The Human Altimeter Activity
This activity can be adapted for any grade. The teacher can illustrate the mathmatical concepts as they see fit.
GPS, Speed of light, Altimetry, Topography, Scientific Method
A laser altimeter is an instrument that is used to learn about the topography, or the shape of the surface, of a planet. That planet could be Earth, Mars, or even Mercury. A laser altimeter can be operated from a plane, a helicopter, or a satellite.
A laser altimeter works by emitting short flashes of laser light, which travels to the surface of the planet, where they are reflected. Part of the reflected laser radiation returns to the laser altimeter, is detected, and stops a time counter which was started when the pulse was sent out.
We know that distance (D) is equal to velocity (V) multiplied by time (t), shown mathematically as D = V x t. In the case of a laser, our velocity will always be the speed of light (c), making our equation D = c x t. If we know how long it takes for the light to travel to the surface and back, we can calculate the total distance the light has traveled. However, the total distance our laser pulse has traveled is really twice the distance our altimeter is from the surface. The measurement, the altimeter's distance from the surface, is called range. Range (R) is one half the total distance.
In order to figure out the exact geographic 3D coordinates (latitude, longitude, elevation) of any surface spot that was hit by a laser pulse, it is necessary to know two more items in addition to the distance: the location of the aircraft or spacecraft from which the measurement was made, and the direction in which the laser altimeter was ÔlookingÔ.
These values are usually obtained through GPS-receivers (for the satellite-based Global Positioning System) in the aircraft and, for reference, on a known location on the ground, and an INS (Inertial Navigation System) onboard the aircraft. With a laser altimeter system composed of these components the absolute coordinates of surface spots can be determined accurately.
Laser altimetry data can be used to map large surface features, like slopes, hills, areas flatness or mountains. Laser altimetry technology is to the point where they can measure features only 10 cm in size! Laser altimeters have been used to map the surface of Mars. And there are many surfaces on Earth that laser altimeters can be used to map. GLAS is a laser altimeter that is going to measure the topography of ice sheets.
Along one side of the room create some "terrain". There are several ways to do this. You could use masking tape to map out a terrain proflie, or you could always make an art project out of it also by getting a large roll of paper and drawing a profile of a city or mountains, etc. and taping it on the ground. This is up to the teacher. But for each student participating, leave a mark on the terrain that is theirs to "measure". Each student should be in front of their mark on the terrain. (See diagram below.)
Each student will represent a pulse of light being emitted from a laser altimeter on a spacecraft or aircraft. They are all given a GPS height to simulate the position of the craft.
- One at a time, a student is tapped on the shoulder to start walking from the starting point towards their mark on the terrain, by a person with a stop watch.
- The student must walk or march at a constant speed because light has a constant velocity. Music with a constant beat may help.
- The person with the stop watch times the person who walks to their mark at a constant pace, and back to their original spot.
- Each student can then calculate their total distance traveled (D), range (R) and thus the topography, or altitude, of the terrain. Remember that the velocity V in this case is the speed of light (c). The speed of light (c) is 3 x 10 8 m/s.
Distance = D
Speed of Light = c
Range = R
Time = t
D = c x t
R = D/2
Topography (altitude of terrain) = GPS Height - R
Have the students the distance from their starting point to ther marks on the terrain with rulers. Compare that with what they determine from the stop watch/music/marching approach and discuss the possible sources of error, ie user errors, not everyone has the same stride, or walks preciscely with the beat of the music. This can be used as an intro to the scientific method.
Animated graphic and some text used from an intro to laser altimetry by GeoLas Consulting