To determine the possibility of powering a portion of The Netherlands on wind energy, the amount of wind power that can be derived from the area must be estimated. To estimate the available wind power, the average wind speed will be referenced. The effective wind speed will then be approximately 1.5 m/s higher than the measured value. To determine the speed of the air at the height of the turbine head, the following formula will be used:
velocity at turbine = (velocity measured)*(height of turbine/height of measurement)^(1/7)
velocity at turbine = (1.5 m/s + 3.8 m/s)*(100 m/10 m)^(1/7) = 7.36 m/s
Using the calculated velocity at the turbine, the power per unit area of the land is calculated as
Power/Area = (pi/400)*density*velocity^3 = (pi/400)*(1.2 )*(7.36)^3 = 3.76 W/m^2
The total area of The Netherlands is 41,000 km^2. Assuming that 10% of the country would be available to wind energy (10% is a high approximation given the dense population of the country) the available power is given as:
Available wind power = (0.10)*(3.76 W/m^2)*(41 x 10^9 m^2) = 15.4 GW
This breaks down per person as
(15.4 x 10^6 kW)*(24 hours)/(16,500,000 people) = 22.4 kWh/(day* person)
Offshore Wind
To determine the amount power that can be generated from offshore wind turbines, the same calculations will be used to determine the available power per unit area as was done for inland wind turbines. The turbine height that will be used is 100 m and the wind measurement height is 15 m.
For the effective wind speed at the turbine:
(1.5 m/s + 7.6 m/s)*(100/15)^(1/7) = 11.9 m/s
To determine the power per unit area of land:
Power/Area = (pi/400)*density*velocity^3 = (pi/400)*(1.2 )*(11.9)^3 = 15.88 W/m^2
Assuming that wind turbines can be installed up to 10 km out from the coastline and that the coastline is 450 km, the total power that could be generated can be determined as:
Power = (15.88 W/m^2)*(450,000 m)*(10,000 m) = 71.5 GW
To convert this into kWh/day per person,
(71.5 x 10^6 kW)*(24 hours/day)/(16,500,000 people) = 104 kWh/day per person
The weight of all the concrete and steel that will be used is determined using a ratio developed from Mckay's method. McKay has stated that 48 kWh per day per person can be produced from 60 million tons of concrete and steel. Setting up a proportion and solving for the unknown weight:
x =(104 kWh)*(60 million tons/48 kWh) = 130 million tons of concrete and steel
That would be the required steel and concrete to create such offshore wind turbines.
Hydro-Electric Power
To determine the potential power that could be developed from hydro-electric generators, the rainfall rate of The Netherlands must be known. The rainfall rate will be specified as the cubic meters of rainfall per second. The average elevation is taken as 322 m. The power can be determined using the potential energy rate created by rainfall.
Rainfall rate = (1.72 x 10^7 cubic meters/year)/(31,536,000 seconds/year) = 0.5454 cubic meters/second
The power can then be calculated by:
Power = (0.5454 cubic meters/sec)*(1000 kg/cubic meter)*(9.81 m/s^2)*(322 m) = 1.72 MW
To convert to kWh per day per person,
(1.72 x 10^3 kW)*(24 hours)/(16,500,000 people) = 0.0025 kWh/day per person
Solar
'The power that could potentially be provided by solar radiation in The Netherlands can be determined using an average of the yearly solar energy per unit area. The average yearly energy value is 1150 kWh/m^2. A factor of 15% will be used as the amount of solar energy that can be converted to electrical energy through the use of solar panels.
(1150 kWh/m^2)*(0.15) = 172.5 kWh/m^2
The area that would need to be covered by solar panels in order to provide all needed power can be calculated as:
(55 kWh/day per person)*(16,500,000 people)*(365 days) = 3.3 x 10^11 kWh
Area required = (3.3 x 10^11)/(172.5 kWh/m^2) = 1.92 x 10^9 sq m = 1.92 x 10^3 sq km
This is nearly 5% of the land area!
That would not be feasible due to the dense population of The Netherlands. To obtain a realistic estimate for the solar power that could be generated, a factor of 1% will be used.
Power = (0.01)*(172.5 kWh/m^2 per year)*(41 x 10^9 m^2)/[(365 days/year)*(16,500,000 people) =
11.74 kWh/day per person
The completed green stack looks like this:
Sources for this post: (14) , (15)