Aspect Ratio given Span Efficiency Factor Calculator

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Two-Dimensional Incompressible Flow

Compressible Flow

Fundamentals of Inviscid and Incompressible Flow

Three-Dimensional Incompressible Flow

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Flow over Airfoils and Wings

Elementary Flows

Flow and Lift Distribution

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✖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%
✖Span Efficiency Factor represents the change in drag with lift of a three-dimensional wing or airplane, as compared with an ideal wing having the same aspect ratio and an elliptical lift distribution.ⓘ Span Efficiency Factor [e_span]			+10% -10%
✖The Induced Drag Coefficient is a dimensionless parameter that describes a relation between the coefficient of the lift and the aspect ratio.ⓘ Induced Drag Coefficient [C_D,i]			+10% -10%

✖Wing Aspect Ratio is defined as the ratio of the square of wingspan to the wing area or wingspan over wing chord for a rectangular planform.ⓘ Aspect Ratio given Span Efficiency Factor [AR]

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Formula

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Aspect Ratio given Span Efficiency Factor

Formula

`"AR" = "C"_{"L"}^2/(pi*"e"_{"span"}*"C"_{"D,i"})`

Example

`"15.03087"=("1.2")^2/(pi*"0.95"*"0.0321")`

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Aspect Ratio given Span Efficiency Factor Solution

STEP 0: Pre-Calculation Summary

Formula Used

Wing Aspect Ratio = Lift Coefficient^2/(pi*Span Efficiency Factor*Induced Drag Coefficient)
AR = C_L^2/(pi*e_span*C_D,i)
This formula uses 1 Constants, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Wing Aspect Ratio - Wing Aspect Ratio is defined as the ratio of the square of wingspan to the wing area or wingspan over wing chord for a rectangular planform.
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.
Span Efficiency Factor - Span Efficiency Factor represents the change in drag with lift of a three-dimensional wing or airplane, as compared with an ideal wing having the same aspect ratio and an elliptical lift distribution.
Induced Drag Coefficient - The Induced Drag Coefficient is a dimensionless parameter that describes a relation between the coefficient of the lift and the aspect ratio.

STEP 1: Convert Input(s) to Base Unit

Lift Coefficient: 1.2 --> No Conversion Required
Span Efficiency Factor: 0.95 --> No Conversion Required
Induced Drag Coefficient: 0.0321 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

AR = C_L^2/(pi*e_span*C_D,i) --> 1.2^2/(pi*0.95*0.0321)

Evaluating ... ...

AR = 15.0308652600314

STEP 3: Convert Result to Output's Unit

15.0308652600314 --> No Conversion Required

FINAL ANSWER

15.0308652600314 ≈ 15.03087 <-- Wing Aspect Ratio

(Calculation completed in 00.004 seconds)

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< 11 Flow over Wings Calculators

Aspect Ratio of Wing given Lift Curve Slope of Finite Wing

Go Wing Aspect Ratio = (2D Lift Curve Slope*(1+Induced Lift Slope Factor))/(pi*(2D Lift Curve Slope/Lift Curve Slope-1))

Lift Curve Slope for Finite Wing

Go Lift Curve Slope = 2D Lift Curve Slope/(1+(2D Lift Curve Slope*(1+Induced Lift Slope Factor))/(pi*Wing Aspect Ratio))

2D Lift Curve Slope of Airfoil given Lift Slope of Finite Wing

Go 2D Lift Curve Slope = Lift Curve Slope/(1-(Lift Curve Slope*(1+Induced Lift Slope Factor))/(pi*Wing Aspect Ratio))

Aspect Ratio given Span Efficiency Factor

Go Wing Aspect Ratio = Lift Coefficient^2/(pi*Span Efficiency Factor*Induced Drag Coefficient)

Aspect Ratio of Wing given Lift Curve Slope of Elliptic Finite Wing

Go Wing Aspect Ratio = 2D Lift Curve Slope/(pi*(2D Lift Curve Slope/Lift Curve Slope-1))

Lift Curve Slope for Elliptic Finite Wing

Go Lift Curve Slope = 2D Lift Curve Slope/(1+2D Lift Curve Slope/(pi*Wing Aspect Ratio))

2D Lift Curve Slope of Airfoil given Lift Slope of Elliptic Finite Wing

Go 2D Lift Curve Slope = Lift Curve Slope/(1-Lift Curve Slope/(pi*Wing Aspect Ratio))

Geometric Angle of Attack given Effective Angle of Attack

Go Geometric Angle of Attack = Effective Angle of Attack+Induced Angle of Attack

Induced Angle of Attack given Effective Angle of Attack

Go Induced Angle of Attack = Geometric Angle of Attack-Effective Angle of Attack

Effective Angle of Attack of Finite Wing

Go Effective Angle of Attack = Geometric Angle of Attack-Induced Angle of Attack

Oswald Efficiency Factor

Go Oswald Efficiency Factor = 1.78*(1-0.045*Wing Aspect Ratio^(0.68))-0.64

Aspect Ratio given Span Efficiency Factor Formula

Wing Aspect Ratio = Lift Coefficient^2/(pi*Span Efficiency Factor*Induced Drag Coefficient)
AR = C_L^2/(pi*e_span*C_D,i)

How does aspect ratio affect aircraft?

The ratio of the length of wings to their width is called the aspect ratio. A high aspect ratio indicates long, narrow wings. Generally, high aspect ratio wings give slightly more lift and enable sustained, endurance flight, while low aspect ratio wings are best for swift maneuverability.

How to Calculate Aspect Ratio given Span Efficiency Factor?

Aspect Ratio given Span Efficiency Factor calculator uses Wing Aspect Ratio = Lift Coefficient^2/(pi*Span Efficiency Factor*Induced Drag Coefficient) to calculate the Wing Aspect Ratio, The Aspect Ratio given Span Efficiency Factor formula calculates the aspect ratio of the wing for the actual lift distribution which is a function of the Fourier series, by using the span efficiency factor. Wing Aspect Ratio is denoted by AR symbol.

How to calculate Aspect Ratio given Span Efficiency Factor using this online calculator? To use this online calculator for Aspect Ratio given Span Efficiency Factor, enter Lift Coefficient (C_L), Span Efficiency Factor (e_span) & Induced Drag Coefficient (C_D,i) and hit the calculate button. Here is how the Aspect Ratio given Span Efficiency Factor calculation can be explained with given input values -> 10.05189 = 1.2^2/(pi*0.95*0.0321).

FAQ

What is Aspect Ratio given Span Efficiency Factor?

The Aspect Ratio given Span Efficiency Factor formula calculates the aspect ratio of the wing for the actual lift distribution which is a function of the Fourier series, by using the span efficiency factor and is represented as AR = C_L^2/(pi*e_span*C_D,i) or Wing Aspect Ratio = Lift Coefficient^2/(pi*Span Efficiency Factor*Induced Drag 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, Span Efficiency Factor represents the change in drag with lift of a three-dimensional wing or airplane, as compared with an ideal wing having the same aspect ratio and an elliptical lift distribution & The Induced Drag Coefficient is a dimensionless parameter that describes a relation between the coefficient of the lift and the aspect ratio.

How to calculate Aspect Ratio given Span Efficiency Factor?

The Aspect Ratio given Span Efficiency Factor formula calculates the aspect ratio of the wing for the actual lift distribution which is a function of the Fourier series, by using the span efficiency factor is calculated using Wing Aspect Ratio = Lift Coefficient^2/(pi*Span Efficiency Factor*Induced Drag Coefficient). To calculate Aspect Ratio given Span Efficiency Factor, you need Lift Coefficient (C_L), Span Efficiency Factor (e_span) & Induced Drag Coefficient (C_D,i). With our tool, you need to enter the respective value for Lift Coefficient, Span Efficiency Factor & Induced Drag 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 Wing Aspect Ratio?

In this formula, Wing Aspect Ratio uses Lift Coefficient, Span Efficiency Factor & Induced Drag Coefficient. We can use 2 other way(s) to calculate the same, which is/are as follows -

Wing Aspect Ratio = 2D Lift Curve Slope/(pi*(2D Lift Curve Slope/Lift Curve Slope-1))
Wing Aspect Ratio = (2D Lift Curve Slope*(1+Induced Lift Slope Factor))/(pi*(2D Lift Curve Slope/Lift Curve Slope-1))

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