Average Wind Direction

Date: 05/21/97 at 20:32:14
From: Josh Morcom
Subject: Average wind direction

We have a weather instrument that records wind direction once every
second. (A numerical value between 0 and 359)
  
Our problem is to calculate average wind direction once each hour
using 3600 samples.
  
Any help that you can give us will be greatly appreciated.

Josh Morcom

Date: 05/22/97 at 05:18:57
From: Doctor Mitteldorf
Subject: Re: Average wind direction
      
Dear Josh,

You may be confused about this problem because it really doesn't have
a clear answer!  Sometimes the idea of an "average wind direction" 
makes sense, but sometimes it won't make any sense at all.

Here's an example of how it CAN make sense.  If the wind blows from 
the east (90 deg) for half an hour and from the south (180 deg) for 
half an hour, you can clearly say that the average wind direction for 
that hour is southeast (180 + 90)/2 = 135 deg.

Here's an example of how it DOESN'T make sense. If the wind blows from
the east (90 deg) for half an hour and from the west (270 deg) for 
half an hour, there really is no average direction at all. You could 
say south, but you could just as well say north.  

Here's what I would do if I were you. First look at the sample "by 
eye" to see if the wind direction was pretty consistent, or if it 
varied all over the map. If it varied too much, and had a lot of N, S, 
E and W in it all in one hour, you just have to say that there is no 
meaning to "average wind direction."

But if it's pretty consistent, then you can keep going. Let's say 
that all the numbers are between 80 and 150 deg. Then you can just 
add them all up and divide by 3600, the usual way you take an average.

It is a little trickier if the wind is coming approximately from the 
north. Then there will be some numbers between 0 and 30, say, and 
some more between 300 and 359. If that's the case, then you might add 
360 to all the LOW numbers before you do the average. For every number 
that's 0-30 you add 360, and for every number that's between 300 and 
359 you keep the same.  Add them all up and divide by 3600 to get the 
answer.

Here's one problem I'll leave you with: Suppose you do all that and 
the answer you get is an average of 368 degrees.  What does that 
really mean?

-Doctor Mitteldorf,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/