Relative Velocity and Vectors

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Relative Velocity and Vectors

Real World Data

Gather Data

Data collection is pretty straightforward. First, go to this flight tracking site (back-up) and click on Track A Flight under the Track a RANDOM FLIGHT section. A random flight is then displayed. There is an animated map that shows a little plane moving, a speed gauge, a compass and an altimeter.

For example, American Airlines flight 1691 was displayed just outside of Lubbock, Tx. It was traveling almost due West at a ground speed of 500 mph and an altitude 35,000 ft. We should change the ground speed into knots (multiply mph by 0.87): Vg=434 knots.

Now, let's look at the wind speed in that general area at that altitude. Go to the Weather Channel's Aviation web site. There is a map with a drop down menu underneath. Select the closest Winds Aloft map to the altitude (34,000 ft in this case) and choose to enlarge it. It should look something like this (click to enlarge):

This looks like a 60 knot wind in a NE direction. This, of course, is an approximation, but that is fine for the purposes of this activity.

Analyze Data

Graphical Analysis

The red arrow represents the ground speed (434 knots due West), the purple arrow is the negative vector for the wind speed (60 knots SW (the wind is in the NE direction), and the blue resultant vector represents the air speed. This image is not to scale, so measuring the length and angle of the wind speed vector would not yield accurate data.

Numerical Analysis

We need to convert the ground and wind speed vectors into component form. The ground speed is in the -X direction, so Vg = -434i + 0j. The wind speed is mostly NE, so Ww = 42i + 42j. Subtracting wind speed from ground speed, the airspeed must be Va = -476i -43j.

Finally, converting the airspeed into magnitude/direction form: Va = 478 knots @ 5 degrees South of West.