Bank Angle Calculator

Coordinated Turns and Bank Angle

In a coordinated aircraft turn, lift tilts inward so horizontal component provides centripetal force and vertical component balances weight. The required bank angle depends on speed, turn radius, and gravitational acceleration.

Bank Angle Formula

$$\tan(\phi) = \frac{v^2}{r \cdot g}$$

$\phi$ is bank angle, $v$ is speed in m/s, $r$ is turn radius in meters, and $g = 9.81$ m/s². Example: 100 knots ($\approx 51.4$ m/s) with a 1000 m radius gives $\tan(\phi) \approx 0.27$, so $\phi \approx 15°$.

Unit Conversions

Convert knots to m/s by multiplying by 0.514444. Convert feet to meters by multiplying by 0.3048. Always use consistent SI units inside the formula before taking the arctangent.

Related tools: Drone Flight Time Calculator and Azimuth Calculator.

Frequently Asked Questions

What is a coordinated turn?

The aircraft yaws so the lift vector points through the apparent vertical felt by occupants. Uncoordinated turns cause slip or skid and extra load on the structure.

Does load factor increase with bank?

Yes. Load factor $n = 1/\cos(\phi)$. At 60° bank, load factor is 2 g.

Can I use this for cars on a banked track?

Yes, for ideal frictionless banking where speed and radius match the design angle. Real vehicles also depend on tire friction.

Why is g fixed at 9.81?

Standard gravity at Earth's surface. Aviation formulas conventionally use 9.81 m/s² unless a specific locale requires otherwise.

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Coordinated Turns and Bank Angle

Bank Angle Formula

Unit Conversions

Frequently Asked Questions

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