Wind Turbine Blade Tip Speed Quiz
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Questions and Answers

What is the theoretical maximum rotor efficiency, also known as Betz efficiency or Betz’s law?

  • 100%
  • 59.3% (correct)
  • 35-45%
  • 75%

    • How does the efficiency of the rotor change if the rotor turns too slowly?

  • The efficiency drops off (correct)
  • The efficiency remains constant
  • The efficiency increases
  • The efficiency reaches 100%

    • What impact does the tower have on wind speed for downwind machines?

  • Decreases wind speed significantly
  • Increases wind speed significantly
  • Causes wind 'shadowing' (correct)
  • No impact on wind speed

    • What effect does the flexing of a blade have on wind turbine noise?

    <p>Increases wind turbine noise</p> Signup and view all the answers

    How much energy can be extracted from the wind under the best operating conditions?

    <p>35-45%</p> Signup and view all the answers

    What is the primary cause of turbulence (stall) in a wind turbine?

    <p>The destruction of the low pressure area by the tumbling wind over the top of the rotor</p> Signup and view all the answers

    How does the angle of attack affect the efficiency of a wind turbine rotor?

    <p>Lower angle of attack leads to higher efficiency</p> Signup and view all the answers

    What is the significance of tip speed ratio in determining the efficiency of a wind turbine rotor?

    <p>Each turbine has a maximum operating efficiency defined by a specific tip speed ratio</p> Signup and view all the answers

    Why does the tip of the turbine blade travel at the highest speed when it is rotating?

    <p>To achieve a specific tip speed ratio for optimal efficiency</p> Signup and view all the answers

    How does apparent wind relate to the efficiency of wind turbine blades?

    <p>Efficiency increases with an increase in apparent wind speed</p> Signup and view all the answers

    What is the tip-speed-ratio (TSR) of a wind turbine with a rotor diameter of 40m and a rotor speed of 1800 rpm?

    <p>4.79</p> Signup and view all the answers

    What is the efficiency of the complete wind turbine (blades, gearbox, generator) when it operates with a TSR of 4.0?

    <p>82%</p> Signup and view all the answers

    At what wind speed does the turbine produce its maximum power output for a Vesta V90 – 3.0 MW turbine with a 90m diameter?

    <p>15 m/s</p> Signup and view all the answers

    Why does the power output level off at 3,000 kW for the Vesta V90 – 3.0 MW turbine?

    <p>Due to the design limit of the blades</p> Signup and view all the answers

    What gear ratio is needed to match the rotor speed (TSR = 4.0) to the generator speed (1800 rpm) for a wind turbine with a rotor diameter of 40m?

    <p>16:1</p> Signup and view all the answers

    What is the formula for tip speed in terms of rotor speed (N), rotor diameter (D), and wind speed (v)?

    <p>π D N / 60v</p> Signup and view all the answers

    How does the optimum spacing of wind turbine towers vary with wind direction?

    <p>It is wider in the wind direction and narrower in the crosswind direction</p> Signup and view all the answers

    How does the wind speed vary with height according to the given expression?

    <p>$V_1 = V_2 + α(h_2 - h_1)$</p> Signup and view all the answers

    Why can't average wind speed be used to predict total energy available?

    <p>The relationship between power and wind speed is nonlinear</p> Signup and view all the answers

    Calculate the energy at 6 m/s using the given formula: Energy (6 m/s) = 1/2 ρAv^3t. What is the result?

    <p>$12 · 1.225 kg/m3 ·1m2 · (6 m/s)^3 · 100 h$</p> Signup and view all the answers

    What is the definition of tip speed?

    <p>The measured speed at the blade tip as it rotates through the air</p> Signup and view all the answers

    What causes considerable stress on the tip of the turbine blade when it is rotating?

    <p>Centrifugal force</p> Signup and view all the answers

    What does the Tip Speed Ratio (TSR) measure?

    <p>The speed of the blade at its tip divided by the wind speed</p> Signup and view all the answers

    Which method of speed control involves shifting the rotor axis out of the wind direction when wind speed exceeds the design limit?

    <p>Yaw and tilt control</p> Signup and view all the answers

    What does 'stall control' involve in terms of speed regulation?

    <p>Shifting the blades into a position such that they stall</p> Signup and view all the answers

    What is the power density in the wind at a height of 50 m, assuming the wind speed at 10 m is 5 m/s?

    <p>102.4 W/m2</p> Signup and view all the answers

    According to the 1/7th power law, how does the power in the wind at the top tip of the rotor compare to that at the lowest point that it falls to?

    <p>45% higher</p> Signup and view all the answers

    What is the estimated friction coefficient α for ground with hedges and shrubs?

    <p>0.20</p> Signup and view all the answers

    Using the 1/7th power law, what is the relationship between wind speed and height (v/vo)3?

    <p>(H/Ho)3α</p> Signup and view all the answers

    What is the ratio of specific power in the wind at the highest point that a rotor blade tip reaches to the lowest point that it falls to, for a wind turbine with a 30-m rotor diameter?

    <p>45% higher</p> Signup and view all the answers

    What is the theoretical maximum rotor efficiency, also known as Betz efficiency or Betz’s law?

    <p>50%</p> Signup and view all the answers

    If the wind speed is increased from 5 m/s to 15 m/s, what will be the expected increase in power output of the wind turbine (in percentage)?

    <p>500%</p> Signup and view all the answers

    What is the efficiency of the wind turbine when the wind speed is 15 m/s and the actual power output is 3,000 kW?

    <p>23.2%</p> Signup and view all the answers

    Why does the power output level off at 3,000 kW according to the provided text?

    <p>Due to the limitation on turbine rotation speed</p> Signup and view all the answers

    What is the rated capacity of the Vestas V164, the world's biggest wind turbine?

    <p>8 MW</p> Signup and view all the answers

    What impact does the tower have on wind speed for downwind machines as mentioned in the text?

    <p>Decreases wind speed</p> Signup and view all the answers

    How much energy can be extracted from the wind under the best operating conditions according to the text?

    <p>$7200 kW</p> Signup and view all the answers

    What is the diameter of the Vestas V164, the world's biggest wind turbine?

    <p>164 m</p> Signup and view all the answers

    What is the overall height of the Vestas V164, the world's biggest wind turbine?

    <p>$220 m</p> Signup and view all the answers

    What is the theoretical maximum rotor efficiency, also known as Betz efficiency or Betz’s law?

    <p>59.3%</p> Signup and view all the answers

    What is the usual way to illustrate rotor efficiency?

    <p>As a function of its tip-speed ratio (TSR)</p> Signup and view all the answers

    What is the significance of the tip speed ratio in determining the efficiency of a wind turbine rotor?

    <p>It determines the efficiency by balancing the rotor speed with the wind speed.</p> Signup and view all the answers

    How much energy can be extracted from the wind under the best operating conditions?

    <p>About 35 to 45 percent</p> Signup and view all the answers

    What is the impact of the tower on wind speed for downwind machines?

    <p>It causes significant wind 'shadowing' as the blades pass behind the tower.</p> Signup and view all the answers

    What is the relationship between wind speed and height according to the 1/7th power law?

    <p>(v/vo)^3</p> Signup and view all the answers

    What is the primary cause of turbulence (stall) in a wind turbine?

    <p>The rotor turning too fast</p> Signup and view all the answers

    What is the definition of tip speed?

    <p>The speed at which the tip of the turbine blade travels when it is rotating</p> Signup and view all the answers

    What is the impact of tower height on wind speed?

    <p>The impact of tower height on wind speed is that it greatly affects wind speed due to the friction that the air experiences as it moves across the earth’s surface.</p> Signup and view all the answers

    Under what conditions does the 1/7th power law provide an approximate value for the friction coefficient?

    <p>For neutral stability conditions, the 1/7th power law provides an approximate value for the friction coefficient.</p> Signup and view all the answers

    What is the significance of using average wind speed to predict energy in the wind?

    <p>The above example dramatically illustrates the inaccuracy associated with using average wind speeds, as the combination of different wind regimes can produce significantly different energy outputs despite the same average wind speed.</p> Signup and view all the answers

    How does the efficiency of wind turbine blades change based on wind speed probability distributions?

    <p>Based on certain common assumptions about wind speed probability distributions, the energy in the wind is typically almost twice the amount that would be found by using the average wind speed.</p> Signup and view all the answers

    What is the relationship between wind speed at different heights and the roughness of the earth’s surface?

    <p>The wind speed at a certain height (v) is affected by the wind speed at a reference height (vo), the friction coefficient (α), and the roughness length (z) of the earth’s surface.</p> Signup and view all the answers

    How does the energy output of wind regimes with different wind speeds compare?

    <p>The combination of 9-m/s and 3-m/s winds produces 75% more energy than winds blowing at a steady 6 m/s, despite having the same average wind speed.</p> Signup and view all the answers

    What is the impact of tower height on wind speed for downwind machines?

    <p>The impact of the roughness of the earth’s surface on wind speed is that surface winds are slowed considerably by high irregularities, such as forests and buildings.</p> Signup and view all the answers

    What is the relationship between energy output and wind speed at different heights?

    <p>The energy in the wind is typically almost twice the amount that would be found by using the average wind speed, under certain common assumptions about wind speed probability distributions.</p> Signup and view all the answers

    What is the tip-speed-ratio (TSR) of a wind turbine with a rotor diameter of 40m and a rotor speed of 1800 rpm?

    <p>4.5</p> Signup and view all the answers

    What is the formula for tip speed in terms of rotor speed (N), rotor diameter (D), and wind speed (v)?

    <p>$ ext{Tip Speed} = rac{N imes D}{2}$</p> Signup and view all the answers

    At what wind speed does the turbine produce its maximum power output for a Vesta V90 – 3.0 MW turbine with a 90m diameter?

    <p>14 m/s</p> Signup and view all the answers

    What is the estimated friction coefficient α for ground with hedges and shrubs?

    <p>0.1</p> Signup and view all the answers

    What is the significance of tip speed ratio in determining the efficiency of a wind turbine rotor?

    <p>It determines how effectively the rotor captures wind energy.</p> Signup and view all the answers

    What causes considerable stress on the tip of the turbine blade when it is rotating?

    <p>Centrifugal force</p> Signup and view all the answers

    What gear ratio is needed to match the rotor speed (TSR = 4.0) to the generator speed (1800 rpm) for a wind turbine with a rotor diameter of 40m?

    <p>2.0</p> Signup and view all the answers

    What is the theoretical maximum rotor efficiency, also known as Betz efficiency or Betz’s law?

    <p>59.3%</p> Signup and view all the answers

    According to the 1/7th power law, how does the power in the wind at the top tip of the rotor compare to that at the lowest point that it falls to?

    <p>The power at the top tip of the rotor is higher than at the lowest point but not proportionally by the cube of the height ratio.</p> Signup and view all the answers

    Study Notes

    Wind Turbine Efficiency

    • Theoretical maximum rotor efficiency, also known as Betz efficiency or Betz's law, is 59.3%.
    • Efficiency of rotor decreases if it turns too slowly.

    Wind Speed and Tower Impact

    • Tower has a significant impact on wind speed for downwind machines.
    • Wind speed varies with height according to the 1/7th power law (v/vo)³.

    Turbine Blade Noise and Flexing

    • Flexing of a blade affects wind turbine noise.

    Energy Extraction and Power Output

    • Maximum energy that can be extracted from the wind under the best operating conditions is 59.3% of the total energy.
    • Power output levels off at 3,000 kW for the Vesta V90 – 3.0 MW turbine.
    • Power output increases with wind speed, but levels off at maximum capacity.

    Tip Speed Ratio and Rotor Efficiency

    • Tip speed ratio (TSR) measures the efficiency of a wind turbine rotor.
    • TSR of a wind turbine with a rotor diameter of 40m and a rotor speed of 1800 rpm is 4.0.
    • Formula for tip speed is (πDN)/60, where N is the rotor speed, D is the rotor diameter, and v is the wind speed.

    Wind Turbine Design and Operation

    • Vestas V164 is the world's biggest wind turbine, with a diameter of 164m and a height of 220m.
    • Rated capacity of the Vestas V164 is 9.5 MW.
    • Tower height has a significant impact on wind speed and energy output.

    Turbulence and Stall

    • Primary cause of turbulence (stall) in a wind turbine is angle of attack.
    • Stall control involves shifting the rotor axis out of the wind direction when wind speed exceeds the design limit.

    Wind Speed Probability Distributions

    • Efficiency of wind turbine blades changes based on wind speed probability distributions.
    • Average wind speed cannot be used to predict energy in the wind.

    Roughness of the Earth's Surface

    • Wind speed at different heights is related to the roughness of the earth's surface.
    • Energy output of wind regimes with different wind speeds compares using the 1/7th power law.

    Gear Ratio and Generator Speed

    • Gear ratio is needed to match the rotor speed (TSR = 4.0) to the generator speed (1800 rpm) for a wind turbine with a rotor diameter of 40m.

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    Description

    Test your knowledge about wind turbine blade tip speed and related concepts with this quiz. Explore topics like tip speed ratio and centrifugal force.

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