Speed of Rotation in RPM Calculator

✖Angle B/W Axis of Radius of Rotation and Line OA is the angle between the axis of rotation of the governor and the line OA, which affects the governor's stability.ⓘ Angle B/W Axis of Radius of Rotation and Line OA [φ]			+10% -10%
✖Mass of Ball is the measure of the amount of matter in a ball, typically measured in units of mass such as grams or kilograms.ⓘ Mass of Ball [m_ball]			+10% -10%

✖Mean Equilibrium Speed in RPM is the speed at which the governor reaches a state of balance, maintaining a stable engine speed under varying loads.ⓘ Speed of Rotation in RPM [N_equillibrium]

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Speed of Rotation in RPM Solution

STEP 0: Pre-Calculation Summary

Formula Used

Mean Equilibrium Speed in RPM = 60/(2*pi)*sqrt((tan(Angle B/W Axis of Radius of Rotation and Line OA))/Mass of Ball)
N_equillibrium = 60/(2*pi)*sqrt((tan(φ))/m_ball)
This formula uses 1 Constants, 2 Functions, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

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)
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Mean Equilibrium Speed in RPM - Mean Equilibrium Speed in RPM is the speed at which the governor reaches a state of balance, maintaining a stable engine speed under varying loads.
Angle B/W Axis of Radius of Rotation and Line OA - (Measured in Radian) - Angle B/W Axis of Radius of Rotation and Line OA is the angle between the axis of rotation of the governor and the line OA, which affects the governor's stability.
Mass of Ball - (Measured in Kilogram) - Mass of Ball is the measure of the amount of matter in a ball, typically measured in units of mass such as grams or kilograms.

STEP 1: Convert Input(s) to Base Unit

Angle B/W Axis of Radius of Rotation and Line OA: 85.6 Degree --> 1.49400183970687 Radian (Check conversion here)
Mass of Ball: 5.9 Kilogram --> 5.9 Kilogram No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

N_equillibrium = 60/(2*pi)*sqrt((tan(φ))/m_ball) --> 60/(2*pi)*sqrt((tan(1.49400183970687))/5.9)

Evaluating ... ...

N_equillibrium = 14.172709918239

STEP 3: Convert Result to Output's Unit

14.172709918239 --> No Conversion Required

FINAL ANSWER

14.172709918239 ≈ 14.17271 <-- Mean Equilibrium Speed in RPM

(Calculation completed in 00.007 seconds)

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< Basics of Governor Calculators

Total Downward Force on Sleeve in Wilson-Hartnell Governor

LaTeX 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

Corresponding Radial Force Required at Each Ball for Spring Loaded Governors

LaTeX 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

LaTeX Go Angle B/W Axis of Radius of Rotation and 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

LaTeX Go Angle B/W Axis of Radius of Rotation and Line OA = atan(Mass of Ball*Mean Equilibrium Angular Speed^2)

Speed of Rotation in RPM Formula

LaTeX Go

Mean Equilibrium Speed in RPM = 60/(2*pi)*sqrt((tan(Angle B/W Axis of Radius of Rotation and Line OA))/Mass of Ball)
N_equillibrium = 60/(2*pi)*sqrt((tan(φ))/m_ball)

What is Porter Governor?

Porter Governor is a modification of Watt Governor with a central load attached to the sleeve. This load moves up and down the central spindle. The additional force increases the speed of revolution required to enable the balls to rise to any predetermined level.

How to Calculate Speed of Rotation in RPM?

Speed of Rotation in RPM calculator uses Mean Equilibrium Speed in RPM = 60/(2*pi)*sqrt((tan(Angle B/W Axis of Radius of Rotation and Line OA))/Mass of Ball) to calculate the Mean Equilibrium Speed in RPM, Speed of Rotation in RPM formula is defined as a measure of the rotational speed of a shaft or other rotating element, typically in a mechanical system, which is crucial in determining the performance and efficiency of the system. Mean Equilibrium Speed in RPM is denoted by N_equillibrium symbol.

How to calculate Speed of Rotation in RPM using this online calculator? To use this online calculator for Speed of Rotation in RPM, enter Angle B/W Axis of Radius of Rotation and Line OA (φ) & Mass of Ball (m_ball) and hit the calculate button. Here is how the Speed of Rotation in RPM calculation can be explained with given input values -> 14.05411 = 60/(2*pi)*sqrt((tan(1.49400183970687))/5.9).

FAQ

What is Speed of Rotation in RPM?

Speed of Rotation in RPM formula is defined as a measure of the rotational speed of a shaft or other rotating element, typically in a mechanical system, which is crucial in determining the performance and efficiency of the system and is represented as N_equillibrium = 60/(2*pi)*sqrt((tan(φ))/m_ball) or Mean Equilibrium Speed in RPM = 60/(2*pi)*sqrt((tan(Angle B/W Axis of Radius of Rotation and Line OA))/Mass of Ball). Angle B/W Axis of Radius of Rotation and Line OA is the angle between the axis of rotation of the governor and the line OA, which affects the governor's stability & Mass of Ball is the measure of the amount of matter in a ball, typically measured in units of mass such as grams or kilograms.

How to calculate Speed of Rotation in RPM?

Speed of Rotation in RPM formula is defined as a measure of the rotational speed of a shaft or other rotating element, typically in a mechanical system, which is crucial in determining the performance and efficiency of the system is calculated using Mean Equilibrium Speed in RPM = 60/(2*pi)*sqrt((tan(Angle B/W Axis of Radius of Rotation and Line OA))/Mass of Ball). To calculate Speed of Rotation in RPM, you need Angle B/W Axis of Radius of Rotation and Line OA (φ) & Mass of Ball (m_ball). With our tool, you need to enter the respective value for Angle B/W Axis of Radius of Rotation and Line OA & Mass of Ball 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 Mean Equilibrium Speed in RPM?

In this formula, Mean Equilibrium Speed in RPM uses Angle B/W Axis of Radius of Rotation and Line OA & Mass of Ball. We can use 1 other way(s) to calculate the same, which is/are as follows -

Mean Equilibrium Speed in RPM = (Minimum equilibrium speed in RPM+Maximum Equilibrium Speed in RPM)/2

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