Knowing the true wind direction and speed on board ship is important for navigation, weather forecasting and safety. However, determining the true wind is not as simple as looking at a wind vane or an anemometer. The ship’s own motion and orientation affect the apparent/relative wind that is observed on deck. To calculate the true wind, one needs to take into account the ship’s speed and heading, as well as the relative wind direction and speed. In relation to this, we will explain how to use vector algebra and trigonometry to find the true wind from the relative wind and the ship’s data.

To understand better, let’s take a look to this example.

Your ship’s heading is 045° T and a speed of 10 knots. The relative wind speed and direction showing on anemometer is 20 knots from 30° relative. Find the true wind speed and direction.

First, create a line for ship’s heading which is 045° T with its speed of 10 knots. Next, from ship’s position create a line with angle of 30° from ship’s heading with the speed of 20 knots (relative wind direction and speed). Then, at the end of the ship’s heading line, transfer the relative wind direction and speed line but in opposite direction. Now, connect the point of the ship to the end of the transferred relative wind line to create a triangle which will be used for calculation.

Based on the given values:

Let’s put own ship’s speed as side “a” = 10

Relative wind speed as side “b” = 20

True wind speed as side “c” = ?

Relative wind as “θ” = 30°

By using the formula for the **Law of Cosines** which is **c² = a² + b² – 2ab * cos θ,**

Let’s get first the true wind speed which the side “c”.

**c² = a² + b² – 2ab * cos θ**

c² = (10²) +(20²) – (2*10*20* cos 30**°)**

c² = 153.6

c = 12.4

Thus,** true wind speed is 12.4 knots.**

**Now let’s get the true wind direction.**

** **Let’s get first the value of angle Ω as shown.

By using again the formula for the law of cosines, we will come up with this equation.

cos Ω = (a² + b² – c²) / (2ab)

In this case, since we’re looking for the angle Ω, so the side “c” will the value of w-r line which is 20 knots, since it is the opposite of the angle Ω.

cos Ω = (a² + b² – c²) / (2ab)

cos Ω =( 12.4² + 10² – 20²) / (2*12.4*10)

cos Ω = (-146.24)/ (248)

cos Ω =-0.59

Ω = 126**°**

**To get the true wind direction, subtract the Ω from 180° (straight line) then add the heading of the ship.**

True wind direction = (180**° – **Ω) + Ship’s heading

True wind direction = (180**° – 126°) + 045°**

**True wind direction = 099 ° T**

To summarize with regards to the given example, when your ship’s heading is 045° T and a speed of 10 knots. The relative wind speed and direction showing on anemometer is 20 knots from 30° relative. The true wind speed 12.4 knots and wind direction is 099 °T.

(You can download the “True Wind Speed and Direction Calculator” here)