Triangulation

Students:

4th grade and up, max of ~32 students, min of ~12

Objective:

To understand the practical and mathematical techniques used to triangulate a position.

Minimum Facilities Required:

• A large open room (gym or multipurpose room, for example) or field
• A noise source that doesn't have to be plugged in (e.g., castanets)
• Two screens that won't impede sound (cloth or paper...)
• Markings (with chalk...) on the walls or floors of the room indicating a letter/number grid
• Gridded paper representation of the room grid.
• Large sheets of paper, pencils, rulers, protractors (optional)
• Walkie talkie (optional but fun)

Organization:

The class is organized into three equally sized groups. One group is assigned to be the noise source (NS). The other groups are each assigned to a Triangulation Station (TS), which are set up behind screens at consecutive corners of the room (the long side of the room is best). The students at the TS have a diagram of the room which is made out as a lettered/numbered grid.

Procedure:

The NS students form a line, more or less equally spaced, and more or less straight (to start with, you can try with curves later). They will toss the noise source from one to the other from one end of the line to the other with each toss at a time signal from the facilitator. This should be done slowly at first. The line should be invisible to the TS teams behind their screens.

In the TS teams, one or two students are chosen as antennas. When they hear a noise, they turn around to be able to hear it evenly out of both ears. (Note that a more advanced group could create equipment to do this using directional microphones and a suitable meter). The teams are challenged to find a way of using this information to figure out where the noise is on the grid, and after a few observations, to be able to call out the location where the noise will come from next. The walkie talkie helps the TS groups communicate their findings to each other - or they may use runners. They may also create a coordinated observation team at a command post that has the information relayed to it from both stations. The goal is to use information gathered at two Triangulation Stations to "triangulate" the location of the noise source.

For groups that respond well to competition, the NS group wins if they get the noise all the way to the end of the line. The TS group wins if they can correctly call out the grid square where the noise will go next.

Teams should rotate so that they all get the chance to be in each position. Ideally, a discussion of the technique they used to record and extrapolate the information can assist them in being more efficient with it on subsequent tries. Once the students get good at this, the speed of the noise toss, or the complexity of the trajectory can be increased.

Enhancements:

To develop a 'guided missile' that will hit a noise making object (not a student!) after a short observation of its trajectory.

To develop a system that will allow the noise maker to be found using only one station (hint: only possible if there is a rule about how the noise changes)

For a less structured environment (e.g., scouts) this can be turned into a game to play in the woods.

Tie-in to Ulysses URAP experiment:

Ulysses, with the WIND spacecraft, uses triangulation techniques to map the trajectory of high-energy electrons as the follow the sun's magnetic field away from the site of solar flare, which occurs on the sun. We can use this information to create a map of the sun's magnetic field.

Tie-in to Earth:

Triangulation techniques are used in surveying and mapping, tracking of aircraft and missiles, and other efforts to locate any emitting object. They can help in finding downed aircraft or lost ships that can still transmit radio signals.