Displacement, Velocity, and Acceleration

Try this

Few mobile devices have the capability to measure small-scale displacements inside of buildings - when it is measured, it is typically done through comparing GPS coordinates. However, another method is to use “dead-reckoning.” In this case, a simple example of linear dead-reckoning can be accomplished by taking the double integration of acceleration data.

While using the Accelerometer tool on a mobile device that is lying flat on the floor of an elevator, ride up or down a reasonable number of levels. Export this data as a .csv file into a data analysis program, such as Logger Pro, Data Studio, or Excel. Take the double integral of the data from the moment you started accelerating at the start of the ride to the moment you stoppped accelerating at the end of the ride. This double integration gives the displacement of the elevator. If possible, compare this double integration to a physically measured value (i.e. counting and measure stair steps) to evaluation.

Challenge yourself

• If you went up in your elevator ride, how would your results (graph, integral, and total displacement) be different if you went down?
• How would the results above be different if your mobile device was oriented differently? Explain.
• What is the percent error in your double integration compared to the physically measured displacement? Explain what factors might account for these differences.