Vertical Tail Moment Arm For Given Lift Curve Slope Calculator

Formula Used:

\[ l_v = \frac{N_v}{C_v \cdot (\beta + \sigma) \cdot Q_v \cdot S_v} \]

Vertical Tail Moment (Nv):

N·m

Vertical Tail Lift Curve Slope (Cv):

1/rad

Sideslip Angle (β):

rad

Sidewash Angle (σ):

rad

Vertical Tail Dynamic Pressure (Qv):

Vertical Tail Area (Sv):

m²

Vertical Tail Moment Arm (lv):

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1. What is the 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 is a crucial parameter in aircraft stability and control calculations.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ l_v = \frac{N_v}{C_v \cdot (\beta + \sigma) \cdot Q_v \cdot S_v} \]

Where:

\( l_v \) — Vertical Tail Moment Arm (m)
\( N_v \) — Vertical Tail Moment (N·m)
\( C_v \) — Vertical Tail Lift Curve Slope (1/rad)
\( \beta \) — Sideslip Angle (rad)
\( \sigma \) — Sidewash Angle (rad)
\( Q_v \) — Vertical Tail Dynamic Pressure (Pa)
\( S_v \) — Vertical Tail Area (m²)

Explanation: This formula calculates the moment arm by dividing the vertical tail moment by the product of lift curve slope, combined angle (sideslip + sidewash), dynamic pressure, and tail area.

3. Importance of Vertical Tail Moment Arm Calculation

Details: Accurate calculation of the vertical tail moment arm is essential for determining aircraft directional stability and control effectiveness. It helps in designing the vertical tail to provide adequate yawing moment for control and stability.

4. Using the Calculator

Tips: Enter all values in appropriate units. Ensure all inputs are positive values. The sideslip and sidewash angles should be in radians. All parameters must be valid for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of the vertical tail moment arm?
A: The vertical tail moment arm determines the effectiveness of the vertical tail in generating yawing moments for directional stability and control.

Q2: How does sideslip angle affect the calculation?
A: Sideslip angle represents the angle between the aircraft centerline and the relative wind, which affects the side force generated by the vertical tail.

Q3: What is sidewash angle and why is it important?
A: Sidewash angle is caused by flow field distortion due to wings and fuselage. It's analogous to downwash for the horizontal tail and affects the effective angle of attack of the vertical tail.

Q4: How does dynamic pressure affect the moment arm calculation?
A: Dynamic pressure represents the kinetic energy of the airflow and directly affects the aerodynamic forces generated by the vertical tail surface.

Q5: What are typical values for vertical tail moment arm?
A: Typical values vary by aircraft type but generally range from several meters for small aircraft to tens of meters for large transport aircraft.