1. True Wind
Prompt: What is a true wind? How is the true wind defined in terms of the reference frame?
Answer – A true wind is a wind vector with magnitude (speed) and direction referenced to the fixed Earth and a direction from which the wind is blowing referenced to true (not magnetic) north.
Direction “from” which the wind is blowing is a convention set by the World Meteorological Organization.

2. Suspect True Direction Data
Facilitator Notes:
Point out the changes (steps) in the true wind direction (DIR) that correspond to turns made by the vessel (changing course [PL_CRS]).
When you see a signal of the motion of the ship in your “true” wind data, that should raise a red flag.

3. Suspect True Speed Data
Facilitator notes:
Note the changes (steps) in true wind speed (SPD) that correspond to changes in vessel speed (PL_SPD).

4. Coordinate Systems Facilitator Notes:
Note the differences between the Earth, ship, and mathematical coordinate systems. Math coordinates have a different zero location and increase counterclockwise.
These differences appear in the equations for true wind calculations.

5. Definitions True Wind (T) – Wind vector with
speed and direction referenced to fixed Earth and
direction from which the wind blows referenced to true north (not magnetic north).
Apparent Wind (A) – Wind vector with
speed referenced to the vessel and
direction from which the wind blows referenced to true north.
Platform-Relative Wind (P) – Wind vector with
speed and direction referenced to the vessel and
direction from which the wind blows referenced to the bow.
Prompt: Ask participants if they are familiar with vectors.
Explain the convention that a Bold letter is a vector. Vectors have both a magnitude AND a direction. Contrast winds with air temperature (scalar value with no direction).
Mention that the apparent wind direction is derived by adjusting the platform wind direction using the heading and zero reference angle for the anemometer.
Facilitator Notes:
Note: “From vs. To” is a common concern between meteorologists and oceanographers (who record currents in the direction to which they flow).
By convention of the World Meteorological Organization – winds are reported with direction from which they blow.

6. Definitions Course Over Ground (C) Heading (hθ)
Vector motion of the vessel with a speed and direction to which the vessel is traveling referenced to true north.
Heading (hθ)
The direction to which the bow of the vessel is pointing referenced to true north.
Facilitator notes:
The magnitude of C and Cθ describe the course vector.
The heading angle can differ from the course angle when the vessel is crabbing due to currents (or strong winds).

7. Definitions Zero-line-reference (Rθ)
The angle between the zero line on the wind vane (anemometer) and the bow of the vessel;
Measured clockwise from the bow.
Facilitator Notes:
The orientation of the anemometer on the vessel must be documented.
Often it is more convenient to orient the zero line on the wind vane in a direction other than the bow (e.g., along a mounting arm, towards the stern, etc.)
Refer to the discussion of the dead zone on most mechanical anemometers from Lesson 2.

8. Impact of 180˚ Error in Rθ Facilitator Notes:
A 180˚ error in platform wind direction generally results in an error in the true wind speed that is less than or equal to double the ship’s speed over the ground.
Such an error can result from an unreported zero line angle toward the stern or an anemometer installed backwards.

9. 1D Example of True Wind Vector Math
Vessel is stationary on a day with true wind blowing directly over the bow.
Facilitator Notes:
Start with a stationary ship with wind blowing directly over the bow.
Anemometer would measure wind of |T| with direction from 0˚.

10. 1D Example of True Wind Vector Math
Vessel moves forward inducing additional wind relative to the vessel.
Facilitator Notes:
When vessel move forward (Course = 0˚, speed |C|), an additional wind induced by the vessel motion (M) will be added to the true wind (T).
Note that M has the same magnitude as C, but with opposite sign (180˚ opposite direction).

11. 1D Example of True Wind Vector Math
A = T + M
T = A – M
M = –C
T = A – (–C) = A + C
Facilitator Notes:
The apparent wind on the vessel, as measured by the anemometer, would be equal to T + M.
Therefore, calculating the true wind requires removing the wind induced by the motion of the vessel (M) from the apparent wind.
Continue discussion with the equations to get final form of T = A + C.
Prompt: As a reminder, what of these vectors do you actually measure?
Answer – Course and apparent wind vectors.

12. Calculation Details Calculate the apparent wind in math coordinates.
A’θ = 270˚ – (hθ+Rθ+Pθ)
|A| = |P|
Adjust the course over ground to math coordinates.
C’θ = 90˚ – Cθ
Facilitator Notes:
Given course vector, platform relative wind vector, heading, and zero reference angle, here are the detailed calculations to derive the true wind.
Note: all calculations are done in math coordinates. Thus the 270˚ accounts for the 180˚ correction for meteorological convention and 90˚ to get to math coordinates.
This graphic has Rθ = 0˚.
In the example, A’ θ = -10˚, C’θ = 45˚

13. Calculation Details Calculate the components of the true wind vector.
Tu = T’u = |A| cos(A’ θ) + |C| cos(C’ θ)
Tv = T’v = |A| sin(A’ θ) + |C| sin(C’ θ)
Calculate the true wind speed and direction from which the wind is blowing.
|T| = (Tu2 + Tv2)0.5
T θ = 270˚ – arctan(Tv/Tu)
NOTE: Arctan function must have a range of -180˚ to +180˚.
Facilitator notes:
U component falls on x axis in math coordinates V component falls on y axis.
Atan2 function in FORTRAN works, but atan will not.
Must also ensure that trigonometric functions will work with input of degrees, if not you need to convert all directions to radians.

14. Averaging Errors Facilitator notes:
Highlight spikes in true wind direction when vessel changes speed and heading.
These are acceleration spikes that result from calculating true winds after averaging input values.
Prompt: What types of motions would result in the acceleration of a an anemometer on a vessel?
Answer: vessel speed change, course change, heading change (turns), pitch, roll, heave.

15. Turning Ship Alters Apparent Wind
Facilitator Notes:
When a vessel turns (in this case while traveling at a steady forward speed over the ground; red), the apparent wind (blue) changes continuously during the turn.
Since the true wind equations are nonlinear (through the sine and cosine functions), they are accurate only when all the input parameters are approximately constant over the averaging period.
In the case above, the turning results in a lack of constancy over the time period of the turn.

16. Incorrect Averaging Method
Course
Speed
Heading
P. Wind Direction
P. Wind Speed
True Wind Direction
True Wind Speed
0.0
5.0
300.0
10.0
350.0
305.0
10.5
340.0
310.0
11.0
330.0
315.0
11.5
320.0
12.0
13.0
13.5
290.0
14.0
280.0
355.0
14.5
270.0
15.0
4.4
331.2
11.7
271.1
8.1
Facilitator Notes:
As an example, say the turn in the previous diagram occurred over one minute and the acquisition system on the vessel records every five seconds.
We wish to calculate a one-minute averaged true wind value.
The data above would represent the conditions during the turn. We assume no ocean currents, so the heading equals the course over the ground.
If the ten input values are vector averaged first over the minute, the resulting true wind direction and speed are shown at the lower right.

17. Correct Averaging Method
Course
Speed
Heading
P. Wind Dir
P. Wind Speed
True Wind Dir
True Wind Speed
0.0
5.0
300.0
10.0
270.0
8.7
350.0
305.0
10.5
266.8
340.0
310.0
11.0
263.8
330.0
315.0
11.5
261.1
320.0
12.0
258.5
8.8
13.0
263.9
9.0
13.5
269.0
290.0
14.0
274.5
9.1
280.0
355.0
14.5
272.4
9.5
15.0
267.1
Facilitator Notes:
The proper way to create the one-minute average is to calculate the true winds for each five-second sample, and then vector average the five-second true winds.
The resultant one-minute average true wind is shown at the lower right.
Note that the difference is ~ 1.0 m/s in this case.

18. Questions?