Lift at given Distance along Wingspan Solution

STEP 0: Pre-Calculation Summary
Formula Used
Lift at Distance = Freestream Density*Freestream Velocity*Circulation at Origin*sqrt(1-(2*Distance from Center to Point/Wingspan)^2)
L = ρ*V*Γo*sqrt(1-(2*a/b)^2)
This formula uses 1 Functions, 6 Variables
Functions Used
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)
Variables Used
Lift at Distance - (Measured in Newton) - The Lift at Distance is the sum of all the forces at that point which causes it to move perpendicular to the direction of flow.
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.
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.
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.
Distance from Center to Point - (Measured in Meter) - Distance from center to point is the length of line segment measured from the center of a body to a particular point.
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.
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
Freestream Velocity: 15.5 Meter per Second --> 15.5 Meter per Second No Conversion Required
Circulation at Origin: 14 Square Meter per Second --> 14 Square Meter per Second No Conversion Required
Distance from Center to Point: 16.4 Millimeter --> 0.0164 Meter (Check conversion here)
Wingspan: 2340 Millimeter --> 2.34 Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
L = ρ*Vo*sqrt(1-(2*a/b)^2) --> 1.225*15.5*14*sqrt(1-(2*0.0164/2.34)^2)
Evaluating ... ...
L = 265.798884212059
STEP 3: Convert Result to Output's Unit
265.798884212059 Newton --> No Conversion Required
FINAL ANSWER
265.798884212059 265.7989 Newton <-- Lift at Distance
(Calculation completed in 00.004 seconds)

Credits

Created by Ravi Khiyani
Shri Govindram Seksaria Institute of Technology and Science (SGSITS), Indore
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National Institute Of Technology (NIT), Hamirpur
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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

Lift at given Distance along Wingspan Formula

Lift at Distance = Freestream Density*Freestream Velocity*Circulation at Origin*sqrt(1-(2*Distance from Center to Point/Wingspan)^2)
L = ρ*V*Γo*sqrt(1-(2*a/b)^2)

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 Lift at given Distance along Wingspan?

Lift at given Distance along Wingspan calculator uses Lift at Distance = Freestream Density*Freestream Velocity*Circulation at Origin*sqrt(1-(2*Distance from Center to Point/Wingspan)^2) to calculate the Lift at Distance, The Lift at given Distance along Wingspan formula calculates the lift for the elliptical lift distribution along the wingspan at the given point from the center of the elliptical distribution. Lift at Distance is denoted by L symbol.

How to calculate Lift at given Distance along Wingspan using this online calculator? To use this online calculator for Lift at given Distance along Wingspan, enter Freestream Density ), Freestream Velocity (V), Circulation at Origin o), Distance from Center to Point (a) & Wingspan (b) and hit the calculate button. Here is how the Lift at given Distance along Wingspan calculation can be explained with given input values -> 265.7989 = 1.225*15.5*14*sqrt(1-(2*0.0164/2.34)^2).

FAQ

What is Lift at given Distance along Wingspan?
The Lift at given Distance along Wingspan formula calculates the lift for the elliptical lift distribution along the wingspan at the given point from the center of the elliptical distribution and is represented as L = ρ*Vo*sqrt(1-(2*a/b)^2) or Lift at Distance = Freestream Density*Freestream Velocity*Circulation at Origin*sqrt(1-(2*Distance from Center to Point/Wingspan)^2). Freestream Density is the mass per unit volume of air far upstream of an aerodynamic body at a given altitude, 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, Circulation at Origin is the circulation when the origin is taken at the center of the bound vortex, Distance from center to point is the length of line segment measured from the center of a body to a particular point & The Wingspan (or just span) of a bird or an airplane is the distance from one wingtip to the other wingtip.
How to calculate Lift at given Distance along Wingspan?
The Lift at given Distance along Wingspan formula calculates the lift for the elliptical lift distribution along the wingspan at the given point from the center of the elliptical distribution is calculated using Lift at Distance = Freestream Density*Freestream Velocity*Circulation at Origin*sqrt(1-(2*Distance from Center to Point/Wingspan)^2). To calculate Lift at given Distance along Wingspan, you need Freestream Density ), Freestream Velocity (V), Circulation at Origin o), Distance from Center to Point (a) & Wingspan (b). With our tool, you need to enter the respective value for Freestream Density, Freestream Velocity, Circulation at Origin, Distance from Center to Point & Wingspan and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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