Angle of Banking Calculator

Turning Radius (\( r \)):

Velocity (\( v \)):

Friction Coefficient (\( \mu \)):

Gravity (\( g \)):

Angle of Banking (\( \theta \)) in degrees:

1. What is the Angle of Banking Calculator?

Definition: This calculator determines the angle of banking (\( \theta \)) required for a vehicle to turn safely based on turning radius, velocity, friction coefficient, and gravity.

Purpose: It assists engineers and drivers in designing and navigating curved roads or tracks.

2. How Does the Calculator Work?

The calculator uses the relationship:

\[ \theta = \arctan\left(\frac{v^2 - r \cdot g \cdot \mu}{r \cdot g + v^2 \cdot \mu}\right) \]

Where:

\( \theta \) — Angle of banking (in degrees)
\( v \) — Velocity
\( r \) — Turning radius
\( g \) — Acceleration due to gravity
\( \mu \) — Friction coefficient (unitless)

Explanation: Enter turning radius, velocity, friction coefficient, and gravity in the chosen units, and the calculator computes the banking angle.

3. Importance of Angle of Banking

Details: The banking angle ensures safe turning by counteracting centrifugal force, critical for road design and vehicle dynamics.

4. Using the Calculator

Tips: Enter positive values for turning radius, velocity, friction coefficient, and gravity, then click "Calculate." Results show the banking angle in degrees (to 5 decimal places, or scientific notation if less than 0.0001).

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