Radius of turn for given wing loading Calculator

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High Load Factor Maneuver

Pull Up and Pull Down Maneuver

✖Wing Loading is the loaded weight of the aircraft divided by the area of the wing.ⓘ Wing Loading [W_S]			+10% -10%
✖Freestream density is the mass per unit volume of air far upstream of an aerodynamic body at a given altitude.ⓘ Freestream density [ρ_∞]			+10% -10%
✖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.ⓘ Lift Coefficient [C_L]			+10% -10%

✖Turn Radius is the radius of the flight path causing the airplane to turn in a circular path.ⓘ Radius of turn for given wing loading [R]

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Formula

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Radius of turn for given wing loading

Formula

`"R" = 2*"W"_{"S"}/("ρ"_{"∞"}*"C"_{"L"}*"[g]")`

Example

`"416.2107m"=2*"5Pa"/("1.225kg/m³"*"0.002"*"[g]")`

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Radius of turn for given wing loading Solution

STEP 0: Pre-Calculation Summary

Formula Used

Turn Radius = 2*Wing Loading/(Freestream density*Lift Coefficient*[g])
R = 2*W_S/(ρ_∞*C_L*[g])
This formula uses 1 Constants, 4 Variables

Constants Used

[g] - Gravitational acceleration on Earth Value Taken As 9.80665

Variables Used

Turn Radius - (Measured in Meter) - Turn Radius is the radius of the flight path causing the airplane to turn in a circular path.
Wing Loading - (Measured in Pascal) - Wing Loading is the loaded weight of the aircraft divided by the area of the wing.
Freestream density - (Measured in Kilogram per Cubic Meter) - Freestream density is the mass per unit volume of air far upstream of an aerodynamic body at a given altitude.
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.

STEP 1: Convert Input(s) to Base Unit

Wing Loading: 5 Pascal --> 5 Pascal No Conversion Required
Freestream density: 1.225 Kilogram per Cubic Meter --> 1.225 Kilogram per Cubic Meter No Conversion Required
Lift Coefficient: 0.002 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

R = 2*W_S/(ρ_∞*C_L*[g]) --> 2*5/(1.225*0.002*[g])

Evaluating ... ...

R = 416.210699174665

STEP 3: Convert Result to Output's Unit

416.210699174665 Meter --> No Conversion Required

FINAL ANSWER

416.210699174665 ≈ 416.2107 Meter <-- Turn Radius

(Calculation completed in 00.004 seconds)

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Created by Vinay Mishra

Indian Institute for Aeronautical Engineering and Information Technology (IIAEIT), Pune

Vinay Mishra has created this Calculator and 300+ more calculators!

Verified by Shikha Maurya

Indian Institute of Technology (IIT), Bombay

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< 25 High Load Factor Maneuver Calculators

Turn rate for given lift coefficient

Go Turn Rate = [g]*(sqrt((Reference Area*Freestream density*Lift Coefficient*Load factor)/(2*Aircraft weight)))

Turn rate for given wing loading

Go Turn Rate = [g]*(sqrt(Freestream density*Lift Coefficient*Load factor/(2*Wing Loading)))

Lift Coefficient for given turn rate

Go Lift Coefficient = 2*Aircraft weight*(Turn Rate^2)/(([g]^2)*Freestream density*Load factor*Reference Area)

Lift Coefficient for given Turn Radius

Go Lift Coefficient = Aircraft weight/(0.5*Freestream density*Reference Area*[g]*Turn Radius)

Radius of turn for given lift coefficient

Go Turn Radius = 2*Aircraft weight/(Freestream density*Reference Area*[g]*Lift Coefficient)

Wing loading for given turn rate

Go Wing Loading = ([g]^2)*Freestream density*Lift Coefficient*Load factor/(2*(Turn Rate^2))

Lift Coefficient for given wing loading and turn radius

Go Lift Coefficient = 2*Wing Loading/(Freestream density*Turn Radius*[g])

Radius of turn for given wing loading

Go Turn Radius = 2*Wing Loading/(Freestream density*Lift Coefficient*[g])

Wing loading for given turn radius

Go Wing Loading = (Turn Radius*Freestream density*Lift Coefficient*[g])/2

Velocity for given pull-up maneuver radius

Go Velocity = sqrt(Turn Radius*[g]*(Load factor-1))

Velocity given Pull-down Maneuver Radius

Go Velocity = sqrt(Turn Radius*[g]*(Load factor+1))

Velocity given Turn Radius for High Load Factor

Go Velocity = sqrt(Turn Radius*Load factor*[g])

Change in Angle of Attack due to Upward Gust

Go Change in Angle of Attack = tan(Gust Velocity/Flight Velocity)

Load Factor given Pull-down Maneuver Radius

Go Load factor = ((Velocity^2)/(Turn Radius*[g]))-1

Load Factor given Pull-UP Maneuver Radius

Go Load factor = 1+((Velocity^2)/(Turn Radius*[g]))

Pull-down maneuver radius

Go Turn Radius = (Velocity^2)/([g]*(Load factor+1))

Pull-up maneuver radius

Go Turn Radius = (Velocity^2)/([g]*(Load factor-1))

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

Go Load factor = (Velocity^2)/([g]*Turn Radius)

Turn radius for high load factor

Go Turn Radius = (Velocity^2)/([g]*Load factor)

Velocity for given pull-up maneuver rate

Go Velocity = [g]*(Load factor-1)/Turn Rate

Load Factor given Pull-Up Maneuver Rate

Go Load factor = 1+(Velocity*Turn Rate/[g])

Pull-down maneuver rate

Go Turn Rate = [g]*(1+Load factor)/Velocity

Pull-up maneuver rate

Go Turn Rate = [g]*(Load factor-1)/Velocity

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

Go Load factor = Velocity*Turn Rate/[g]

Turn rate for high load factor

Go Turn Rate = [g]*Load factor/Velocity

Radius of turn for given wing loading Formula

Turn Radius = 2*Wing Loading/(Freestream density*Lift Coefficient*[g])
R = 2*W_S/(ρ_∞*C_L*[g])

How do you calculate wing area?

In aerodynamics, the surface area of a wing is calculated by looking at the wing from a top-down view and measuring the wing area. This surface area is also known as the planform area. The planform area is a significant value when calculating the performance of an aeroplane.

How to Calculate Radius of turn for given wing loading?

Radius of turn for given wing loading calculator uses Turn Radius = 2*Wing Loading/(Freestream density*Lift Coefficient*[g]) to calculate the Turn Radius, The Radius of turn for given wing loading depends upon the altitude, lift coefficient, and wing loading of the aircraft. Turn Radius is denoted by R symbol.

How to calculate Radius of turn for given wing loading using this online calculator? To use this online calculator for Radius of turn for given wing loading, enter Wing Loading (W_S), Freestream density (ρ_∞) & Lift Coefficient (C_L) and hit the calculate button. Here is how the Radius of turn for given wing loading calculation can be explained with given input values -> 416.2107 = 2*5/(1.225*0.002*[g]).

FAQ

What is Radius of turn for given wing loading?

The Radius of turn for given wing loading depends upon the altitude, lift coefficient, and wing loading of the aircraft and is represented as R = 2*W_S/(ρ_∞*C_L*[g]) or Turn Radius = 2*Wing Loading/(Freestream density*Lift Coefficient*[g]). Wing Loading is the loaded weight of the aircraft divided by the area of the wing, Freestream density is the mass per unit volume of air far upstream of an aerodynamic body at a given altitude & 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.

How to calculate Radius of turn for given wing loading?

The Radius of turn for given wing loading depends upon the altitude, lift coefficient, and wing loading of the aircraft is calculated using Turn Radius = 2*Wing Loading/(Freestream density*Lift Coefficient*[g]). To calculate Radius of turn for given wing loading, you need Wing Loading (W_S), Freestream density (ρ_∞) & Lift Coefficient (C_L). With our tool, you need to enter the respective value for Wing Loading, Freestream density & Lift Coefficient and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Turn Radius?

In this formula, Turn Radius uses Wing Loading, Freestream density & Lift Coefficient. We can use 4 other way(s) to calculate the same, which is/are as follows -

Turn Radius = (Velocity^2)/([g]*Load factor)
Turn Radius = 2*Aircraft weight/(Freestream density*Reference Area*[g]*Lift Coefficient)
Turn Radius = (Velocity^2)/([g]*(Load factor-1))
Turn Radius = (Velocity^2)/([g]*(Load factor+1))

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