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Rotor Radius given Tip Speed Ratio Calculator

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✖Tip Speed Ratio is the ratio of the speed of the tip of a wind turbine blade.ⓘ Tip Speed Ratio [λ]			+10% -10%
✖Free Stream Wind Speed is the speed of wind that occurs naturally in the atmosphere, unaffected by any obstacles or wind turbines.ⓘ Free Stream Wind Speed [V_∞]			+10% -10%
✖Angular Velocity of Rotor is the speed at which the rotor blades of a wind turbine rotate around their axis.ⓘ Angular Velocity of Rotor [ω]			+10% -10%

✖Rotor Radius is the distance from the axis of rotation to the tip of the blade in a rotor.ⓘ Rotor Radius given Tip Speed Ratio [R]

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Rotor Radius given Tip Speed Ratio Solution

STEP 0: Pre-Calculation Summary

Formula Used

Rotor Radius = (Tip Speed Ratio*Free Stream Wind Speed)/Angular Velocity of Rotor
R = (λ*V_∞)/ω
This formula uses 4 Variables

Variables Used

Rotor Radius - (Measured in Meter) - Rotor Radius is the distance from the axis of rotation to the tip of the blade in a rotor.
Tip Speed Ratio - Tip Speed Ratio is the ratio of the speed of the tip of a wind turbine blade.
Free Stream Wind Speed - (Measured in Meter per Second) - Free Stream Wind Speed is the speed of wind that occurs naturally in the atmosphere, unaffected by any obstacles or wind turbines.
Angular Velocity of Rotor - (Measured in Radian per Second) - Angular Velocity of Rotor is the speed at which the rotor blades of a wind turbine rotate around their axis.

STEP 1: Convert Input(s) to Base Unit

Tip Speed Ratio: 2.2 --> No Conversion Required
Free Stream Wind Speed: 0.168173 Meter per Second --> 0.168173 Meter per Second No Conversion Required
Angular Velocity of Rotor: 0.504722 Revolution per Minute --> 0.0528543642408134 Radian per Second (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

R = (λ*V_∞)/ω --> (2.2*0.168173)/0.0528543642408134

Evaluating ... ...

R = 7.00000095194232

STEP 3: Convert Result to Output's Unit

7.00000095194232 Meter --> No Conversion Required

FINAL ANSWER

7.00000095194232 ≈ 7.000001 Meter <-- Rotor Radius

(Calculation completed in 00.004 seconds)

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Power Extracted by Rotor given Power Coefficient of Wind Machine

LaTeX Go Power Extracted by Rotor = Power Coefficient of Wind Machine*(0.5*Density of Air*pi*(Rotor Radius^2)*Free Stream Wind Speed^3)

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LaTeX 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

LaTeX 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

LaTeX 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

Rotor Radius given Tip Speed Ratio Formula

LaTeX Go

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

What is Rotar Radius?

The Rotor Radius is the distance from the center of a wind turbine’s rotor (hub) to the tip of one of its blades. It defines the rotor's swept area, which is crucial in determining the amount of wind energy the turbine can capture. A larger rotor radius allows for a greater swept area, increasing the potential energy that can be converted into electricity.

How to Calculate Rotor Radius given Tip Speed Ratio?

Rotor Radius given Tip Speed Ratio calculator uses Rotor Radius = (Tip Speed Ratio*Free Stream Wind Speed)/Angular Velocity of Rotor to calculate the Rotor Radius, The Rotor Radius given Tip Speed Ratio is the radius of rotation of the rotor i.e. distance from the tip of the blade to the axis of rotation. Rotor Radius is denoted by R symbol.

How to calculate Rotor Radius given Tip Speed Ratio using this online calculator? To use this online calculator for Rotor Radius given Tip Speed Ratio, enter Tip Speed Ratio (λ), Free Stream Wind Speed (V_∞) & Angular Velocity of Rotor (ω) and hit the calculate button. Here is how the Rotor Radius given Tip Speed Ratio calculation can be explained with given input values -> 6.999959 = (2.2*0.168173)/0.0528543642408134.

FAQ

What is Rotor Radius given Tip Speed Ratio?

The Rotor Radius given Tip Speed Ratio is the radius of rotation of the rotor i.e. distance from the tip of the blade to the axis of rotation and is represented as R = (λ*V_∞)/ω or Rotor Radius = (Tip Speed Ratio*Free Stream Wind Speed)/Angular Velocity of Rotor. Tip Speed Ratio is the ratio of the speed of the tip of a wind turbine blade, Free Stream Wind Speed is the speed of wind that occurs naturally in the atmosphere, unaffected by any obstacles or wind turbines & Angular Velocity of Rotor is the speed at which the rotor blades of a wind turbine rotate around their axis.

How to calculate Rotor Radius given Tip Speed Ratio?

The Rotor Radius given Tip Speed Ratio is the radius of rotation of the rotor i.e. distance from the tip of the blade to the axis of rotation is calculated using Rotor Radius = (Tip Speed Ratio*Free Stream Wind Speed)/Angular Velocity of Rotor. To calculate Rotor Radius given Tip Speed Ratio, you need Tip Speed Ratio (λ), Free Stream Wind Speed (V_∞) & Angular Velocity of Rotor (ω). With our tool, you need to enter the respective value for Tip Speed Ratio, Free Stream Wind Speed & Angular Velocity of Rotor 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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