Physics MCP Server

Uses numerical integration (RK4) to solve motion equations with: - Quadratic drag force: F_drag = 0.5 * ρ * v² * Cd * A - Magnus force (spin effects): F_magnus = 0.5 * ρ * Cl * A * ω * r * v - Wind effects (constant wind vector) - Variable air density (altitude and temperature effects) This provides REALISTIC trajectories for sports balls, projectiles, and other objects moving through air or water. Compare with calculate_projectile_motion (no drag) to see dramatic differences! Common drag coefficients (Cd): - Sphere: 0.47 (default) - Baseball: 0.4 - Golf ball: 0.25 (dimples reduce drag) - Football (American): 0.05-0.15 (orientation-dependent) - Basketball: 0.55 - Soccer ball: 0.25 - Skydiver (belly-down): 1.0-1.3 - Streamlined car: 0.25-0.35 Args: initial_velocity: Launch velocity in m/s angle_degrees: Launch angle in degrees (0-90) mass: Object mass in kg cross_sectional_area: Cross-section perpendicular to motion in m² initial_height: Launch height in meters (default 0) drag_coefficient: Drag coefficient Cd (default 0.47 for sphere) fluid_density: Fluid density in kg/m³ (air=1.225, water=1000) gravity: Gravitational acceleration m/s² (default 9.81) time_step: Integration time step in seconds (default 0.01) max_time: Maximum simulation time in seconds (default 30) spin_rate: Spin rate in rad/s for Magnus force (default 0, no spin) spin_axis: Spin axis unit vector [x, y, z] (default [0, 0, 1] = vertical) wind_velocity: Wind velocity [vx, vy] in m/s (default [0, 0], no wind) altitude: Altitude above sea level in meters (default 0, affects air density) temperature: Air temperature in Celsius (default 15, affects air density) Returns: Dict containing: - max_height: Maximum altitude reached (m) - range: Horizontal distance traveled (m) - time_of_flight: Total flight time (s) - impact_velocity: Speed at landing (m/s) - impact_angle: Angle at landing (degrees below horizontal) - trajectory_points: [[x, y], ...] for plotting - energy_lost_to_drag: Energy dissipated by drag (J) - initial_kinetic_energy: Initial KE (J) - final_kinetic_energy: Final KE (J) - lateral_deflection: Lateral deflection from spin/wind (m) - magnus_force_max: Maximum Magnus force magnitude (N) - wind_drift: Total wind drift (m) - effective_air_density: Effective air density used (kg/m³) Example - Baseball curveball (2500 rpm backspin): result = await calculate_projectile_with_drag( initial_velocity=40.23, # 90 mph angle_degrees=10, mass=0.145, cross_sectional_area=0.0043, drag_coefficient=0.4, spin_rate=261.8, # 2500 rpm = 261.8 rad/s spin_axis=[0, 0, 1] # Backspin (vertical axis) ) # Backspin increases range and height! Example - Golf ball at altitude (Denver, 1600m): result = await calculate_projectile_with_drag( initial_velocity=70, angle_degrees=12, mass=0.0459, cross_sectional_area=0.00143, drag_coefficient=0.25, altitude=1600, # Denver elevation temperature=20 # Summer day ) # Less air resistance = longer drive! Example - Soccer free kick with wind: result = await calculate_projectile_with_drag( initial_velocity=25, angle_degrees=15, mass=0.43, cross_sectional_area=0.0388, drag_coefficient=0.25, wind_velocity=[5, 0], # 5 m/s tailwind spin_rate=50, # Sidespin for curve spin_axis=[0, 1, 0] # Horizontal axis ) # Wind drift + Magnus curve!