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 radius of rotation of the rotor.
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.
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.
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
Angular Velocity of Rotor: 15 Revolution per Minute --> 1.57079632671491 Radian per Second (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
R = (λ*V)/ω --> (2.2*10)/1.57079632671491
Evaluating ... ...
R = 14.0056349928
STEP 3: Convert Result to Output's Unit
14.0056349928 Meter --> No Conversion Required
FINAL ANSWER
14.0056349928 14.00563 Meter <-- Rotor Radius
(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

Rotor Radius given Tip Speed Ratio Formula

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

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 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 -> 14.00563 = (2.2*10)/1.57079632671491.

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 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 & Angular Velocity of Rotor is the time rate at which the rotor rotates, or revolves about its 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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