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Radius of Turn for given Lift Coefficient Formula

GoTurn radius for high load factor Formula

GoRadius of Turn for given Wing Loading 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 = 2 \cdot \frac{W}{ρ ∞ \cdot S \cdot [g] \cdot C L}

R - Turn Radius?W - Aircraft Weight?ρ_∞ - Freestream Density?S - Reference Area?C_L - Lift Coefficient?[g] - Gravitational acceleration on Earth?

Radius of Turn for given Lift Coefficient Example

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Here is how the Radius of Turn for given Lift Coefficient equation looks like with Values.

Here is how the Radius of Turn for given Lift Coefficient equation looks like with Units.

Here is how the Radius of Turn for given Lift Coefficient equation looks like.

29495.2464 = 2 \cdot \frac{1800}{1.225 \cdot 5.08 \cdot 9.8066 \cdot 0.002}

29495.2464m = 2 \cdot \frac{1800N}{1.225kg/m³ \cdot 5.08m² \cdot 9.8066m/s² \cdot 0.002}

29495.2464 = 2 \cdot \frac{1800}{1.225 \cdot 5.08 \cdot 9.8066 \cdot 0.002}

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Radius of Turn for given Lift Coefficient Solution

Follow our step by step solution on how to calculate Radius of Turn for given Lift Coefficient?

FIRST Step Consider the formula

R = 2 \cdot \frac{W}{ρ ∞ \cdot S \cdot [g] \cdot C L}

Next Step Substitute values of Variables

∴

R = 2 \cdot \frac{1800N}{1.225kg/m³ \cdot 5.08m² \cdot [g] \cdot 0.002}

Next Step Substitute values of Constants

∴

R = 2 \cdot \frac{1800N}{1.225kg/m³ \cdot 5.08m² \cdot 9.8066m/s² \cdot 0.002}

Next Step Prepare to Evaluate

∴

R = 2 \cdot \frac{1800}{1.225 \cdot 5.08 \cdot 9.8066 \cdot 0.002}

Next Step Evaluate

∴

R = 29495.2463982046m

LAST Step Rounding Answer

∴

R = 29495.2464m

Radius of Turn for given Lift Coefficient Formula Elements

Variables

Constants

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

Aircraft Weight

Aircraft Weight is the total aircraft weight at any moment during the flight or ground operation.

Symbol: W

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Aircraft Weight

Freestream Density

Freestream Density is the mass per unit volume of air far upstream of an aerodynamic body at a given altitude.

Symbol: ρ_∞

Measurement: DensityUnit: kg/m³

Note: Value can be positive or negative.

Formulas to find Freestream Density

Reference Area

The Reference Area is arbitrarily an area that is characteristic of the object being considered. For an aircraft wing, the wing's planform area is called the reference wing area or simply wing area.

Symbol: S

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Reference Area

Lift Coefficient

The Lift Coefficient is a dimensionless coefficient that relates the lift generated by a lifting body to the fluid density around the body, the fluid velocity and an associated reference area.

Symbol: C_L

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Lift Coefficient

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

Other Formulas to find Turn Radius

Go Turn radius for high load factor

R = \frac{v^{2}}{[g] \cdot n}

Go Radius of Turn for given Wing Loading

R = 2 \cdot \frac{W S}{ρ ∞ \cdot C L \cdot [g]}

Other formulas in High Load Factor Maneuver category

Go Velocity given Turn Radius for High Load Factor

v = \sqrt{R \cdot n \cdot [g]}

Go Load factor for given turn radius for high-performance fighter aircraft

n = \frac{v^{2}}{[g] \cdot R}

Go Turn Rate for High Load Factor

ω = [g] \cdot \frac{n}{v}

Go Load factor for given turn rate for high-performance fighter aircraft

n = v \cdot \frac{ω}{[g]}

How to Evaluate Radius of Turn for given Lift Coefficient?

Radius of Turn for given Lift Coefficient evaluator uses Turn Radius = 2*Aircraft Weight/(Freestream Density*Reference Area*[g]*Lift Coefficient) to evaluate the Turn Radius, Radius of Turn for given Lift Coefficient is a measure of the turning radius required for an aircraft to maintain a specific lift coefficient. This formula relates the turn radius to aircraft weight, freestream density, reference area, gravitational acceleration, and the desired lift coefficient. Understanding and applying this formula is essential for pilots and engineers in optimizing aircraft maneuverability and stability based on desired lift characteristics. Turn Radius is denoted by R symbol.

How to evaluate Radius of Turn for given Lift Coefficient using this online evaluator? To use this online evaluator for Radius of Turn for given Lift Coefficient, enter Aircraft Weight (W), Freestream Density (ρ_∞), Reference Area (S) & Lift Coefficient (C_L) and hit the calculate button.

FAQs on Radius of Turn for given Lift Coefficient

What is the formula to find Radius of Turn for given Lift Coefficient?

The formula of Radius of Turn for given Lift Coefficient is expressed as Turn Radius = 2*Aircraft Weight/(Freestream Density*Reference Area*[g]*Lift Coefficient). Here is an example- 29495.25 = 2*1800/(1.225*5.08*[g]*0.002).

How to calculate Radius of Turn for given Lift Coefficient?

With Aircraft Weight (W), Freestream Density (ρ_∞), Reference Area (S) & Lift Coefficient (C_L) we can find Radius of Turn for given Lift Coefficient using the formula - Turn Radius = 2*Aircraft Weight/(Freestream Density*Reference Area*[g]*Lift Coefficient). This formula also uses Gravitational acceleration on Earth constant(s).

What are the other ways to Calculate Turn Radius?

Here are the different ways to Calculate Turn Radius-

Turn Radius=(Velocity^2)/([g]*Load Factor)
Turn Radius=2*Wing Loading/(Freestream Density*Lift Coefficient*[g])

Can the Radius of Turn for given Lift Coefficient be negative?

No, the Radius of Turn for given Lift Coefficient, measured in Length cannot be negative.

Which unit is used to measure Radius of Turn for given Lift Coefficient?

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

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Radius of Turn for given Lift Coefficient Formula

​GoTurn radius for high load factor Formula

​GoRadius of Turn for given Wing Loading Formula

Radius of Turn for given Lift Coefficient Example

Radius of Turn for given Lift Coefficient Solution

Radius of Turn for given Lift Coefficient Formula Elements

Other Formulas to find Turn Radius

Other formulas in High Load Factor Maneuver category

How to Evaluate Radius of Turn for given Lift Coefficient?

FAQs on Radius of Turn for given Lift Coefficient

Variable Name

GoTurn radius for high load factor Formula

GoRadius of Turn for given Wing Loading Formula