The problem of the second wind turbine – a note on a common but flawed wind power estimation method

Several recent wind power estimates suggest how this renewable resource can meet all of the current and future global energy demand with little impact on the atmosphere. These estimates are calculated using observed wind speeds in combination with specifications of wind turbine size and density to quantify the extractable wind power. Here we show that this common methodology is flawed because it does not account for energy removal by the turbines that is necessary to ensure the conservation of energy. We will first illustrate the common but flawed methodology using parameters from a recent global quantification of wind power in a simple experimental setup. For a small number of turbines at small scales, the conservation of energy hardly results in a difference when compared to the common method. However, when applied at large to global scales, the ability of radiative gradients to generate a finite amount of kinetic energy needs to be taken into account. Using the same experimental setup, we use the simplest method to ensure the conservation of energy to show a non-negligble decrease in wind velocity after the first turbine that will successively result in lower extraction of the downwind turbines. We then show how the conservation of energy inevitably results in substantially lower estimates of wind power at the global scale. Because conservation of energy is fundamental, we conclude that ultimately environmental constraints set the upper limit for wind power availability at the larger scale rather than detailed engineering specifications of the wind turbine design and placement.