Question:

What will the outcome be if the rotor blades of a wind turbine are halved?

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Diameter of rotor: 30m

Generator rotation speed rating : 1500 rpm

Gear box ratio: 1:48

a) Convert the rpm to rad/s to find the angular velocity (w) of the high speed shaft,

w_o (high speed shaft)=1500/60 X 2π=157 rad/s…………………………….(1)

The angular velocity of the low speed shaft is 1/48 of that of the high speed shaft due to the gearbox,

Therfore

w (low speed shaft)=157/48=3.2 rad/s……………………………………….(2)

We can now find the velocity (v) at the tips of the blades by the equation.

V=wr

V=3.2 X 15………………………………………………………………………(3)

V=48 m/s

If the wind speed now increases and the velocity of the blade tips increases by 10 m/s in 5 seconds, the following results will occur;

New Velocity=48 10=58m/s

V=wr……………………………………………………………………..(4)

58=w X 15

w( low speed shaft)= 3.9 rad/s

High speed shaft=low speed shaft X Gear box ratio…….……………..(5)

w=3.9 X 48

w (new angular velocity high speed shaft)=187.2 rad/s

The new RPM of the high speed shaft will be:

187.2/2π X 60=1788 an increase of 288 RPM........................................

The angular acceleration of the high speed shaft is found by the formula;

w=w_o αt………………………………………………(7)

Where (t) = time

187.2=157 α 5

α= (187.2-157)/5

Angular acceleration (α) = 6 rad/s2

______________________________________...

If the rotor length was now halved to a diameter of 15 metres;

From equation (2)

V=wr

V=3.2 X 7.5

V=24 m/s

If the wind increased at the same rate, therefore the rotor tip speed increases by 10m/s in 5 seconds, then;

New Velocity=24 10=34 m/s

V=wr

34=w X 7.5

w( low speed shaft)= 4.5 rad/s

High speed shaft=low speed shaft X Gear box ratio

w=4.5 X 48

w (high speed shaft)=216 rad/s

The new RPM of the high speed shaft will be:

216/2π X 60=2063 rpm

an increase of 563 rpm.

The new angular acceleration is as follows

From equation (7)

α= (216-157)/5

Angular acceleration (α) = 11.8 rad/s2

IS THIS CORRECT AND WHY WILL THE ACCELERATION INCREASE?

PLEASE HELP

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1 ANSWERS


  1. it must be due to the weight issue and velocity through the air due to the size reduction !  

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