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| Fig. 1: Schematic of a buoyant air turbine. (Image source: B. Suo.) |
A wind turbine is a device that converts the kinetic energy of the wind to electrical energy. Traditional ground based wind turbine harvest winds below 200 meters to the ground level. Since the wind kinetic energy is proportional to the speed it blows, the power generated by a ground based wind turbine is limited to wind speed. Thus, to harvest more energy from wind, one would seek for places where the wind blows stronger. Buoyant Air Turbines (BATs) address this by lifting the rotor to higher altitudes, tapping those faster, more consistent winds to generate more electricity.
Fig. 1 illustrates how a buoyant air turbine works. A buoyant shell filled with helium gas lifts the turbine to high altitudes where the wind is stronger and steadier. [1] The central turbine spins as the wind blows through and collects power. A few tethers connecting the BAT to a ground station carrier electrical current generated by the turbine. The power can thus be transmitted to local power grids. The tethers also serve to control the height of the BAT.
If we make a simple assumption that the power generated by the turbine is proportional to the speed of the wind it collects, we realize that it is not guaranteed a BAT can deliver constant power since the wind speed at a certain altitude can change over time. Therefore, a BAT needs to adjust its height accordingly to find an optimal wind speed. Generally, higher the altitude, stronger the wind. When the wind speed is low, the BAT can automatically increase the height by releasing longer tethers and vice versa.
Let's now calculate how much power a buoyant air turbine can generate. We shall make a few naive assumptions to ease our calculations. Firstly, let's assume that there is only one turbine per BAT. Secondly, we assume that the wind is blowing head on to the turbine. We also assume that at the optimal wind speed, the effective cross section of a turbine is around half of the physical cross section of the blade disc. We are now ready to derive a power formula. We start by recognizing that power is energy per unit time:
| P | = | E t |
= | 1/2 m v2 t |
where E is the kinetic energy carried by the wind blowing through the turbine, t is the time and v is the speed of the wind. Given a certain wind speed v, we are left to determine the mass per unit time. We shall assume that in a given time t, the volume that a chunk of air travels through is a cylinder with a base area set by the cross section of a blade disc and the height set by the wind speed v times the time duration t.
| V | = | Avt |
We recall that the volume of a matter is equal to its mass divided by its density. We can thus combine these two expressions to obtain the mass per unit time. Therefore, the power can be expressed as
| P | = | 1 2 |
ρ v3 A |
where ρ=1.225 kg/m3 is the mass density of air, v is the wind speed and A is the effective cross-section area. This formula implies that the power is determined by the wind speed and effective cross-section area. A major selling point for BAT is that it can harvest high speed wind at high altitude. The power of 3 in the wind velocity term indicates that a small increase in the wind speed can have a dramatic effect on the power output. However, if the goal is to beat over traditional ground based wind turbines, one would also need to consider the size restriction of the BAT's turbine blade. Let's have a rough order of magnitude estimate on the power a BAT can deliver. Earlier BAT models developed by Altaeros Energies has a size of a few meters and can fly to a height of 2000 feet. [2] Earlier models developed by Altaeros Energies has a 10-meter diameter inflatable shell and at its maximum power output, BAT can collect wind with a speed of 10 - 15 m/s. [3,4] Let's thus assume that a BAT has a turbine blade length of 3 m, and collects wind with a speed of 15 m/s. The power is thus
| P | = | 1 2 |
× 1.225 kg/m3 × (15 m/s)3 × | 1 2 |
× π × (3m)2 | = | 29 kW |
Compared with modern ground-based wind turbines, which produce power in the megawatt range, buoyant air turbines deliver only tens of kilowatts. [5] As a result, they are poorly suited to meeting city-scale electricity demand, which is measured in gigawatts. As illustrated by the equations above, given a certain wind speed, a major limitation is the effective cross-sectional area one could achieve in capturing the wind. In earlier prototypes, the rotor diameter is limited to no more than tens of meters, which is smaller than that of a traditional ground based turbine. [3]
As compared to traditional ground based turbines, BAT offers several advantages. By lifting turbines hundreds of meters above the ground, BAT can capture wind streams that are both faster and less intermittent, which can stabilize the overall energy output. Another advantage lies in its mobility. BATs can be transported and installed with far less infrastructure than traditional turbines. This makes it attractive to remote communities, disaster-relief scenarios, or regions where constructing tall towers is impractical. Moreover, the modularity of BAT systems allows operators to adjust altitude in real time, optimizing performance in changing atmospheric conditions.
Despite these benefits, BAT also comes with certain limitations and challenges. One of the key challenges is the restricted turbine diameter imposed by the dimension of the inflatable shell. Since power scales with the swept area of the rotor, this size constraint limits the maximum achievable output. Moreover, stability and safety at high altitude are also concerns. High altitude operations expose BATs to severe weather like icing, thunderstorm and gusts which could complicates the aerodynamics control and tether design. Besides, the long conductive tether can introduce resistive losses and mechanical stresses when transmitting power, adding more challenges to perform maintenance.
Economically, BATs are promising and attracting but not competitive at the scale of national energy grids. Their relatively modest power out put typically in the tens to hundreds of kilowatts for current designs limits their use in large scale renewable portfolios. While future multi-turbine BAT platforms may help close this gap, these remain early-stage concepts that face engineering and regulatory hurdles.
© Bingcheng Suo. The author warrants that the work is the author's own and that Stanford University provided no input other than typesetting and referencing guidelines. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.
[1] C. L. Archer et al., "Global Assessment of High-Altitude Wind Power," Energies 2, 2, (2009).
[2] C. Vermillion, T. Grunnagle, and I. Kolmanovsky, "Modeling and Control Design For a Prototype Lighter-Than-Air Wind Energy System " IEEE 6315434, American Control Conference, 27 Jun 12.
[3] U. Ahrens, M. Diehl, and R. Schmehl, Airborne Wind Energy (Springer, 2013).
[4] J. Samson et al., "Multivariable Control of a Lighter than Air System," IEEE 6915149, UKACC Intl. Conf. on Control, 9 Jul 14.
[5] O. Friedman, "Wind Turbines," Physics 240, Stanford University, Fall 2021.