Physics $333$ Problem Set #$3$

Question $1-$ Vesta Windmills

To find an ideal placement of a turbine, we need to understand at what wind speeds turbine would operate most efficiently. You might think you want to run it at full power, but if you're not efficient, the excessive wear on the turbine could be costly$.$

A common word turbine is the Vesta V$90-3\mathrm{.}0$ MW $($turbine diameter $=90m).$ The actual power produced by the turbine as a function of wind speed is plotted below.

Use data from the graph to find the efficiency of Vesta windmill. You will need to read them off the graph and reproduce it in some plotting tool, such as Excel.

a$)$ Plot the theoretical power that can be obtained from this wind turbine.

b$)$ Plot the efficiency of the Vesta V$90-3\mathrm{.}0$ MW as a function of wind speed.

c$)$ How does the efficiency which you found compare to the Betz efficiency? As the wind speed increases, why does the efficiency change?

Question $2-$ Designing a Vesta Wind Farm

Wayne bought a hilly, cougar$-$filled piece of land, that happened to have the highest average winds in Saskatchewan. He now gets paid by the government to house $82$ windmills on it$,$ a few of which are shown below. Below the windmills he raises organic buffalo, which have eyes as deep as the void space, and in his other land he grows organic alfalfa. Not bad for a romantic.

Assume the wind turbines are the Vesta V$90-3\mathrm{.}0$ MW turbine and that the average wind speed is $12\frac{m}{s}.$

Estimate how much land area these windmills occupy.

How much power do the $82$ windmills generate?

How many homes in Saskatoon do they power? When searching the data you need, keep in mind that this question asks about total $($electricity $+$ gas$)$ power consumption per a household in Saskatoon.

Physics $333$ Problem Set #$3$

Question $1-$ Vesta Windmills

To find an ideal placement of a turbine, we need to understand at what wind speeds turbine would operate most efficiently. You might think you want to run it at full power, but if you're not efficient, the excessive wear on the turbine could be costly$.$

A common word turbine is the Vesta V$90-3\mathrm{.}0$ MW $($turbine diameter $=90m).$ The actual power produced by the turbine as a function of wind speed is plotted below.

Use data from the graph to find the efficiency of Vesta windmill. You will need to read them off the graph and reproduce it in some plotting tool, such as Excel.

a$)$ Plot the theoretical power that can be obtained from this wind turbine.

b$)$ Plot the efficiency of the Vesta V$90-3\mathrm{.}0$ MW as a function of wind speed.

c$)$ How does the efficiency which you found compare to the Betz efficiency? As the wind speed increases, why does the efficiency change?