Induced Drag for Wings having Elliptic Lift Distribution Calculator

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Introduction and Governing Equations

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Lift and Drag Polar

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Preliminary Aerodynamics

✖Lift force is the component of the total force acting on a body that is perpendicular to the direction of the fluid flow.ⓘ Lift Force [F_L]			+10% -10%
✖Dynamic pressure, also referred to as velocity pressure, is a specific type of pressure associated with the kinetic energy per unit volume of a moving fluid.ⓘ Dynamic Pressure [q]			+10% -10%
✖Lateral plane span is set of all linear combinations of 2 non-parallel vectors u and v is called the span of u and v.ⓘ Lateral plane span [b_W]			+10% -10%

✖Induced drag is primarily caused by the formation of wingtip vortices, which are created due to the pressure difference between the upper and lower surfaces of a lifting wing.ⓘ Induced Drag for Wings having Elliptic Lift Distribution [D_i]

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Formula

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Induced Drag for Wings having Elliptic Lift Distribution

Formula

`"D"_{"i"} = ("F"_{"L"}^2)/(3.14*"q"*"b"_{"W"}^2)`

Example

`"0.015605N"=(("10.5N")^2)/(3.14*"10Pa"*("15m")^2)`

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Induced Drag for Wings having Elliptic Lift Distribution Solution

STEP 0: Pre-Calculation Summary

Formula Used

Induced Drag = (Lift Force^2)/(3.14*Dynamic Pressure*Lateral plane span^2)
D_i = (F_L^2)/(3.14*q*b_W^2)
This formula uses 4 Variables

Variables Used

Induced Drag - (Measured in Newton) - Induced drag is primarily caused by the formation of wingtip vortices, which are created due to the pressure difference between the upper and lower surfaces of a lifting wing.
Lift Force - (Measured in Newton) - Lift force is the component of the total force acting on a body that is perpendicular to the direction of the fluid flow.
Dynamic Pressure - (Measured in Pascal) - Dynamic pressure, also referred to as velocity pressure, is a specific type of pressure associated with the kinetic energy per unit volume of a moving fluid.
Lateral plane span - (Measured in Meter) - Lateral plane span is set of all linear combinations of 2 non-parallel vectors u and v is called the span of u and v.

STEP 1: Convert Input(s) to Base Unit

Lift Force: 10.5 Newton --> 10.5 Newton No Conversion Required
Dynamic Pressure: 10 Pascal --> 10 Pascal No Conversion Required
Lateral plane span: 15 Meter --> 15 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

D_i = (F_L^2)/(3.14*q*b_W^2) --> (10.5^2)/(3.14*10*15^2)

Evaluating ... ...

D_i = 0.0156050955414013

STEP 3: Convert Result to Output's Unit

0.0156050955414013 Newton --> No Conversion Required

FINAL ANSWER

0.0156050955414013 ≈ 0.015605 Newton <-- Induced Drag

(Calculation completed in 00.020 seconds)

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National Institute of Technology, Hamirpur (NITH), Himachal Pradesh

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< 21 Lift and Drag Polar Calculators

Drag Coefficient for given zero-lift drag coefficient

Go Drag Coefficient = Zero-lift drag coefficient+((Lift Coefficient^2)/(pi*Oswald Efficiency Factor*Aspect Ratio of a wing))

Drag Coefficient for given parasite drag coefficient

Go Drag Coefficient = Parasite Drag coefficient+((Lift Coefficient^2)/(pi*Oswald Efficiency Factor*Aspect Ratio of a wing))

Coefficient of Drag due to lift

Go Coefficient of drag due to lift = (Lift Coefficient^2)/(pi*Oswald Efficiency Factor*Aspect Ratio of a wing)

Modern Lift Equation

Go Lift on Airfoil = (Lift Coefficient*Air Density*Aircraft Gross Wing Area*Fluid Velocity^2)/2

Induced drag given span efficiency factor

Go Induced Drag = Drag Coefficient*Density of Material*Velocity^2*Reference Area/2

Lift given induced drag

Go Lift Force = sqrt(Induced Drag*3.14*Dynamic Pressure*Lateral plane span^2)

Induced Drag for Wings having Elliptic Lift Distribution

Go Induced Drag = (Lift Force^2)/(3.14*Dynamic Pressure*Lateral plane span^2)

Coefficient of lift given drag

Go Lift Coefficient = (Gross Weight*Drag Coefficient)/Drag Force

Coefficient of drag given drag

Go Drag Coefficient = (Lift Coefficient*Drag Force)/Gross Weight

Drag

Go Drag Force = Gross Weight/Lift Coefficient/Drag Coefficient

Lift coefficient given drag coefficient

Go Lift Coefficient = Lift Force/Drag Force*Drag Coefficient

Drag coefficient given lift coefficient

Go Drag Coefficient = Lift Coefficient*Drag Force/Lift Force

Lift given drag coefficient

Go Lift Force = Lift Coefficient/Drag Coefficient*Drag Force

Drag given lift coefficient

Go Drag Force = Lift Force*Drag Coefficient/Lift Coefficient

Parasite Drag Coefficient at zero lift

Go Zero-lift drag coefficient = Drag Coefficient-Coefficient of drag due to lift

Lift given lift coefficient

Go Lift Force = Lift Coefficient*Dynamic Pressure

Drag given drag coefficient

Go Drag Force = Drag Coefficient*Dynamic Pressure

Lift coefficient new

Go Lift Coefficient = Lift Force/Dynamic Pressure

Drag coefficient new

Go Drag Coefficient = Drag Force/Dynamic Pressure

Lift given aerodynamic force

Go Lift Force = Aerodynamic Force-Drag Force

Drag given aerodynamic force

Go Drag Force = Aerodynamic Force-Lift Force

Induced Drag for Wings having Elliptic Lift Distribution Formula

Induced Drag = (Lift Force^2)/(3.14*Dynamic Pressure*Lateral plane span^2)
D_i = (F_L^2)/(3.14*q*b_W^2)

What is induced drag?

Induced Drag is an inevitable consequence of lift and is produced by the passage of an aerofoil (e.g. wing or tailplane) through the air. Air flowing over the top of a wing tends to flow inwards because the decreased pressure over the top surface is less than the pressure outside the wing tip.

How to Calculate Induced Drag for Wings having Elliptic Lift Distribution?

Induced Drag for Wings having Elliptic Lift Distribution calculator uses Induced Drag = (Lift Force^2)/(3.14*Dynamic Pressure*Lateral plane span^2) to calculate the Induced Drag, Induced Drag for Wings having Elliptic Lift Distribution is defined as the amount of induced downwash in the vicinity of the wing of the plane with acting dynamic pressure. Induced Drag is denoted by D_i symbol.

How to calculate Induced Drag for Wings having Elliptic Lift Distribution using this online calculator? To use this online calculator for Induced Drag for Wings having Elliptic Lift Distribution, enter Lift Force (F_L), Dynamic Pressure (q) & Lateral plane span (b_W) and hit the calculate button. Here is how the Induced Drag for Wings having Elliptic Lift Distribution calculation can be explained with given input values -> 0.015605 = (10.5^2)/(3.14*10*15^2).

FAQ

What is Induced Drag for Wings having Elliptic Lift Distribution?

Induced Drag for Wings having Elliptic Lift Distribution is defined as the amount of induced downwash in the vicinity of the wing of the plane with acting dynamic pressure and is represented as D_i = (F_L^2)/(3.14*q*b_W^2) or Induced Drag = (Lift Force^2)/(3.14*Dynamic Pressure*Lateral plane span^2). Lift force is the component of the total force acting on a body that is perpendicular to the direction of the fluid flow, Dynamic pressure, also referred to as velocity pressure, is a specific type of pressure associated with the kinetic energy per unit volume of a moving fluid & Lateral plane span is set of all linear combinations of 2 non-parallel vectors u and v is called the span of u and v.

How to calculate Induced Drag for Wings having Elliptic Lift Distribution?

Induced Drag for Wings having Elliptic Lift Distribution is defined as the amount of induced downwash in the vicinity of the wing of the plane with acting dynamic pressure is calculated using Induced Drag = (Lift Force^2)/(3.14*Dynamic Pressure*Lateral plane span^2). To calculate Induced Drag for Wings having Elliptic Lift Distribution, you need Lift Force (F_L), Dynamic Pressure (q) & Lateral plane span (b_W). With our tool, you need to enter the respective value for Lift Force, Dynamic Pressure & Lateral plane span 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 Induced Drag?

In this formula, Induced Drag uses Lift Force, Dynamic Pressure & Lateral plane span. We can use 1 other way(s) to calculate the same, which is/are as follows -

Induced Drag = Drag Coefficient*Density of Material*Velocity^2*Reference Area/2

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