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apparent wind formula

14464 Views 5 Replies 5 Participants Last post by  ericsmith3d
is there a formula that can figure apparent wind direction to true wind direction. also for speed of wind. with the sailboat going 6 knots at a 45 degree angle to a 15 knot wind apparent on the boat - what would be the true wind angle an speed? i'm not a racing sailor but a cruiser with curiousity.
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This all I know.

True-Wind Calculator Formulas
** Apparent-Wind (AW) and Apparent-Wind Degrees off the bow (D) are known. }

Y = 90 - D
a = AW * ( cos Y )
bb = AW * ( sin Y )
b = bb - BS
True-Wind Speed = (( a * a ) + ( b * b )) 1/2
True-Wind Angle = 90-arctangent ( b / a )

Apparent-Wind Calculator Formulas
** True-Wind (TW) and Apparent-Wind Degrees off the bow (D) are known. }

Y = 90 - D
a = TW * ( cos Y )
b = TW * ( sin Y )
bb = b + BS
Apparent-Wind Speed = (( a * a ) + ( bb * bb )) 1/2
Apparent-Wind Angle = 90- arctangent ( bb / a )

True and Apparent Wind Calculator
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true wind angle= 66.5 degrees
true wind speed= 11.5 kts

USSailling has a nice page to calculate for you, but if you want the formula just click on the calculate button and you will be given the formula for both true and apparent.
True and Apparent Wind Calculator

EDIT: beat me to it Gryzio
exactly what i was looking for. Thank you.
now to practice that, just using my head- i don't think so.
In practical terms the tricky part is knowing your apparent wind angle without a vane and gauge that give you the angle. Speed is simple now with GPS, and true wind is easy to find old-school if you just shoot into the wind briefly while watching your compass.

If you're trig-challenged like me, but know true wind and speed, and boatspeed, then you can do a qick pencil plot an a chart and just measure the long AW line.
Slight change:
True-Wind Speed = (( a * a ) + ( b * b )) 1/2
should be
True-Wind Speed = (( a * a ) + ( b * b )) ^1/2
i.e. it's the square root of the sum of the squared sides, the Pythagorean Theorem.
Same for the formula for Apparent-Wind Speed.
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