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Apparent wind is thewind experienced by a moving object.

Theapparent wind is the wind experienced by an observer in motion and is therelative velocity of the wind in relation to the observer.^{[citation needed]}

Thevelocity of the apparent wind is thevector sum of thevelocity of the headwind (which is the velocity a moving object would experience in still air) plus thevelocity of the true wind. The headwind is theadditive inverse of the object's velocity; therefore, thevelocity of the apparent wind can also be defined as a vector sum of thevelocity of the true wind minus thevelocity of the object.^{[citation needed]}

Insailing,apparent wind is the speed and direction of wind indicated by a wind instrument (anemometer) on amoving craft (on water, land or ice) in undisturbed air. It is composed of thecombined speeds and directions of the craft and wind observed by astationary wind instrument—thetrue wind. A true wind coming from the bow increases the apparent wind induced by the speed of the craft, coming from the stern it decreases apparent wind, and coming from the side the apparent wind angle and speed change according to the combined speed and direction of each the craft and the true wind. Apparent wind is important to sailors in order to set sail angle with respect to the wind and to anticipate how much power the wind will generate on apoint of sail. Apparent wind differs in speed and direction from thetrue wind that is experienced by a stationary observer and composed of the true wind speed (TWS) and true wind direction (TWD) or the TWS and true wind angle (TWA) relative to the boat if it were stationary.^[1]Innautical terminology, apparent wind is measured inknots anddegrees.

Note that a number of additional factors come into play when converting the measurements from the masthead anemometer into the true wind if a high degree of accuracy is required, including the following:^[2][3][4]

• Leeway (or drift on power vessels) - Factors like water currents or slipping sideways due to wind (leeway) mean that the direction a craft is pointing often does not exactly match its actual direction of travel. This must be corrected for when converting apparent wind angle to true wind direction. The same effect is found when the craft is altering course.
• Mast twist - the rigging loads often put a significant amount of torsion on the mast, especially if the rig has runners, so it is twisted along its length
• Mast rotation - many racingmultihulls have a mast that can be rotated, so the anemometer reading needs to be corrected by the angle of rotation of the mast
• Heel angle - this is a simple trigonometric correction
• Upwash from the sails - the airflow around the top of the mast is distorted by the presence of the sails. This effect varies with the sails set at the time, the wind speed and the point of sail, but is noticed by the true wind angle changing from port to starboard tack, and the true wind speed changing from when beating to running
• Boat motions - as the masthead is so distant from the centre of motion of the craft, inertial effect on both the wind vane and the anemometer cups can be significant when the craft is moving, especially when pitching and rolling
• Wind shear - there can be a significant change in both wind speed and direction between the water's surface and the top of the mast, especially in conditions of unstable, light airs. The wind instruments are just measuring conditions at the masthead, and these are not necessarily the same at all heights

In the presence of a current, the true wind is considered to be that measured on the craft drifting with the water over the bottom, and wind with respect to the sea bed as theground orgeographical wind.^{[citation needed]}

Theapparent wind on board (a boat) is often quoted as a speed measured by amastheadtransducer containing ananemometer andwind vane that measures wind speed inknots and wind direction in degrees relative to theheading of the boat. Modern instrumentation can calculate the true wind velocity when the apparent wind and boat speed and direction are input.^{[citation needed]}

Insailboat racing, and especially inspeed sailing, apparent wind is a vital factor, when determining thepoints of sail a sailboat can effectively travel in. A vessel traveling at increasing speed relative to theprevailing 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 lowangles will cause a loss of accelerating force. This constitutes the main limitation to the speed of wind-driven vessels and vehicles.^{[citation needed]}

Windsurfers and certain types of boats are able to sail faster than the true wind. These include fastmultihulls and someplaning monohulls.Ice-sailors andland-sailors also usually fall into this category, because of their relatively low amount ofdrag orfriction.^{[citation needed]}

The AC72 foiling catamarans used in the America's Cup are an example of this phenomenon, as the boats sail through the water at up to double the environmental wind speed. 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.^[5]

Infixed-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-basedairport traffic, as well as most mid-sized and large birds generally take off and land facing upwind for the same reason.^{[citation needed]}

This sectiondoes notcite anysources. Please helpimprove this section byadding citations to reliable sources. Unsourced material may be challenged andremoved. Find sources: "Apparent wind" – news ·newspapers ·books ·scholar ·JSTOR(September 2016) (Learn how and when to remove this message)

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

Where:

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

The above formula is derived from theLaw of cosines and using${\displaystyle \cos ({\alpha }^{\prime })=\cos ({180}^{\circ }-\alpha )=-\cos (\alpha )}$.

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

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

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

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

and

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

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

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

• http://www.csgnetwork.com/twscorcalc.html
• https://www.tecepe.com.br/nav/inav_c11.htm.

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