"""Sports Projectile Motion Examples: Comparing Drag vs. No Drag.
This example demonstrates the dramatic impact of air resistance on sports
balls. Compare realistic trajectories (with drag) to ideal/vacuum conditions.
Common drag coefficients (Cd):
- Baseball: 0.4
- Golf ball (dimpled): 0.25
- Basketball: 0.55
- Soccer ball: 0.25
- Tennis ball: 0.55
- Football (American): 0.05-0.15
"""
from chuk_mcp_physics.models import ProjectileWithDragRequest, ProjectileMotionRequest
from chuk_mcp_physics.kinematics import calculate_projectile_with_drag
from chuk_mcp_physics.providers.analytic import AnalyticProvider
def baseball_90mph_fastball():
"""Compare baseball pitch with and without drag."""
print("\n" + "=" * 70)
print("⚾ BASEBALL: 90 mph Fastball")
print("=" * 70)
# 90 mph = 40.23 m/s
velocity = 40.23
angle = 10.0 # Low angle pitch
height = 1.8 # Pitcher's release height
# WITH DRAG (realistic)
with_drag = ProjectileWithDragRequest(
initial_velocity=velocity,
angle_degrees=angle,
initial_height=height,
mass=0.145, # kg (baseball)
drag_coefficient=0.4, # baseball Cd
cross_sectional_area=0.0043, # π * (0.037m)² for baseball
fluid_density=1.225, # air density
)
result_drag = calculate_projectile_with_drag(with_drag)
# WITHOUT DRAG (vacuum/ideal)
provider = AnalyticProvider()
no_drag = ProjectileMotionRequest(
initial_velocity=velocity,
angle_degrees=angle,
initial_height=height,
)
import asyncio
result_nodrag = asyncio.run(provider.calculate_projectile_motion(no_drag))
print("\n📍 Initial Conditions:")
print(f" Velocity: {velocity} m/s (90 mph)")
print(f" Angle: {angle}°")
print(f" Height: {height} m")
print(" Mass: 0.145 kg")
print(" Drag coefficient: 0.4")
print("\n🌪️ WITH AIR RESISTANCE (Realistic):")
print(f" Range: {result_drag.range:.1f} m ({result_drag.range * 3.28:.1f} ft)")
print(f" Max height: {result_drag.max_height:.1f} m")
print(f" Flight time: {result_drag.time_of_flight:.2f} s")
print(f" Impact velocity: {result_drag.impact_velocity:.1f} m/s")
print(f" Energy lost to drag: {result_drag.energy_lost_to_drag:.1f} J")
print("\n🌌 WITHOUT AIR RESISTANCE (Vacuum):")
print(f" Range: {result_nodrag.range:.1f} m ({result_nodrag.range * 3.28:.1f} ft)")
print(f" Max height: {result_nodrag.max_height:.1f} m")
print(f" Flight time: {result_nodrag.time_of_flight:.2f} s")
print("\n📊 DRAG IMPACT:")
print(f" Range reduction: {(1 - result_drag.range / result_nodrag.range) * 100:.1f}%")
print(f" Energy dissipated: {result_drag.energy_lost_to_drag:.1f} J")
print(
f" ({result_drag.energy_lost_to_drag / result_drag.initial_kinetic_energy * 100:.1f}% of initial energy)"
)
def golf_drive():
"""Compare golf drive with and without drag."""
print("\n" + "=" * 70)
print("⛳ GOLF: Pro Drive (155 mph clubhead speed)")
print("=" * 70)
velocity = 70.0 # m/s (~155 mph)
angle = 12.0 # Optimal launch angle for distance
height = 0.0
# WITH DRAG (realistic)
with_drag = ProjectileWithDragRequest(
initial_velocity=velocity,
angle_degrees=angle,
initial_height=height,
mass=0.0459, # kg (golf ball)
drag_coefficient=0.25, # dimpled golf ball (reduced Cd)
cross_sectional_area=0.00143, # π * (0.0213m)² for golf ball
fluid_density=1.225,
)
result_drag = calculate_projectile_with_drag(with_drag)
# WITHOUT DRAG
provider = AnalyticProvider()
no_drag = ProjectileMotionRequest(
initial_velocity=velocity,
angle_degrees=angle,
initial_height=height,
)
import asyncio
result_nodrag = asyncio.run(provider.calculate_projectile_motion(no_drag))
print("\n📍 Initial Conditions:")
print(f" Velocity: {velocity} m/s ({velocity * 2.237:.0f} mph)")
print(f" Angle: {angle}°")
print(" Mass: 0.0459 kg")
print(" Drag coefficient: 0.25 (dimpled)")
print("\n🌪️ WITH AIR RESISTANCE (Realistic):")
print(f" Range: {result_drag.range:.1f} m ({result_drag.range * 1.094:.1f} yards)")
print(f" Max height: {result_drag.max_height:.1f} m")
print(f" Flight time: {result_drag.time_of_flight:.2f} s")
print(f" Impact velocity: {result_drag.impact_velocity:.1f} m/s")
print("\n🌌 WITHOUT AIR RESISTANCE (Vacuum):")
print(f" Range: {result_nodrag.range:.1f} m ({result_nodrag.range * 1.094:.1f} yards)")
print(f" Max height: {result_nodrag.max_height:.1f} m")
print("\n📊 DRAG IMPACT:")
print(f" Range reduction: {(1 - result_drag.range / result_nodrag.range) * 100:.1f}%")
print(" ⚠️ Dimples reduce drag by ~50% (Cd 0.47 → 0.25)!")
print(f" Without dimples, range would be ~{result_drag.range * 0.7:.1f} m")
def basketball_three_pointer():
"""Compare basketball 3-point shot with and without drag."""
print("\n" + "=" * 70)
print("🏀 BASKETBALL: 3-Point Shot")
print("=" * 70)
velocity = 7.5 # m/s
angle = 48.0 # High arc shot
height = 2.0 # Release height
# WITH DRAG (realistic)
with_drag = ProjectileWithDragRequest(
initial_velocity=velocity,
angle_degrees=angle,
initial_height=height,
mass=0.624, # kg (basketball)
drag_coefficient=0.55, # basketball Cd
cross_sectional_area=0.0456, # π * (0.12m)² for basketball
fluid_density=1.225,
)
result_drag = calculate_projectile_with_drag(with_drag)
# WITHOUT DRAG
provider = AnalyticProvider()
no_drag = ProjectileMotionRequest(
initial_velocity=velocity,
angle_degrees=angle,
initial_height=height,
)
import asyncio
result_nodrag = asyncio.run(provider.calculate_projectile_motion(no_drag))
print("\n📍 Initial Conditions:")
print(f" Velocity: {velocity} m/s")
print(f" Angle: {angle}° (high arc)")
print(f" Release height: {height} m")
print(" Mass: 0.624 kg")
print(" Target: 6.75 m (3-point line)")
print("\n🌪️ WITH AIR RESISTANCE (Realistic):")
print(f" Range: {result_drag.range:.2f} m")
print(f" Max height: {result_drag.max_height:.2f} m")
print(f" Flight time: {result_drag.time_of_flight:.2f} s")
print(f" Impact velocity: {result_drag.impact_velocity:.1f} m/s")
print("\n🌌 WITHOUT AIR RESISTANCE (Vacuum):")
print(f" Range: {result_nodrag.range:.2f} m")
print(f" Max height: {result_nodrag.max_height:.2f} m")
print("\n📊 DRAG IMPACT:")
print(f" Range reduction: {(1 - result_drag.range / result_nodrag.range) * 100:.1f}%")
print(
f" For 3-point shots, drag reduces range by ~{result_nodrag.range - result_drag.range:.2f} m"
)
def soccer_penalty_kick():
"""Compare soccer penalty kick with and without drag."""
print("\n" + "=" * 70)
print("⚽ SOCCER: Penalty Kick")
print("=" * 70)
velocity = 25.0 # m/s (~56 mph)
angle = 10.0 # Low angle
height = 0.3 # Ball on ground
# WITH DRAG
with_drag = ProjectileWithDragRequest(
initial_velocity=velocity,
angle_degrees=angle,
initial_height=height,
mass=0.43, # kg (soccer ball)
drag_coefficient=0.25, # modern soccer ball
cross_sectional_area=0.0388, # π * (0.111m)² for soccer ball
fluid_density=1.225,
)
result_drag = calculate_projectile_with_drag(with_drag)
# WITHOUT DRAG
provider = AnalyticProvider()
no_drag = ProjectileMotionRequest(
initial_velocity=velocity,
angle_degrees=angle,
initial_height=height,
)
import asyncio
result_nodrag = asyncio.run(provider.calculate_projectile_motion(no_drag))
print("\n📍 Initial Conditions:")
print(f" Velocity: {velocity} m/s ({velocity * 2.237:.0f} mph)")
print(f" Angle: {angle}°")
print(" Mass: 0.43 kg")
print(" Goal distance: 11 m (penalty spot)")
print("\n🌪️ WITH AIR RESISTANCE (Realistic):")
print(f" Range: {result_drag.range:.1f} m")
print(f" Max height: {result_drag.max_height:.2f} m")
print(f" Flight time: {result_drag.time_of_flight:.3f} s")
print(f" Time to goal (11m): ~{11 / velocity:.3f} s")
print("\n🌌 WITHOUT AIR RESISTANCE (Vacuum):")
print(f" Range: {result_nodrag.range:.1f} m")
print(f" Max height: {result_nodrag.max_height:.2f} m")
print("\n📊 DRAG IMPACT:")
print(f" Range reduction: {(1 - result_drag.range / result_nodrag.range) * 100:.1f}%")
print(" Less impact at short distances!")
if __name__ == "__main__":
print("\n" + "🎾 " * 20)
print("SPORTS PROJECTILES: THE IMPACT OF AIR RESISTANCE")
print("🎾 " * 20)
print("\nThis example demonstrates how drag dramatically affects sports balls.")
print("Real-world trajectories (WITH drag) vs ideal/vacuum conditions (NO drag).")
baseball_90mph_fastball()
golf_drive()
basketball_three_pointer()
soccer_penalty_kick()
print("\n" + "=" * 70)
print("💡 KEY TAKEAWAYS")
print("=" * 70)
print("1. Drag reduces projectile range by 20-70% depending on velocity and shape")
print("2. Higher velocity = more drag force (quadratic relationship)")
print("3. Golf ball dimples reduce drag coefficient by ~50%!")
print("4. Baseball range reduced by ~40% due to air resistance")
print("5. Drag effect increases with projectile speed (v²)")
print("\n✅ Always include drag for realistic sports simulations!")
print()
