The Simple Numbers Behind Offshore Wind Power
Offshore wind maths comes down to one simple question:
How much electricity can we make from wind, and how do we deliver it efficiently?
At first, this may sound complicated.
However, the maths is simpler than it looks.
Most offshore wind calculations use only:
- Multiplication
- Squaring
- Cubing
- Percentages
So, let’s build the maths step by step.
1. Start with Wind Speed
Everything begins with wind speed.
Wind speed tells us how fast the air is moving.
It is measured in metres per second (m/s).
Examples
- 5 m/s = gentle breeze
- 10 m/s = strong wind
- 25 m/s = storm conditions
When winds become too strong, turbines shut down for safety.
At this stage, there is no maths yet.
We are simply measuring wind.
2. Why Wind Speed Matters So Much
This is the most important idea in offshore wind maths.
If wind speed doubles, power increases by eight times.
That sounds surprising, but it happens because wind power depends on wind speed cubed.
In simple terms:
More wind = much more power
Even small increases in wind speed can make a huge difference.
3. The Main Power Equation
The basic wind power equation is:
Power = ½ × Air Density × Swept Area × Wind Speed³
That may look intimidating.
However, it becomes much easier when broken into parts.
Power depends on four main things:
- Air density
- Blade size
- Wind speed
- Efficiency
Let’s look at each one.
4. Air Density
Air may seem weightless, but it has mass.
Because of this, moving air carries energy.
Typical offshore air density is about:
1.225 kg/m³
You do not usually calculate this yourself.
Engineers normally use standard values.
A simple idea to remember is:
Denser air = more energy
5. Blade Size (Swept Area)
Turbine blades sweep out a huge circular area.
The bigger this area, the more wind energy the turbine can capture.
The area of a circle is:
Area = π × radius²
Example
If blade length is 100 metres:
Area = 3.14 × 100² = 31,400 m²
That is a huge area.
Also, blade size matters a lot.
If blade length doubles, swept area becomes four times larger.
That is why offshore turbines are so large.
6. Wind Speed Cubed — The Big Factor
This is where power rises dramatically.
Example 1
If wind speed is 10 m/s:
10³ = 1,000
Example 2
If wind speed rises to 12 m/s:
12³ = 1,728
That is a 72% increase in power from a fairly small increase in wind speed.
So, wind speed matters more than almost anything else.
7. Putting It Together
Let’s try a simple example.
Suppose:
- Air density = 1.225
- Blade length = 100 m
- Swept area = 31,400 m²
- Wind speed = 10 m/s
Using the wind power equation gives:
Raw wind power ≈ 19.2 MW
This is the total energy flowing through the spinning area.
However, turbines cannot capture all of it.
8. Why Turbines Cannot Capture All Wind Energy
A turbine cannot remove all energy from the wind.
If it did, the air behind the turbine would stop moving completely.
That is not physically possible.
Betz Limit
The maximum theoretical energy a turbine can capture is:
59.3%
Real turbines usually capture around:
40–50%
So, actual power is always lower than raw wind power.
9. Power vs Energy
This difference is very important.
Power
Power tells you how fast electricity is produced.
Measured in:
- Watts (W)
- Kilowatts (kW)
- Megawatts (MW)
Energy
Energy tells you how much electricity is produced over time.
Measured in:
- kWh
- MWh
- GWh
Formula:
Energy = Power × Time
Example
A 10 MW turbine running for 5 hours produces:
10 × 5 = 50 MWh
10. Capacity Factor
Turbines do not run at full power all the time.
Wind changes constantly.
That is why we use capacity factor.
Capacity factor compares actual output to maximum possible output.
Formula:
Capacity Factor = Actual Energy ÷ Maximum Possible Energy
Typical offshore wind capacity factors are:
45–60%
Example
Maximum possible output = 100 MWh
Actual output = 50 MWh
50 ÷ 100 = 50%
So the capacity factor is 50%.
11. Electricity Losses in Cables
Electricity loses some energy as heat while travelling through cables.
More current usually means more loss.
That is why offshore wind farms increase voltage before sending electricity to shore.
A simple rule is:
Higher voltage = Lower current = Lower losses
This helps reduce wasted energy.
12. AC vs DC
Offshore wind farms use either:
- AC (Alternating Current)
- DC (Direct Current)
AC
- Current changes direction
- Common in electricity networks
- More losses over long distances
DC
- Current flows one way
- Lower losses over long distances
Because of this, long offshore cable links often use DC.
13. Scaling Up to a Wind Farm
A wind farm is simply many turbines working together.
Formula:
Total Power = Power per Turbine × Number of Turbines
Example
Suppose a wind farm has:
- 80 turbines
- Each rated at 12 MW
Total power:
12 × 80 = 960 MW
That is nearly 1 gigawatt of power.
14. Carbon Savings
Offshore wind also reduces carbon emissions.
A simple way to estimate carbon savings is:
CO₂ Saved = Electricity Generated × Carbon Intensity of Fossil Fuel
Example:
If fossil fuel generation produces:
400 kg CO₂ per MWh
Then:
1,000 MWh of wind power saves about 400 tonnes of CO₂
That is a major environmental benefit.
In Short
Most offshore wind maths comes down to five main things:
- Wind speed
- Blade size
- Efficiency
- Time
- Energy losses
That is really all you need.
Once you understand these numbers, offshore wind maths becomes much easier to follow.