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Wind power pros/cons and output: 1.25 m blade

Short answer

Advantages are renewable, clean, low operating cost, quick installation, and land use below turbines; disadvantages are variability, limited sites, noise, visual impact, and bird risk. Using P = 0.5 rho A v^3 Cp with blade radius 1.25 m and Cp 0.3, the output is about 3.71 kW.

List out the advantages and disadvantages of wind power. Estimate electric power output from a wind turbine that has turbine blade length of 1.25 m and wind speed of 16 m/sec. Assume that air density is 1.23 kg/m³ and power coefficient is 0.3.

Advantages of wind power

  • Renewable and clean; no fuel cost and no CO₂ emission in operation.
  • Low operating cost; quick to install; modular.
  • Land around turbines can be used for farming.
  • Good for remote and hybrid (wind–solar–hydro) systems.

Disadvantages of wind power

  • Output is variable and unpredictable (P∝v3P \propto v^3); needs storage or backup.
  • Suitable sites are limited; high capital cost per kW for small units.
  • Noise, visual impact, danger to birds.
  • Low air density at high altitude reduces power.

Power output

P=12ρAv3Cp,A=πr2P = \frac{1}{2}\rho A v^3 C_p, \qquad A = \pi r^2

Given: r=1.25r = 1.25 m, v=16v = 16 m/s, ρ=1.23\rho = 1.23 kg/m³, Cp=0.3C_p = 0.3.

A=π×1.252=4.909 m2Pw=0.5×1.23×4.909×163=0.5×1.23×4.909×4096=12,365 WP=0.3×12,365=3,710 W\begin{aligned} A &= \pi \times 1.25^2 = 4.909\ \text{m}^2 \\ P_w &= 0.5 \times 1.23 \times 4.909 \times 16^3 \\ &= 0.5 \times 1.23 \times 4.909 \times 4096 = 12{,}365\ \text{W} \\ P &= 0.3 \times 12{,}365 = 3{,}710\ \text{W} \end{aligned}

Answer: Electric power output ≈3.71\approx 3.71 kW.

✓ Answer checked by Claude Opus 5.5 (high effort)

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