Gearing Ratio Given Hinge Moment Coefficient Calculator

Gearing Ratio Formula:

\[ Gearing\ Ratio = \frac{Stick\ Force}{C_{he} \times 0.5 \times \rho \times V^2 \times S_e \times c_e} \]

Stick Force:

Newton

Hinge Moment Coefficient:

Density (ρ):

kg/m³

Flight Velocity (V):

m/s

Elevator Area (Sₑ):

m²

Elevator Chord (cₑ):

Gearing Ratio:

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1. What is Gearing Ratio?

Gearing Ratio is a measure of the mechanical advantage provided by the control system of an aircraft. It represents the relationship between the stick force applied by the pilot and the resulting hinge moment on the control surface.

2. How Does the Calculator Work?

The calculator uses the Gearing Ratio formula:

\[ Gearing\ Ratio = \frac{Stick\ Force}{C_{he} \times 0.5 \times \rho \times V^2 \times S_e \times c_e} \]

Where:

\( Stick\ Force \) — Force exerted on the control column (Newton)
\( C_{he} \) — Hinge Moment Coefficient
\( \rho \) — Density of the fluid (kg/m³)
\( V \) — Flight Velocity (m/s)
\( S_e \) — Elevator Area (m²)
\( c_e \) — Elevator Chord (m)

Explanation: The formula calculates the mechanical advantage in the aircraft's control system by considering aerodynamic forces and control surface characteristics.

3. Importance of Gearing Ratio Calculation

Details: Accurate Gearing Ratio calculation is crucial for aircraft control system design, ensuring proper force feedback to the pilot, and maintaining flight stability and control characteristics.

4. Using the Calculator

Tips: Enter all values in appropriate units. Stick force in Newtons, density in kg/m³, velocity in m/s, elevator area in m², and elevator chord in meters. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of Gearing Ratio in aircraft design?
A: Gearing Ratio determines the mechanical advantage in the control system, affecting pilot workload and aircraft handling characteristics.

Q2: How does Hinge Moment Coefficient affect Gearing Ratio?
A: Higher hinge moment coefficients require more stick force for the same control surface deflection, resulting in different gearing ratios.

Q3: What are typical values for Gearing Ratio?
A: Gearing Ratio values vary significantly depending on aircraft type and control system design, typically ranging from 0.1 to 10 1/m.

Q4: How does flight velocity affect Gearing Ratio?
A: Higher flight velocities increase aerodynamic forces, which affects the hinge moment and consequently the gearing ratio.

Q5: Can this calculator be used for other control surfaces?
A: While specifically designed for elevators, the same principle can be applied to ailerons and rudders with appropriate coefficient values.