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Calculating Wind Speed and Direction

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Flight Instructor

I'm trying to figure out how to calculate wind speed and wind direction given a Course, True Airspeed, Ground Speed, and Heading.

I'm sure Vector subtraction is used to figure this out, anyone know exactly what the math is behind this?


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1 Answers

  1. Best Answer

    Wesley Beard on Nov 30, 2010

    The math behind the equation requires the use of vectors and triangle geometry.  You are required to break each vector down into its vertical and horizontal component.  Subtract the GS vector from the TAS vector for each vertical and horizontal value and the wind speed is calculated using pythagoream theorem A^2 + B^2 = C^2 where C is the wind speed.  The wind direction is calculated using the arctan function and checking if the wind is a headwind of a tailwind
    WS = Wind Speed
    WD = Wind Direction
    TC = True Course
    TH = True Heading
    TAS = True Airspeed
    GS = Groundspeed
    Here is the formula for the wind speed (you can use this in Excel provided you use Named Ranges)
    WS =ROUND(SQRT(((SIN(RADIANS(MOD(TH, 360)))*TAS)-(SIN(RADIANS(MOD(TC, 360)))*GS))^2 +((COS(RADIANS(MOD(TH, 360)))*TAS)-(COS(RADIANS(MOD(TC, 360)))*GS))^2), 0)
    Breaking down the formula, we are using pythagoream theorem WS = square root([Horizontal Value Difference]^2 + [Vertical Value Difference]^2) and rouding the number to the nearest whole number
    Here is the formula for the wind direction
    WD =ROUND(MOD(DEGREES(ATAN(((SIN(RADIANS(MOD(TH, 360)))*TAS)-(SIN(RADIANS(MOD(TC, 360)))*GS))/((COS(RADIANS(MOD(TH, 360)))*TAS)-(COS(RADIANS(MOD(TC, 360)))*GS))))+IF(((COS(RADIANS(MOD(TH, 360)))*TAS)-(COS(RADIANS(MOD(TC, 360)))*GS))<0, 180, 0), 360), 0)
    Breaking down this formula, we are getting the arctangent([Horizontal Value Difference] / [Vertical Value Difference]) and then checking the sign of the [Vertical Value Difference] and adding 180 if it is negative.
    To simplify the calculations into manageable chunks, open up excel and copy these into a cell.  When you copy the formula change the name of the cell to what it equals or change to the appropriate cell (A1)
    GSH = SIN(RADIANS(MOD(TC, 360)))*GS ‘Horizontal Portion of GS Vector
    GSV = COS(RADIANS(MOD(TC, 360)))*GS ‘Vertical Portion of GS Vector
    TASH = SIN(RADIANS(MOD(TH, 360)))*TAS ‘Horizontal Portion of TAS Vector
    TASV = COS(RADIANS(MOD(TH, 360)))*TAS ‘Vertical Portion of TAS Vector
    DeltaH = TASH-GSH  ‘Horizontal Vector Difference
    DeltaV = TASV-GSV ‘Vertical Vector Difference
    WS = ROUND(SQRT(DeltaH^2 +DeltaV^2), 0) ‘Pythagoream Theorem rounded
    WD = ROUND(MOD(DEGREES(ATAN(DeltaH/DeltaV))+IF(DeltaV<0, 180, 0), 360), 0) ‘arc tangent plus check for Vertical Vector Difference sign

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