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Need help-Wind Turbine Investigation

Need help-Wind Turbine Investigation

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The following experiment enables you to:

  • Measure the energy in the wind.
  • Assess a commercially available wind turbine in an environmental wind tunnel.
  • Determine the power curve of a wind turbine and obtain cut-in speeds
  • Calculate the coefficient of performance of a turbine
  • Calculate the Solidity and Tip-speed ratio.
  • See how the energy is converted stored and utilised.
  • Examine the Beaufort wind scale.


The power available to a wind turbine is the kinetic energy passing per unit time in a column of air with the same cross sectional area A as the wind turbine rotor, travelling with a wind speed U0. Thus the available power is proportional to the cube of the wind speed. See the figure below.


The equipment is provided by Marlec and the following information is from their web page but has been modified slightly for this labsheet.

The Rutland 913 is designed for marine use on board coastal and ocean going yachts usually over 10m in length. This unit will generate enough power to serve both domestic and engine batteries on board.
The Rutland 913 is a popular sight in marinas, thousands are in use worldwide, boat owners like it’s clean, aerodynamic lines and its quiet and continuous operation. Without doubt this latest marine model accumulates more energy than any other comparable windcharger available, you’ll always see a Rutland spinning in the lightest of breezes!

  • Low wind speed start up of less than 3m/s
  • Generates 90w @ 37m/s, 24w @ 20 m/s
  • Delivers up to 250w
  • Modern, durable materials for reliability on the high seas
  • SR200 Regulator – Shunt type voltage regulator prevents battery overcharge


During this experiment you will make use of the following equations to calculate key parameters

Key formulae

Energy in the wind E = (watts)

Swept area of rotor A=πR2


Electrical power output P=VxI (watts)


Coefficient of performance


Tip speed ratio




Solidity = blade area/swept area


R is the rotor radius (m)

ρ is air density say 1.23 kg/m3

Uo is the wind speed (m/s)

V is voltage (volts)

I is current (amps)

ω (rads/sec) is the angular velocity of the rotor found from


 where N is the rotor speed in revs/min






Step 1         Ensure that everything is setup for you and switch on the tunnel.

Step 2         Adjust the wind speed and let it stabilize

Step 3         Measure the wind speed, voltage and current

Step 4         If available measure the rotor speed with the stroboscope.

Repeat steps 2 – 4 for other wind speeds up to a maximum of 10m/s if achievable.


Gather your data by completing tables 1 and 2


Wind speed

Uo  (m/s)



Effect on land Output voltage

V (volts)

Output current

I (amps)

Rotor speed

N (revs/min)

Table 1 measured data


Calculate the following

Rotor radius use a ruler to measure from center to tip of turbine R =
Swept area A=πR2


A =
Blade area = blade area + hub area

do your best!

Solidity = blade area / swept area.   =

Table 2 measured data




Now analyse your data by completing table 3.


Energy in the wind Electrical power Coefficient of performance Tip speed ratio
E =  (watts) P = V x I




(or column 2 /column 1)

Table 3 Analyse your data


Present your data:

Now present your results in graphical format to give you a better understanding of the data you have gathered and analysed.


Use excel and the x-y scatter chart for this.


Graph 1

Plot the values Uo (x-axis) against P (y1-axis) and E (y2-axis).


Graph 2

Plot the values of Uo (x-axis) against Cp (y-axis).


What conclusions do you draw?


How efficiently are you converting the kinetic energy in the wind into electrical energy that is stored chemically in the batteries?


Write up the laboratory formally and submit to turnitin. Please ensure presentation is clear and quote fully any references.



The Beaufort Wind Speed Scale

Wind Speed at 10m height Description Wind Turbine
Effect on
Effect at
0 0.0 -0.4 Calm None Smoke rises vertically Mirror smooth
1 0.4 -1.8 Light None Smoke drifts; vanes unaffected small ripples
2 1.8 -3.6 Light None Leaves move slightly Definite waves
3 3.6 -5.8 Light Small turbines start – e.g. for pumping Leaves in motion; Flags extend Occasional breaking crest
4 5.8 -8.5 Moderate Start up for electrical generation Small branches move Larger waves; White crests common
5 8.5 -11.0 Fresh Useful power Generation at 1/3 capacity Small trees sway Extensive white crests
6 11.0 -14.0 Strong Rated power range Large branches move Larger waves; foaming crests
7 14.0 -17.0 Strong Full capacity Trees in motion Foam breaks from crests
8 17.0 -21.0 Gale Shut down initiated Walking difficult Blown foam
9 21.0 -25.0 Gale All machines shut down Slight structural damage Extensive blown foam
10 25.0 -29.0 Strong gale Design criteria against damage Trees uprooted; much structural damage Large waves with long breaking crests
11 29.0 -34.0 Strong gale Widespread damage
12 >34.0 Hurricane Serious damage Disaster conditions Ships hidden in wave troughs

Supplementary Theory

The power available to a wind turbine is the kinetic energy passing per unit time in a column of air with the same cross sectional area A as the wind turbine rotor, travelling with a wind speed u0. Thus the available power is proportional to the cube of the wind speed.

We can see that the power achieved is highly dependent on the wind speed. Doubling the wind speed increases the power eightfold but doubling the turbine area only doubles the power. Thus optimising the siting of wind turbines in the highest wind speed areas has significant benefit and is critical for the best economic performance. Information on power production independently of the turbine characteristics is normally expressed as a flux, i.e. power per unit area or power density in W/m2. Thus assuming a standard atmosphere with density at 1.225kg/s :

Wind speed m/s     Power W/m squared               5.0                76.6              10.0               612.5              15.0              2067.2              20.0              4900.0              25.0              9570.3

The density of the air will also have an effect on the total power available. The air is generally less dense in warmer climates and also decreases with height. The air density can range from around 0.9 kg/m3 to 1.4kg/m3. This effect is very small in comparison to the variation of wind speed.


In practice all of the kinetic energy in the wind cannot be converted to shaft power since the air must be able to flow away from the rotor area. The Betz criterion, derived using the principles of conservation of momentum and conservation of energy gives a maximum possible turbine efficiency, or power coefficient, of 59%. In practise power coefficients of 20 – 30 % are common. The section on Aerodynamics discusses these matters in detail.


Most wind turbines are designed to generate maximum power at a fixed wind speed. This is known as Rated Power and the wind speed at which it is achieved the Rated Wind Speed. The rated wind speed chosen to fit the local site wind regime, and is often about 1.5 times the site mean wind speed.

The power produced by the wind turbine increases from zero, below the cut in wind speed, (usually around 5m/s but again varies with site) to the maximum at the rated wind speed. Above the rated wind speed the wind turbine continues to produce the same rated power but at lower efficiency until shut down is initiated if the wind speed becomes dangerously high, i.e. above 25 to 30m/s (gale force). This is the cut out wind speed. The exact specifications for designing the energy capture of a turbine depend on the distribution of wind speed over the year at the site.


Performance calculations


Power coefficient Cp is the ratio of the power extracted by the rotor to the power available in the wind.

It can be shown that the maximum possible value of the power coefficient is 0.593 which is referred to as the Betz limit.


Pe is the extracted power by the rotor (W)

V¥ is the free stream wind velocity (m/s)

A is area normal to wind         (m2)

ρ is density of the air              (kg/m3)



The tip speed ratio (l) is the ratio of the speed of the blade tip to the free stream wind speed.




w is the angular velocity of the rotor (rads/sec), and

R is the tip radius (m)


This relation holds for the horizontal axis machine which is the focus of these notes.


The solidity (g) is the ratio of the blade area to the swept frontal area (face area) of the machine


Blade area = number of blades * mean chord length * radius = N.c.R


Mean chord length is the average width of the blade facing the wind.


Swept frontal area is pR2

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