"""Advanced Projectile Motion Examples: Magnus Force, Wind, and Altitude.
This example demonstrates the enhanced features of calculate_projectile_with_drag:
- Spin effects (Magnus force) for curveballs, slices, hooks
- Wind effects (tailwind, headwind, crosswind)
- Altitude and temperature effects on air density
All calculations include realistic air resistance and show dramatic differences
compared to ideal vacuum conditions.
"""
from chuk_mcp_physics.models import ProjectileWithDragRequest
from chuk_mcp_physics.kinematics import calculate_projectile_with_drag
def baseball_curveball_vs_fastball():
"""Compare baseball curveball (topspin) vs fastball (backspin)."""
print("\n" + "=" * 70)
print("⚾ BASEBALL: Curveball vs Fastball (Spin Effects)")
print("=" * 70)
velocity = 35.0 # m/s (~78 mph curveball)
# Fastball with backspin (Magnus force lifts ball)
fastball = ProjectileWithDragRequest(
initial_velocity=velocity,
angle_degrees=0, # Level pitch
mass=0.145,
drag_coefficient=0.4,
cross_sectional_area=0.0043,
spin_rate=200.0, # rad/s (~1900 rpm backspin)
spin_axis=[0, 0, 1], # Backspin (lifts)
)
# Curveball with topspin (Magnus force drops ball)
curveball = ProjectileWithDragRequest(
initial_velocity=velocity,
angle_degrees=0, # Level pitch
mass=0.145,
drag_coefficient=0.4,
cross_sectional_area=0.0043,
spin_rate=200.0, # rad/s (~1900 rpm topspin)
spin_axis=[0, 0, -1], # Topspin (drops)
)
result_fastball = calculate_projectile_with_drag(fastball)
result_curveball = calculate_projectile_with_drag(curveball)
print("\n📊 Initial Conditions:")
print(f" Velocity: {velocity} m/s (78 mph)")
print(" Angle: 0° (level pitch)")
print(" Spin: 200 rad/s (~1900 rpm)")
print("\n🔝 FASTBALL (Backspin - Magnus lifts):")
print(f" Max height: {result_fastball.max_height:.2f} m")
print(f" Range: {result_fastball.range:.1f} m")
print(f" Magnus force: {result_fastball.magnus_force_max:.2f} N (upward)")
print(f" Flight time: {result_fastball.time_of_flight:.3f} s")
print("\n🔽 CURVEBALL (Topspin - Magnus drops):")
print(f" Max height: {result_curveball.max_height:.2f} m")
print(f" Range: {result_curveball.range:.1f} m")
print(f" Magnus force: {result_curveball.magnus_force_max:.2f} N (downward)")
print(f" Flight time: {result_curveball.time_of_flight:.3f} s")
print("\n💡 SPIN EFFECT:")
height_diff = result_fastball.max_height - result_curveball.max_height
print(f" Height difference: {height_diff:.2f} m ({height_diff * 39.37:.1f} inches)")
print(" Backspin makes fastball 'rise' relative to curveball")
def golf_denver_vs_sea_level():
"""Compare golf drive at Denver (altitude) vs sea level."""
print("\n" + "=" * 70)
print("⛳ GOLF: Denver (1600m altitude) vs Sea Level")
print("=" * 70)
velocity = 70.0 # m/s (~155 mph)
angle = 12.0
# Sea level (standard conditions)
sea_level = ProjectileWithDragRequest(
initial_velocity=velocity,
angle_degrees=angle,
mass=0.0459,
drag_coefficient=0.25,
cross_sectional_area=0.00143,
altitude=0.0,
temperature=15.0, # Standard temperature
spin_rate=200.0, # Backspin
spin_axis=[0, 0, 1],
)
# Denver (high altitude = less air density)
denver = ProjectileWithDragRequest(
initial_velocity=velocity,
angle_degrees=angle,
mass=0.0459,
drag_coefficient=0.25,
cross_sectional_area=0.00143,
altitude=1600.0, # Denver elevation
temperature=20.0, # Warm summer day
spin_rate=200.0, # Same backspin
spin_axis=[0, 0, 1],
)
result_sea = calculate_projectile_with_drag(sea_level)
result_denver = calculate_projectile_with_drag(denver)
print("\n📍 Initial Conditions:")
print(f" Velocity: {velocity} m/s ({velocity * 2.237:.0f} mph)")
print(f" Angle: {angle}°")
print(" Backspin: 200 rad/s")
print("\n🌊 SEA LEVEL (0m altitude, 15°C):")
print(f" Air density: {result_sea.effective_air_density:.3f} kg/m³")
print(f" Range: {result_sea.range:.1f} m ({result_sea.range * 1.094:.1f} yards)")
print(f" Max height: {result_sea.max_height:.1f} m")
print(f" Energy lost to drag: {result_sea.energy_lost_to_drag:.1f} J")
print("\n🏔️ DENVER (1600m altitude, 20°C):")
print(f" Air density: {result_denver.effective_air_density:.3f} kg/m³")
print(f" Range: {result_denver.range:.1f} m ({result_denver.range * 1.094:.1f} yards)")
print(f" Max height: {result_denver.max_height:.1f} m")
print(f" Energy lost to drag: {result_denver.energy_lost_to_drag:.1f} J")
print("\n📊 ALTITUDE ADVANTAGE:")
range_gain = result_denver.range - result_sea.range
print(f" Extra distance: {range_gain:.1f} m ({range_gain * 1.094:.1f} yards)")
print(f" Percentage gain: {(range_gain / result_sea.range) * 100:.1f}%")
density_ratio = result_denver.effective_air_density / result_sea.effective_air_density
print(f" Air density ratio: {density_ratio:.2%}")
print(f" ⚠️ Balls fly ~{(1 - density_ratio) * 100:.1f}% farther in Denver!")
def soccer_free_kick_with_wind():
"""Soccer free kick with crosswind and sidespin."""
print("\n" + "=" * 70)
print("⚽ SOCCER: Free Kick with Crosswind + Sidespin")
print("=" * 70)
velocity = 28.0 # m/s (~63 mph)
angle = 12.0
# No wind, no spin
basic = ProjectileWithDragRequest(
initial_velocity=velocity,
angle_degrees=angle,
mass=0.43,
drag_coefficient=0.25,
cross_sectional_area=0.0388,
wind_velocity=[0.0, 0.0],
spin_rate=0.0,
)
# With crosswind
with_wind = ProjectileWithDragRequest(
initial_velocity=velocity,
angle_degrees=angle,
mass=0.43,
drag_coefficient=0.25,
cross_sectional_area=0.0388,
wind_velocity=[5.0, 0.0], # 5 m/s crosswind
spin_rate=0.0,
)
# With sidespin (bending shot)
with_spin = ProjectileWithDragRequest(
initial_velocity=velocity,
angle_degrees=angle,
mass=0.43,
drag_coefficient=0.25,
cross_sectional_area=0.0388,
wind_velocity=[0.0, 0.0],
spin_rate=80.0, # rad/s sidespin
spin_axis=[0, 1, 0], # Horizontal spin axis
)
# With BOTH wind and spin
combined = ProjectileWithDragRequest(
initial_velocity=velocity,
angle_degrees=angle,
mass=0.43,
drag_coefficient=0.25,
cross_sectional_area=0.0388,
wind_velocity=[5.0, 0.0], # Crosswind
spin_rate=80.0, # Sidespin
spin_axis=[0, 1, 0],
)
result_basic = calculate_projectile_with_drag(basic)
result_wind = calculate_projectile_with_drag(with_wind)
result_spin = calculate_projectile_with_drag(with_spin)
result_combined = calculate_projectile_with_drag(combined)
print("\n📍 Initial Conditions:")
print(f" Velocity: {velocity} m/s ({velocity * 2.237:.0f} mph)")
print(f" Angle: {angle}°")
print(" Goal distance: ~25m (typical free kick)")
print("\n⚪ BASIC (no wind, no spin):")
print(f" Range: {result_basic.range:.1f} m")
print(f" Lateral deflection: {result_basic.lateral_deflection:.2f} m")
print("\n💨 WITH CROSSWIND (5 m/s, no spin):")
print(f" Range: {result_wind.range:.1f} m")
print(f" Wind drift: {result_wind.wind_drift:.2f} m")
print("\n🌀 WITH SIDESPIN (80 rad/s, no wind):")
print(f" Range: {result_spin.range:.1f} m")
print(f" Lateral deflection: {result_spin.lateral_deflection:.2f} m (Magnus curve)")
print(f" Magnus force: {result_spin.magnus_force_max:.2f} N")
print("\n🌪️ WITH BOTH (wind + spin):")
print(f" Range: {result_combined.range:.1f} m")
print(f" Total lateral movement: {result_combined.lateral_deflection:.2f} m")
print(f" Wind drift: {result_combined.wind_drift:.2f} m")
print(f" Magnus force: {result_combined.magnus_force_max:.2f} N")
print(" 💡 Combined effects can bend ball around wall!")
def tennis_serve_hot_vs_cold():
"""Tennis serve on hot day vs cold day (temperature affects air density)."""
print("\n" + "=" * 70)
print("🎾 TENNIS: Serve on Hot Day vs Cold Day")
print("=" * 70)
velocity = 55.0 # m/s (~123 mph pro serve)
angle = 0.0 # Flat serve
# Cold day
cold_day = ProjectileWithDragRequest(
initial_velocity=velocity,
angle_degrees=angle,
initial_height=2.5, # High contact point
mass=0.058, # Tennis ball
drag_coefficient=0.55,
cross_sectional_area=0.00338, # π * (0.0328m)²
temperature=5.0, # Cold day (41°F)
spin_rate=100.0, # Topspin
spin_axis=[0, 0, -1],
)
# Hot day
hot_day = ProjectileWithDragRequest(
initial_velocity=velocity,
angle_degrees=angle,
initial_height=2.5,
mass=0.058,
drag_coefficient=0.55,
cross_sectional_area=0.00338,
temperature=35.0, # Hot day (95°F)
spin_rate=100.0, # Same topspin
spin_axis=[0, 0, -1],
)
result_cold = calculate_projectile_with_drag(cold_day)
result_hot = calculate_projectile_with_drag(hot_day)
print("\n📍 Initial Conditions:")
print(f" Velocity: {velocity} m/s ({velocity * 2.237:.0f} mph)")
print(" Height: 2.5 m (contact point)")
print(" Topspin: 100 rad/s")
print("\n❄️ COLD DAY (5°C / 41°F):")
print(f" Air density: {result_cold.effective_air_density:.3f} kg/m³")
print(f" Range: {result_cold.range:.1f} m")
print(f" Max height: {result_cold.max_height:.2f} m")
print(f" Energy lost: {result_cold.energy_lost_to_drag:.1f} J")
print("\n🔥 HOT DAY (35°C / 95°F):")
print(f" Air density: {result_hot.effective_air_density:.3f} kg/m³")
print(f" Range: {result_hot.range:.1f} m")
print(f" Max height: {result_hot.max_height:.2f} m")
print(f" Energy lost: {result_hot.energy_lost_to_drag:.1f} J")
print("\n📊 TEMPERATURE EFFECT:")
range_diff = result_hot.range - result_cold.range
print(f" Extra distance (hot): {range_diff:.2f} m")
print(f" Percentage difference: {(range_diff / result_cold.range) * 100:.1f}%")
print(" 💡 Hot air = thinner air = less drag = faster serves!")
if __name__ == "__main__":
print("\n" + "🌟 " * 20)
print("ADVANCED PROJECTILE PHYSICS: Magnus Force, Wind & Altitude")
print("🌟 " * 20)
print("\nDemonstrating enhanced features:")
print(" • Magnus force (spin effects on trajectory)")
print(" • Wind effects (tailwind, headwind, crosswind)")
print(" • Altitude effects (air density changes with elevation)")
print(" • Temperature effects (air density changes with temperature)")
baseball_curveball_vs_fastball()
golf_denver_vs_sea_level()
soccer_free_kick_with_wind()
tennis_serve_hot_vs_cold()
print("\n" + "=" * 70)
print("💡 KEY TAKEAWAYS")
print("=" * 70)
print("1. Backspin creates lift (Magnus force), topspin creates drop")
print("2. Golf balls fly ~10% farther in Denver due to thin air")
print("3. Crosswind + sidespin combine for dramatic trajectory bends")
print("4. Hot weather reduces air density = less drag = longer shots")
print("5. These effects are crucial for realistic sports simulations!")
print("\n✅ All effects computed with full 3D physics simulation (RK4)")
print()
