We have been examining how one might study sports such as paragliding in 3-D using ArcGIS Explorer. We mapped the GPS track of the paraglider, and how to calculate vertical change and vertical velocity. Let us now calculate the total flight length.

As my ESRI colleague Matt took off from Alyeska Ski Resort, Alaska, above, he took his first coordinate. His last coordinate was collected upon his touchdown over an hour later. From his GPS track, select his first and last coordinate:

Latitude, Longitude, Date, Time, Altitude(m)
61.041198,-149.051793, 06/21/2007,06:21:20, 1802.609
60.967984,-149.119363, 06/21/2007,07:42:52, 50.12598

One can use simple math to roughly calculate the distance between two points in miles by the formula: sqrt(x * x + y * y)
where x = 69.1 * (lat2 - lat1)
and y = 53.0 * (lon2 - lon1)

Using the values for Matt’s flight:
X = 69.1 * (60.967984 - 61.041198) yields x = 5.059 miles
y = 53.0 * (149.119363 – 149.051793) yields y = 3.581 miles
The total distance is then: sqrt (5.059 * 5.059 + 3.581 * 3.581), which yields a distance of 6.198 miles, or 9.97471 kilometers.

An improved distance can be found by the same formula sqrt(x * x + y * y),
but where x = 69.1 * (lat2 - lat1)
and y = 69.1 * (lon2 - lon1) * cos(lat1/57.3)
Using these values yields 5.47406 miles, or 8.80964km of horizontal distance.

Paragliders move in the vertical dimension too, of course. Matt descended from 1802.609 meters to 50.12598 meters, or 1752.48302 meters total. Use the Pythagorean Theorem to determine the total distance that incorporates both the horizontal and vertical distances:

Total distance = sqrt ((8,809.64m * 8,809.64m) + (1752.48302m * 1752.48302m), which yields 8,982.25m or 8.98 km.

Remember that this total is straight line distance. Matt’s actual winding course down the valley can be calculated from importing the track into ArcMap, measuring it, and then applying the Pythagorean Theorem to account for the altitude lost.

Matt traveled 8.98 km in 1:21:32 (or, 1.359 hours), or 6.608 km/per hour, or 4.11 mph. One of the attractions of paragliding might be that one glides along at the pace of a brisk walk. However, in a paraglider, one must pay much more attention to what one is doing!

-Joseph Kerski, Education Manager.