Ratio of Length of Arm to Length of Link Calculator

✖Angle of inclination of link to vertical is the angle formed by the intersection of the arm and the x-axis.ⓘ Angle of Inclination of Link to Vertical [β]			+10% -10%
✖Angle of inclination of arm to vertical is the angle formed by the intersection of the arm and the x-axis.ⓘ Angle of Inclination of Arm to Vertical [α]			+10% -10%

✖Ratio of Length of Link to Length of Arm is equal to the ratio of tan of their inclination angle.ⓘ Ratio of Length of Arm to Length of Link [q]

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Formula

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Ratio of Length of Arm to Length of Link

Formula

`"q" = tan("β")/tan("α")`

Example

`"0.700208"=tan("35°")/tan("45°")`

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Ratio of Length of Arm to Length of Link Solution

STEP 0: Pre-Calculation Summary

Formula Used

Ratio of Length of Link to Length of Arm = tan(Angle of Inclination of Link to Vertical)/tan(Angle of Inclination of Arm to Vertical)
q = tan(β)/tan(α)
This formula uses 1 Functions, 3 Variables

Functions Used

tan - The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle., tan(Angle)

Variables Used

Ratio of Length of Link to Length of Arm - Ratio of Length of Link to Length of Arm is equal to the ratio of tan of their inclination angle.
Angle of Inclination of Link to Vertical - (Measured in Radian) - Angle of inclination of link to vertical is the angle formed by the intersection of the arm and the x-axis.
Angle of Inclination of Arm to Vertical - (Measured in Radian) - Angle of inclination of arm to vertical is the angle formed by the intersection of the arm and the x-axis.

STEP 1: Convert Input(s) to Base Unit

Angle of Inclination of Link to Vertical: 35 Degree --> 0.610865238197901 Radian (Check conversion here)
Angle of Inclination of Arm to Vertical: 45 Degree --> 0.785398163397301 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

q = tan(β)/tan(α) --> tan(0.610865238197901)/tan(0.785398163397301)

Evaluating ... ...

q = 0.700207538209746

STEP 3: Convert Result to Output's Unit

0.700207538209746 --> No Conversion Required

FINAL ANSWER

0.700207538209746 ≈ 0.700208 <-- Ratio of Length of Link to Length of Arm

(Calculation completed in 00.004 seconds)

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< 13 Basics of Governor Calculators

Total Downward Force on Sleeve in Wilson-Hartnell Governor

Go Force = Mass on Sleeve*Acceleration due to Gravity+(Tension in the auxiliary spring*Distance of auxiliary spring from mid of lever)/Distance of main spring from mid point of lever

Speed of Rotation in RPM

Go Mean Equilibrium Speed in RPM = 60/(2*pi)*sqrt((tan(Angle b/w axis of radius of rotation & line OA))/Mass of Ball)

Ratio of Length of Arm to Length of Link

Go Ratio of Length of Link to Length of Arm = tan(Angle of Inclination of Link to Vertical)/tan(Angle of Inclination of Arm to Vertical)

Corresponding Radial Force Required at Each Ball for Spring Loaded Governors

Go Corresponding Radial Force Required at Each Ball = (Force Required at Sleeve to Overcome Friction*Length of sleeve arm of lever)/(2*Length of ball arm of lever)

Angle between Axis of Radius of Rotation and Line Joining Point on Curve to Origin O

Go Angle b/w axis of radius of rotation & line OA = atan(Controlling Force/Radius of Rotation if Governor is in Mid-Position)

Angle between Axis of Radius of Rotation and Line Joining Point on Curve to Origin

Go Angle b/w axis of radius of rotation & line OA = atan(Mass of Ball*Mean Equilibrium Angular Speed^2)

Mean Equilibrium Speed in RPM

Go Mean Equilibrium Speed in RPM = (Minimum equilibrium speed in r.p.m+Maximum equilibrium speed in r.p.m)/2

Mean Equilibrium Angular Speed

Go Mean Equilibrium Angular Speed = (Minimum equilibrium angular speed+Maximum equilibrium angular speed)/2

Sleeve Load for Decrease in Speed Value when Taking Friction into Account

Go Sleeve load for decrease in speed = Total load on sleeve-Force Required at Sleeve to Overcome Friction

Sleeve Load for Increase in Speed Value when Taking Friction into Account

Go Sleeve load for increase in speed = Total load on sleeve+Force Required at Sleeve to Overcome Friction

Increased Speed

Go Increased Speed = Mean Equilibrium Speed in RPM*(1+Percentage Increase in Speed)

Governor Power

Go Power = Mean Effort*Lift of Sleeve

Height of Watt Governor

Go Height of Governor = 895/(Speed in RPM^2)

Ratio of Length of Arm to Length of Link Formula

Ratio of Length of Link to Length of Arm = tan(Angle of Inclination of Link to Vertical)/tan(Angle of Inclination of Arm to Vertical)
q = tan(β)/tan(α)

What is governor?

A governor is a system that is used to maintain the mean speed of an engine, within certain limits, under fluctuating load conditions. It does this by regulating and controlling the amount of fuel supplied to the engine.

How to Calculate Ratio of Length of Arm to Length of Link?

Ratio of Length of Arm to Length of Link calculator uses Ratio of Length of Link to Length of Arm = tan(Angle of Inclination of Link to Vertical)/tan(Angle of Inclination of Arm to Vertical) to calculate the Ratio of Length of Link to Length of Arm, The Ratio of Length of Arm to Length of Link is equal to the ratio of tan of their inclination angle. Ratio of Length of Link to Length of Arm is denoted by q symbol.

How to calculate Ratio of Length of Arm to Length of Link using this online calculator? To use this online calculator for Ratio of Length of Arm to Length of Link, enter Angle of Inclination of Link to Vertical (β) & Angle of Inclination of Arm to Vertical (α) and hit the calculate button. Here is how the Ratio of Length of Arm to Length of Link calculation can be explained with given input values -> 0.700208 = tan(0.610865238197901)/tan(0.785398163397301).

FAQ

What is Ratio of Length of Arm to Length of Link?

The Ratio of Length of Arm to Length of Link is equal to the ratio of tan of their inclination angle and is represented as q = tan(β)/tan(α) or Ratio of Length of Link to Length of Arm = tan(Angle of Inclination of Link to Vertical)/tan(Angle of Inclination of Arm to Vertical). Angle of inclination of link to vertical is the angle formed by the intersection of the arm and the x-axis & Angle of inclination of arm to vertical is the angle formed by the intersection of the arm and the x-axis.

How to calculate Ratio of Length of Arm to Length of Link?

The Ratio of Length of Arm to Length of Link is equal to the ratio of tan of their inclination angle is calculated using Ratio of Length of Link to Length of Arm = tan(Angle of Inclination of Link to Vertical)/tan(Angle of Inclination of Arm to Vertical). To calculate Ratio of Length of Arm to Length of Link, you need Angle of Inclination of Link to Vertical (β) & Angle of Inclination of Arm to Vertical (α). With our tool, you need to enter the respective value for Angle of Inclination of Link to Vertical & Angle of Inclination of Arm to Vertical and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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