calculate_banking_angle
Calculate the ideal banking angle for a banked curve where no friction is needed to maintain a turn at a given speed, using velocity, radius, and gravity inputs.
Instructions
Calculate ideal banking angle: θ = arctan(v² / (rg)).
For a banked curve, the ideal angle where no friction is needed
to maintain the turn at a given speed.
Args:
velocity: Speed in m/s
radius: Turn radius in meters
gravity: Gravitational acceleration in m/s² (default 9.81)
Returns:
Dict containing:
- angle_radians: Banking angle in radians
- angle_degrees: Banking angle in degrees
Tips for LLMs:
- Faster speed → steeper banking angle
- Tighter turn → steeper banking angle
- NASCAR tracks banked ~30° for high-speed turns
- At ideal angle, normal force provides all centripetal force
Example - Highway exit ramp:
result = await calculate_banking_angle(
velocity=25, # m/s (90 km/h)
radius=100 # meter radius turn
)
# θ ≈ 32.5°Input Schema
TableJSON Schema
| Name | Required | Description | Default |
|---|---|---|---|
| velocity | Yes | ||
| radius | Yes | ||
| gravity | No |