Banked Curve Calculator
Calculate ideal banking angle using tan θ = v²/(rg) or maximum safe speed.
What Is Banked Curve Calculator?
The formula Calculate ideal banking angle using tan θ = v²/(rg) or maximum safe speed., derives directly from fundamental physics principles.
Understanding this relationship enables both analytical calculation and intuitive reasoning about physical systems.
Applications span multiple fields of science and engineering. This calculator handles the arithmetic while you focus on the physics.
Ensure inputs are in SI units for correct results.
Formula Reference Table
| Solve For | Formula | Notes |
|---|---|---|
| Ideal bank angle | tan θ = v²/(rg) | θ in degrees |
| Ideal speed | v = √(rg·tan θ) | m/s |
| Ideal radius | r = v²/(g·tan θ) | m |
| With friction (max v) | v_max = √(rg·(tan θ+μ)/(1−μ·tan θ)) | μ = friction coeff |
| With friction (min v) | v_min = √(rg·(tan θ−μ)/(1+μ·tan θ)) | Minimum speed before sliding in |
| Normal force | N = mg/cos θ | Load factor = 1/cosθ |
3 Worked Examples
Speed 72 km/h = 20 m/s, radius = 100 m.
- tan θ = v²/(rg) = 400/(100×9.81) = 0.408
- θ = arctan(0.408) = 22.2°
Bank angle 33°, radius 305 m. Ideal speed?
- v = √(305×9.81×tan(33°)) = √(305×9.81×0.6494)
- v = √(1944) = 44.1 m/s = 159 km/h
v = 250 km/h = 69.4 m/s, θ = 15°.
- r = v²/(g×tan θ) = 4816/(9.81×0.2679) = 1,835 m
Real-World Applications
Common Mistakes to Avoid
Use SI.
Check geometry/conditions.
Formula assumes ideal conditions.
Check conventions.
Verify squared/sqrt terms.
Frequently Asked Questions
Related Physics Calculators
Formula Explorer connections
Interpretation: This formula is the rotational counterpart of linear mechanics, relating angle, angular motion, torque, inertia or rotational energy. Assumption: Define the rotation axis and sign convention. Rigid-body behavior, no slipping, steady rotation or negligible bearing losses may be assumed.