Induced Angle of Attack given Coefficient of Lift Solution

STEP 0: Pre-Calculation Summary
Formula Used
Induced Angle of Attack = Reference Area Origin*Lift Coefficient Origin/(pi*Wingspan^2)
αi = S0*Cl/(pi*b^2)
This formula uses 1 Constants, 4 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Variables Used
Induced Angle of Attack - (Measured in Radian) - The Induced Angle of Attack is the angle between the local relative wind and the direction of freestream velocity.
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 Origin - Lift Coefficient Origin 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.
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
Reference Area Origin: 2.21 Square Meter --> 2.21 Square Meter No Conversion Required
Lift Coefficient Origin: 1.5 --> No Conversion Required
Wingspan: 2340 Millimeter --> 2.34 Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
αi = S0*Cl/(pi*b^2) --> 2.21*1.5/(pi*2.34^2)
Evaluating ... ...
αi = 0.192708976678221
STEP 3: Convert Result to Output's Unit
0.192708976678221 Radian -->11.0414110379491 Degree (Check conversion here)
FINAL ANSWER
11.0414110379491 11.04141 Degree <-- Induced Angle of Attack
(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

Induced Angle of Attack given Coefficient of Lift Formula

Induced Angle of Attack = Reference Area Origin*Lift Coefficient Origin/(pi*Wingspan^2)
αi = S0*Cl/(pi*b^2)

How does angle of attack affect the airfoil?

An increase in the angle of attack results in an increase in both lift and induced drag, up to a point. Too high an angle of attack (usually around 17 degrees) and the airflow across the upper surface of the aerofoil become detached, resulting in a loss of lift, otherwise known as a Stall.

How to Calculate Induced Angle of Attack given Coefficient of Lift?

Induced Angle of Attack given Coefficient of Lift calculator uses Induced Angle of Attack = Reference Area Origin*Lift Coefficient Origin/(pi*Wingspan^2) to calculate the Induced Angle of Attack, The Induced angle of attack given coefficient of lift formula calculates the angle between the direction of the freestream velocity and the local relative wind. Induced Angle of Attack is denoted by αi symbol.

How to calculate Induced Angle of Attack given Coefficient of Lift using this online calculator? To use this online calculator for Induced Angle of Attack given Coefficient of Lift, enter Reference Area Origin (S0), Lift Coefficient Origin (Cl) & Wingspan (b) and hit the calculate button. Here is how the Induced Angle of Attack given Coefficient of Lift calculation can be explained with given input values -> 632.6263 = 2.21*1.5/(pi*2.34^2).

FAQ

What is Induced Angle of Attack given Coefficient of Lift?
The Induced angle of attack given coefficient of lift formula calculates the angle between the direction of the freestream velocity and the local relative wind and is represented as αi = S0*Cl/(pi*b^2) or Induced Angle of Attack = Reference Area Origin*Lift Coefficient Origin/(pi*Wingspan^2). 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 Origin 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 & The Wingspan (or just span) of a bird or an airplane is the distance from one wingtip to the other wingtip.
How to calculate Induced Angle of Attack given Coefficient of Lift?
The Induced angle of attack given coefficient of lift formula calculates the angle between the direction of the freestream velocity and the local relative wind is calculated using Induced Angle of Attack = Reference Area Origin*Lift Coefficient Origin/(pi*Wingspan^2). To calculate Induced Angle of Attack given Coefficient of Lift, you need Reference Area Origin (S0), Lift Coefficient Origin (Cl) & Wingspan (b). With our tool, you need to enter the respective value for Reference Area Origin, Lift Coefficient Origin & Wingspan 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 Angle of Attack?
In this formula, Induced Angle of Attack uses Reference Area Origin, Lift Coefficient Origin & Wingspan. We can use 3 other way(s) to calculate the same, which is/are as follows -
  • Induced Angle of Attack = Lift Coefficient Origin/(pi*Wing Aspect Ratio ELD)
  • Induced Angle of Attack = Circulation at Origin/(2*Wingspan*Freestream Velocity)
  • Induced Angle of Attack = -(Downwash/Freestream Velocity)
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