Radius of Turn for given Wing Loading Calculator

Turn Radius Formula:

\[ R = \frac{2 \times WS}{\rho_{\infty} \times C_L \times [g]} \]

Turn Radius (R):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Turn Radius Formula?

The Turn Radius formula calculates the radius of the flight path causing an airplane to turn in a circular path. It is derived from the balance of centrifugal and lift forces during a coordinated turn.

2. How Does the Calculator Work?

The calculator uses the Turn Radius formula:

\[ R = \frac{2 \times WS}{\rho_{\infty} \times C_L \times [g]} \]

Where:

\( R \) — Turn Radius (m)
\( WS \) — Wing Loading (Pa)
\( \rho_{\infty} \) — Freestream Density (kg/m³)
\( C_L \) — Lift Coefficient
\( [g] \) — Gravitational acceleration (9.80665 m/s²)

Explanation: The formula shows that turn radius increases with higher wing loading and decreases with higher air density, lift coefficient, or gravitational acceleration.

3. Importance of Turn Radius Calculation

Details: Calculating turn radius is crucial for aircraft maneuverability analysis, flight path planning, and understanding aircraft performance characteristics during turning maneuvers.

4. Using the Calculator

Tips: Enter wing loading in Pascals, freestream density in kg/m³, and lift coefficient. All values must be positive numbers greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What factors affect turn radius?
A: Turn radius is affected by wing loading, air density, lift coefficient, and gravitational acceleration. Higher speeds and lower lift coefficients generally result in larger turn radii.

Q2: How does altitude affect turn radius?
A: At higher altitudes where air density decreases, turn radius increases for the same wing loading and lift coefficient.

Q3: What is typical turn radius for commercial aircraft?
A: Commercial aircraft typically have turn radii ranging from several kilometers at cruise to hundreds of meters during approach and landing phases.

Q4: How can pilots reduce turn radius?
A: Pilots can reduce turn radius by increasing bank angle (which increases lift coefficient), reducing speed, or flying at lower altitudes with higher air density.

Q5: Are there limitations to this formula?
A: This formula assumes a coordinated turn with constant speed and altitude, and may not account for all real-world factors like wind, aircraft structural limits, or pilot technique.