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Turn radius Formula

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Turn Radius is the radius of the flight path causing the airplane to turn in a circular path. Check FAQs

R = \frac{V^{2}}{[g] \cdot \sqrt{(n^{2}) - 1}}

R - Turn Radius?V - Flight Velocity?n - Load Factor?[g] - Gravitational acceleration on Earth?

Turn radius Example

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Here is how the Turn radius equation looks like with Values.

Here is how the Turn radius equation looks like with Units.

Here is how the Turn radius equation looks like.

8466.4578 = \frac{200^{2}}{9.8066 \cdot \sqrt{({1.11}^{2}) - 1}}

8466.4578m = \frac{{200m/s}^{2}}{9.8066m/s² \cdot \sqrt{({1.11}^{2}) - 1}}

8466.4578 = \frac{200^{2}}{9.8066 \cdot \sqrt{({1.11}^{2}) - 1}}

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Turn radius Solution

Follow our step by step solution on how to calculate Turn radius?

FIRST Step Consider the formula

R = \frac{V^{2}}{[g] \cdot \sqrt{(n^{2}) - 1}}

Next Step Substitute values of Variables

∴

R = \frac{{200m/s}^{2}}{[g] \cdot \sqrt{({1.11}^{2}) - 1}}

Next Step Substitute values of Constants

∴

R = \frac{{200m/s}^{2}}{9.8066m/s² \cdot \sqrt{({1.11}^{2}) - 1}}

Next Step Prepare to Evaluate

∴

R = \frac{200^{2}}{9.8066 \cdot \sqrt{({1.11}^{2}) - 1}}

Next Step Evaluate

∴

R = 8466.45775110158m

LAST Step Rounding Answer

∴

R = 8466.4578m

Turn radius Formula Elements

Variables

Constants

Functions

Turn Radius

Turn Radius is the radius of the flight path causing the airplane to turn in a circular path.

Symbol: R

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Turn Radius

Flight Velocity

Flight Velocity refers to the speed at which an aircraft moves through the air.

Symbol: V

Measurement: SpeedUnit: m/s

Note: Value should be greater than 0.

Formulas to find Flight Velocity

Load Factor

Load Factor is the ratio of the aerodynamic force on the aircraft to the gross weight of the aircraft.

Symbol: n

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Load Factor

Gravitational acceleration on Earth

Gravitational acceleration on Earth means that the velocity of an object in free fall will increase by 9.8 m/s2 every second.

Symbol: [g]

Value: 9.80665 m/s²

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other formulas in Turning Flight category

Go Load Factor given Turn Rate

n = \sqrt{{(V \cdot \frac{ω}{[g]})}^{2} + 1}

Go Velocity for given turn rate

V = [g] \cdot \frac{\sqrt{n^{2} - 1}}{ω}

Go Turn rate

ω = [g] \cdot \frac{\sqrt{n^{2} - 1}}{V}

Go Load Factor given Turn Radius

n = \sqrt{1 + {(\frac{V^{2}}{[g] \cdot R})}^{2}}

How to Evaluate Turn radius?

Turn radius evaluator uses Turn Radius = Flight Velocity^2/([g]*sqrt((Load Factor^2)-1)) to evaluate the Turn Radius, Turn Radius is a measure of the circular path an aircraft follows during a turn, calculated by considering the velocity, load factor, and gravitational force, providing a critical indicator of an aircraft's maneuverability and stability. Turn Radius is denoted by R symbol.

How to evaluate Turn radius using this online evaluator? To use this online evaluator for Turn radius, enter Flight Velocity (V) & Load Factor (n) and hit the calculate button.

FAQs on Turn radius

What is the formula to find Turn radius?

The formula of Turn radius is expressed as Turn Radius = Flight Velocity^2/([g]*sqrt((Load Factor^2)-1)). Here is an example- 4910.376 = 200^2/([g]*sqrt((1.11^2)-1)).

How to calculate Turn radius?

With Flight Velocity (V) & Load Factor (n) we can find Turn radius using the formula - Turn Radius = Flight Velocity^2/([g]*sqrt((Load Factor^2)-1)). This formula also uses Gravitational acceleration on Earth constant(s) and Square Root (sqrt) function(s).

Can the Turn radius be negative?

No, the Turn radius, measured in Length cannot be negative.

Which unit is used to measure Turn radius?

Turn radius is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Turn radius can be measured.

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Turn radius Formula

Turn radius Example

Turn radius Solution

Turn radius Formula Elements

Other formulas in Turning Flight category

How to Evaluate Turn radius?

FAQs on Turn radius

Variable Name