Wing Loading for given Turn Rate Calculator

✖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%
✖Load Factor is the ratio of the aerodynamic force on the aircraft to the gross weight of the aircraft.ⓘ Load Factor [n]			+10% -10%
✖Turn Rate is the rate at which an aircraft executes a turn expressed in degrees per second.ⓘ Turn Rate [ω]			+10% -10%

✖Wing Loading is the loaded weight of the aircraft divided by the area of the wing.ⓘ Wing Loading for given Turn Rate [W_S]

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Formula

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Wing Loading for given Turn Rate

Formula

W S = ({[g]}^{2}) \cdot ρ ∞ \cdot C L \cdot \frac{n}{2 \cdot (ω^{2})}

Example

354.6108 Pa = ({[g]}^{2}) \cdot 1.225 kg/m³ \cdot 0.002 \cdot \frac{1.2}{2 \cdot ({1.144 degree/s}^{2})}

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Wing Loading for given Turn Rate Solution

STEP 0: Pre-Calculation Summary

Formula Used

Wing Loading = ([g]^2)*Freestream Density*Lift Coefficient*Load Factor/(2*(Turn Rate^2))
W_S = ([g]^2)*ρ_∞*C_L*n/(2*(ω^2))
This formula uses 1 Constants, 5 Variables

Constants Used

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

Variables Used

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.
Load Factor - Load Factor is the ratio of the aerodynamic force on the aircraft to the gross weight of the aircraft.
Turn Rate - (Measured in Radian per Second) - Turn Rate is the rate at which an aircraft executes a turn expressed in degrees per second.

STEP 1: Convert Input(s) to Base Unit

Freestream Density: 1.225 Kilogram per Cubic Meter --> 1.225 Kilogram per Cubic Meter No Conversion Required
Lift Coefficient: 0.002 --> No Conversion Required
Load Factor: 1.2 --> No Conversion Required
Turn Rate: 1.144 Degree per Second --> 0.0199665666428114 Radian per Second (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

W_S = ([g]^2)*ρ_∞*C_L*n/(2*(ω^2)) --> ([g]^2)*1.225*0.002*1.2/(2*(0.0199665666428114^2))

Evaluating ... ...

W_S = 354.610753867053

STEP 3: Convert Result to Output's Unit

354.610753867053 Pascal --> No Conversion Required

FINAL ANSWER

354.610753867053 ≈ 354.6108 Pascal <-- Wing Loading

(Calculation completed in 00.020 seconds)

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Created by Vinay Mishra

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

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< High Load Factor Maneuver Calculators

Velocity given Turn Radius for High Load Factor

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

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)

Turn Rate for High Load Factor

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

Wing Loading for given Turn Rate Formula

Wing Loading = ([g]^2)*Freestream Density*Lift Coefficient*Load Factor/(2*(Turn Rate^2))
W_S = ([g]^2)*ρ_∞*C_L*n/(2*(ω^2))

Does wing area include fuselage?

The wing-area of an aircraft refers to the entire trapezoid, including the portion buried inside the fuselage.

How to Calculate Wing Loading for given Turn Rate?

Wing Loading for given Turn Rate calculator uses Wing Loading = ([g]^2)*Freestream Density*Lift Coefficient*Load Factor/(2*(Turn Rate^2)) to calculate the Wing Loading, The Wing Loading for given Turn Rate refers to the weight supported by the aircraft's wings per unit area, this formula computes the wing loading required to sustain the specified turn rate under given aerodynamic conditions, it leverages the balance between lift and gravitational forces during the turn. Wing Loading is denoted by W_S symbol.

How to calculate Wing Loading for given Turn Rate using this online calculator? To use this online calculator for Wing Loading for given Turn Rate, enter Freestream Density (ρ_∞), Lift Coefficient (C_L), Load Factor (n) & Turn Rate (ω) and hit the calculate button. Here is how the Wing Loading for given Turn Rate calculation can be explained with given input values -> 354.6108 = ([g]^2)*1.225*0.002*1.2/(2*(0.0199665666428114^2)).

FAQ

What is Wing Loading for given Turn Rate?

The Wing Loading for given Turn Rate refers to the weight supported by the aircraft's wings per unit area, this formula computes the wing loading required to sustain the specified turn rate under given aerodynamic conditions, it leverages the balance between lift and gravitational forces during the turn and is represented as W_S = ([g]^2)*ρ_∞*C_L*n/(2*(ω^2)) or Wing Loading = ([g]^2)*Freestream Density*Lift Coefficient*Load Factor/(2*(Turn Rate^2)). 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, Load Factor is the ratio of the aerodynamic force on the aircraft to the gross weight of the aircraft & Turn Rate is the rate at which an aircraft executes a turn expressed in degrees per second.

How to calculate Wing Loading for given Turn Rate?

The Wing Loading for given Turn Rate refers to the weight supported by the aircraft's wings per unit area, this formula computes the wing loading required to sustain the specified turn rate under given aerodynamic conditions, it leverages the balance between lift and gravitational forces during the turn is calculated using Wing Loading = ([g]^2)*Freestream Density*Lift Coefficient*Load Factor/(2*(Turn Rate^2)). To calculate Wing Loading for given Turn Rate, you need Freestream Density (ρ_∞), Lift Coefficient (C_L), Load Factor (n) & Turn Rate (ω). With our tool, you need to enter the respective value for Freestream Density, Lift Coefficient, Load Factor & Turn Rate 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 Wing Loading?

In this formula, Wing Loading uses Freestream Density, Lift Coefficient, Load Factor & Turn Rate. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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