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"Automobiles, Racing Mathematics."
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Score with race car math
\"Use math to solve problems about various famous races and drivers, all while learning race car facts\"-- Provided by publisher.
Book
Research on aerodynamic characteristics of vehicle platoon under crosswind conditions based on Ahmed body
Purpose
The purpose of this paper is to study the aerodynamic characteristics of Ahmed body in longitudinal and lateral platoons under crosswind by computational fluid dynamics simulation. It helps to improve the aerodynamic characteristics of vehicles by providing theoretical basis and engineering direction for the development and progress of intelligent transportation.
Design/methodology/approach
A two-car platoon model is used to compare with the experiment to prove the accuracy of the simulation method. The simplified Ahmed body model and the Reynolds Averaged N-S equation method are used to study the aerodynamic characteristics of vehicles at different distances under cross-winds.
Findings
When the longitudinal distance x/L = 0.25, the drag coefficients of the middle and trailing cars at β = 30° are improved by about 272% and 160% compared with β = 10°. The side force coefficients of the middle and trailing cars are increased by 50% and 62%. When the lateral distance y/W = 0.25, the side force coefficients of left and middle cars at β = 30° are reduced by 38% and 37.5% compared with β = 10°. However, the side force coefficient of the right car are increased by about 84.3%.
Originality/value
Most of the researches focus on the overtaking process, and there are few researches on the neat lateral platoon. The innovation of this paper is that in addition to studying the aerodynamic characteristics of longitudinal driving, the aerodynamic characteristics of neat lateral driving are also studied, and crosswind conditions are added. The authors hope to contribute to the development of intelligent transportation.
Journal Article
Aerodynamic characteristics of the race car in pitch and roll attitude
Purpose
Aerodynamics plays a crucial role in enhancing the performance of race cars. Due to the low ride height, the aerodynamic components of race cars are affected by ground effects. The changes in pitch and roll attitudes during the car’s movement impact its ride height. This study aims to analyze the aerodynamic characteristics of race cars under specific pitch and roll attitudes to understand the underlying aerodynamic mechanisms. This paper focuses on the aerodynamic characteristics of racing cars under variations in body posture associated with different vehicle ride heights. It examines not only the force and pressure distribution resulting from changes in the overall vehicle posture but also the flow field behavior of both surface flow and off‑body flow. Analyzing individual components reveals the impact of the front wing on the overall aerodynamic performance and aerodynamic balance of the racing car under these posture variations.
Design/methodology/approach
The grid strategy for the computational fluid dynamics (CFD) method was established under baseline conditions and compared with the results from wind tunnel experiments. The CFD approach was further employed to investigate the aerodynamic characteristics of the racing car under varying body postures associated with different vehicle ride heights. Emphasis is placed on the overall aerodynamic performance of the vehicle and the various components’ influence on the changing trends of aerodynamic forces. By considering the surface pressure distribution of the car, the primary reasons behind the changes in aerodynamic forces for each component are investigated. In addition, the surface flow and detached flow (wake and vortex distributions) of the car were observed to gain insights into the overall flow field behavior under different attitudes.
Findings
The findings indicate that both pitch and roll attitudes result in a considerable loss of downforce on the front wing compared with other components, thereby affecting the overall downforce and aerodynamic balance of the vehicle.
Originality/value
This paper focuses on the aerodynamic characteristics of racing cars under variations in body posture associated with different vehicle ride heights. It examines not only the force and pressure distribution resulting from changes in the overall vehicle posture but also the flow field behavior of both surface flow and off-body flow. Analyzing individual components reveals the impact of the front wing on the overall aerodynamic performance and aerodynamic balance of the racing car under these posture variations.
Journal Article
Driving STEM Education via Motorsports a Closer Look at Donk Racing — A Work in Process Paper
This work-in-progress research paper describes a community-based study to better understand the attraction of underrepresented minorities to an unconventional motorsport , Donk racing, as a pathway to STEM discovery. This study detects an unconscious attraction to STEM in African American youth who enjoy motorsports, especially automobile and motorcycle racing. Uncovering the attraction to STEM early in the educational process yields an opportunity to address the missing connections leading to career choices that provide greater social mobility and meet a national need. A research team has been working passionately on a groundbreaking study centered around the intriguing intersection of motorsports and STEM (Science, Technology, Engineering, and Mathematics) education. This mixed-method study seeks to understand the connection between academic preferences and career choices through the lens of motorsports enthusiasts.
Journal Article
Trajectory Tracking Control in Real-Time of Dual-Motor-Driven Driverless Racing Car Based on Optimal Control Theory and Fuzzy Logic Method
To improve the accuracy and timeliness of the trajectory tracking control of the driverless racing car during the race, this paper proposes a track tracking control method that integrates the rear wheel differential drive and the front wheel active steering based on optimal control theory and fuzzy logic method. The model of the lateral track tracking error of the racing car is established. The model is linearized and discretized, and the quadratic optimal steering control problem is constructed. Taking advantage of the differential drive of dual-motor-driven racing car, the dual motors differential drive fuzzy controller is designed and integrated driving with active steering control. Simulation analysis and actual car verification show that this integrated control method can ensure that the car tracks different race tracks well and improve the track tracking control accuracy by nearly 30%.
Journal Article
Energy flow of a 2018 FIA F1 racing car and proposed changes to the powertrain rules
In the last few years, the different teams have dramatically improved the directly injected, electrically assisted turbocharged, internal combustion engine of FIA F1 hybrid electric cars. With limited fuel flow rate, but unlimited boost, the engine is now delivering peak power at fuel conversion efficiencies about 45% running lean stratified with the help of some sort of jet ignition. The paper analyses the energy flow of a FIA F1 hybrid electric car covering one lap of the Monte Carlo race track of length 3.370 km. The amount of energy recovered is minimal, at the most 2 of the 9.77 MJ of braking energy, or 20.6%. The fuel consumption per lap, 1.16 kg of fuel, or 50.34 MJ of fuel energy, needed to deliver the 16.28-18.28 MJ of propulsive energy, at an outstanding average efficiency of 32 to 36%, may still be dramatically reduced. New rules are thus proposed to promote the development of technical features that could be beneficial to passenger car applications, from advanced turbo-compounding, to enhanced thermal and mechanical energy recovery, and better hybridization.
Journal Article
Effects of Seat Belts and Shock Absorbers on the Safety of Racing Car Drivers
This paper aimed to study the behavior of a body (dummy) that was in a race car in the event of a frontal collision with a wall in order to see what loads were acting on the dummy. Based on a complex car model, equipped with two safety system seat belts and a shock absorption system, the behavior of the dummy was obtained following frontal collision of the car–dummy assembly. The accelerations were obtained at different points of the dummy’s body and the force that appeared on the seat belts were determined. The Gibbs–Appell method was used to assess the response of the system based on the equations of motion in a problem involving shocks. This paper demonstrates that the revisited old principle of mechanics can offer an interesting and convenient means to obtain results in a short time. FEM and Altair Hyperworks software II was used to model the system. It can be used to determine whether a seat belt is able to work if it has defects during use, such as scratches, cigarette burns or animal bites.
Journal Article
Corvettes, Curve Fitting, and Calculus
Sometimes the best mathematics problems come from the most unexpected situations. Last summer, a Corvette raced down a local quarter-mile drag strip. The driver, a family member, provided the spectators with time and distance-traveled data from his time slip and asked \"Can you calculate how many seconds it took me to go from 0 to 60 mph?\" Although initially this question seemed like a straightforward one, it was soon clear that depending on the solution strategy and assumptions, different answers were possible. Thus began the ongoing discussions with colleagues--and with high school mathematics teacher friends over pizza and with mechanical engineer family members at holiday dinners--to collectively decide on the \"best\" method. The mathematical discussions that arose on how to best solve the problem prompted two questions: (1) What makes this problem so intriguing? and (2) What would students do? Any interesting mathematical task will likely encourage teachers to wonder what aspects of the task make it special. The authors of this article wanted to know why this problem generated these mathematical conversations and how they could incorporate it into a calculus class. Insights from colleagues and students revealed several qualities of the problem that they believe contribute to its intrigue and worth. What they found illustrates what they consider to be three hallmarks of a good problem: (1) The problem solver must decide what mathematics to introduce; (2) The task users real-life data; and (3) The task requires mathematical modeling. A nonroutine task with three hallmarks of a good problem offers the flexibility to model real-life, messy data.
Journal Article
A Theoretical and Experimental Investigation of the Effects of Inverted Wings Modifications on the Stability and Aerodynamic Performance of a Sedan Car at Cornering
This research examines the impact of cornering on the aerodynamic forces and stability of a Nissan Versa (Almera) passenger sedan car by introducing novel modifications. These modifications included single inverted wings with end plates as a front spoiler, double‐element inverted wings with end plates as a rear spoiler, and incorporating the ground as a diffuser under the car trunk. The goal is to enhance the performance and stability of conventional passenger cars. To ensure the accuracy of the numerical data, the study utilized multiple methodologies to model the turbulence model, ultimately selecting the most suitable option. This involved comparing numerical data with wind tunnel experimental data using force balance and pressure distribution. Once validated, the computational fluid dynamics (CFD) was employed to analyze the vehicle's aerodynamic performance relative to the straight‐line condition under cornering conditions. The car simulation in a cornering condition was conducted at a representative Reynolds number based on the vehicle length of about 1.3 × 107. The study discovered that asymmetry was a recurring theme regarding surface pressure distribution, with greater prominence under cornering conditions. All modified models exhibited a more favorable lift‐to‐drag ratio than the baseline, indicating improved aerodynamic efficiency. The underbody double‐element diffuser proved most effective for enhancing fuel efficiency and stability. Mesh refinement with a polyhedral algorithm consisting of 11.27 million elements and a computational domain with a frontal area of 91.8 m2 and a curved length of 31 m (˜7 times car length) was crucial for achieving accurate and repeatable results. The study employed multiple turbulence models within the CFD framework. The realizable k‐ε model was chosen due to its balance between accuracy and computational cost for all Nissan Versa models. These findings are limited to the selected parameters and wind tunnel conditions, and further investigations might be needed for extreme driving scenarios.
Journal Article
Aerodynamic and Structural Design of a 2022 Formula One Front Wing Assembly
The aerodynamic loads generated in a wing are critical in its structural design. When multi-element wings with wingtip devices are selected, it is essential to identify and to quantify their structural behaviour to avoid undesirable deformations which degrade the aerodynamic performance. This research investigates these questions using numerical methods (Computational Fluid Dynamics and Finite Elements Analysis), employing exhaustive validation methods to ensure the accuracy of the results and to assess their uncertainty. Firstly, a thorough investigation of four baseline configurations is carried out, employing Reynolds Averaged Navier–Stokes equations and the k-ω SST (Shear Stress Transport) turbulence model to analyse and quantify the most important aerodynamic and structural parameters. Several structural configurations are analysed, including different materials (metal alloys and two designed fibre-reinforced composites). A 2022 front wing is designed based on a bidimensional three-element wing adapted to the 2022 FIA Formula One regulations and its structural components are selected based on a sensitivity analysis of the previous results. The outcome is a high-rigidity-weight wing which satisfies the technical regulations and lies under the maximum deformation established before the analysis. Additionally, the superposition principle is proven to be an excellent method to carry out high-performance structural designs.
Journal Article