How to Measure Direction and Speed of True Wind on Moving Boat

Xiang Zheng Tu

With an anemometer, people can easily measure the direction and speed of natural wind or true wind. The true wind is the term most commonly used to describe sailing wind, without the effects of the motion of the boat. On a moving boat, the measured wind is no longer the true wind instead of apparent wind. The apparent wind is the wind experienced by an observer in motion and is the relative velocity of the wind in relation to the observer. On the moving boat the apparent wind is a product of three other winds: the true wind, tide wind, and motion wind.

Tide wind is the wind created by the motion of the water relative to the land. Motion wind is the wind created by the movement of the boat through the water. By combining these two winds we have boatspeed wind (speed through the water, not speed over ground).

It can be seen that the true wind is a derived number, not a measured number like the apparent wind. This means we cannot physically measure the true wind angle or the true wind speed on the moving boat. We need to calculate it using the apparent wind angle, apparent wind speed, and the boatspeed.

These measured numbers are put through something called “the wind triangle.” The end result is the true wind angle and the true wind speed. These calculations are much more useful to the sailor as they reference the sailing wind outside of the boat and allow them to think strategically.

Fortunately a highly integrated thermopile motion sensing unit has been developed. This unit can measure the speeds of the winds coming from three different directions as shown in the above figure. There are three winds blowing toward the moving boat. One is the boatspeed wind consisting of two components: the boat speed and the true wind component in the forward direction of the moving boat. The second one is the true wind component in the side perpendicular direction of the moving boat. The third one is a combination wind of the boatspeed wind and the true wind, which blows toward the moving boat at 45 degree angle to the forward direction. The combination wind also consists of two components. One is the boatspeed wind component in the direction at 45 degree to the forward direction. The other is the true wind component in the direction at α angle to the side perpendicular direction of the moving boat. The sensing unit contains three thermopile motion sensors that are disposed in the three wind passages, respectively. In operation of the sensing unit, the sensors measure each wind speeds and send out signals V_Forward, V_45digree, and V_Side, which represent their individual wind speeds. 

Reference the above figure, the following equations can be established based on basic trigonometric formulas:

V_Forward = u + ν cos α,                                    (1)

V_45degree = u cos 45⁰ + (v cos α) cos 45⁰,      (2)

V _Side  = ν sin α ,                                             (3)

where u is the speed of the boatspeed wind, v is the speed of the true wind. This is a system of ternary linear equations. The three variables u, v and α in the system can be found by substituting the measured values of V_Forward, V_45degree  and V_Side and cos 45⁰ = 21/2 /2 into the system, and solving the system.

The thermopile motion sensors actually are the thermal flow sensors produced by POSIFA Microsystems. A thermal flow sensor comprises a heater, two thermopiles and a thermal insulated base recessed in a silicon chip and supporting the heater and thermopiles. The sensor measures fluid mass flow rate by means of the heat convected from the heater surface to the flowing fluid. The sensor and the fluid can move in relation to each other. If the sensor is still and the fluid flows the sensor is functioned as a thermal flow sensor. If the fluid is still and the sensor moves the sensor is functioned as a thermopile motion sensor. This is based on the fact that any moving object can produce an apparent wind.

A simple example for the apparent wind is that a man is a riding bicycle on a day when there is no wind. Although the wind speed is zero, the rider will feel a breeze on the bicycle due to the bicycle is moving through the air. This is the apparent wind. On the windless day, the measured apparent wind will always be directly in front and equal in speed to the speed of the bicycle.

Another example is in sailing. The apparent wind is the actual flow of air acting upon a sail. It is the wind as it appears to the sailor on a moving vessel. It differs in speed and direction from the true wind that is experienced by a stationary observer.

In all these examples the thermal flow sensors or the thermopile motion sensors can be used to measure the speeds of the moving objects.