Angular Velocity of Rotor given Tip Speed Ratio Solution

STEP 0: Pre-Calculation Summary
Formula Used
Angular Velocity of Rotor = (Tip Speed Ratio*Free Stream Wind Speed)/Rotor Radius
ω = (λ*V)/R
This formula uses 4 Variables
Variables Used
Angular Velocity of Rotor - (Measured in Radian per Second) - Angular Velocity of Rotor is the time rate at which the rotor rotates, or revolves about its axis.
Tip Speed Ratio - Tip Speed Ratio is the ratio of the speed of the blade tip to the free stream wind speed.
Free Stream Wind Speed - (Measured in Meter per Second) - Free Stream Wind Speed is the velocity of the free stream which is the air far upstream of an aerodynamic body i.e. before the body has a chance to deflect, slow down or compress the air.
Rotor Radius - (Measured in Meter) - Rotor Radius is the radius of rotation of the rotor.
STEP 1: Convert Input(s) to Base Unit
Tip Speed Ratio: 2.2 --> No Conversion Required
Free Stream Wind Speed: 10 Meter per Second --> 10 Meter per Second No Conversion Required
Rotor Radius: 7 Meter --> 7 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ω = (λ*V)/R --> (2.2*10)/7
Evaluating ... ...
ω = 3.14285714285714
STEP 3: Convert Result to Output's Unit
3.14285714285714 Radian per Second -->30.0120749845714 Revolution per Minute (Check conversion here)
FINAL ANSWER
30.0120749845714 30.01207 Revolution per Minute <-- Angular Velocity of Rotor
(Calculation completed in 00.004 seconds)

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Free Stream Wind Speed given Drag Coefficient
Go Free Stream Wind Speed = sqrt(Drag Force/(0.5*Density of air VC*pi*Rotor Radius^2*Drag Coefficient))
Power Extracted by Rotor given Power Coefficient of Wind Machine
Go Power Extracted by Rotor = Power Coefficient of Wind Machine*(0.5*Density of Air*pi*(Rotor Radius^2)*Free Stream Wind Speed^3)
Power Coefficient of Wind Machine
Go Power Coefficient of Wind Machine = Power Extracted by Rotor/(0.5*Density of Air*pi*Rotor Radius^2*Free Stream Wind Speed^3)
Lift Coefficient of Blade of Wind Rotor
Go Lift Coefficient of Blade of Wind Rotor = Lift Force/(0.5*Density of air VC*pi*Rotor Radius^2*Free Stream Wind Speed^2)
Lift Force given Lift Coefficient of Blade
Go Lift Force = Lift Coefficient of Blade of Wind Rotor*0.5*Density of air VC*pi*Rotor Radius^2*Free Stream Wind Speed^2
Drag Coefficient of Blade of Wind Rotor
Go Drag Coefficient = Drag Force/(0.5*Density of air VC*pi*Rotor Radius^2*Free Stream Wind Speed^2)
Solidity of Wind Machine
Go Solidity of Wind Machine = (Number of Blades in Wind turbine*Mean Chord of Blades)/(pi*Rotor Radius)
Number of Blades of Wind Turbine given Solidity of Wind Turbine
Go Number of Blades in Wind turbine = (Solidity of Wind Machine*pi*Rotor Radius)/Mean Chord of Blades
Mean Chord of Blades given Solidity of Wind Machine
Go Mean Chord of Blades = (Solidity of Wind Machine*pi*Rotor Radius)/Number of Blades in Wind turbine
Angular Velocity of Rotor given Tip Speed Ratio
Go Angular Velocity of Rotor = (Tip Speed Ratio*Free Stream Wind Speed)/Rotor Radius
Rotor Radius given Tip Speed Ratio
Go Rotor Radius = (Tip Speed Ratio*Free Stream Wind Speed)/Angular Velocity of Rotor
Tip Speed Ratio
Go Tip Speed Ratio = (Angular Velocity of Rotor*Rotor Radius)/Free Stream Wind Speed

Angular Velocity of Rotor given Tip Speed Ratio Formula

Angular Velocity of Rotor = (Tip Speed Ratio*Free Stream Wind Speed)/Rotor Radius
ω = (λ*V)/R

Is higher tip speed ratio better?

The tip-speed ratio is related to efficiency, with the optimum varying with blade design. Higher tip speeds result in higher noise levels and require stronger blades due to larger centrifugal forces.

How to Calculate Angular Velocity of Rotor given Tip Speed Ratio?

Angular Velocity of Rotor given Tip Speed Ratio calculator uses Angular Velocity of Rotor = (Tip Speed Ratio*Free Stream Wind Speed)/Rotor Radius to calculate the Angular Velocity of Rotor, The Angular Velocity of Rotor given Tip Speed Ratio is the time rate at which the rotor rotates, or revolves about its axis. Angular Velocity of Rotor is denoted by ω symbol.

How to calculate Angular Velocity of Rotor given Tip Speed Ratio using this online calculator? To use this online calculator for Angular Velocity of Rotor given Tip Speed Ratio, enter Tip Speed Ratio (λ), Free Stream Wind Speed (V) & Rotor Radius (R) and hit the calculate button. Here is how the Angular Velocity of Rotor given Tip Speed Ratio calculation can be explained with given input values -> 286.5942 = (2.2*10)/7.

FAQ

What is Angular Velocity of Rotor given Tip Speed Ratio?
The Angular Velocity of Rotor given Tip Speed Ratio is the time rate at which the rotor rotates, or revolves about its axis and is represented as ω = (λ*V)/R or Angular Velocity of Rotor = (Tip Speed Ratio*Free Stream Wind Speed)/Rotor Radius. Tip Speed Ratio is the ratio of the speed of the blade tip to the free stream wind speed, Free Stream Wind Speed is the velocity of the free stream which is the air far upstream of an aerodynamic body i.e. before the body has a chance to deflect, slow down or compress the air & Rotor Radius is the radius of rotation of the rotor.
How to calculate Angular Velocity of Rotor given Tip Speed Ratio?
The Angular Velocity of Rotor given Tip Speed Ratio is the time rate at which the rotor rotates, or revolves about its axis is calculated using Angular Velocity of Rotor = (Tip Speed Ratio*Free Stream Wind Speed)/Rotor Radius. To calculate Angular Velocity of Rotor given Tip Speed Ratio, you need Tip Speed Ratio (λ), Free Stream Wind Speed (V) & Rotor Radius (R). With our tool, you need to enter the respective value for Tip Speed Ratio, Free Stream Wind Speed & Rotor Radius 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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