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Solving For True Wind Direction

Your vessel is on course  180°T, speed 22 knots. The apparent wind is from 70° off the port bow, speed 20 knots. The true wind direction and the speed of the wind are________.

 Given:                Own course = 180°T
                            Own speed = 22 knots
                      Apparent angle =  70°
             Apparent wind speed = 20 knots

What is asked: 
  1. True wind direction
  2. True wind speed
Solution:   

 Note: We have to solve first the true wind speed before we can proceed into solving true wind direction. Regarding how to solve "true wind speed", I'll refer you my other post so that I can proceed directly to solve for the true wind direction. Here's the link: solving for true wind speed.

This is the formula for true wind direction: 

True Wind Directon = Apparent wind speed² - True Wind Speed² - Own Speed²
÷ 2 x True Wind Speed x Own Speed. Then inv cosine.

And then the result will be added or subtracted to Own Course.

True Wind Direction=20²-24²-22²÷2x24x22
                                           -660÷(2x24x22) = -0.625 inv COS = 129°

Now, Own Course 180°-129°= 51° is the True Wind Direction. I subtract because the apparent wind is in the bow. You might ask, what if the apparent wind is located at the quarter? You have to add it.


  
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