use in a frontal impact with a vertical wall. A model with finite elements is used to describe the entire car–driver shock-absorber assembly. The von Mises stresses calculated for both cases under consideration are below the tensile strength. The tensions arising in the belt and the accelerations required at various points of the driver's body are determined by both the properties of the utilized polyester and the chosen construction variant. The obtained results justify the use of the three-point and four-point belt in the cases of both common and race cars. [ABSTRACT FROM AUTHOR]

The yaw acceleration required for circuit driving is determined by the time variation of the yaw rate due to two factors: corner radius and velocity at the center of gravity. Torque vectoring systems have the advantage where the yaw moment can be changed only by the longitudinal force without changing the lateral force of the tires, which greatly affects lateral acceleration. This is expected to improve the both the spinning performance and the orbital performance, which are usually in a trade-off relationship. In this study, we proposed a yaw moment control technology that actively utilized a power unit with a brake system, which was easy to implement in a system, and compared the performance of vehicles equipped with and without the proposed system using the Milliken Research Associates moment method for quasi-steady-state analysis. The performances of lateral acceleration and yaw moment were verified using the same method, and a variable corner radius simulation for circuit driving was used to compare time and performance. The results showed the effectiveness of the proposed system.

The yaw acceleration required for circuit driving is determined by the time variation of the yaw rate due to two factors: corner radius and velocity at the center of gravity. Torque vectoring systems have the advantage where the yaw moment can be changed only by the longitudinal force without changing the lateral force of the tires, which greatly affects lateral acceleration. This is expected to improve the both the spinning performance and the orbital performance, which are usually in a trade-off relationship. In this study, we proposed a yaw moment control technology that actively utilized a power unit with a brake system, which was easy to implement in a system, and compared the performance of vehicles equipped with and without the proposed system using the Milliken Research Associates moment method for quasi-steady-state analysis. The performances of lateral acceleration and yaw moment were verified using the same method, and a variable corner radius simulation for circuit driving was used to compare time and performance. The results showed the effectiveness of the proposed system. [ABSTRACT FROM AUTHOR]

Polyester is currently the main material used for the manufacture of safety belts used in car transport for the protection of passengers and the driver. The seat belt is the main passive safety element used in vehicle engineering. In this work, the behavior of two safety belts, one with three-point fastening and the other with four-point fastening, which equip the seat of a racing car used in Formula Student for use in a frontal impact with a vertical wall. A model with finite elements is used to describe the entire car–driver shock-absorber assembly. The von Mises stresses calculated for both cases under consideration are below the tensile strength. The tensions arising in the belt and the accelerations required at various points of the driver’s body are determined by both the properties of the utilized polyester and the chosen construction variant. The obtained results justify the use of the three-point and four-point belt in the cases of both common and race cars.

The purpose of this study is to identify the initial lateral and vertical location and angle of attack of a GT4-style rear wing on the rear downforce for an Aston Martin DB7 Vantage, prior to installation. The tests were completed with a two-dimensional model, using the Computational Fluid Dynamics (CFD) software, Fluent Ansys. The tests were completed using a range of velocities: 60–80 mph. Optimization of the position of the rear wing aerodynamic device was permitted under the Motorsport UK rules for multiple race series. The results show that while the drag decreases the farther back the wing is located, the desired configuration for the rear wing with regard to downforce is when it is positioned ca. 1850 mm back from the center point of the car, with an attack angle of 5°. Unusually, this is to the front of the boot/rear deck, but it is remarkably similar to where Aston Martin set the rear wing on their Le Mans car in 1995, above where the rear windscreen met the boot hinge, which was based upon wind tunnel studies using a scale model. Our results suggest that while 2D simulations of these types cannot give absolute values for downforce due to aerodynamic device location, they can provide low costs, fast simulation time, and a route for a wide range of cars, making the approach accessible to club motorsports, unlike complex 3D simulation and wind tunnel experimentation.

The wheel loads of a race car have been estimated in view of structural durability assessments. First, the front left double‐wishbone suspension of a rear‐wheel‐drive race vehicle has been instrumented; then, wheel loads have been estimated by means of four approaches: (i) a geometric matrix (GM) method, (ii) a feedforward neural network (FNN) approach applied to the fully instrumented suspension (FIS), (iii) a FNN approach involving a reduced number of sensors (the partially instrumented suspension (PIS)) and an inertial measurement unit (IMU), and (iv) a linear modeling approach (LM). After having trained the FNNs by using suspension signals acquired in a racetrack as inputs and related tire forces measured with the GM method as targets, the FNN‐based methods have been validated on three different racetracks by comparing the estimated loads with those estimated by means of the GM method. According to the results achieved, the FNN approaches are effective for the estimation of the wheel forces. Highlights: A double‐wishbone suspension was instrumented to measure the wheel fatigue loads.A geometric matrix method was formulated to measure the loads simply from equilibrium.Two NNs were formulated, with fully and partially instrumented suspension, respectively.Both NNs were trained and successfully estimated the wheel loads in track driving. [ABSTRACT FROM AUTHOR]

The objective of this work is to design an upper stage steering system for the Formula FSAE car “Omega” that will effectively translate driver input force to the rack and pinion. The system consists of a steering wheel, steering shafts, universal joints, a quick release mechanism, and connection points to the car. Critical loads have been determined, and the final design has been validated using finite element analysis to ensure the safety of the assembly during normal operation and worst-scenario cases. The design key factors were performance, weight, cost, ergonomics, maintainability, manufacturability and reliability.

Nonlinear effects and external disturbances can severely impact the control of an autonomous race car at the handling limits. State-of-the-art approaches do not take these uncertainties explicitly into account in the design process and are therefore prone to failure. To overcome this limitation, we present a robust control design based on tube model predictive control (TMPC). It is based on a simplified friction limited point-mass model and an additive disturbance for the lateral and longitudinal dynamics. Instead of nominal predictions, it leverages an approximate tube of reachable sets over the prediction horizon to guarantee constraint satisfaction. The resulting optimisation problem can be posed in the form of a standard quadratic programme by tightening the input and state constraints. The computational burden is therefore the same as in the nominal case. We benchmark our controller on a Hardware-in-the-Loop testbench with a nonlinear dual-track model and a combined Pacejka tyre model. The results demonstrate that the TMPC controller reduces the constraint violations while achieving comparable lap-times in contrast to an MPC controller and an infinite time LQR controller. It manages to apply caution when needed while maintaining a similar level of performance and is therefore considered to be superior in practical applications. [ABSTRACT FROM AUTHOR]

The purpose of this study is to identify the initial lateral and vertical location and angle of attack of a GT4-style rear wing on the rear downforce for an Aston Martin DB7 Vantage, prior to installation. The tests were completed with a two-dimensional model, using the Computational Fluid Dynamics (CFD) software, Fluent Ansys. The tests were completed using a range of velocities: 60–80 mph. Optimization of the position of the rear wing aerodynamic device was permitted under the Motorsport UK rules for multiple race series. The results show that while the drag decreases the farther back the wing is located, the desired configuration for the rear wing with regard to downforce is when it is positioned ca. 1850 mm back from the center point of the car, with an attack angle of 5°. Unusually, this is to the front of the boot/rear deck, but it is remarkably similar to where Aston Martin set the rear wing on their Le Mans car in 1995, above where the rear windscreen met the boot hinge, which was based upon wind tunnel studies using a scale model. Our results suggest that while 2D simulations of these types cannot give absolute values for downforce due to aerodynamic device location, they can provide low costs, fast simulation time, and a route for a wide range of cars, making the approach accessible to club motorsports, unlike complex 3D simulation and wind tunnel experimentation. [ABSTRACT FROM AUTHOR]

The search for high aerodynamic performance of a race car is one of the main aspects of the design process. The flow around the basic body shape is complicated by the presence of the rotating wheels. This is especially true in race cars on which the wheels are not shrouded, where the effects on the flow field are considerable. Despite this, few works have focused on the flow around the rotating wheels. In this paper, CFD techniques were used to provide a detailed analysis of the flow structures generated by the interaction between a multielement inverted wing and the wheel of an open-wheel race car. In the first part, the CFD approach was validated for the isolated wheel case by comparing the results with experimental and numerical data from the literature. The wheel was analyzed both in stationary and unsteady flow conditions. Then, the CFD model was adopted to study the interaction of the flow structures between the wheel with the real grooves on the tire and the front wing of a Formula 1 car. Three different configurations were considered in order to differentiate the individual effects. The discussions were supported by the values of the aerodynamic performance coefficients and flow contours. [ABSTRACT FROM AUTHOR]

Modern motorsport limited slip differentials (LSD) have evolved to become highly adjustable, allowing the torque bias that they generate to be tuned in the corner entry, apex and corner exit phases of typical on-track manoeuvres. The task of finding the optimal torque bias profile under such varied vehicle conditions is complex. This paper presents a nonlinear optimal control method which is used to find the minimum time optimal torque bias profile through a lane change manoeuvre. The results are compared to traditional open and fully locked differential strategies, in addition to considering related vehicle stability and agility metrics. An investigation into how the optimal torque bias profile changes with reduced track-tyre friction is also included in the analysis. The optimal LSD profile was shown to give a performance gain over its locked differential counterpart in key areas of the manoeuvre where a quick direction change is required. The methodology proposed can be used to find both optimal passive LSD characteristics and as the basis of a semi-active LSD control algorithm.

The objective of this work is to design an upper stage steering system for the Formula FSAE car "Omega" that will effectively translate driver input force to the rack and pinion. The system consists of a steering wheel, steering shafts, universal joints, a quick release mechanism, and connection points to the car. Critical loads have been determined, and the final design has been validated using finite element analysis to ensure the safety of the assembly during normal operation and worst-scenario cases. The design key factors were performance, weight, cost, ergonomics, maintainability, manufacturability and reliability. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of the link between the driving style of an ideal driver, modelled as an optimal controller, and fundamental set-up parameters of a vehicle in the GP2 motorsport class. The aim is to evaluate quantitatively how set-up parameters, like distribution of aerodynamic loads, weight and roll stiffness between front and rear axles, affect the driving style, encoded in the shape of the optimal trajectory and in the acceleration, brake and steer inputs. To this aim, we develop an optimization code that includes a double-track vehicle model capable of solving the minimum lap-time problem (MLTP) on a given track. The track is represented via NURBS curves and the MLTP is framed and solved as an optimal control problem by transcription into a nonlinear program using direct collocation. To assess the accuracy of the vehicle model and the optimization pipeline, we also validate our results against real telemetry data. The developed software framework lends itself to easily perform both sensitivity analysis and concurrent trajectory planning and set-up parameter optimization: this is obtained by simple promotion of static parameters of interests to variables in the optimal control problem. Some results along these lines are also included. [ABSTRACT FROM AUTHOR]

While several papers dealing with the kinematic of mechanisms that approximate the well-known Ackermann steering are available, apparently there are no contributions related to the effect of Ackermann steering on vehicle performance. This work focuses on the effect of Ackermann steering and parallel steering on the performance of a racing car, after a discussion on the different definitions of Ackermann steering ratio available in the literature. Three scenarios are considered: steady turning, slalom and a circuit lap. Nonlinear optimal control techniques are employed to assess the maximum performance. A Formula SAE car model is used and validated against experimental data in acceleration, steady turning and slalom. Then the same model is employed to investigate the effect of different steering layouts. [ABSTRACT FROM AUTHOR]

The methodology used for the reconstruction of a high-profile Sprint Car accident that was captured by at least three different video recording devices is presented in two parts. Part I discusses a classical method of an accident reconstruction, and Part II discusses matchmoving technique to accurately analyze the video footage of the accident. Accidents captured on video are unlike most simple car collision evaluations and require expert knowledge from experienced professionals. Understanding the race car vehicle dynamics as it relates to recorded video footage allows a proper methodology to be followed in order to gather and process the evidence needed to provide meaningful data to the trier of fact. This paper discusses the classical process to reconstruct the accident as well as the currently acceptable scientific methodologies that were used to collect and interpolate the available scientific evidence. A visualization of the vehicles involved, Sprint Car #13 (SC#13) and Sprint Car #14 (SC#14), is shown in Figure 1. [ABSTRACT FROM AUTHOR]

Computational model was developed to investigate aerodynamic forces acting on a closed-wheel race car. A particular focus was on the effects of ground clearance and rake angle on aerodynamic drag and lift forces. Computations were performed for a steady viscous fluid flow using the realizable k-ε turbulence model and non-equilibrium wall functions. The computational results indicate a strong influence of ground clearance and rake angle on aerodynamic loading of a race car. The largest drag force coefficient was obtained for the largest ground clearance. The drag force coefficient for the squatting car is larger by 5% compared to the reference case, where the both front and rear ground clearances are 100 mm. For the nose-diving car, the drag force coefficient is equal to the reference case. Increasing the ground clearance caused a negligible increase in the lift force coefficient in comparison with the reference case. A decrease in the ground clearance yielded an increase in the lift force coefficient. The largest positive lift force coefficient was obtained for a squatting car, whereas the largest negative lift force coefficient was observed for a nose-diving car. While the favorable aerodynamic downforce acting on front wheels is larger for a nose-diving car, for rear wheels it is larger for a squatting car.

The search for high aerodynamic performance of a race car is one of the main aspects of the design process. The flow around the basic body shape is complicated by the presence of the rotating wheels. This is especially true in race cars on which the wheels are not shrouded, where the effects on the flow field are considerable. Despite this, few works have focused on the flow around the rotating wheels. In this paper, CFD techniques were used to provide a detailed analysis of the flow structures generated by the interaction between a multielement inverted wing and the wheel of an open-wheel race car. In the first part, the CFD approach was validated for the isolated wheel case by comparing the results with experimental and numerical data from the literature. The wheel was analyzed both in stationary and unsteady flow conditions. Then, the CFD model was adopted to study the interaction of the flow structures between the wheel with the real grooves on the tire and the front wing of a Formula 1 car. Three different configurations were considered in order to differentiate the individual effects. The discussions were supported by the values of the aerodynamic performance coefficients and flow contours.

This paper shows a software stack capable of planning a minimum curvature trajectory for an autonomous race car on the basis of an occupancy grid map and introduces a controller design that allows to follow the trajectory at the handling limits. The minimum curvature path is generated using a quadratic optimisation problem (QP) formulation. The key contributions of this paper are the extension of the QP for an improved accuracy of the curvature approximation, the introduction of curvature constraints and the iterative invocation of the QP to significantly reduce linearisation errors in corners. On the basis of the resulting raceline, a velocity profile is calculated using a forward-backward-solver that considers the velocity dependent longitudinal and lateral acceleration limits of the car. The advantages and disadvantages of the proposed trajectory planning approach are discussed critically with respect to practical experience from various racetracks. The software stack showed to be robust in a real world environment as it ran successfully on the Roborace DevBot during the Berlin Formula E event in May 2018. The lap time achieved was within a tenth of a second of a human driver and the car reached about 150 k m / h and 80% of its acceleration limits. [ABSTRACT FROM AUTHOR]

Computational model was developed to investigate aerodynamic forces acting on a closed-wheel race car. A particular focus was on the effects of ground clearance and rake angle on aerodynamic drag and lift forces. Computations were performed for a steady viscous fluid flow using the realizable k-ε turbulence model and non-equilibrium wall functions. The computational results indicate a strong influence of ground clearance and rake angle on aerodynamic loading of a race car. The largest drag force coefficient was obtained for the largest ground clearance. The drag force coefficient for the squatting car is larger by 5% compared to the reference case, where the both front and rear ground clearances are 100 mm. For the nose-diving car, the drag force coefficient is equal to the reference case. Increasing the ground clearance caused a negligible increase in the lift force coefficient in comparison with the reference case. A decrease in the ground clearance yielded an increase in the lift force coefficient. The largest positive lift force coefficient was obtained for a squatting car, whereas the largest negative lift force coefficient was observed for a nose-diving car. While the favorable aerodynamic downforce acting on front wheels is larger for a nose-diving car, for rear wheels it is larger for a squatting car. [ABSTRACT FROM AUTHOR]

The steady Reynolds-Averaged Navier-Stokes (RANS) method with the Realizable k   turbulence model was used to analyze the flow field around a race car (generic Formula One). This study was conducted using the ANSYS software package. The numerical simulations were conducted at a Reynolds number based on the race car model (14.9×106). The time-averaged velocity field, flow topology, velocity magnitude, static pressure magnitude and vortex regions of the flow fields are presented in this paper. The measurements were performed on the vertical and cross-sectional planes. The results are presented graphically, showing the main characteristics of the flow field around the whole race car, whereas most previous studies only mention the flow field around individual components of race cars. The Realizable k  turbulence model results showed consistency with the valuable validation data, which helps to elucidate the flow field around a model generic Formula one race car.

The dynamics of race cars is an extremely broad issue, as there are many factors which have an impact on a race car's behaviour on the road. This study examines the relationship between lap time of a race car and different adjustments of front and rear wheel tracks. The analysis is performed using VI-CarRealTime simulation tool provided by VI-grade, a global leader in racing simulation tools. To explain the difference between the front/rear wheel track ratios, the values of side slip angle in corners are used. The best adjustment is determined.

This paper presents a braking strategy analysis for a Formula SAE electric race car. The proposed braking strategy aims to increase the recovery energy by a relevant distribution of the braking forces between the rear and front wheels. A mathematical model of the car is presented, and a simulation is performed in Matlab-Simulink. The model is organized using the energetic macroscopic representation graphical formalism. A real racetrack driving cycle is considered. Three braking strategies are compared considering the energy recovery and the vehicle stability. The simulation results show that the proposed strategy enables higher energy recovery while avoiding locking on both rear and front wheels. As in such a race the driving range is fixed, the reduction in energy consumption can be used to reduce the battery size. The battery weight can thus be decreased to improve the vehicle performance during competition.

Currently, the autonomous driving technique is attracting increasing research focus from all over the world. Generally, the control systems of an autonomous vehicle include environment perception, path planning and path tracking control systems. In this paper, the path tracking control issue of the autonomous vehicle will be focused on. Few of the previous proposed path tracking controllers consider the vehicle driving and handling limit, which degenerates the potential of the autonomous vehicle to finish the desired path as quick as possible. To this end, this paper proposes a path tracking controller for autonomous vehicle, which aims at pushing it to the driving and handling limit. The limit dynamic performance of the autonomous vehicle is represented by the G-G diagram, which indicates the acceleration capability of the autonomous vehicle. The G-G diagram is obtained by phase portrait method and it is validated by a modified FSAE racing car. Finally, a path tracking controller based on the G-G diagram is proposed. The simulation validation results demonstrate the effectiveness of the proposed controller. [ABSTRACT FROM AUTHOR]

In this paper, we investigate an optimal control problem in which the objective is to decelerate a simplified vehicle model, subject to input constraints, from a given initial velocity down to zero by minimizing a quadratic cost functional. The problem is of interest because, although it involves apparently simple drift-less dynamics, a minimizing trajectory does not exist over the admissible input trajectories. This problem is motivated by a minimum-time problem for a fairly complex car vehicle model on a race track. Numerical computations run on the car trajectory optimization problem provide evidence of convergence issues and of an apparently unmotivated ripple in the steer angle. Characterizing this ripple behavior is important to fully understand and exploit minimizing vehicle trajectories. We are able to isolate the key features of this chattering behavior in a very simple dynamics/objective setting. We show that the cost functional has an infimum, but an admissible minimizing input trajectory does not exist. We also show that the infimum can be arbitrarily approximated by bang-bang inputs with a sufficiently large number of switches. We reproduce this phenomenon in numerical computations and characterize it by means of non-existence of admissible minimizing trajectories. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The steady Reynolds-Averaged Navier-Stokes (RANS) method with the Realizable k - ε turbulence model was used to analyze the flow field around a race car (generic Formula One). This study was conducted using the ANSYS software package. The numerical simulations were conducted at a Reynolds number based on the race car model (14.9×106). The time-averaged velocity field, flow topology, velocity magnitude, static pressure magnitude and vortex regions of the flow fields are presented in this paper. The measurements were performed on the vertical and cross-sectional planes. The results are presented graphically, showing the main characteristics of the flow field around the whole race car, whereas most previous studies only mention the flow field around individual components of race cars. The Realizable k - ε turbulence model results showed consistency with the valuable validation data, which helps to elucidate the flow field around a model generic Formula one race car. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel approach to compute minimum-time trajectories for a two-track car model, including tires and (quasi-static) longitudinal and lateral load transfer. Given the car model and a planar track, including lane boundaries, our goal is to find a trajectory of the car minimizing the traveling time subject to steering and tire limits. Moreover, we enforce normal force constraints to avoid wheel liftoff. Based on a projection operator nonlinear optimal control technique, we propose a minimum-time trajectory generation strategy to compute the fastest car trajectory. Numerical computations are presented on two testing scenarios, a 90° turn and a real testing track. The computations allow us to both demonstrate the efficiency and accuracy of the proposed approach and highlight important features of the minimum-time trajectories. Finally, we integrate our strategy into a commercial vehicle dynamics software, thus computing minimum-time trajectories for a complex multibody vehicle model. The matching between the predicted trajectory and the one of the commercial toolbox further highlights the effectiveness of the proposed methodology. [ABSTRACT FROM PUBLISHER]