# Apparent wind

V = boat speed, H = head wind, W = true wind, A = apparent wind, α = pointing angle, β = angle of apparent wind

Apparent wind is the wind experienced by a moving object.

## Definition 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.

Apparent wind velocity is the vector sum of the true wind and the headwind an object would experience in still air. The headwind velocity in still air is inverse of the object's velocity, therefore the apparent wind can also be defined as a vector subtraction: the Velocity of the wind minus the Velocity of the object.

## A simple example

Suppose you are riding a bicycle on a day when there is no wind. Although the wind speed is zero (people sitting still feel no breeze), you will feel a breeze on the bicycle due to the fact that you are moving through the air. This is the apparent wind. On the windless day, the apparent wind will always be directly in front and equal in speed to the speed of the bicycle.

Now suppose there is a 5 mph wind coming directly from the north. If you pedal at 10 mph due north, you will feel an apparent wind of 15 mph from the north. But if you pedal 10 mph due south, you will feel an apparent wind of 5 mph from the south. The apparent wind is not only different in speed than the true wind (except when you are standing still), but may also be different in direction.

In these simple examples, the motion is parallel to the true wind which makes it easy to calculate the speed and direction of the apparent wind in relation to true wind speed (relative to the earth). When the motion is not parallel to the wind, one must use trigonometry to calculate the apparent wind. Vector mathematics might also be useful in some cases.

## Apparent wind in sailing

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 nautical terminology, these properties of the apparent wind are normally expressed in knots and degrees. On boats, apparent wind is measured (see "Instruments" below) or "felt on face / skin" if on a dinghy or looking at any telltales or wind indicators on board. True wind needs to be calculated or stop the boat.

## Instruments

The apparent wind on-board (a boat) is often quoted as a speed measured by a masthead transducer containing an anemometer and wind vane that measures wind speed in knots and wind direction in degrees relative to the heading of the boat. Modern instrumentation can calculate the true wind velocity when the apparent wind and boat velocity & direction are input.

## Implications on sailing speeds

In sailboat racing, and especially in speed sailing, apparent wind is a vital factor, when determining the points of sail a sail-boat can effectively travel in. A vessel traveling at increasing speed relative to the prevailing wind will encounter the wind driving the sail at a decreasing angle and increasing velocity. Eventually, the increased drag and diminished degree of efficiency of a sail at extremely low angles will cause a loss of accelerating force. This constitutes the main limitation to the speed of wind-driven vessels and vehicles.

Windsurfers and certain types of boats are able to sail faster than the true wind. These include fast multihulls and some planing monohulls. Ice-sailors and land-sailors also usually fall into this category, because of their relatively low amount of drag or friction.

In the foiling AC72 America's cup catamarans,the boats sail through the water at up to double the environmental wind strength. The effect of this is to radically change the apparent wind direction when sailing "downwind". In these boats the forward speed is so great that the apparent wind is always forward-at an angle that varies between 2 and 4 degrees to the wing sail. This means that AC72's are effectively tacking downwind, although at a greater angle than the normal 45 degree upwind angle,usually between 50 and 70 degrees.[1]

## Other areas of relevance

In fixed-wing aircraft, apparent wind is what is experienced on-board and it determines the necessary speeds for take-off and landing. Aircraft carriers generally steam directly upwind at maximum speed, in order to increase apparent wind and reduce the necessary take-off velocity. Land-based airport traffic, as well as most mid-sized and large birds generally take off and land facing upwind for the same reason.

## Calculating Apparent velocity and angle

$A = \sqrt{W^2 + V^2 +2WV\cos{\alpha}}$

Where:

• $V$ = velocity (boat speed over ground, always > 0)
• $W$ = true wind velocity (always > 0)
• $\alpha$ = true pointing angle in degrees (0 = upwind, 180 = downwind)
• $A$ = apparent wind velocity (always > 0)

The above formula is derived from the Law of cosines and using $\cos(\alpha') = \cos(180^\circ-\alpha) = -\cos(\alpha)$.

The angle of apparent wind ($\beta$) can be calculated from the measured velocity of the boat and wind using the inverse cosine in degrees ($\arccos$)

$\beta = \arccos \left( \frac{W\cos \alpha+V}{A} \right) = \arccos \left( \frac{W\cos \alpha+V}{\sqrt{W^2 + V^2 +2WV\cos{\alpha}}} \right)$

If the velocity of the boat and the velocity and the angle of the apparent wind are known, for instance from a measurement, the true wind velocity and direction can be calculated with:

$W = \sqrt{A^2 + V^2 - 2AV\cos{\beta}}$

and

$\alpha = \arccos \left( \frac{A\cos \beta-V}{W} \right) = \arccos \left( \frac{A\cos \beta-V}{\sqrt{A^2 + V^2 -2AV\cos{\beta}}} \right)$

Note: Due to quadrant ambiguity, this equation for $\alpha$ is only valid when the apparent winds are coming from the starboard direction (0° < β < 180°). For port apparent winds (180° < β < 360° or 0° > β > -180°), the true pointing angle (α) has the opposite sign:

$\alpha = -\arccos \left( \frac{A\cos \beta-V}{W} \right) = -\arccos \left( \frac{A\cos \beta-V}{\sqrt{A^2 + V^2 -2AV\cos{\beta}}} \right)$

## References

1. ^ TVNZ Live America's cup Broadcast.Interview with Tom Schnackenburg. 22/9/2013