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The Wind Triangle

Have you ever wondered about the magic behind the E6B flight computers and flight planning programs? The calculation of ground speed and true heading is one of the basic elements in air navigation. The wind triangle method is the foundation for all flight planning devices and computer software. The wind triangle is a vectors representation of the desired course, wind, correction angle and velocities. The various problems can be solved either by mathematical computations or graphical representation.
With the aid of a compass, protractor and a graph paper anyone can solve any wind triangle problem.

True Course (TC) is the desired ground track measured clockwise from the Geographic True North. The TC is noted by a single arrow.
True Heading (TH) is the heading to be flown to maintain the desired track measured clockwise from the Geographic True North. The TH is noted by a double arrow.
Wind Direction (W) is the direction from which the wind is coming measured clockwise from the Geographic True North. The Wind Direction is noted by a triple arrow.
The Ground Speed (GS) is proportional to the True Course, the True Airspeed (TAS) is proportional to the True Heading (TH) and the Wind Velocity (V) is proportional to the Wind Direction (W).

Wind Triangle

    Graphic solution examples:
       
      Given:
       
      True Course - 045  
      True Airspeed - 100kts.  
      Wind/Velocity - 360/20kts  
       
      Find:  
       
      True Heading - TH 
      Ground Speed - GS  
First Step      Second Step      Third Step
    a. The True Course is plotted in a 45 angle to the True North.
    b. The wind direction (360) is plotted to point A. 20 kts. (2 squares) is measured from point A to point B.
    c. The compass is set to 10 squares (100 kts.). With point B as the center, a radius that intersects the True Course is plotted defining point C.
To obtain the ground speed, the line CA is measured. GS=92 kts (using the scale of 1 square = 10 kts.).
To obtain True Heading, the wind correction angle 5 is subtracted from the True Course (wind coming from the left). TH=045-5=040.
 
Top

Similarly, problems such as finding the wind direction and velocity can be obtained when the TC, TH, TAS and GS are known.

      Given:
       
      TH - 070
      TC - 045
      TAS - 120kts.
      GS - 110kts.
       
      Find:
       
      Wind Direction and Velocity.

First Step      Second Step      Third Step

    a. The True Course and True Heading are plotted converging at point A.
    b. Using a scale, the True Airspeed is measured from A on the True Heading line and the Ground Speed is
    measured on the True Course line defining points B and C.
    c. The line connecting point B and C represents the Wind Direction and velocity. The wind is blowing from Point
    C to Point B. The wind direction is measured relative to the true north. It should be remembered that that wind is
    noted by the direction it comes from. In this example the wind coming from the southeast (120). The Velocity is
    measured using the same scale used to measure the True Airspeed and the Ground Speed. The Wind Speed here
    is 45kts.

    It is the scope of this article to demonstrate the effect of the wind on flight. Advanced mathematical solutions are not offered here.


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    Last update May 17, 2005
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