I recently discussed how one might map and study a 3-D sport such as paragliding using ArcGIS Explorer. Mapping paths in the horizontal and vertical dimensions is just one of many interdisciplinary activities possible from paragliders or any other object from which you can obtain GPS tracks. Integrating mathematics and physics is easy through the analysis of the resulting coordinates and elevation values.

For example, examine the GPS track below from my ESRI colleague Matt as he began his flight at Alyeska Ski Resort near the Cook Inlet, Alaska (http://www.alyeskaresort.com).

Latitude, Longitude Date, time Altitude(m)
61.041198,-149.051793 06/21/2007,06:21:20 1802.609
61.041198,-149.051342 06/21/2007,06:23:13 1809.819
61.041241,-149.051471 06/21/2007,06:24:06 1812.703
61.041219,-149.051535 06/21/2007,06:24:41 1813.664

Have students calculate the rate at which Matt’s altitude rose during his launch: He rose 11.55 meters in 3 minutes and 21 seconds, at a rate of 3.44 meters per minute, or .057 meters per second.

Soon after, Matt rapidly lost altitude as he flew down the valley toward the Cook Inlet, as shown in the data below:

Latitude, Longitude Date, time Altitude(m)
61.014011,-149.046321 06/21/2007,06:59:57 1240.238
61.014290,-149.049239 06/21/2007,07:00:14 1217.167
61.014075,-149.050763 06/21/2007,07:00:23 1204.669
61.013303,-149.052222 06/21/2007,07:00:35 1188.327

Have your students calculate Matt’s descent: 51.911 meters in 38 seconds, or 1.366 meters per second. His descent was 24 times faster in the vertical dimension than his increase in altitude during takeoff. At this rate, I am sure that Matt felt the wind in his hair! Ask students to visualize these numbers by showing them a photograph of this part of the flight:

The numbers also make sense when one maps the data using ArcGIS Explorer:

Paragliding is only the beginning. Try mapping and analyzing other objects for which you can obtain horizontal and vertical data. Today, phenomena are tracked on, above, and even below the surface of our world as never before. For example, after analyzing the paragliding data that I have posted on ArcLessons, you might analyze whale migration data using WhaleNet (http://whale.wheelock.edu/Welcome.html).

In the next blog, I discuss how one can calculate Matt’s total distance traveled.

-Joseph Kerski, Education Manager.