EE6623 Chap.1 Wind Resource and Available Power
Wind Resource and Available Power
Start with the air stream
Available wind power is a resource calculation before it is a turbine calculation. Air crossing the rotor plane has mass because density multiplies the swept volume, and it has kinetic energy because that mass moves. Combining mass flow with kinetic energy produces the familiar dependence on one half, air density, swept area and the cube of wind speed.
Rebuilding that path makes the exponents memorable and supplies the first unit check.
Give every factor its own physical job
Density is linear, swept area depends on the square of rotor radius, and wind speed is cubed. A ratio comparison should show those three factors separately before any numbers are entered.
Temperature, pressure and altitude normally act through density, while tower height can change the wind speed predicted by a site profile. Mixing these corrections into one unexplained multiplier hides the reason a result changes and makes an inverted ratio difficult to spot.
Hub height changes the input
A power-law profile estimates wind speed at a new height from a measured reference speed and a site exponent.
The exponent depends on terrain and surface roughness, so it must be stated rather than treated as universal. Correct the wind speed to hub height first, then cube that corrected value in the available-power equation. An altitude-related density correction belongs on a different line.
Resource power is not electrical output
The air stream contains available power.
The rotor captures a fraction described by a power coefficient. Mechanical and electrical stages introduce further limits and losses. Label each output as available, captured, shaft or grid power before applying the next factor.
That notation prevents a coefficient being used twice and prepares the transition to the turbine power curve, where control can deliberately stop electrical output following the cube law.
Use direction and scale as final checks
Larger density, area or speed must increase available power.
A ten per cent increase in diameter produces a twenty-one per cent area increase, while a ten per cent speed increase produces about a thirty-three per cent resource increase. Energy requires a time interval after power is known. Kilowatts multiplied by hours give kilowatt-hours; watts multiplied by seconds give joules. A final answer should state both the unit and the conversion boundary.
What this chapter covers
- 01
Mass flow through swept area
- 02
The wind-speed cube law
- 03
Air density, temperature and pressure
- 04
Hub-height power-law correction
- 05
Available, captured and electrical power
- 06
Energy from power and time
Worked example · free
Calculate available and captured wind power
- 2Convert diameter to radius and find swept area.
- 3Evaluate one half density area speed cubed.
- 3Apply the rotor coefficient once and label the boundary.
Key terms
- Swept Area
- The circular area passed through by the rotating blades, calculated from rotor radius.
- Air Density
- Air mass per unit volume, which changes available wind power linearly.
- Power Coefficient
- The fraction of available air-stream power captured aerodynamically by the rotor.
- Hub Height
- The elevation of the rotor centre, used when estimating the wind speed seen by the machine.
- Specific Power
- Power expressed per unit swept area for comparing the strength of a wind resource or turbine loading.
Wind Resource and Available Power FAQ
Why is wind speed cubed in the power equation?
Mass crossing the rotor each second already grows linearly with wind speed, while kinetic energy per unit mass grows with speed squared. Multiplying those effects produces a cube. That is why a modest speed change can dominate a larger linear change in density.
Does high altitude always improve wind power?
Higher altitude can bring faster wind, but lower pressure usually reduces air density. Evaluate the speed and density effects separately, cubing only the speed ratio. The site improves available power only when the speed gain outweighs the density reduction and any other changed factor.
When can I use a wind-power ratio?
Use a ratio when comparing conditions with a known relationship and cancel factors that remain unchanged. Keep density linear, area proportional to diameter squared, and speed cubed. Do not use the cube-law output ratio across a rated-power or shutdown region of the turbine curve.
Exam move
Begin by deriving the available-power equation from a cylinder of air crossing the rotor plane. Say aloud which part contributes density, area, one speed factor from mass flow and two speed factors from kinetic energy. Next build a ratio card with density to the first power, diameter to the second power through area, and speed to the third power. Work comparisons symbolically so common quantities cancel before numbers enter.
For height questions, write reference speed and height, target height and the stated terrain exponent on separate lines. Correct speed first and apply density separately. For every numerical result, add a boundary label: air stream, rotor, shaft or grid. Then perform three checks. Direction must agree with the changed input, units must end in power or energy as requested, and magnitude must fit the rotor scale.
Once this is stable, practise mixed cases that change diameter, density and speed together. Finish by asking whether both operating points are below rated speed. If a point lies on the rated or shutdown region, explain why resource scaling no longer equals electrical-output scaling. Keep one error log for diameter used as radius, percentage used without converting to a ratio, and time units mixed between seconds and hours.
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