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Wind Speed Calculator. True, Apparent.

Posted on by Katamarans

True Wind, Apparent Wind Calculator

Try this tool if you would like to convert true wind speed and direction to apparent and vice-versa.

Normally you know your speed over ground (SOG) and you are either inputting TWS and TWA to find the Apparent values or the AWS and AWA to find the true values.

Wind Calculator

Enter three or four values to calculate the missing one or two.

This tool is a sailing wind calculator designed to help you determine the relationship between True Wind and Apparent Wind.

In sailing, the True Wind is the actual speed and direction of the wind over the water, while the Apparent Wind is the wind speed and direction you feel on the boat, which is a combination of the true wind and the wind created by the boat’s movement.

How the Tool Works

The tool works by treating wind and boat speed as vectors. A vector is a quantity with both magnitude (speed) and direction. The fundamental principle is that the Apparent Wind vector is the sum of the True Wind vector and the Boat Speed vector.

true wind to apparent wind calculator
  1. Vector Decomposition: The tool takes the speed and angle you enter for each value (True Wind Speed, True Wind Angle, and Boat Speed) and breaks them down into their horizontal (X) and vertical (Y) components. This is done using trigonometry:
    • X=speed×cos(angle)
    • Y=speed×sin(angle)
  2. Vector Addition: To find the missing value(s), the tool adds or subtracts the known vectors’ components. For example, to find the Apparent Wind, it adds the X and Y components of the True Wind and Boat Speed vectors.
  3. Vector Composition: Once the combined X and Y components are found for the missing value, the tool uses the Pythagorean theorem to calculate the new speed (the vector’s magnitude) and the atan2 function to calculate the new angle (the vector’s direction). This process is repeated to solve for any missing values.

Here are the mathematical formulas used by the wind calculator, presented with a guide to the symbols. These equations are a direct representation of the vector calculations performed in the code.

Mathematical Formulae

Guide to Symbols

  • W: True Wind Speed (TWS)
  • V: Boat Speed (SOG)
  • α: The angle between the boat’s course and the true wind, in radians (TWA)
  • atan2(y,x): This is a programming function that correctly calculates the angle in degrees from the X and Y components of a vector. It is a more robust alternative to the arccos function.

These formulae are what the tool uses to solve for the missing values. The code converts angles to radians for calculation and then back to degrees for display.

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