Induced Angle Of Attack Given Circulation At Origin Calculator

Formula Used:

\[ \alpha_i = \frac{\Gamma_o}{2 \cdot b \cdot V_{\infty}} \]

Induced Angle of Attack (αi):

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1. What is Induced Angle of Attack?

The induced angle of attack is the angle between the local relative wind and the direction of freestream velocity. It results from the downwash produced by the wing's trailing vortices and affects the effective angle of attack experienced by the airfoil sections.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \alpha_i = \frac{\Gamma_o}{2 \cdot b \cdot V_{\infty}} \]

Where:

\( \alpha_i \) — Induced angle of attack (radians)
\( \Gamma_o \) — Circulation at origin (m²/s)
\( b \) — Wingspan (m)
\( V_{\infty} \) — Freestream velocity (m/s)

Explanation: This formula calculates the induced angle of attack based on the circulation at the origin, wingspan, and freestream velocity.

3. Importance of Induced Angle of Attack

Details: Understanding and calculating the induced angle of attack is crucial for aerodynamic analysis, particularly in determining the effective angle of attack and induced drag of aircraft wings. It plays a significant role in wing performance and efficiency calculations.

4. Using the Calculator

Tips: Enter circulation at origin in m²/s, wingspan in meters, and freestream velocity in m/s. All values must be positive numbers greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is circulation in aerodynamics?
A: Circulation is a measure of the rotational component of flow around a body, related to the lift generated by the wing according to the Kutta-Joukowski theorem.

Q2: How does wingspan affect induced angle of attack?
A: Larger wingspans generally result in smaller induced angles of attack, as the downwash effect is distributed over a larger area.

Q3: What is the relationship between induced angle of attack and induced drag?
A: Induced drag is directly related to the induced angle of attack. A larger induced angle of attack typically results in higher induced drag.

Q4: Can induced angle of attack be negative?
A: Typically, induced angle of attack is positive for conventional wing configurations, but certain conditions or wing designs might result in negative values.

Q5: How accurate is this calculation for real-world applications?
A: This formula provides a fundamental theoretical calculation. For precise real-world applications, additional factors such as wing geometry, airfoil characteristics, and flight conditions should be considered.