What Is The Formula For Wind Speed?

Wind speed refers to the rate at which air moves horizontally past a given point. It is usually measured by anemometers at weather stations in units like kilometers per hour or miles per hour. Knowing the wind speed is important for a variety of applications, such as predicting weather, estimating energy production from wind turbines, determining airplane takeoff and landing patterns, and assessing impacts on structures.

Wind speed can change rapidly based on the weather and geography, so there are mathematical formulas and scales used to measure and quantify wind speeds for analysis and standard comparisons.

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Wind Speed Units

There are several common units used to measure wind speed:

Miles per hour (mph) – This is a commonly used unit in the United States to measure wind speed. 1 mph is approximately 1.6 km/h.
Kilometers per hour (km/h) – This metric unit is used to measure wind speed internationally. 1 km/h is approximately 0.62 mph.

Knots – This nautical unit measures a ship’s speed through water. 1 knot is equal to 1.15 mph or 1.85 km/h.
Meters per second (m/s) – The SI unit of wind speed is meters per second. 1 m/s is approximately 2.24 mph or 3.6 km/h.

Of these units, meters per second is the standard scientific measure, while knots, miles per hour and kilometers per hour are common everyday units used in weather forecasts and reports. The choice of unit depends on the country and context.

Beaufort Wind Force Scale

The Beaufort Wind Force Scale is an empirical measure developed in 1805 by British Royal Navy officer Sir Francis Beaufort that relates wind speed to observed conditions at sea or on land (https://www.weather.gov/mfl/beaufort). The scale categorizes wind speeds into 13 force numbers from 0 to 12, with each number corresponding to a range of wind speeds, a classification name, and a description of observed conditions.

For example, Force 6 on the Beaufort scale corresponds to “strong breeze” with wind speeds from 22-27 knots. At this force level, “large branches in motion; whistling heard in telephone wires; umbrellas used with difficulty” (https://www.spc.noaa.gov/faq/tornado/beaufort.html). This qualitative description of wind effects gives an intuitive sense of the wind conditions. The scale starts at Force 0 for winds less than 1 knot (calm) and goes up to Force 12 for hurricane-force winds over 64 knots.

Though initially designed for sailors to estimate wind speed based on visual observations, the Beaufort scale remains useful today for describing wind intensity and assessing conditions on land. It provides a standardized way to communicate the degree of windiness, making it a popular reference tool among meteorologists and weather forecasters (https://www.rmets.org/metmatters/beaufort-wind-scale).

Factors Affecting Wind Speed

There are several key factors that influence wind speed:

Pressure gradient force – Winds blow from areas of high pressure to areas of low pressure. The greater the difference in pressure, the stronger the wind speed. This pressure gradient force is the primary driver of wind flow.

Coriolis force – The rotation of the Earth causes moving air to be deflected to the right in the Northern Hemisphere and to the left in the Southern Hemisphere. This impacts wind direction more than speed.

Friction – Surface drag slows winds closer to the ground. Friction has a greater impact over land than over water. Wind speed generally increases with altitude.

Temperature – Temperature differences create pressure gradient forces. Warm air rises while cold air sinks, causing winds. Large temperature variations between air masses lead to stronger pressure gradients and faster winds.

Moisture – Dry air flows more readily than moist air. The mixing of moist and dry air masses can create winds as they attempt to reach equilibrium.

Terrain – Mountains, valleys, bodies of water, and other geographic features can channel winds, block their passage, or cause turbulence. Winds are generally faster over smooth, open terrain.

Seasons – The strength and position of global pressure systems vary throughout the year, leading to seasonal wind patterns like monsoons and trade winds.

Calculating Wind Speed

The wind speed formula relates the speed of an object to the frequency shift in the sound or electromagnetic waves bouncing off it. This phenomenon is known as the Doppler effect. The formula is:

Wind Speed = (Change in Frequency/Original Frequency) x Speed of Sound

Where:

Change in Frequency is the difference between the transmitted and received frequency of the wave.

Original Frequency is the known frequency of the transmitted wave.
Speed of Sound is a constant (~343 m/s).

The Doppler effect allows devices like anemometers and LIDAR to calculate wind speed by analyzing the change in frequency of waves reflecting off moving air particles. The greater the frequency shift, the faster the wind speed.

This formula relates the physical phenomena of sound/light waves to the motion of air particles. By understanding the relationship between frequency, speed, and motion, we can quantify wind speed.

Anemometers

Anemometers are instruments used for measuring wind speed and are one of the most common tools used in meteorology. They work by using rotating cups or propellers to catch the wind. The spin of the cups or propellers is then converted into wind speed measurements.

Most anemometers have 3-4 cups or propellers mounted horizontally on the end of a vertical shaft. As wind blows into the cups, it causes them to spin. The rate of spin is directly proportional to the wind speed – the faster the spin, the higher the wind speed. There are different types of anemometers that convert this spin into a measurable reading through various methods, but they all operate on this basic principle of using the wind’s force to make the cups rotate.

Some advanced anemometers use ultrasonic signals or lasers to measure wind speed without any moving parts. But the classic spinning cup or propeller design is still widely used for its simplicity and reliability. The key advantage of anemometers is that they provide a direct, real-time reading of wind speed from the environment.

Anemometers are a critical tool for meteorologists and weather stations to quantify wind conditions. They allow for standardized wind speed measurements from different locations to analyze weather systems. Anemometers positioned at different heights also help study vertical wind profiles. Overall, anemometers form the backbone of wind speed data collection used in weather forecasting and climatological analysis.
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Average Wind Speed

Average wind speed can vary significantly depending on geographic location and local climate. According to data from the National Climatic Data Center, the average wind speed across the continental United States is around 10 mph. However, wind speeds tend to be higher in flatter inland areas and along coastlines. The highest average wind speeds in the U.S. are found in parts of the Midwest, Great Plains, and coastal New England where average wind speeds range from 12-14 mph. Some specific locations with very high average wind speeds include Amarillo, TX with 13.9 mph and Nantucket, MA with a 15.4 mph average.

In general, wind speeds tend to be lower in areas of high elevation and complex terrain like mountain ranges since the landscape blocks and slows wind flow. Major cities, forests, and other areas with many buildings, trees, and obstructions also experience slower average wind speeds. The lowest average wind speeds in the contiguous U.S. are found in dense urban areas and forests like Atlanta, GA with a 6.9 mph average and elements of the Appalachian Mountains where average speeds can dip below 5 mph.

Across the globe, the highest average wind speeds are found in coastal areas, on islands, and in other locations exposed to consistent winds blowing across oceans. The windiest place on Earth is Commonwealth Bay in Antarctica which experiences average wind speeds of 50 mph generated by katabatic winds blowing off the polar ice sheet.

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High Wind Events

Higher than average wind speeds are often caused by significant high wind weather events such as tropical cyclones, tornados, and thunderstorms. Hurricanes are large, intense tropical storms with winds greater than 74 mph. Hurricanes generate some of the highest wind speeds and are often the most destructive for coastal locations. Tropical storms are slightly less intense than hurricanes with sustained windspeeds between 39-73 mph. However, they can still cause substantial damage over large swaths of land. According to the Chemical Safety Board, hurricanes alone cause roughly 84 deaths and $54 billion in damage per year in the U.S.

Tornadoes are violent, rotating columns of air in contact with the ground. They are spawned by powerful thunderstorms and can generate very localized, extreme wind speeds called tornado vortex winds that can exceed 250 mph in the most extreme and destructive tornadoes. These winds can cause catastrophic damage to structures and are one of the primary risks tornados pose to human life. According to the National Storm Shelter Association, tornadoes cause approximately 70 deaths and 1500 injuries each year in the U.S.

Thunderstorms themselves can also generate very high, straight-line wind gusts exceeding 100 mph in some cases. These thunderstorm winds can cause significant damage over areas 10-100 miles wide along the leading edge of a thunderstorm. According to the National Weather Service, thunderstorm winds account for half of all severe reports and most wind damage related insurance claims in the U.S.

Impacts of Wind Speed

Wind speed can have various impacts on the natural environment and human structures. Higher wind speeds apply greater force on objects in their path. According to a study from the University of Delaware, offshore wind farms can influence local weather patterns including precipitation and wind speed depending on the farm’s size and distance from shore (https://www.udel.edu/udaily/2020/december/offshore-wind-farms-onshore-precipitation/).

In terms of impacts on vegetation, strong winds can damage trees and agricultural crops. Windthrow refers to trees being uprooted by wind, which is more likely to occur in saturated soil conditions. Wind can also damage branches and disrupt pollination. For crops, high winds can cause lodging, where stems are bent over, reducing yield. Additionally, wind removes moisture from soil through evapotranspiration, causing drought stress in plants.

For structures and buildings, wind load is the lateral force exerted by wind. Strong winds impose positive pressure on windward sides and negative pressure on leeward sides. Buildings must be designed to withstand wind loads to avoid structural failures. Hurricane-force winds can generate enough force to damage roofs, walls, doors and windows. Wind-borne debris carried by extremely high winds can also cause damage. Bridges are particularly vulnerable to wind effects due to their long exposed surfaces and flexibility.

Conclusion

In conclusion, accurately measuring wind speed is critical in a variety of fields and applications. Weather forecasters rely on accurate wind speed data to predict and warn about imminent storms. Wind energy companies need reliable wind speed measurements to identify optimal locations for wind farms and optimize turbine performance. Architects and engineers factor wind load calculations based on wind speed into building designs to ensure structural integrity. Ship captains and aviators use real-time wind speed information to chart safe courses. Researchers analyze wind patterns and speeds to study climate change trends and impacts.

As this article has shown, a wide range of instruments like anemometers, weather vanes, and wind socks have been developed over centuries to quantify wind speed. While visually estimating wind speed based on environmental cues has some utility, using calibrated scientific instruments provides much more precise and standardized measurements. As technology advances, new remote sensing tools like LIDAR allow for higher-resolution wind speed mapping over large areas. Having access to accurate, real-time wind speed data from multiple sources allows everyone from meteorologists and engineers to renewable energy developers and construction firms to make smarter decisions and operate more safely and efficiently. The ability to accurately measure wind speed has unlocked many insights into weather patterns, climate impacts, and wind energy potential to benefit society.