Please read the document 'Introduction to quiz', which contains all the information you need to solve the quiz questions.' as decimal separator.

Please read the document 'Introduction to quiz', which contains all the information you need to solve the quiz questions.

When typing your results, please use '.' as decimal separator.

Keep the decimals till you get result to have better approximation. Only result in with 0.1 approximation.

You will now use the equations derived in the practical quiz to calculate the weight of a turbine blade.In the further questions, use the following information together with the information shown in Table 1:

Length of the bladeL=86m

L=86mRated wind speedV_r=11 m/s

Vr

​=11m/sDensity of airrho_{air} = 1.2 kg/m^3

ρair

​=1.2kg/m3

Acceleration of gravityg= 10 m/s^2

g=10m/s2

Blade height at root sectionh_0^{flap} = 2m

h0

flap

​=2mBlade width at root sectionh_0^{edge} = 4m

h0

edge

​=4m

Data

The properties of the three materials to be investigated are given in Table 1. The composite material data is for unidirectional (UD) composites with a fibre volume fraction of 55-60 %

55−60% . The carbon fibre composite data is for a low cost carbon fibre. The provided data for fatigue limits corresponds to approximately 10^8 -10^9

108

−109

 cycles.

MaterialDensity (rho

ρ)StiffnessStrengthFatigue limitAluminium2700 kg/m^3

2700kg/m3

70 GPa

70GPa300 MPa

300MPa150 MPa

150MPaUD glass fibre composite1900 kg/m^3

1900kg/m3

44 GPa

44GPa1000 MPa

1000MPa180 MPa

180MPaUD carbon fibre composite1600 kg/m^3

1600kg/m3

120 GPa

120GPa2000 MPa

2000MPa300 MPa

300MPa

Table 1. Properties of three materials

Question 1.

Calculate the mass (in metric tons) of a blade made of Aluminum, M_{blade}^{Al}

Mblade

Al

​ , setting the stress limit equal to fatigue limit of the material, sigma_0^{Al} = 150 MPa

σ0

Al

​=150MPa.