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Gearing Ratio Formula

GoGearing Ratio for given Stick Force Formula

GoGearing Ratio given Hinge Moment Coefficient Formula

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Gearing Ratio is a measure of the mechanical advantage provided by the control system of an aircraft. Check FAQs

𝑮 = \frac{δ e}{𝒍 s \cdot δ s}

𝑮 - Gearing Ratio?δ_e - Elevator Deflection Angle?𝒍_s - Stick Length?δ_s - Stick Deflection Angle?

Gearing Ratio Example

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Here is how the Gearing Ratio equation looks like with Values.

Here is how the Gearing Ratio equation looks like with Units.

Here is how the Gearing Ratio equation looks like.

0.9302 = \frac{0.1}{0.215 \cdot 0.5}

0.9302m⁻¹ = \frac{0.1rad}{0.215m \cdot 0.5rad}

0.9302 = \frac{0.1}{0.215 \cdot 0.5}

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Gearing Ratio Solution

Follow our step by step solution on how to calculate Gearing Ratio?

FIRST Step Consider the formula

𝑮 = \frac{δ e}{𝒍 s \cdot δ s}

Next Step Substitute values of Variables

∴

𝑮 = \frac{0.1rad}{0.215m \cdot 0.5rad}

Next Step Prepare to Evaluate

∴

𝑮 = \frac{0.1}{0.215 \cdot 0.5}

Next Step Evaluate

∴

𝑮 = 0.930232558139535m⁻¹

LAST Step Rounding Answer

∴

𝑮 = 0.9302m⁻¹

Gearing Ratio Formula Elements

Variables

Gearing Ratio

Gearing Ratio is a measure of the mechanical advantage provided by the control system of an aircraft.

Symbol: 𝑮

Measurement: Reciprocal LengthUnit: m⁻¹

Note: Value should be greater than 0.

Formulas to find Gearing Ratio

Elevator Deflection Angle

The Elevator Deflection Angle is the angle made by the elevator of an aircraft with the horizontal for an applied stick force.

Symbol: δ_e

Measurement: AngleUnit: rad

Note: Value can be positive or negative.

Formulas to find Elevator Deflection Angle

Stick Length

Stick Length is the length of the control stick (to move the control surface) of an aircraft.

Symbol: 𝒍_s

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Stick Length

Stick Deflection Angle

Stick Deflection Angle is the angle made by the control stick (used to move control surface) of an aircraft with the vertical.

Symbol: δ_s

Measurement: AngleUnit: rad

Note: Value can be positive or negative.

Formulas to find Stick Deflection Angle

Other Formulas to find Gearing Ratio

Go Gearing Ratio for given Stick Force

𝑮 = \frac{𝙁}{𝑯 𝒆}

Go Gearing Ratio given Hinge Moment Coefficient

𝑮 = \frac{𝙁}{Ch e \cdot 0.5 \cdot ρ \cdot V^{2} \cdot S e \cdot c e}

Other formulas in Stick Forces and Hinge Moments category

Go Elevator Hinge moment coefficient

Ch e = \frac{𝑯 𝒆}{0.5 \cdot ρ \cdot V^{2} \cdot S e \cdot c e}

Go Elevator Hinge Moment given Hinge Moment Coefficient

𝑯 𝒆 = Ch e \cdot 0.5 \cdot ρ \cdot V^{2} \cdot S e \cdot c e

Go Flight Velocity given Elevator Hinge Moment Coefficient

V = \sqrt{\frac{𝑯 𝒆}{Ch e \cdot 0.5 \cdot ρ \cdot S e \cdot c e}}

Go Elevator Area given Hinge Moment Coefficient

S e = \frac{𝑯 𝒆}{Ch e \cdot 0.5 \cdot ρ \cdot V^{2} \cdot c e}

How to Evaluate Gearing Ratio?

Gearing Ratio evaluator uses Gearing Ratio = Elevator Deflection Angle/(Stick Length*Stick Deflection Angle) to evaluate the Gearing Ratio, Gearing Ratio is a measure of the mechanical advantage of a control system, calculated by dividing the elevator deflection angle by the product of the stick length and stick deflection angle, providing insight into the system's responsiveness and sensitivity. Gearing Ratio is denoted by 𝑮 symbol.

How to evaluate Gearing Ratio using this online evaluator? To use this online evaluator for Gearing Ratio, enter Elevator Deflection Angle (δ_e), Stick Length (𝒍_s) & Stick Deflection Angle (δ_s) and hit the calculate button.

FAQs on Gearing Ratio

What is the formula to find Gearing Ratio?

The formula of Gearing Ratio is expressed as Gearing Ratio = Elevator Deflection Angle/(Stick Length*Stick Deflection Angle). Here is an example- 0.930233 = 0.1/(0.215*0.5).

How to calculate Gearing Ratio?

With Elevator Deflection Angle (δ_e), Stick Length (𝒍_s) & Stick Deflection Angle (δ_s) we can find Gearing Ratio using the formula - Gearing Ratio = Elevator Deflection Angle/(Stick Length*Stick Deflection Angle).

What are the other ways to Calculate Gearing Ratio?

Here are the different ways to Calculate Gearing Ratio-

Gearing Ratio=Stick Force/Hinge Moment
Gearing Ratio=Stick Force/(Hinge Moment Coefficient*0.5*Density*Flight Velocity^2*Elevator Area*Elevator Chord)

Can the Gearing Ratio be negative?

No, the Gearing Ratio, measured in Reciprocal Length cannot be negative.

Which unit is used to measure Gearing Ratio?

Gearing Ratio is usually measured using the 1 per Meter[m⁻¹] for Reciprocal Length. 1 per Kilometer[m⁻¹], 1 per Mile[m⁻¹], 1 per Yard[m⁻¹] are the few other units in which Gearing Ratio can be measured.

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