Subjects
Physics, Geography, MathematicsAim and Purpose
To determine the position of the receiver by using runtime measurements taken with GPS-receiving devices.Materials
- GPS receiving devices (ideally, three units are needed; but experiment can also be done with one unit only)
- a big open meadow or field (at least 50 to 100 m in width and length)
- a watch/timepiece with seconds indicator
- a long measuring tape, if available
Pre-requisites
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Basic knowledge on how to use a GPS device
Time needed
For the experiment, a two-hour lesson should be scheduled to allow time for analysis and discussion.
Procedure
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Divide the class into groups of five. Each group member is assigned a role. One member acts as
Receiver and is given the watch/timepiece, one member acts as Recorder and the three other members act as
Transmitters. The three students acting as Transmitters are each given a GPS-device.
The GPS-devices should be able to indicate the time accurately to the nearest second, as well as the exact velocity.
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The Transmitters take different positions on the meadow/field, as far apart as possible from one anotehr.
The Receiver and the Recorder take position on any place on the field they like. The distances between
the three Transmitters are measured and noted down by the Recorder. By using runtime measurements,
the students should be able to determine the position of the Receiver. To begin with, the Receiver and the
Recorder give one of the Satellite Signals a sign (by waving or yelling) to start walking. Satellite Signal No. 1
takes a mental note of the starting time indicated on his GPS-device and then walks with constant speed towards
the position of the Receiver. Upon his arrival, the Receiver takes note of the arrival time using the watch/timepiece.
The Recorder writes down the arrival time, as well as the start time and velocity indicated on the GPS-device.
The same procedure is repeated with Transmitters No. 2 and No. 3.
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It would be an advantage to perform the experiment on a football field whose area size (usually 60mx100m) is
already known and to position the Transmitters in the corners. In the absence of a football field, it
would be necessary to measure the distances between the three Transmitters. It is also recommended that
the Transmitters walk at a speed of around 2 to 7 km/h (depending on the quality of the GPS-device),
in order to avoid erroneous readings of velocity on the GPS-device.
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In the analysis, the distances should be scaled down and drawn true to scale as much as possible.
Note down the scale ratio.
Then, convert the velocity readings into m/s. Compute the runtime by subtracting the start time from the arrival time.
Afterwards you may compute the distance that each Transmitter walked from its starting position to the
position of the Receiver.
Now, draw circles with the distances from starting point to Receiver as radius. By using trilateration, you should be
able to determine the position of the Receiver.
- After following the above procedures, the students will realise that initially, the circles they have drawn do not show a clear intersecting point. The reason could lie in several occuring inaccuracies but mainly due to lack of synchronisation of the clocks. At this point, it should be mentioned that this problem is not uncommon in GPS. The time error in the experiment, which is reflected as a distance error, can be reduced by repeating the runtime measurements with synchronised clocks. The drawing can then be improved using the corrected runtime measurements, after which a clearer position of the Receiver can be determined.
Worksheet for Transmitter as website or as printable rtf-file
Worksheet for Receiver as website or as printable rtf-file
Worksheet for Recorder as website or as printable rtf-file
