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It only takes a minute to sign up. What is the best way to average wind direction?

### Vector Unit Calculator

I have found many conflicting suggestions elsewhere. This is to be used to produce a windrose where the input must have one record per hour, but the data provided has several records per hour. While it's not quite meaningless to average the direction of the wind, it's ill-defined in many cases imagine that you have a perfect east wind and a perfect west wind and you want to find the direction of their average!

It also has the advantage that it's rotationally invariant ; rotating the entire assemblage by any constant value for instance, making your north wind a northeast wind and your east wind a southeast wind will give an average that's the average of the initial data rotated by that amount. Note that in the case where the average is ill-defined, this method will yield a zero vector for the combined wind's direction, and so it correctly breaks down when trying to find an angle from that result.

Question is old, but I found this in Wikipedia, which might be the "average of sin" stuff you wrote in your question:. Consider the following three angles as an example: 10, 20, and 30 degrees.

Intuitively, calculating the mean would involve adding these three angles together and dividing by 3, in this case indeed resulting in a correct mean angle of 20 degrees. By rotating this system anticlockwise through 15 degrees the three angles become degrees, 5 degrees and 15 degrees.

The naive mean is now degrees, which is the wrong answer, as it should be 5 degrees. Assuming you use the standard meterological convention that wind direction is the source direction of winds i. Given two arrays containing wind speed WS and wind direction WDin degrees observations, the vector mean wind direction is calculated as follows:. Alternately, the unit vector mean wind direction can be calculated by omitting the wind speed components.

The unit vector mean wind direction is often a good approximation to the scalar mean wind direction which is a more involved calculation. The implementation of the arctan2 or atan2 function is important: most programming languages respect the atan2 y, x convention but spreadsheets tend to reverse the arguments as atan2 x, y.

You probably want to take the magnitude of the wind into account. A good solution would be to take the vectors of wind direction, add them all together and divide by the number of samples.

For example, in the above case the average speed would be.The wind is described as having both a direction and a magnitude speedand it is therefore a vector quantity. Although the wind is a vector quantity, the wind direction and speed can be treated separately as scalar values. In collecting wind data, samples are typically collected at a high frequency and then averaged over a time period of a few minutes to an hour.

Depending on the application and the instrumentation, the data may be vector averaged, scalar averaged or averaged using both techniques. In scalar averaging wind data, instruments such as a cup or propeller anemometer and a wind vane are used to make independent measurements of the wind speed and direction.

Philips respironics trilogy 100 priceThe instruments are sampled at regular intervals and simple arithmetic averages of the outputs are calculated over the averaging period. In vector averaging, either the orthogonal components of the wind are measured directly with a wind instrument or the speed and direction are measured with an anemometer and a wind vane and then they are used to derive the orthogonal components.

To obtain the vector-averaged speed and direction, the components are summed and vector averaged at the end of the averaging time.

Brooklyn synthDuring periods of moderate to high wind speeds, the difference between vector and scalar averages will be small. In the case of wind speed, vector-averaged speeds will never be larger than the scalar-averaged values and will generally be lower.

Larger differences will occur with greater wind direction variancewhich typically occurs at lower wind speeds below about 2 meters per second.

As an extreme example, suppose we had a constant wind from the north at 5 meters per second for 5 minutes followed by a constant wind of 5 meters per second from the south for 5 minutes. If we calculated both the vector and scalar averages for the minute period, the vector-averaged speed would be zero, whereas the scalar-averaged speed would be 5 meters per second.

In most real-world situations, the wind direction variability is much less than this extreme example. In moderate wind speeds, say above about 5 meters per second, the wind direction standard deviation sigma theta is typically about 5 to 10 degrees, and the difference between the scalar and vector averages of wind speed will generally be within one to two tenths of a meter per second.

Shown below are some actual wind speed data from a m meteorological tower equipped with a cup anemometer and wind vane:. Both vector- and scalar-averaged speeds were recorded. The vector- and scalar-averaged speeds were obtained with the same anemometer and wind vane, but the averages were derived using the different vector and scalar averaging techniques.

### Crosswind Calculator

These data were averaged over minute periods. Also plotted on the figure below are the corresponding measurements of sigma theta. As shown in this figure, there is very little difference between the vector- and scalar averaged speeds above about 5 meters per second, although the vector-averaged speeds are slightly lower.

Sigma theta values during these periods of higher speeds generally are below about 10 degrees.

How to setup logout macro poeAt lower speeds, larger departures between the vector and scalar speeds occur and the corresponding sigma theta values become large. In the case of wind direction, there will also be differences between vector and scalar averages, particularly at lower speeds.This calculator performs all vector operations. You can add, subtract, find length, find dot and cross product, check if vectors are dependant.

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I have U and V wind component data and I would like to calculate wind direction from these values in R. I have used the following code to try and obtain wind direction column tdbut I am not convinced that the returned angles are those that I want i.

86.330395 & luftkolben!!!! 2 x o-ring für erreger hilti te 76 atcI would appreciate any advice on whether my method is correct, and if not how I could correctly obtain the desired wind direction values.

While Calculating wind direction from U and V components of the wind using lapply or ifelse was helpful, the code did work with my data, and I am sure that there is an easier away to obtain wind direction. Many thanks! Then you must convert this wind vector to the meteorological convention of the direction the wind is coming from:.

While the accepted answer has the right idea it has a flaw. As mentioned in the comments one does not need to normalize the u and v component in order to use atan2 on them.

When not normalizing the components atan2 0,0 happily returns 0. So not only is normalizing not necessary, it also introduces an error. Please also be aware that the most common function signature of atan2 is atan2 y, x -- Microsoft Excel being an exception.

This leads to a Southerly wind degrees for a [0,1] vector, a Northerly wind 0 degrees for a [0,-1] vector, a South Westerly wind degrees for a [1,1] vector:. Learn more. Asked 6 years, 2 months ago. Active 1 month ago.

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## Online calculator. Angle between vectors.

Emily Emily 5 5 gold badges 11 11 silver badges 27 27 bronze badges. Active Oldest Votes. You want an answer in cardinal coordinates which increase clockwise and have a zero on the y-axis. To convert unit circle to cardinal coordinates, you must subtract the unit circle angle from A number followed by a "x10" to some exponent is in scientific notation to conserve space. The standard rules of algebra apply to all the formulas. The geostrophic wind approximations are broken into its two horizontal components.

The "U" component represents the east-west component of the wind while the "V" component represents the north-south component. The two formulas for the U and V component of wind are as follows.

These formulas are extremely tedious and complicated to use. Breaking up the equations into individual terms is probably the easiest way to tackle this calculation. Thankfully, some terms are present in both equations, which will save us some time and effort. To calculate the maximum, prevailing wind speed and direction, you will want to select two points of reference that when connected by a line, will create a line that is perpendicular to the isobars on a typical surface weather map.

This will calculate the maximum pressure gradient between the two points and calculate the most likely prevailing wind. For the example calculation, suppose you are in San Francisco and you want to estimate the wind speed between you and a weather data buoy miles to the northwest, which happens to create the perpendicular line described in the previous paragraph. Let's suppose that the temperature in San Francisco is 60 degrees Fahrenheit and the temperature over the data buoy is 50 degrees Fahrenheit and let's further assume that the atmospheric pressure in San Francisco is millibars and the pressure over the data buoy is millibars.

The latitude of San Francisco is approximately Let's start with term 1 from the equation and calculate the individual terms. This is where vector calculus, right triangles and sin and cosine functions come in handy. The buoy is miles to the northwest, or at the end of a line that is 45 degrees to the north of west and miles long. You can construct a right triangle with the 90 degree angle due west of San Francisco as in the following diagram. Both X and Y must be converted to meters to be used in the equation.

One mile equals If you want to convert U and V from meters per second into miles per hour, use the following conversion factors. To calculate the final answer, we need to combine the U and V components to get the actual wind speed and direction.

The easiest way is to use a vector triangle, similar to the one used previously in the distance calculations. The trigonometric functions can be utilized again as shown below. Note: The minus sign in front of the U component answer indicates an easterly component to the wind, or in other words, a wind that blows from east to west.

A positive U component would mean that the wind is blowing from west to east.

Vw cffb engine problemsThe positive V component answer indicates a southerly component to the wind, or in other words, a wind that blows from south to north. A negative V component would mean that the wind is blowing from north to south.By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service.

Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields.

It only takes a minute to sign up. What is the best way to average wind direction? I have found many conflicting suggestions elsewhere. This is to be used to produce a windrose where the input must have one record per hour, but the data provided has several records per hour.

While it's not quite meaningless to average the direction of the wind, it's ill-defined in many cases imagine that you have a perfect east wind and a perfect west wind and you want to find the direction of their average! It also has the advantage that it's rotationally invariant ; rotating the entire assemblage by any constant value for instance, making your north wind a northeast wind and your east wind a southeast wind will give an average that's the average of the initial data rotated by that amount.

Note that in the case where the average is ill-defined, this method will yield a zero vector for the combined wind's direction, and so it correctly breaks down when trying to find an angle from that result.

Question is old, but I found this in Wikipedia, which might be the "average of sin" stuff you wrote in your question:. Consider the following three angles as an example: 10, 20, and 30 degrees. Intuitively, calculating the mean would involve adding these three angles together and dividing by 3, in this case indeed resulting in a correct mean angle of 20 degrees. By rotating this system anticlockwise through 15 degrees the three angles become degrees, 5 degrees and 15 degrees.

The naive mean is now degrees, which is the wrong answer, as it should be 5 degrees. Assuming you use the standard meterological convention that wind direction is the source direction of winds i. Given two arrays containing wind speed WS and wind direction WDin degrees observations, the vector mean wind direction is calculated as follows:.

Alternately, the unit vector mean wind direction can be calculated by omitting the wind speed components. The unit vector mean wind direction is often a good approximation to the scalar mean wind direction which is a more involved calculation. The implementation of the arctan2 or atan2 function is important: most programming languages respect the atan2 y, x convention but spreadsheets tend to reverse the arguments as atan2 x, y.

You probably want to take the magnitude of the wind into account.

**Understand your E6B! Obtaining wind direction and speed.**

A good solution would be to take the vectors of wind direction, add them all together and divide by the number of samples. For example, in the above case the average speed would be.

This method also has the nice property that it generalizes easily to higher dimensions which, though it might not be relevant for your work, is often an indicator that you're on the right track. Sign up to join this community. The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered.

Calculate average wind direction Ask Question. Asked 8 years, 10 months ago. Active 6 months ago. Viewed 26k times.These tools can be used to construct or resolve a vector. All answers are provided to three decimal places.

These tools only support integers and decimals, fractions are not allowed. How do I solve this. What effect do the ff.

## Online calculator. Angle between vectors.

These tools only support integers and decimals, fractions are not allowed Vector Construction Kits Construct a vector from its individual horizontal x or i and vertical y or j components Add up to three vectors to form a new vector Vector Decomposition Resolve a vector into its horizontal and vertical components Convert from polar coordinates to cartesian coordinates.

Magnitude of the vector's horizontal component Magnitude of the vector's vertical component. Magnitude of 1st vector Direction of 1st vector Magnitude of 2nd vector Direction of 2nd vector Magnitude of 3rd vector optional Direction of 3rd vector.

Vector Magnitude R, radius Vector direction angle, in degrees. Calculate the force of gravity on the 1-kg mass if it were 3. Be sure to use negative signs for any values that are in the opposite direction.

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