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True WindTrue Wind

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Suspect True Direction DataSuspect True Direction Data

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Suspect True Speed DataSuspect True Speed Data

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Coordinate SystemsCoordinate Systems

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DefinitionsDefinitions• 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.

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DefinitionsDefinitions• Course Over Ground (C)

• 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.

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DefinitionsDefinitions

• 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.

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Impact of 180˚ Error in RImpact of 180˚ Error in Rθθ

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1D Example of True Wind Vector Math1D Example of True Wind Vector Math

• Vessel stationary on day with true wind is blowing directly over the bow.

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1D Example of True Wind Vector Math1D Example of True Wind Vector Math

• Vessel moves forward inducing additional wind relative to the vessel.

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1D Example of True Wind Vector Math1D Example of True Wind Vector Math

• T = A – M

• M = –C

• T = A – (–C) = A + C

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Calculation DetailsCalculation Details

1. Calculate the apparent wind in math coordinates.A’θ = 270˚ – (hθ+Rθ+Pθ)

|A| = |P|

1. Adjust the course over ground to math coordinates.C’θ = 90˚ – Cθ

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Calculation DetailsCalculation Details3. 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 wind is blowing.|T| = (Tu

2 + Tv2)0.5

T θ = 270˚ – arctan(Tv/Tu)

• Arctan function must have a range of -180˚ to +180˚.

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Averaging ErrorsAveraging Errors

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Turning Ship Alters Apparent WindTurning Ship Alters Apparent Wind

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Incorrect Averaging MethodIncorrect Averaging MethodCourse Speed Heading P. Wind

DirectionP. Wind Speed

True Wind Direction

True Wind Speed

0.0 5.0 0.0 300.0 10.0

350.0 5.0 350.0 305.0 10.5

340.0 5.0 340.0 310.0 11.0

330.0 5.0 330.0 315.0 11.5

320.0 5.0 320.0 320.0 12.0

310.0 5.0 310.0 330.0 13.0

300.0 5.0 300.0 340.0 13.5

290.0 5.0 290.0 350.0 14.0

280.0 5.0 280.0 355.0 14.5

270.0 5.0 270.0 0.0 15.0

315.0 4.4 315.0 331.2 11.7 271.1 8.1

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Correct Averaging MethodCorrect Averaging MethodCourse Speed Heading P. Wind

DirP. Wind Speed

True Wind Dir

True Wind Speed

0.0 5.0 0.0 300.0 10.0 270.0 8.7

350.0 5.0 350.0 305.0 10.5 266.8 8.7

340.0 5.0 340.0 310.0 11.0 263.8 8.7

330.0 5.0 330.0 315.0 11.5 261.1 8.7

320.0 5.0 320.0 320.0 12.0 258.5 8.8

310.0 5.0 310.0 330.0 13.0 263.9 9.0

300.0 5.0 300.0 340.0 13.5 269.0 9.0

290.0 5.0 290.0 350.0 14.0 274.5 9.1

280.0 5.0 280.0 355.0 14.5 272.4 9.5

270.0 5.0 270.0 0.0 15.0 270.0 10.0

267.1 9.0

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Questions?Questions?