Freestream Velocity Given Induced Angle Of Attack Calculator

Formula Used:

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

Freestream Velocity:

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1. What is Freestream Velocity?

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. It represents the undisturbed flow velocity in the absence of any obstacles or disturbances.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( V_{\infty} \) — Freestream Velocity (m/s)
\( \Gamma_o \) — Circulation at Origin (m²/s)
\( b \) — Wingspan (m)
\( \alpha_i \) — Induced Angle of Attack (rad)

Explanation: This formula calculates the freestream velocity based on circulation, wingspan, and induced angle of attack, which are fundamental parameters in aerodynamic analysis.

3. Importance of Freestream Velocity Calculation

Details: Accurate calculation of freestream velocity is crucial for aerodynamic performance analysis, aircraft design, and understanding the flow characteristics around aerodynamic bodies. It helps in determining lift, drag, and other important aerodynamic properties.

4. Using the Calculator

Tips: Enter circulation at origin in m²/s, wingspan in meters, and induced angle of attack in radians. All values must be positive and valid for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: What is circulation in aerodynamics?
A: Circulation is a fundamental concept in aerodynamics that represents the integral of velocity around a closed loop. It's directly related to the lift generated by an airfoil.

Q2: How does wingspan affect freestream velocity?
A: Larger wingspan typically results in lower induced drag, which can affect the relationship between circulation and freestream velocity in the formula.

Q3: What is induced angle of attack?
A: Induced angle of attack is the angle between the local relative wind and the direction of freestream velocity, caused by the downwash from the wing's trailing vortices.

Q4: Are there limitations to this formula?
A: This formula is based on simplified aerodynamic theory and may have limitations in complex flow situations or when dealing with three-dimensional effects not accounted for in the basic formulation.

Q5: What units should be used for input values?
A: Circulation should be in square meters per second (m²/s), wingspan in meters (m), and induced angle of attack in radians (rad) for consistent results.