Add project files.

Car simulation.slnx

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+<Solution>
+  <Project Path="Car simulation/Car simulation.csproj" />
+</Solution>

Car simulation/Car simulation.csproj

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+<Project Sdk="Microsoft.NET.Sdk">
+
+  <PropertyGroup>
+    <OutputType>Exe</OutputType>
+    <TargetFramework>net10.0</TargetFramework>
+    <RootNamespace>Car_simulation</RootNamespace>
+    <ImplicitUsings>enable</ImplicitUsings>
+    <Nullable>enable</Nullable>
+  </PropertyGroup>
+
+  <ItemGroup>
+    <PackageReference Include="SFML.Net" Version="2.6.1" />
+  </ItemGroup>
+
+</Project>

Car simulation/Car.cs

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+using static SFML.Window.Mouse;
+
+namespace Car_simulation
+{
+    public class Car
+    {
+        public Vector2 Position = new Vector2(0, 0);
+        public Vector2 Velocity = new Vector2(0, 0);
+        public float Speed => Velocity.Length;
+
+        public float Mass = 1500f; // kg
+        public int WheelCount = 4;
+        public int DrivenWheels = 2;
+
+        public float ThrottleInput = 0f;
+        public float BrakeInput = 0f;
+        public float ClutchInput = 1f; // 0 = engaged, 1 = disengaged
+        public bool ForceClutch = false;
+        public float SteeringInput = 0f;
+
+        // Aerodynamics
+        private const float AirDensity = 1.225f;
+        public float DragCoefficient = 0.1f;
+        public float FrontalArea = 2.2f; // m²
+        public float RollingResistanceCoefficient = 0.015f;
+
+        // Components
+        public Engine Engine;
+        public Drivetrain Drivetrain;
+        public WheelSystem WheelSystem;
+
+        private EngineSound _engineSound;
+        private bool _audioEnabled = true;
+
+        public Car()
+        {
+            Engine = new Engine();
+            WheelSystem = new WheelSystem();
+            Drivetrain = new Drivetrain(Engine, WheelSystem);
+
+            // Initial setup
+            WheelSystem.WheelCount = WheelCount;
+            WheelSystem.DrivenWheels = DrivenWheels;
+
+            InitializeAudio();
+        }
+
+        private void InitializeAudio()
+        {
+            try
+            {
+                _engineSound = new EngineSound();
+                _engineSound.SetEngineState(Engine.IdleRPM, 0f);
+                _engineSound.StartSound();
+
+            }
+            catch (Exception ex)
+            {
+                Console.WriteLine($"Audio initialization failed: {ex.Message}");
+                _audioEnabled = false;
+            }
+        }
+
+        public void Update(float deltaTime)
+        {
+            Engine.Throttle = ThrottleInput;
+            Drivetrain.ClutchEngagement = 1f - ClutchInput; // Convert: 0 input = 1 engagement
+
+            if (ForceClutch)
+                Drivetrain.ClutchEngagement = 0f;
+
+            float resistanceTorque = CalculateResistanceTorque();
+            WheelSystem.ResistanceTorque = resistanceTorque;
+
+            Drivetrain.Update(deltaTime);
+            WheelSystem.ApplyResistance(deltaTime);
+
+            float engineLoad = Drivetrain.CalculateEngineLoad(deltaTime);
+            Engine.Update(deltaTime, engineLoad);
+
+            UpdateVehicleMotion(deltaTime);
+            ApplyBraking(deltaTime);
+
+            if (_audioEnabled)
+            {
+                UpdateAudio();
+            }
+        }
+
+        private void UpdateAudio()
+        {
+            try
+            {
+                float throttle = Engine.GetActualThrottle();
+                _engineSound.SetEngineState(Engine.RPM, throttle);
+            }
+            catch (Exception ex)
+            {
+                Console.WriteLine($"Audio update error: {ex.Message}");
+            }
+        }
+
+        private void UpdateVehicleMotion(float deltaTime)
+        {
+            // Calculate net force
+            float tractiveForce = CalculateTractiveForce();
+            float resistanceForce = CalculateTotalResistanceForce();
+            float netForce = tractiveForce - resistanceForce;
+
+            // Calculate acceleration: a = F / m
+            float acceleration = netForce / Mass;
+
+            // Update velocity: v = v₀ + a·Δt
+            if (Velocity.Length > 0)
+            {
+                Vector2 direction = Velocity.Normalized();
+                float newSpeed = Velocity.Length + acceleration * deltaTime;
+                newSpeed = Math.Max(newSpeed, 0); // Don't go backwards without reverse gear
+                Velocity = direction * newSpeed;
+            }
+            else
+            {
+                // Starting from standstill
+                Velocity = new Vector2(acceleration * deltaTime, 0);
+            }
+
+            Position += Velocity * deltaTime;
+
+            // Sync wheel speed with actual vehicle speed (with slip allowance)
+            float currentWheelSpeed = Velocity.Length;
+            WheelSystem.SetSpeed(currentWheelSpeed);
+        }
+
+        private float CalculateTractiveForce()
+        {
+            // 1. Get the torque available at the wheels
+            float wheelTorque = Drivetrain.ClutchTorque * Drivetrain.Efficiency;
+
+            // 2. Convert torque to theoretical force: F = τ / r
+            float theoreticalForce = wheelTorque / WheelSystem.Radius;
+
+            // 3. Account for weight distribution and driven wheels
+            // Normal load on driven wheels = (DrivenWheels / WheelCount) * Weight
+            float drivenWheelNormalLoad = (DrivenWheels / (float)WheelCount) * Mass * 9.81f;
+
+            // 4. Calculate maximum tractive force based on friction (tire grip)
+            float frictionCoefficient = 1.2f; // Typical tire on dry asphalt
+            float maxTractiveForce = drivenWheelNormalLoad * frictionCoefficient;
+
+            // 5. Limit the force by what the tires can actually grip
+            // Also handle direction (forward/reverse)
+            if (theoreticalForce > 0)
+            {
+                return Math.Min(theoreticalForce, maxTractiveForce);
+            }
+            else
+            {
+                // For reverse or engine braking
+                return Math.Max(theoreticalForce, -maxTractiveForce);
+            }
+        }
+
+        private void ApplyBraking(float deltaTime)
+        {
+            if (BrakeInput <= 0) return;
+
+            float brakeTorque = BrakeInput * 500f; // 500 Nm max brake torque
+
+            WheelSystem.ApplyTorque(-brakeTorque, deltaTime);
+        }
+
+        public float CalculateTotalResistanceForce()
+        {
+            float dragForce = CalculateDragForce();
+            float rollingForce = CalculateRollingResistanceForce();
+            return dragForce + rollingForce;
+        }
+
+        private float CalculateDragForce()
+        {
+            // F_drag = 0.5 * ρ * Cd * A * v²
+            float speed = Speed;
+            return 0.5f * AirDensity * DragCoefficient * FrontalArea * speed * speed;
+        }
+
+        private float CalculateRollingResistanceForce()
+        {
+            // F_rolling = C_r * m * g
+            return RollingResistanceCoefficient * Mass * 9.81f;
+        }
+
+        // Convert resistance force to wheel torque
+        public float CalculateResistanceTorque()
+        {
+            float totalForce = CalculateTotalResistanceForce();
+            return totalForce * WheelSystem.Radius;
+        }
+
+        public void DisplayUpdate()
+        {
+            Console.SetCursorPosition(0, 0);
+            Console.WriteLine($"Engine Energy: {Engine.FlywheelEnergy,7:F0} J");
+            Console.WriteLine($"Engine Torque: {Engine.GetTorqueOutput(),7:F0} Nm");
+            Console.WriteLine($"Engine RPM: {Engine.RPM,7:F0}");
+            Console.WriteLine($"Wheel Energy: {WheelSystem.WheelEnergy,7:F0} J");
+            Console.WriteLine($"Wheel RPM: {WheelSystem.RPM,7:F0}");
+            Console.WriteLine($"Vehicle: {Speed * 3.6f,7:F1} km/h");
+            Console.WriteLine($"Throttle: {Engine.GetActualThrottle() * 100,6:F1}%");
+            Console.WriteLine($"Power: {Engine.CurrentPower / 1000,6:F1} kW");
+            Console.WriteLine($"Transmitted: {Drivetrain.TransmittedPower / 1000,6:F1} kW");
+            Console.WriteLine($"Brake: {BrakeInput * 100,6:F1}%");
+            Console.WriteLine($"Clutch: {ClutchInput * 100,6:F1}% disengaged");
+            Console.WriteLine($"Speed Diff: {Drivetrain.GetSpeedDifferenceRPM(),6:F0} RPM");
+            Console.WriteLine($"Clutch T: {Drivetrain.ClutchTorque,6:F0} Nm");
+            Console.WriteLine($"Resistance: {CalculateTotalResistanceForce(),6:F1} N");
+            Console.WriteLine($"Drag: {CalculateDragForce(),6:F1} N");
+            Console.WriteLine($"Rolling: {CalculateRollingResistanceForce(),6:F1} N");
+            Console.WriteLine($"Gear: {Drivetrain.GetCurrentGearName(),3} (Ratio: {Drivetrain.GearRatio:F2}:1)");
+        }
+    }
+}

Car simulation/Drivetrain.cs

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+namespace Car_simulation
+{
+    public class Drivetrain
+    {
+        // Connected components
+        public Engine Engine { get; private set; }
+        public WheelSystem WheelSystem { get; private set; }
+
+        private int currentGear = 1;
+        public float[] GearRatios { get; set; } =
+        {
+            3.8f,   // 1st - Lower for better launch
+            2.5f,   // 2nd
+            1.8f,   // 3rd
+            1.3f,   // 4th
+            1.0f,   // 5th - Direct drive
+            0.8f,   // 6th - Overdrive
+            0.65f   // 7th - Double overdrive (optional)
+        };
+        public float FinalDriveRatio { get; set; } = 5.0f;
+        public float Efficiency { get; set; } = 0.95f;
+        public float ClutchEngagement { get; set; } = 0f; // 0 = disengaged, 1 = fully engaged
+
+        // Calculated
+        public float GearRatio => GetCurrentGearRatio();
+        public float TotalRatio => GearRatio * FinalDriveRatio;
+
+        // Clutch properties
+        public float ClutchStiffness { get; set; } = 500f; // Nm/(rad/s) - how strongly clutch pulls speeds together
+        public float MaxClutchTorque { get; set; } = 4500f; // Maximum torque clutch can transmit
+
+        // State
+        public float SpeedDifference { get; private set; } // rad/s
+        public float ClutchTorque { get; private set; }
+        public float TransmittedPower { get; private set; }
+
+        private float previousWheelOmega = 0f;
+
+        public Drivetrain(Engine engine, WheelSystem wheelSystem)
+        {
+            Engine = engine;
+            WheelSystem = wheelSystem;
+            previousWheelOmega = wheelSystem.AngularVelocity;
+        }
+
+        public void GearUp()
+        {
+            if (currentGear < GearRatios.Length)
+            currentGear++;
+        }
+
+        public void GearDown()
+        {
+            if (currentGear > 1)
+            currentGear--;
+        }
+
+        private float GetCurrentGearRatio()
+        {
+            if (currentGear == 0) return 0f; // Neutral
+            if (currentGear == -1) return -3.5f; // Reverse (example ratio)
+            if (currentGear > 0 && currentGear <= GearRatios.Length)
+                return GearRatios[currentGear - 1];
+            return 0f; // Invalid gear
+        }
+
+        public float CalculateSpeedDifference()
+        {
+            if (TotalRatio == 0) return 0f;
+
+            float engineOmega = Engine.AngularVelocity;
+            float wheelOmega = WheelSystem.AngularVelocity;
+            float expectedWheelOmega = engineOmega / TotalRatio;
+
+            SpeedDifference = wheelOmega - expectedWheelOmega;
+            return SpeedDifference;
+        }
+
+        public float CalculateClutchTorque()
+        {
+            if (ClutchEngagement <= 0.01f)
+            {
+                ClutchTorque = 0;
+                return 0f;
+            }
+
+            CalculateSpeedDifference();
+
+            float torque = -SpeedDifference * ClutchStiffness * ClutchEngagement;
+            torque = Math.Clamp(torque, -MaxClutchTorque, MaxClutchTorque);
+
+            float actualThrottle = Engine.GetActualThrottle();
+            float availableEngineTorque = Engine.GetTorqueOutput();
+
+            float maxTorqueAtClutch = maxEngineTorque * TotalRatio * Efficiency;
+
+            torque = maxTorqueAtClutch;
+
+
+            ClutchTorque = torque;
+            return torque;
+        }
+
+        public void ApplyDrivetrainWork(float deltaTime)
+        {
+            if (ClutchEngagement <= 0.01f || TotalRatio == 0)
+            {
+                ClutchTorque = 0;
+                TransmittedPower = 0;
+                return;
+            }
+
+            CalculateSpeedDifference();
+            float clutchTorque = CalculateClutchTorque();
+
+            bool engineDrivingWheels = clutchTorque > 0;
+            bool wheelsDrivingEngine = clutchTorque < 0;
+
+            if (engineDrivingWheels)
+            {
+                // Engine -> Wheels (normal driving)
+                ApplyEngineToWheels(clutchTorque, deltaTime);
+            }
+            else if (wheelsDrivingEngine)
+            {
+                // Wheels -> Engine (engine braking)
+                ApplyWheelsToEngine(clutchTorque, deltaTime);
+            }
+
+            TransmittedPower = clutchTorque * SpeedDifference;
+        }
+
+        private void ApplyEngineToWheels(float clutchTorque, float deltaTime)
+        {
+            // Existing logic for engine driving wheels
+            float netWheelTorque = clutchTorque * Efficiency - WheelSystem.ResistanceTorque;
+            float netEngineTorque = -clutchTorque / TotalRatio;
+
+            // Apply to both
+            Engine.ApplyTorque(netEngineTorque, deltaTime);
+            WheelSystem.ApplyTorque(netWheelTorque, deltaTime);
+        }
+
+        private void ApplyWheelsToEngine(float clutchTorque, float deltaTime)
+        {
+            // Wheels driving engine (engine braking)
+            // Negative clutchTorque means wheels are trying to spin engine faster
+
+            float wheelTorque = clutchTorque; // Negative value
+            float engineTorque = -clutchTorque / TotalRatio; // Positive resistance
+
+            // Apply resistance to wheels
+            WheelSystem.ApplyTorque(wheelTorque, deltaTime);
+
+            Engine.ApplyTorque(-engineTorque, deltaTime); // Negative = slowing
+        }
+
+        public float GetEquivalentInertiaAtEngine()
+        {
+            float wheelInertia = WheelSystem.GetTotalInertia();
+            return Engine.MomentOfInertia + (wheelInertia * TotalRatio * TotalRatio);
+        }
+
+        public float CalculateEngineLoad(float deltaTime)
+        {
+            if (ClutchEngagement <= 0.01f) return 0f;
+
+            float wheelResistanceTorque = WheelSystem.ResistanceTorque;
+            float engineLoadTorque = wheelResistanceTorque / (TotalRatio * Efficiency);
+
+            float inertiaLoad = CalculateInertiaLoad(deltaTime);
+
+            return engineLoadTorque + inertiaLoad;
+        }
+
+        private float CalculateInertiaLoad(float deltaTime)
+        {
+            float wheelAlpha = (WheelSystem.AngularVelocity - previousWheelOmega) / deltaTime;
+            previousWheelOmega = WheelSystem.AngularVelocity;
+
+            float inertiaTorque = wheelAlpha * WheelSystem.GetTotalInertia();
+            return inertiaTorque / (TotalRatio * TotalRatio * Efficiency);
+        }
+
+        public void Update(float deltaTime)
+        {
+            ApplyDrivetrainWork(deltaTime);
+        }
+
+        // Helper methods
+        public float GetSpeedDifferenceRPM()
+        {
+            return SpeedDifference * PhysicsUtil.RAD_PER_SEC_TO_RPM;
+        }
+
+        public string GetCurrentGearName()
+        {
+            return currentGear switch
+            {
+                -1 => "R",
+                0 => "N",
+                _ => currentGear.ToString()
+            };
+        }
+    }
+}

Car simulation/Engine.cs

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+namespace Car_simulation
+{
+    public class Engine
+    {
+        // Energy state
+        public float FlywheelEnergy { get; set; } // Joules
+
+        // Values
+        public float RPM => GetRPM();
+        public float AngularVelocity => GetOmega();
+        public float CurrentPower { get; private set; }
+
+        // Physical properties
+        public float MomentOfInertia { get; set; } = 0.25f; // kg·m²
+        public float IdleRPM { get; set; } = 800f;
+        public float StallSpeed { get; set; } = 200f;
+        public float Throttle { get; set; } = 0f;
+        public bool IsRunning => RPM > StallSpeed;
+
+        // Torque characteristics
+        public Dictionary<float, float> TorqueCurve { get; set; } = new()
+        {
+            // RPM - Torque Nm
+            { 0f, 0f },
+            { 800f, 150f },   // Idle
+            { 2000f, 200f },  // Peak torque
+            { 4500f, 250f },
+            { 7200f, 250f },
+            { 9200f, 250f },
+            { 10000f, 200f },
+            { 11000f, 0f }
+        };
+
+        public Engine()
+        {
+            // Start with idle energy
+            FlywheelEnergy = GetEnergyFromRPM(IdleRPM);
+        }
+
+        // Calculations
+
+        public float CalculateFrictionEnergy(float deltaTime)
+        {
+            // Real friction torque data for 2.0L engine (Nm)
+            float frictionTorque;
+
+            if (RPM < 500) frictionTorque = 15f;  // Static/breakaway
+            else if (RPM < 1000) frictionTorque = 14f;
+            else if (RPM < 2000) frictionTorque = 16f;
+            else if (RPM < 3000) frictionTorque = 18f;
+            else if (RPM < 4000) frictionTorque = 21f;
+            else if (RPM < 5000) frictionTorque = 25f;
+            else if (RPM < 6000) frictionTorque = 30f;
+            else if (RPM < 7000) frictionTorque = 36f;
+            else frictionTorque = 44f;
+
+            float frictionPower = frictionTorque * AngularVelocity;
+            return frictionPower * deltaTime;
+        }
+
+        private float CalculateCombustionEnergy(float deltaTime)
+        {
+            float torque = GetTorqueOutput() * GetActualThrottle();
+            return torque * AngularVelocity * deltaTime;
+        }
+
+        private float CalculateLoadEnergy(float deltaTime, float loadTorque)
+        {
+            return loadTorque * AngularVelocity * deltaTime;
+        }
+
+        // Get
+
+        public float GetActualThrottle()
+        {
+            float idleThrottle = Math.Max((IdleRPM - RPM) / 10, 0);
+            return Math.Clamp(Throttle + idleThrottle, 0, 1);
+        }
+
+        public float GetOmega()
+        {
+            if (FlywheelEnergy <= 0) return 0;
+                return MathF.Sqrt(2f * FlywheelEnergy / MomentOfInertia);
+        }
+
+        public float GetRPM()
+        {
+            return GetOmega() * PhysicsUtil.RAD_PER_SEC_TO_RPM;
+        }
+
+        // Set
+
+        public float GetEnergyFromRPM(float rpm)
+        {
+            float omega = rpm * PhysicsUtil.RPM_TO_RAD_PER_SEC;
+            return 0.5f * MomentOfInertia * omega * omega;
+        }
+
+        // torque curve
+        public float GetTorqueOutput()
+        {
+            if (RPM <= 0) return 0;
+
+            var points = TorqueCurve.OrderBy(p => p.Key).ToList();
+
+            if (RPM <= points.First().Key) return points.First().Value;
+            if (RPM >= points.Last().Key) return points.Last().Value;
+
+            for (int i = 0; i < points.Count - 1; i++)
+            {
+                if (RPM >= points[i].Key && RPM <= points[i + 1].Key)
+                {
+                    float t = (RPM - points[i].Key) / (points[i + 1].Key - points[i].Key);
+                    return PhysicsUtil.Lerp(points[i].Value, points[i + 1].Value, t);
+                }
+            }
+
+            return 0f;
+        }
+
+        public void ApplyTorque(float torque, float deltaTime)
+        {
+            if (torque == 0) return;
+
+            float work = torque * AngularVelocity * deltaTime;
+
+            FlywheelEnergy += work;
+            FlywheelEnergy = Math.Max(FlywheelEnergy, 0);
+        }
+
+        public void Update(float deltaTime, float loadTorque)
+        {
+            float combustionEnergy = CalculateCombustionEnergy(deltaTime);
+            float frictionEnergy = CalculateFrictionEnergy(deltaTime);
+            float loadEnergy = CalculateLoadEnergy(deltaTime, loadTorque);
+
+            float netEnergy = combustionEnergy - frictionEnergy - loadEnergy;
+            CurrentPower = netEnergy / deltaTime;
+            FlywheelEnergy += netEnergy;
+            FlywheelEnergy = Math.Max(FlywheelEnergy, 0);
+        }
+    }
+}

Car simulation/EngineSound.cs

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+using SFML.Audio;
+using SFML.System;
+using System;
+
+namespace Car_simulation
+{
+    public class EngineSound : SoundStream
+    {
+        // Audio properties - smaller buffer for less latency
+        private const uint SAMPLE_RATE = 44100;
+        private const ushort CHANNEL_COUNT = 2; // Stereo
+        private const float BUFFER_DURATION = 0.01f; // 10ms instead of 50ms!
+
+        // Engine sound properties - NO SMOOTHING for instant response
+        private volatile float _currentRPM = 800f; // volatile for thread safety
+        private volatile float _currentThrottle = 0f;
+        private float _volume = 0.3f;
+        private bool _isPlaying = false;
+
+        // Harmonic series - DIRECT RPM TO FREQUENCY
+        private float[] _harmonicRatios = { 1f, 2f, 4f, 6f };
+        private float[] _harmonicAmplitudes = { 1f, 0.3f, 0.1f, 0.05f };
+        private float[] _harmonicPhases = new float[4];
+
+        // Engine configuration - for direct RPM calculation
+        public int CylinderCount { get; set; } = 4;
+        public float FiringFrequencyMultiplier => CylinderCount / 2f; // 4-stroke engines
+
+        // For RPM to frequency mapping
+        private float _rpmToHzFactor;
+
+        private Random _random = new Random();
+
+        public EngineSound()
+        {
+            Initialize(CHANNEL_COUNT, SAMPLE_RATE);
+
+            // Calculate direct conversion factor
+            // RPM to Hz: (RPM / 60) × (Cylinders / 2) for 4-stroke
+            _rpmToHzFactor = (1f / 60f) * (CylinderCount / 2f);
+
+            // Initialize phases
+            for (int i = 0; i < _harmonicPhases.Length; i++)
+            {
+                _harmonicPhases[i] = (float)(_random.NextDouble() * 2 * Math.PI);
+            }
+
+            Console.WriteLine($"EngineSound initialized: {BUFFER_DURATION * 1000:F0}ms buffer, {CylinderCount} cylinders");
+        }
+
+        // CALL THIS FROM YOUR PHYSICS THREAD - INSTANT UPDATE
+        public void SetEngineState(float rpm, float throttle)
+        {
+            // NO LOCK, NO SMOOTHING - DIRECT ASSIGNMENT
+            _currentRPM = rpm;
+            _currentThrottle = throttle;
+
+            // Volume based on throttle (instant)
+            _volume = 0.1f + 0.4f * throttle;
+        }
+
+        public void StartSound()
+        {
+            if (!_isPlaying)
+            {
+                Play();
+                _isPlaying = true;
+            }
+        }
+
+        public void StopSound()
+        {
+            if (_isPlaying)
+            {
+                Stop();
+                _isPlaying = false;
+            }
+        }
+
+        protected override bool OnGetData(out short[] samples)
+        {
+            // SMALLER BUFFER: 10ms instead of 50ms
+            int sampleCount = (int)(SAMPLE_RATE * BUFFER_DURATION) * 2; // *2 for stereo
+            samples = new short[sampleCount];
+
+            // Get current values ONCE per buffer (not per sample)
+            float rpm = _currentRPM;
+            float throttle = _currentThrottle;
+            float volume = _volume;
+
+            // DIRECT RPM TO FREQUENCY - NO SMOOTHING
+            float baseFrequency = rpm * _rpmToHzFactor; // (RPM/60) × (cylinders/2)
+
+            // Pre-calculate harmonic frequencies
+            float[] harmonicFrequencies = new float[_harmonicRatios.Length];
+            float[] phaseIncrements = new float[_harmonicRatios.Length];
+
+            for (int h = 0; h < _harmonicRatios.Length; h++)
+            {
+                harmonicFrequencies[h] = baseFrequency * _harmonicRatios[h];
+                phaseIncrements[h] = harmonicFrequencies[h] * 2f * MathF.PI / SAMPLE_RATE;
+            }
+
+            // Calculate roughness factor
+            float roughness = 0.02f * throttle;
+
+            // Generate sound
+            for (int i = 0; i < sampleCount; i += 2)
+            {
+                float sampleValue = 0f;
+
+                // Sum all harmonics
+                for (int h = 0; h < _harmonicRatios.Length; h++)
+                {
+                    sampleValue += MathF.Sin(_harmonicPhases[h]) * _harmonicAmplitudes[h];
+                    _harmonicPhases[h] += phaseIncrements[h];
+
+                    if (_harmonicPhases[h] > 2f * MathF.PI)
+                        _harmonicPhases[h] -= 2f * MathF.PI;
+                }
+
+                // Add roughness
+                sampleValue += (float)(_random.NextDouble() * 2 - 1) * roughness;
+
+                // Apply volume
+                sampleValue *= volume;
+
+                // Clamp and convert
+                sampleValue = Math.Clamp(sampleValue, -1f, 1f);
+                short sample = (short)(sampleValue * 32767);
+
+                // Stereo
+                samples[i] = sample;
+                samples[i + 1] = sample;
+            }
+
+            return true;
+        }
+
+        protected override void OnSeek(Time timeOffset)
+        {
+            // Reset phases
+            for (int i = 0; i < _harmonicPhases.Length; i++)
+            {
+                _harmonicPhases[i] = (float)(_random.NextDouble() * 2 * Math.PI);
+            }
+        }
+    }
+}

Car simulation/IPhysicsObject.cs

@@ -0,0 +1,14 @@
+using System;
+using System.Collections.Generic;
+using System.Numerics;
+using System.Text;
+
+namespace Car_simulation
+{
+    public interface IPhysicsObject
+    {
+        Vector2 Position { get; }
+        float GetResistanceForce(Vector2 carPosition, float carSpeed);
+        float GetTractionCoefficient(Vector2 carPosition);
+    }
+}

Car simulation/Program.cs

@@ -0,0 +1,211 @@
+using Car_simulation;
+using SFML.Window;
+using SFML.Graphics;
+using SFML.System;
+using System.Diagnostics;
+
+internal class Program
+{
+    Car car = new Car();
+    private bool _isRunning = true;
+
+    private RenderWindow _window;
+
+    // Timing for physics
+    private Clock _clock = new Clock();
+    private Time _timePerUpdate = Time.FromSeconds(1.0f / 60.0f); // 60 FPS physics
+    private Time _accumulatedTime = Time.Zero;
+    private long _updateCount = 0;
+
+    private Dictionary<Keyboard.Key, bool> _previousKeyStates = new Dictionary<Keyboard.Key, bool>();
+    private Dictionary<Keyboard.Key, bool> _currentKeyStates = new Dictionary<Keyboard.Key, bool>();
+
+    private static void Main(string[] args)
+    {
+        Program program = new Program();
+        program.Run();
+    }
+
+    private void Run()
+    {
+        _window = new RenderWindow(new VideoMode(800, 600), "Car Simulation", Styles.Default);
+        _window.SetVisible(true);
+        _window.SetFramerateLimit(60);
+        _window.SetKeyRepeatEnabled(false);
+
+        _window.Closed += (sender, e) => _isRunning = false;
+        _window.KeyPressed += OnKeyPressed;
+        _window.KeyReleased += OnKeyReleased;
+
+        InitializeTrackedKeys();
+
+        _clock.Restart();
+
+        while (_isRunning && _window.IsOpen)
+        {
+            _window.DispatchEvents();
+
+            Time elapsed = _clock.Restart();
+            _accumulatedTime += elapsed;
+
+            while (_accumulatedTime >= _timePerUpdate)
+            {
+                ProcessInput(_timePerUpdate.AsSeconds());
+                car.Update(_timePerUpdate.AsSeconds());
+                _accumulatedTime -= _timePerUpdate;
+                _updateCount++;
+
+                if (_accumulatedTime >= Time.FromSeconds(0.2f))
+                {
+                    _accumulatedTime = _timePerUpdate;
+                }
+            }
+
+            UpdateDisplay();
+            UpdatePreviousKeyStates();
+        }
+
+        _window.Close();
+        Console.WriteLine($"\nSimulation stopped after {_updateCount} updates");
+    }
+
+    private void InitializeTrackedKeys()
+    {
+        // Initialize all keys we care about
+        var keysToTrack = new Keyboard.Key[]
+        {
+            Keyboard.Key.W,
+            Keyboard.Key.Up,
+            Keyboard.Key.Down,
+            Keyboard.Key.B,
+            Keyboard.Key.Space,
+            Keyboard.Key.Left,
+            Keyboard.Key.Right,
+            Keyboard.Key.Escape
+        };
+
+        foreach (var key in keysToTrack)
+        {
+            _currentKeyStates[key] = false;
+            _previousKeyStates[key] = false;
+        }
+    }
+
+    private void OnKeyPressed(object sender, KeyEventArgs e)
+    {
+        var key = e.Code;
+
+        // Update current state
+        if (_currentKeyStates.ContainsKey(key))
+        {
+            _currentKeyStates[key] = true;
+        }
+    }
+
+    private void OnKeyReleased(object sender, KeyEventArgs e)
+    {
+        var key = e.Code;
+
+        // Update current state
+        if (_currentKeyStates.ContainsKey(key))
+        {
+            _currentKeyStates[key] = false;
+        }
+    }
+
+    private void ProcessInput(float deltaTime)
+    {
+        // quit
+        if (IsKeyDown(Keyboard.Key.Escape))
+        {
+            _isRunning = false;
+            return;
+        }
+
+        // force clutch
+        car.ForceClutch = (IsKeyDown(Keyboard.Key.Space));
+
+        // throttle
+        if (IsKeyDown(Keyboard.Key.W))
+        {
+            car.ThrottleInput = Math.Min(car.ThrottleInput + 2f * deltaTime, 1.0f);
+        }
+        else
+        {
+            car.ThrottleInput = Math.Max(car.ThrottleInput - 10f * deltaTime, 0f);
+        }
+
+        // brake
+        if (IsKeyDown(Keyboard.Key.B))
+        {
+            car.BrakeInput = Math.Min(car.BrakeInput + 0.5f * deltaTime, 1.0f);
+        }
+        else
+        {
+            car.BrakeInput = Math.Max(car.BrakeInput - 1f * deltaTime, 0f);
+        }
+
+        // clutch
+        if (IsKeyDown(Keyboard.Key.Up))
+        {
+            car.ClutchInput = Math.Min(car.ClutchInput + 1f * deltaTime, 1.0f);
+        }
+        else if (IsKeyDown(Keyboard.Key.Down))
+        {
+            car.ClutchInput = Math.Max(car.ClutchInput - 1f * deltaTime, 0f);
+        }
+
+        // clutch
+        if (IsKeyDown(Keyboard.Key.Up))
+        {
+            car.ClutchInput = Math.Min(car.ClutchInput + 1f * deltaTime, 1.0f);
+        }
+        else if (IsKeyDown(Keyboard.Key.Down))
+        {
+            car.ClutchInput = Math.Max(car.ClutchInput - 1f * deltaTime, 0f);
+        }
+
+        // gear
+        if (WasKeyPressed(Keyboard.Key.Left))
+        {
+            car.Drivetrain.GearDown();
+        }
+        else if (WasKeyPressed(Keyboard.Key.Right))
+        {
+            car.Drivetrain.GearUp();
+        }
+    }
+
+    private void UpdatePreviousKeyStates()
+    {
+        var keys = new List<Keyboard.Key>(_currentKeyStates.Keys);
+        foreach (var key in keys)
+        {
+            _previousKeyStates[key] = _currentKeyStates[key];
+        }
+    }
+
+    private bool IsKeyDown(Keyboard.Key key)
+    {
+        return _currentKeyStates.ContainsKey(key) && _currentKeyStates[key];
+    }
+
+    private bool WasKeyPressed(Keyboard.Key key)
+    {
+        return IsKeyDown(key) &&
+               (!_previousKeyStates.ContainsKey(key) || !_previousKeyStates[key]);
+    }
+
+    private void UpdateDisplay()
+    {
+        _window.Clear(Color.Black);
+
+        // Render car or simulation visualization here
+        // For example, if car has Draw() method:
+        // car.Draw(_window);
+
+        car.DisplayUpdate(); // If this updates console display
+
+        _window.Display();
+    }
+}

Car simulation/Util.cs

@@ -0,0 +1,45 @@
+using System;
+using System.Collections.Generic;
+using System.Text;
+
+namespace Car_simulation
+{
+    public class Util
+    {
+        public static float Lerp(float a, float b, float t)
+        {
+            return a + (b - a) * t;
+        }
+    }
+
+    public static class PhysicsUtil
+    {
+        public const float G = 9.81f;
+        public const float AirDensity = 1.225f;
+
+        public static float Lerp(float a, float b, float t)
+        {
+            t = Math.Clamp(t, 0f, 1f);
+            return a + (b - a) * t;
+        }
+
+        public static float RPMToOmega(float rpm) => rpm * MathF.PI * 2f / 60f;
+        public static float OmegaToRPM(float omega) => omega * 60f / (2f * MathF.PI);
+
+        // Calculate kinetic energy: 0.5 * I * ω²
+        public static float CalculateRotationalEnergy(float inertia, float omega)
+        {
+            return 0.5f * inertia * omega * omega;
+        }
+
+        // Calculate omega from energy: ω = sqrt(2E / I)
+        public static float CalculateOmegaFromEnergy(float energy, float inertia)
+        {
+            if (energy <= 0) return 0;
+            return MathF.Sqrt(2f * energy / inertia);
+        }
+
+        public const float RAD_PER_SEC_TO_RPM = 60f / (2f * MathF.PI);  // ≈ 9.549
+        public const float RPM_TO_RAD_PER_SEC = (2f * MathF.PI) / 60f;  // ≈ 0.1047
+    }
+}

Car simulation/Vector2.cs

@@ -0,0 +1,39 @@
+public struct Vector2
+{
+    public float X, Y;
+
+    public Vector2(float x, float y) { X = x; Y = y; }
+
+    public float Length => MathF.Sqrt(X * X + Y * Y);
+    public float LengthSquared => X * X + Y * Y;
+
+    // Returns a normalized copy
+    public Vector2 Normalized()
+    {
+        float length = Length;
+        if (length > 0.0001f)
+            return new Vector2(X / length, Y / length);
+        return new Vector2(0, 0);
+    }
+
+    // Normalizes in place
+    public void Normalize()
+    {
+        float length = Length;
+        if (length > 0.0001f)
+        {
+            X /= length;
+            Y /= length;
+        }
+    }
+
+    // Static normalize
+    public static Vector2 Normalize(Vector2 v) => v.Normalized();
+
+    // Operators
+    public static Vector2 operator *(Vector2 v, float s) => new Vector2(v.X * s, v.Y * s);
+    public static Vector2 operator *(float s, Vector2 v) => new Vector2(v.X * s, v.Y * s);
+    public static Vector2 operator /(Vector2 v, float s) => new Vector2(v.X / s, v.Y / s);
+    public static Vector2 operator +(Vector2 a, Vector2 b) => new Vector2(a.X + b.X, a.Y + b.Y);
+    public static Vector2 operator -(Vector2 a, Vector2 b) => new Vector2(a.X - b.X, a.Y - b.Y);
+}

Car simulation/WheelSystem.cs

@@ -0,0 +1,92 @@
+namespace Car_simulation
+{
+    public class WheelSystem
+    {
+        // Physical properties
+        public float Radius { get; set; } = 0.3f; // meters
+        public float Inertia { get; set; } = 2.0f; // kg·m² per wheel
+        public int WheelCount { get; set; } = 4;
+        public int DrivenWheels { get; set; } = 2; // 2WD
+
+        // State
+        public float WheelEnergy { get; set; } = 0f; // Joules
+        public float AngularVelocity => GetOmega();
+        public float RPM => GetRPM();
+        public float Speed => GetSpeed();
+        public float ResistanceTorque { get; set; } = 0f;
+
+        // Calculations
+        public float GetTotalInertia()
+        {
+            return Inertia * WheelCount;
+        }
+
+        public float GetOmega()
+        {
+            if (WheelEnergy <= 0 || GetTotalInertia() <= 0) return 0f;
+            return MathF.Sqrt(2f * WheelEnergy / GetTotalInertia());
+        }
+
+        public float GetRPM()
+        {
+            return AngularVelocity * PhysicsUtil.RAD_PER_SEC_TO_RPM;
+        }
+
+        public float GetSpeed()
+        {
+            return AngularVelocity * Radius;
+        }
+
+        public float GetEnergyFromSpeed(float speed)
+        {
+            float omega = speed / Radius;
+            return 0.5f * GetTotalInertia() * omega * omega;
+        }
+
+        public void SetSpeed(float speed)
+        {
+            WheelEnergy = GetEnergyFromSpeed(speed);
+        }
+
+        // Apply work to the wheels
+        public void ApplyWork(float work)
+        {
+            WheelEnergy += work;
+            WheelEnergy = Math.Max(WheelEnergy, 0);
+        }
+
+        public void ApplyTorque(float torque, float deltaTime)
+        {
+            if (torque == 0) return;
+            float work = torque * AngularVelocity * deltaTime;
+            ApplyWork(work);
+        }
+
+        public void ApplyResistance(float deltaTime)
+        {
+            if (ResistanceTorque <= 0 || AngularVelocity == 0) return;
+
+            float omega = AngularVelocity;
+
+            if (MathF.Abs(omega) < 0.1f)
+            {
+                // Check if we have enough torque to overcome static friction
+                // For now, just return without applying resistance to allow startup
+                return;
+            }
+
+            float resistanceSign = -MathF.Sign(omega);
+            float alpha = (resistanceSign * ResistanceTorque) / GetTotalInertia();
+
+            float omegaNew = omega + alpha * deltaTime;
+
+            if (MathF.Sign(omegaNew) != MathF.Sign(omega))
+            {
+                omegaNew = 0;
+            }
+
+            float energyNew = 0.5f * GetTotalInertia() * omegaNew * omegaNew;
+            WheelEnergy = Math.Max(energyNew, 0);
+        }
+    }
+}