Freestream Velocity given Circulation at Origin 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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Lift Distribution

Elementary Flows

Flow and Lift Distribution

Flow over Airfoils and Wings

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Elliptical Lift Distribution

General Lift Distribution

✖The Wingspan (or just span) of a bird or an airplane is the distance from one wingtip to the other wingtip.ⓘ Wingspan [b]			+10% -10%
✖Circulation at Origin is the circulation when the origin is taken at the center of the bound vortex.ⓘ Circulation at Origin [Γ_o]			+10% -10%
✖Reference Area Origin 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.ⓘ Reference Area Origin [S₀]			+10% -10%
✖The Lift Coefficient ELD 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 ELD [C_L,ELD]			+10% -10%

✖The Freestream Velocity is the velocity of air far upstream of an aerodynamic body, that is before the body has a chance to deflect, slow down or compress the air.ⓘ Freestream Velocity given Circulation at Origin [V_∞]

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Formula

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Freestream Velocity given Circulation at Origin

Formula

`"V"_{"∞"} = pi*"b"*"Γ"_{"o"}/(2*"S"_{"0"}*"C"_{"L,ELD"})`

Example

`"15.62735m/s"=pi*"2340mm"*"14m²/s"/(2*"2.21m²"*"1.49")`

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Freestream Velocity given Circulation at Origin Solution

STEP 0: Pre-Calculation Summary

Formula Used

Freestream Velocity = pi*Wingspan*Circulation at Origin/(2*Reference Area Origin*Lift Coefficient ELD)
V_∞ = pi*b*Γ_o/(2*S₀*C_L,ELD)
This formula uses 1 Constants, 5 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Freestream Velocity - (Measured in Meter per Second) - The Freestream Velocity is the velocity of air far upstream of an aerodynamic body, that is before the body has a chance to deflect, slow down or compress the air.
Wingspan - (Measured in Meter) - The Wingspan (or just span) of a bird or an airplane is the distance from one wingtip to the other wingtip.
Circulation at Origin - (Measured in Square Meter per Second) - Circulation at Origin is the circulation when the origin is taken at the center of the bound vortex.
Reference Area Origin - (Measured in Square Meter) - Reference Area Origin 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.
Lift Coefficient ELD - The Lift Coefficient ELD 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

Wingspan: 2340 Millimeter --> 2.34 Meter (Check conversion here)
Circulation at Origin: 14 Square Meter per Second --> 14 Square Meter per Second No Conversion Required
Reference Area Origin: 2.21 Square Meter --> 2.21 Square Meter No Conversion Required
Lift Coefficient ELD: 1.49 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V_∞ = pi*b*Γ_o/(2*S₀*C_L,ELD) --> pi*2.34*14/(2*2.21*1.49)

Evaluating ... ...

V_∞ = 15.6273460068028

STEP 3: Convert Result to Output's Unit

15.6273460068028 Meter per Second --> No Conversion Required

FINAL ANSWER

15.6273460068028 ≈ 15.62735 Meter per Second <-- Freestream Velocity

(Calculation completed in 00.004 seconds)

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< 20 Elliptical Lift Distribution Calculators

Lift at given Distance along Wingspan

Go Lift at Distance = Freestream Density*Freestream Velocity*Circulation at Origin*sqrt(1-(2*Distance from Center to Point/Wingspan)^2)

Circulation at Origin in Elliptical Lift Distribution

Go Circulation at Origin = 2*Freestream Velocity*Reference Area Origin*Lift Coefficient Origin/(pi*Wingspan)

Coefficient of Lift given Circulation at Origin

Go Lift Coefficient ELD = pi*Wingspan*Circulation at Origin/(2*Freestream Velocity*Reference Area Origin)

Freestream Velocity given Circulation at Origin

Go Freestream Velocity = pi*Wingspan*Circulation at Origin/(2*Reference Area Origin*Lift Coefficient ELD)

Lift of Wing given Circulation at Origin

Go Lift Force = (pi*Freestream Density*Freestream Velocity*Wingspan*Circulation at Origin)/4

Circulation at Origin given Lift of Wing

Go Circulation at Origin = 4*Lift Force/(Freestream Density*Freestream Velocity*Wingspan*pi)

Induced Angle of Attack given Coefficient of Lift

Go Induced Angle of Attack = Reference Area Origin*Lift Coefficient Origin/(pi*Wingspan^2)

Circulation at given Distance along Wingspan

Go Circulation = Circulation at Origin*sqrt(1-(2*Distance from Center to Point/Wingspan)^2)

Coefficient of Lift given Induced Drag Coefficient

Go Lift Coefficient ELD = sqrt(pi*Wing Aspect Ratio ELD*Induced Drag Coefficient ELD)

Aspect Ratio given Induced Drag Coefficient

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

Induced Drag Coefficient given Aspect Ratio

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

Induced Angle of Attack given Circulation at Origin

Go Induced Angle of Attack = Circulation at Origin/(2*Wingspan*Freestream Velocity)

Freestream Velocity given Induced Angle of Attack

Go Freestream Velocity = Circulation at Origin/(2*Wingspan*Induced Angle of Attack)

Circulation at Origin given Induced Angle of Attack

Go Circulation at Origin = 2*Wingspan*Induced Angle of Attack*Freestream Velocity

Induced Angle of Attack given Aspect Ratio

Go Induced Angle of Attack = Lift Coefficient Origin/(pi*Wing Aspect Ratio ELD)

Aspect Ratio given Induced Angle of Attack

Go Wing Aspect Ratio ELD = Lift Coefficient ELD/(pi*Induced Angle of Attack)

Coefficient of Lift given Induced Angle of Attack

Go Lift Coefficient ELD = pi*Induced Angle of Attack*Wing Aspect Ratio ELD

Induced Angle of Attack given Downwash

Go Induced Angle of Attack = -(Downwash/Freestream Velocity)

Downwash in Elliptical Lift Distribution

Go Downwash = -Circulation at Origin/(2*Wingspan)

Circulation at Origin given Downwash

Go Circulation at Origin = -2*Downwash*Wingspan

Freestream Velocity given Circulation at Origin Formula

Freestream Velocity = pi*Wingspan*Circulation at Origin/(2*Reference Area Origin*Lift Coefficient ELD)
V_∞ = pi*b*Γ_o/(2*S₀*C_L,ELD)

Why is an elliptical lift distribution ideal?

The energy in that vortex appears to the aircraft as 'lift induced drag'. The aerodynamicist tries to design the tip to keep induced drag low. An elliptical lift distribution is best for this purpose. The shape producing this varies with speed, altitude, and other factors, so tips vary from design to design.

How to Calculate Freestream Velocity given Circulation at Origin?

Freestream Velocity given Circulation at Origin calculator uses Freestream Velocity = pi*Wingspan*Circulation at Origin/(2*Reference Area Origin*Lift Coefficient ELD) to calculate the Freestream Velocity, The freestream velocity given circulation at origin formula calculates the velocity of the fluid flowing around the wing when the circulation at the origin is given which is constant for the elliptical lift distribution. Freestream Velocity is denoted by V_∞ symbol.

How to calculate Freestream Velocity given Circulation at Origin using this online calculator? To use this online calculator for Freestream Velocity given Circulation at Origin, enter Wingspan (b), Circulation at Origin (Γ_o), Reference Area Origin (S₀) & Lift Coefficient ELD (C_L,ELD) and hit the calculate button. Here is how the Freestream Velocity given Circulation at Origin calculation can be explained with given input values -> 15.62735 = pi*2.34*14/(2*2.21*1.49).

FAQ

What is Freestream Velocity given Circulation at Origin?

The freestream velocity given circulation at origin formula calculates the velocity of the fluid flowing around the wing when the circulation at the origin is given which is constant for the elliptical lift distribution and is represented as V_∞ = pi*b*Γ_o/(2*S₀*C_L,ELD) or Freestream Velocity = pi*Wingspan*Circulation at Origin/(2*Reference Area Origin*Lift Coefficient ELD). The Wingspan (or just span) of a bird or an airplane is the distance from one wingtip to the other wingtip, Circulation at Origin is the circulation when the origin is taken at the center of the bound vortex, Reference Area Origin 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 & The Lift Coefficient ELD 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 Freestream Velocity given Circulation at Origin?

The freestream velocity given circulation at origin formula calculates the velocity of the fluid flowing around the wing when the circulation at the origin is given which is constant for the elliptical lift distribution is calculated using Freestream Velocity = pi*Wingspan*Circulation at Origin/(2*Reference Area Origin*Lift Coefficient ELD). To calculate Freestream Velocity given Circulation at Origin, you need Wingspan (b), Circulation at Origin (Γ_o), Reference Area Origin (S₀) & Lift Coefficient ELD (C_L,ELD). With our tool, you need to enter the respective value for Wingspan, Circulation at Origin, Reference Area Origin & Lift Coefficient ELD 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 Freestream Velocity?

In this formula, Freestream Velocity uses Wingspan, Circulation at Origin, Reference Area Origin & Lift Coefficient ELD. We can use 1 other way(s) to calculate the same, which is/are as follows -

Freestream Velocity = Circulation at Origin/(2*Wingspan*Induced Angle of Attack)

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