Marine Wind Calculator
True & Apparent Wind Calculation • Tactical Plotting Board
Wind Vector Triangle (Velocity Triangle)
In maritime navigation and marine meteorology, the following conventions are standard:
- True Wind (TWD / TWS) — The direction the wind is blowing from relative to Earth, and its true speed.
- Vessel Course & Speed (COG / Vs) — The direction the vessel is moving towards and its speed through water or over ground.
- Headwind from Vessel Motion — The airflow produced purely by forward speed, directed straight into the bow:
-Vs. - Apparent Wind (AWD / AWS) — The vector resultant of true wind and the ship's speed wind, as measured by onboard masthead anemometers.
W_A = W_T + V_S (Apparent = True + Vessel Speed)
W_T = W_A - V_S (True = Apparent - Vessel Speed)
Cartesian projections (X = East, Y = North):
X_s = V_s * sin(COG), Y_s = V_s * cos(COG)
X_t = X_a - X_s, Y_t = Y_a - Y_s
V_t = sqrt(X_t² + Y_t²), TWD = (atan2(X_t, Y_t) * 180 / π + 360) mod 360
The Navigator's Rule ("Wind Shifts Forward")
Whenever a vessel gathers forward speed, the apparent wind always shifts forward (heads toward the bow) relative to the true wind. On close-hauled (upwind) points of sail, apparent wind speed increases significantly, producing greater heel and rig loads, whereas on downwind runs (broad reach, running) apparent wind drops markedly.
Points of Sail Relative to True Wind Angle (TWA)
| Relative Angle (TWA) | Point of Sail | Key Characteristics |
|---|---|---|
| 0° – 10° | Head to Wind (In Irons) | No-go zone, sails luff, direct headwind, maximum apparent wind |
| 10° – 80° | Close-Hauled | Upwind sailing, substantial heel, elevated apparent wind speed |
| 80° – 100° | Beam Reach | Wind directly on the beam (traversing 90°), fast and balanced |
| 100° – 170° | Broad Reach | Off-the-wind sailing, optimal cruising speed and gentle motion |
| 170° – 180° | Dead Run (Running) | Wind directly from astern, apparent wind speed is at its lowest |
True Wind Calculator: Solving the Marine Velocity Triangle for Bridge Teams
Maintaining situational awareness on a commercial vessel’s navigation bridge requires constant analysis of prevailing weather dynamics. While shipboard anemometers provide precise readouts of wind speed and direction across the deckhouse, they record Apparent Wind (AWS / AWD). Apparent wind is the resultant vector combining the atmospheric air movement and the artificial airflow generated by the vessel’s own speed through the water or over ground.
For meteorological reporting, passage planning, heavy weather maneuvering, and synoptic weather observation, the bridge team must isolate the True Wind (TWS / TWD) relative to the sea surface. The NavLib True Wind Calculator provides deck officers, shipmasters, and marine surveyors with an automated mathematical engine that resolves the velocity triangle instantaneously without manual plotting sheets.
Navigational Conventions
In accordance with international IMO and World Meteorological Organization (WMO) standards, all marine wind directions represent the azimuth or compass bearing FROM WHICH the air mass approaches:
True Wind (TWD / TWS): direction (000 to 359 degrees True) and velocity of the meteorological wind across the ocean surface.
Vessel Motion (COG / SOG): course over ground and speed of the ship.
Apparent Wind (AWD / AWS): relative wind direction and velocity measured by anemometers on the masthead.
Mathematical Framework and Projection Formulas
The calculation engine solves vector addition and subtraction by resolving velocities into orthogonal Cartesian components (X representing Easting, Y representing Northing):
Ship Motion Components:
X_s = V_s * sin(COG)
Y_s = V_s * cos(COG)
Apparent to True Wind Conversion (AWD to TWD): Using anemometer speed V_a and relative angle AWA:
For Starboard wind: AWD = (COG + AWA) modulo 360 degrees
For Port wind: AWD = (COG – AWA + 360) modulo 360 degrees
Apparent wind components: X_a = V_a * sin(AWD), Y_a = V_a * cos(AWD)
True wind components: X_t = X_a – X_s, Y_t = Y_a – Y_s
True wind speed: V_t = square root of (X_t * X_t + Y_t * Y_t)
True wind direction: TWD = (atan2(X_t, Y_t) * 180 / Pi + 360) modulo 360 degrees
True to Apparent Wind Conversion (TWD to AWD): Converting meteorological forecasts into anticipated relative forces:
True wind components: X_t = V_t * sin(TWD), Y_t = V_t * cos(TWD)
Resultant apparent components: X_a = X_t + X_s, Y_a = Y_t + Y_s
Apparent wind speed: V_a = square root of (X_a * X_a + Y_a * Y_a)
Apparent wind direction: AWD = (atan2(X_a, Y_a) * 180 / Pi + 360) modulo 360 degrees
Operational Insights: Head-Wind Shift Dynamics
As a vessel moves ahead, the apparent wind always shifts toward the bow compared to the true wind vector.
On head-to-wind or close-hauled courses, the ship’s own speed stacks directly against incoming air masses, drastically amplifying apparent wind speed and wind resistance.
On running courses (broad reach or dead run), the vessel runs with the wind, lowering apparent wind speed and reducing bridge wind chill.
The integrated tactical radar display provides visual vector triangle validation, featuring selectable North-Up and Course-Up presentations alongside automated Beaufort Scale grading.