Offshore Wind Maths Explained

Offshore wind maths answers one simple question:

How much electricity can we make from the wind, and how do we move it to people safely and efficiently?

We’ll build up the maths slowly, using only what’s needed.

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1. Measuring Wind Speed (The Starting Point)

Wind speed tells us how fast the air is moving.

Units

• Wind speed is measured in metres per second (m/s)
• Example:
  • 5 m/s = gentle breeze
  • 10 m/s = strong wind
  • 25 m/s = storm (turbines shut down)

No maths yet — just measurement.

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2. Why Wind Speed Matters So Much

Here’s the most important idea in offshore wind maths:

If wind speed doubles, power increases by eight times.

This happens because of a cube (³) in the equation.

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3. The Core Power Equation (Explained Gently)

The equation for power from wind is:$$P = \frac{1}{2} \rho A v^3$$

Let’s break this down one piece at a time.

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What Each Symbol Means

Symbol	Meaning	Plain English
$P$	Power (watts)	How much electricity is produced
$\rho$	Air density	How “heavy” the air is
$A$	Area	Size of the spinning blades
$v$	Wind speed	How fast the wind blows

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4. Air Density (ρ)

Air has mass, even though we can’t see it.

• Typical offshore air density:

$$\rho = 1.225 \, \text{kg/m}^3$$

You do not calculate this — engineers use standard values.

Think of it as:

Heavier air = more energy

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5. Swept Area (A): Why Bigger Blades Matter

The blades sweep a circular area.

Circle area equation:

$$A = \pi r^2$$

Where:

• $r$ = blade length
• $\pi$ ≈ 3.14

Example:

If blade length = 100 m:$$A = 3.14 \times 100^2 = 31{,}400 \, \text{m}^2$$

Doubling blade length = four times the area.

That’s why offshore turbines are huge.

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6. Wind Speed Cubed (v³) — The Big One

This is the key part.

Example:

If wind speed = 10 m/s:$$v^3 = 10 \times 10 \times 10 = 1{,}000$$

If wind speed increases to 12 m/s:$$12^3 = 1{,}728$$

That’s 72% more power from just a small wind increase.

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7. Putting It All Together (Simple Example)

Let’s calculate power step by step.

Given:

• Air density = 1.225
• Blade length = 100 m → area = 31,400 m²
• Wind speed = 10 m/s

Equation:

$$P = \frac{1}{2} \times 1.225 \times 31{,}400 \times 10^3$$

Step-by-step:

1. $10^3 = 1{,}000$103=1,000
2. $0.5 \times 1.225 = 0.6125$0.5×1.225=0.6125
3. $0.6125 \times 31{,}400 = 19{,}235$0.6125×31,400=19,235
4. $19{,}235 \times 1{,}000 = 19.2 \text{ MW}$19,235×1,000=19.2 MW

That’s the raw wind power.

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8. Why Turbines Don’t Capture All That Power

Turbines cannot take all the energy from wind.

Betz Limit

Maximum possible capture:$$59.3\%$$

Real turbines achieve:

• 40–50%

So we multiply by efficiency:$$P_\text{actual} = P \times 0.45$$

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9. Power vs Energy (Very Important)

Power (Watts)

• How fast electricity is produced

Energy (Watt-hours)

• How much electricity is produced over time

Equation:

$$\text{Energy} = \text{Power} \times \text{Time}$$

Example:

• Turbine power = 10 MW
• Time = 5 hours

$$10 \times 5 = 50 \text{ MWh}$$

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10. Capacity Factor (Why Turbines Don’t Run at Full Power)

Wind changes constantly.

Capacity factor equation:

$$\text{Capacity Factor} = \frac{\text{Actual Energy}}{\text{Maximum Possible Energy}}$$

Offshore wind typically:

• 45–60%

Example:

• Max possible = 100 MWh
• Actual = 50 MWh

$$50 ÷ 100 = 0.5 = 50\%$$

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11. Electricity Losses in Cables

Electricity loses energy as heat.

Loss equation:

$$P_\text{loss} = I^2 R$$

Where:

• $I$ = current
• $R$ = resistance

Why voltage is increased:

Higher voltage → lower current → lower losses

That’s why offshore substations step voltage up.

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12. AC vs DC (Basic Maths Difference)

AC:

• Voltage changes direction
• More losses over long distances

DC:

• Constant direction
• Fewer losses offshore

Loss comparison:$$\text{Loss} \propto \text{Distance}$$

DC grows more slowly with distance.

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13. Scaling Up: Wind Farms

Total power:$$\text{Total Power} = \text{Power per turbine} \times \text{Number of turbines}$$Total Power=Power per turbine×Number of turbines

Example:

• 12 MW turbine
• 80 turbines

$$12 \times 80 = 960 \text{ MW}$$

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14. Carbon Savings (Simple Arithmetic)

Equation:

$$\text{CO₂ saved} = \text{Energy} \times \text{Carbon intensity}$$

If fossil fuel = 400 kg CO₂/MWh
Wind = ~0 kg CO₂/MWh

Then:$$1{,}000 \text{ MWh} \Rightarrow 400 \text{ tonnes CO₂ saved}$$

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15. That’s All the Maths You Need

Every offshore wind calculation comes back to:

1. Wind speed
2. Blade size
3. Efficiency
4. Time
5. Losses

No calculus. No advanced physics. Just:

• Multiplication
• Squaring
• Cubing
• Percentages