Gearing ratio Calculator

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Static Stability and Control

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Stick Forces and Hinge Moments

✖The elevator deflection angle is the angle made by the elevator of an aircraft with the horizontal for an applied stick force.ⓘ Elevator Deflection Angle [δ_e]			+10% -10%
✖Stick length is the length of the control stick (to move the control surface) of an aircraft.ⓘ Stick Length [𝒍_s]			+10% -10%
✖Stick deflection angle is the angle made by the control stick (used to move control surface) of an aircraft with the vertical.ⓘ Stick Deflection Angle [δ_s]			+10% -10%

✖Gearing ratio is a measure of the mechanical advantage provided by the control system of an aircraft.ⓘ Gearing ratio [𝑮]

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Formula

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Gearing ratio

Formula

`"𝑮" = "δ"_{"e"}/("𝒍"_{"s"}*"δ"_{"s"})`

Example

`"0.930233m⁻¹"="0.1rad"/("0.215m"*"0.5rad")`

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Gearing ratio Solution

STEP 0: Pre-Calculation Summary

Formula Used

Gearing Ratio = Elevator Deflection Angle/(Stick Length*Stick Deflection Angle)
𝑮 = δ_e/(𝒍_s*δ_s)
This formula uses 4 Variables

Variables Used

Gearing Ratio - (Measured in 1 per Meter) - Gearing ratio is a measure of the mechanical advantage provided by the control system of an aircraft.
Elevator Deflection Angle - (Measured in Radian) - The elevator deflection angle is the angle made by the elevator of an aircraft with the horizontal for an applied stick force.
Stick Length - (Measured in Meter) - Stick length is the length of the control stick (to move the control surface) of an aircraft.
Stick Deflection Angle - (Measured in Radian) - Stick deflection angle is the angle made by the control stick (used to move control surface) of an aircraft with the vertical.

STEP 1: Convert Input(s) to Base Unit

Elevator Deflection Angle: 0.1 Radian --> 0.1 Radian No Conversion Required
Stick Length: 0.215 Meter --> 0.215 Meter No Conversion Required
Stick Deflection Angle: 0.5 Radian --> 0.5 Radian No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

𝑮 = δ_e/(𝒍_s*δ_s) --> 0.1/(0.215*0.5)

Evaluating ... ...

𝑮 = 0.930232558139535

STEP 3: Convert Result to Output's Unit

0.930232558139535 1 per Meter --> No Conversion Required

FINAL ANSWER

0.930232558139535 ≈ 0.930233 1 per Meter <-- Gearing Ratio

(Calculation completed in 00.004 seconds)

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Credits

Created by Vinay Mishra

Indian Institute for Aeronautical Engineering and Information Technology (IIAEIT), Pune

Vinay Mishra has created this Calculator and 300+ more calculators!

Verified by Maiarutselvan V

PSG College of Technology (PSGCT), Coimbatore

Maiarutselvan V has verified this Calculator and 300+ more calculators!

< 23 Stick Forces and Hinge Moments Calculators

Flight velocity for given stick force

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

Gearing Ratio given Hinge Moment Coefficient

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

Hinge Moment Coefficient given Stick Force

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

Elevator Chord Length given Stick Force

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

Elevator Area given Stick Force

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

Elevator Stick Force Given Hinge Moment Coefficient

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

Flight Velocity given Elevator Hinge Moment Coefficient

Go Flight Velocity = sqrt(Hinge Moment/(Hinge Moment Coefficient*0.5*Density*Elevator Area*Elevator Chord))

Elevator Chord Length given Hinge Moment Coefficient

Go Elevator Chord = Hinge Moment/(Hinge Moment Coefficient*0.5*Density*Flight Velocity^2*Elevator Area)

Elevator Area given Hinge Moment Coefficient

Go Elevator Area = Hinge Moment/(Hinge Moment Coefficient*0.5*Density*Flight Velocity^2*Elevator Chord)

Elevator Hinge moment coefficient

Go Hinge Moment Coefficient = Hinge Moment/(0.5*Density*Flight Velocity^2*Elevator Area*Elevator Chord)

Elevator Hinge Moment given Hinge Moment Coefficient

Go Hinge Moment = Hinge Moment Coefficient*0.5*Density*Flight Velocity^2*Elevator Area*Elevator Chord

Stick deflection angle for given stick force

Go Stick Deflection Angle = Hinge Moment*Elevator Deflection Angle/(Stick Force*Stick Length)

Stick length for given stick force

Go Stick Length = Hinge Moment*Elevator Deflection Angle/(Stick Force*Stick Deflection Angle)

Elevator Stick Force

Go Stick Force = Elevator Deflection Angle*Hinge Moment/(Stick Length*Stick Deflection Angle)

Elevator deflection angle for given stick force

Go Elevator Deflection Angle = Stick Force*Stick Length*Stick Deflection Angle/Hinge Moment

Hinge moment for given stick force

Go Hinge Moment = Stick Force*Stick Length*Stick Deflection Angle/Elevator Deflection Angle

Stick deflection angle for given gearing ratio

Go Stick Deflection Angle = Elevator Deflection Angle/(Stick Length*Gearing Ratio)

Control stick length for given gearing ratio

Go Stick Length = Elevator Deflection Angle/(Gearing Ratio*Stick Deflection Angle)

Gearing ratio

Go Gearing Ratio = Elevator Deflection Angle/(Stick Length*Stick Deflection Angle)

Elevator Deflection Angle given Gearing Ratio

Go Elevator Deflection Angle = Gearing Ratio*Stick Length*Stick Deflection Angle

Elevator Stick Force given Gearing Ratio

Go Stick Force = Gearing Ratio*Hinge Moment

Hinge moment for given gearing ratio

Go Hinge Moment = Stick Force/Gearing Ratio

Gearing ratio for given stick force

Go Gearing Ratio = Stick Force/Hinge Moment

Gearing ratio Formula

Gearing Ratio = Elevator Deflection Angle/(Stick Length*Stick Deflection Angle)
𝑮 = δ_e/(𝒍_s*δ_s)

What are the two requirements for longitudinal static stability?

The center of gravity must lie ahead of the neutral point for positive stability (positive static margin).

How to Calculate Gearing ratio?

Gearing ratio calculator uses Gearing Ratio = Elevator Deflection Angle/(Stick Length*Stick Deflection Angle) to calculate the Gearing Ratio, The Gearing ratio is a function of elevator deflection angle, stick length and stick deflection angle. Gearing Ratio is denoted by 𝑮 symbol.

How to calculate Gearing ratio using this online calculator? To use this online calculator for Gearing ratio, enter Elevator Deflection Angle (δ_e), Stick Length (𝒍_s) & Stick Deflection Angle (δ_s) and hit the calculate button. Here is how the Gearing ratio calculation can be explained with given input values -> 0.5 = 0.1/(0.215*0.5).

FAQ

What is Gearing ratio?

The Gearing ratio is a function of elevator deflection angle, stick length and stick deflection angle and is represented as 𝑮 = δ_e/(𝒍_s*δ_s) or Gearing Ratio = Elevator Deflection Angle/(Stick Length*Stick Deflection Angle). The elevator deflection angle is the angle made by the elevator of an aircraft with the horizontal for an applied stick force, Stick length is the length of the control stick (to move the control surface) of an aircraft & Stick deflection angle is the angle made by the control stick (used to move control surface) of an aircraft with the vertical.

How to calculate Gearing ratio?

The Gearing ratio is a function of elevator deflection angle, stick length and stick deflection angle is calculated using Gearing Ratio = Elevator Deflection Angle/(Stick Length*Stick Deflection Angle). To calculate Gearing ratio, you need Elevator Deflection Angle (δ_e), Stick Length (𝒍_s) & Stick Deflection Angle (δ_s). With our tool, you need to enter the respective value for Elevator Deflection Angle, Stick Length & Stick Deflection Angle and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Gearing Ratio?

In this formula, Gearing Ratio uses Elevator Deflection Angle, Stick Length & Stick Deflection Angle. We can use 2 other way(s) to calculate the same, which is/are as follows -

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

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