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Asked by: Eddie
vectors General Aviation
Hi there, i was wondering whether you could explain how to find the ground speed of an aircraft using vectors and information such as direction/speed of wind, heading, speed of aircraft in the air and also how to draw it out.
John D. Collins
on Dec 03, 2012
A vector has a magnitude and a direction. They are normally drawn as a line with an arrow head on one end whose length is proportional to the magnitude and the direction of the vector is in the same direction as the arrow head points to . If you know two vectors and their relative directions they are added together graphically by connecting the head of one to the tail of the other. If you know the relative direction of the two vectors, you can orient the second vector at an angle equal to the relative direction between the two vectors. You can draw a third vector that is a straight line between the tail of the first vector to the head of the second vector. This is the vector sum. If you know the heading and TAS of the aircraft, that forms one vector. The second vector is the wind speed and its direction. By orienting them head to tail and doing the vector addition, you get a resultant vector that is the course and groundspeed.
Unfortunately, this is not of much use for flight planning, because although you know the aircraft TAS from your POH performance charts, you are trying to determine the heading to fly to maintain a given course. You also know the groundspeed direction because this is your intended course, but not its value. From your winds aloft briefing you know the wind direction and its velocity, so this vector is known. You can use mathematics and trigonometry to solve for the missing items using variations of the law of cosines. but the E6B wind side is a neat tool to aid in a vector solution. It has both a circular rotating part and a translating part, The rotating part is a circle marked in degrees with an outer scale also marked in degrees. In the center of the rotating part is a hole or reference point. The translating part has curved lines at regular intervals and is marked in the center with a vertical line and marked in TAS, it also has radial lines that will be used to represent the wind correction angle.
You rotate the circle until the direction of the wind is shown at the top center of the E6B. Using the translating part’s scale to measure a relative value with the center hole, you place a pencil mark equal in length to the winds aloft as measured above the center hole. Example, assume the winds are from 330 at 30 Kts. Align the circular part to 330. Slide the translating part until something easy to use to determine a relative value, I choose 100. At the point where the center line crosses 130 make a mark (this is 30 from the center hole) and represents the wind. Now rotate the circular part until the course is on the center line. Usually the wind mark will be off to one side or the other. The speed lines that are marked near the center continue on either side of the translating part curved in both directions. Slide the translating part of the E6B until the wind mark just touches your true airspeed. Read your true airspeed as the value under the hole in the center of the circle. The wind correction angle is read off of the radial lines on the translating part.
Think of the wind vector being drawn from the wind mark to the center hole with the head of the vector at the hole and the mark is the tail. The translating part along one of the radial lines that touches the wind mark is the TAS vector with the head of the vector at the point where it touches the wind mark. The resultant vector is the center line which represents your course and the ground speed which is read under the hole. Head to tail, head to tail.
This verbal description is much easier to do visually than to write about.
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on Dec 08, 2012
Before I would trust my E6B, I did a couple of these calculations. Setting up the vector drawing was the tricky part. I ended up with two different drawings, one for when there was a head wind, and one for when there was a tail wind. You need to solve the small wind triangle for the x and y vectors along the direction of travel (green lines).
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on Aug 05, 2014
Hi. Similarly with Eddie, I am trying to find ground speed of an aircraft using wind speed and wind direction. However, I am using matlab but I don’t know how to proceed. Any ideas of how to write a code in matlab for this vector calcs, to end up with ground speed?
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