Mathematical study of wind and wind power

Summary: Wind and wind power have been mathematically studied for centuries as an energy source and promise to be increasingly important energy sources.

Wind is omnipresent. There are few parts of the world that are not affected by the wind, from the pleasant breezes off a lake to the terrifying destruction of hurricanes and tornados. Historically, wind was one of the most important sources of energy; it drove sailing ships and was key to driving some pre-industrial revolution machines, such as windmills. Being able to master the wind was a key component in the fate of empires. For example, in 1588, it is said that the Spanish Armada of Catholic King Philip II was defeated by a “strong Protestant wind” that forced his fleet off course and prevented a vulnerable England under the reign of Queen Elizabeth I from being invaded. In the wake of the steam engine, developed by James Watt in the 1760s, and the emergence of coal-powered machines during the Industrial Revolution, the age of wind and sail began to decline for much of the industrialized world. Many cite this shift to fossil fuel sources as a cause of the rise in carbon dioxide, other greenhouse gasses (GHGs), and the global warming phenomenon, and there is a movement toward returning to wind as one source of clean energy.

Mathematicians and scientists have long been involved in the study of wind and wind energy. Posidonius of Rhodes (c. 135–51 b.c.e.) theorized about clouds, mist, wind, and rain. Francis Beaufort (1774–1857) developed a mathematical scale to describe wind speed. Twenty-first-century engineer Michael Klemen has explored mathematical issues of wind data acquisition as a function of time and estimated wind resource availability for power generation. Mathematicians continue to contribute to these fields and to the exploration of related phenomena like solar winds, which are believed to have first been observed by astronomer John Herschel during his observations of Halley’s comet in 1835.

History

Seventeenth-century mathematician Evangelista Torricelli was reputed to be skilled in making instruments and he is often credited with inventing the barometer. He also conducted research about weather and is believed to have given the first correct explanation of wind when he said, “winds are produced by differences of air temperature, and hence density, between two regions of the earth.” In the seventeenth and eighteenth centuries, mathematician Philippe de La Hire studied instruments to measure climate, including temperature, pressure, and wind speed. He went on to collect data using these instruments at the Paris Observatory. In the nineteenth century, William Ferrel proposed a model for wind circulation, which was the first recorded theory to explain the westerly winds in the middle latitudes of both the northern and southern hemispheres. Ferrel cells are phenomena where air flows eastward and towards the pole near the Earth’s surface, but westward and toward the equator at higher altitudes. The Beaufort wind scale was also named in the nineteenth century after Francis Beaufort, a British Rear Admiral who reportedly extended the work of many individuals in trying to standardize wind measurement and description. The invention of the cup anemometer by astronomer and physicist John Robinson in the middle of the same century aided in measuring winds and reputedly helped popularize the measure. The Beaufort wind scale was later revised by meteorologist George Simpson in the early twentieth century. Mathematician Lewis Richardson is widely considered a pioneer of mathematical weather prediction. He applied the method of finite differences and other mathematical methods in his Weather Prediction by Numerical Process in 1922. Wind is often mathematically modeled as a fluid, and some of Richardson’s work was an extension of studies regarding water flow in peat. The Richardson number is a function involving gradients of temperature and wind velocity. Edward Milne, his contemporary, studied wind and sound, helping to refine huge binaural listening trumpets used to detected aircraft at night during World War I. In the twenty-first century, mathematicians often model various aspects of wind and wind power, including the wind movement through plant canopies using first and second order closure techniques; the probability of bird collisions with wind turbine rotors using statistical methods and calculus; descriptions and predictions of surface wind in mountainous terrain using statistical methods, geometry, vectors, and other mathematical functions; and the wind flow or turbulence over many types of surfaces, including turbine blades, ocean waves, automobiles, and structures.

U.S. Wind Research and Applications

The first wind system to generate electricity in the United States was built by Charles Brush in the late nineteenth century. However, there was relatively little development in that area until the energy crises of the 1970s, which motivated people to seek alternative sources of electricity, such as wind. The 1990s and the 2000s saw technological advances, decreasing turbine costs, and the emergence of popular and political support for wind energy. At the start of the twenty-first century, the U.S. government aimed to have 20% of all electricity generated by wind by 2030. Moreover, statistical studies and other data suggest that wind should be able to compete on a cost-effective basis with traditional fossil fuel sources. Some reports even estimate that wind will account for 26% of the increase in renewable energy production by 2035, though this extrapolation may not be reliable. Wind has shown a number of advantages compared to other forms of electricity production: it does not emit greenhouse gasses while in operation, it is freely available, it is not subject to energy security concerns, there are no waste products, and the maintenance costs are relatively low compared to traditional or nuclear generating facilities. For energy sources such as wind and nuclear, the emissions occur during the construction phase and tend to be associated with the amount of concrete and steel used in the facilities. Wind energy also faces technological problems with intermittency, as electricity can only be produced while the wind is blowing and this problem had been studied by mathematicians.

For example, the Weibull correlation model, based on the Weibull distribution named for mathematician (Ernst) Waloddi Weibull, estimates energy outputs with reduced uncertainty versus previous models, which is potentially useful for preventative operation and maintenance strategies. The National Renewable Energy Laboratory offers both wind data sets and has developed many mathematical models to explore wind energy grids, economic impact of wind energy, and even a model called Village Power Optimization Model for Renewables (ViPOR), which is a computational tool that facilitates the design of a village electrification system using the lowest cost combination of centralized and isolated power generation. Beyond land-based power generation, scientists and engineers like Maximillian Platzer and Nesrin Sarigul-Klijn are exploring the potential benefits of a return to wind energy as a supplement for large, ocean-going ships.

Bibliography

Huler, Scott. Defining the Wind: The Beaufort Scale and How a Nineteenth-Century Admiral Turned Science Into Poetry. New York: Three Rivers Press, 2004.

Shepherd, William, and Li Zhang. Electricity Generation Using Wind Power. Singapore: World Scientific Publishing Company, 2010.

Walker, Gabrielle. An Ocean of Air: Why the Wind Blows and Other Mysteries of the Atmosphere. London: Bloomsbury, 2007.