Vertical Tail Moment Arm For Given Yawing Moment Coefficient Calculator

Formula Used:

\[ l_v = \frac{C_n}{S_v \cdot Q_v \cdot C_v \cdot (\beta + \sigma) / (S \cdot b \cdot Q_w)} \]

Yawing Moment Coefficient (Cn):

Vertical Tail Area (Sv):

m²

Vertical Tail Dynamic Pressure (Qv):

Vertical Tail Lift Curve Slope (Cv):

1/rad

Sideslip Angle (β):

rad

Sidewash Angle (σ):

rad

Reference Area (S):

m²

Wingspan (b):

Wing Dynamic Pressure (Qw):

Vertical Tail Moment Arm (lv):

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1. What is Vertical Tail Moment Arm?

The Vertical Tail Moment Arm is the distance between the centroid of the vertical tail shape and the center of gravity of the aircraft. It represents the lever arm through which the vertical tail forces act to produce yawing moments.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ l_v = \frac{C_n}{S_v \cdot Q_v \cdot C_v \cdot (\beta + \sigma) / (S \cdot b \cdot Q_w)} \]

Where:

\( l_v \) — Vertical Tail Moment Arm (m)
\( C_n \) — Yawing Moment Coefficient
\( S_v \) — Vertical Tail Area (m²)
\( Q_v \) — Vertical Tail Dynamic Pressure (Pa)
\( C_v \) — Vertical Tail Lift Curve Slope (1/rad)
\( \beta \) — Sideslip Angle (rad)
\( \sigma \) — Sidewash Angle (rad)
\( S \) — Reference Area (m²)
\( b \) — Wingspan (m)
\( Q_w \) — Wing Dynamic Pressure (Pa)

Explanation: This formula calculates the moment arm required for the vertical tail to produce a specific yawing moment coefficient given various aerodynamic parameters.

3. Importance of Vertical Tail Moment Arm

Details: The vertical tail moment arm is crucial for aircraft directional stability and control. It determines the effectiveness of the vertical tail in generating yawing moments to counteract disturbances and maintain directional stability.

4. Using the Calculator

Tips: Enter all required parameters with appropriate units. Ensure all values are positive where applicable (areas, pressures, spans, etc.). The calculator will compute the vertical tail moment arm needed to achieve the specified yawing moment coefficient.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of the yawing moment coefficient?
A: The yawing moment coefficient quantifies the aircraft's tendency to rotate about its vertical axis. It's crucial for directional stability and control analysis.

Q2: How does sidewash angle affect the calculation?
A: Sidewash angle, caused by flow field distortion due to wings and fuselage, affects the effective angle of attack seen by the vertical tail, thus influencing its effectiveness.

Q3: What is typical range for vertical tail moment arm?
A: The moment arm varies significantly by aircraft type but generally ranges from several meters for small aircraft to tens of meters for large commercial jets.

Q4: How does dynamic pressure affect the result?
A: Higher dynamic pressure on the vertical tail relative to the wing increases its effectiveness, allowing for a shorter moment arm to achieve the same yawing moment.

Q5: Can this calculator be used for aircraft design?
A: Yes, this calculator is useful for preliminary aircraft design to determine the required vertical tail moment arm for desired directional stability characteristics.