Primitive Navigation - Small Angle Approximation


This is an in-section activity created by John Huth for his Primitive Navigation course where students walk small distances and use their analysis to learn small angle approximation, statistics, and prepares them for future assignments. 

In section, the students go outside, we put out a tape measure of 100 ft, the students walk the distance counting paces. The students walk 100 feet four times. They count how many paces it takes to walk 100 feet, we also record their walking speed, converting into miles per hour. We also record their pace turnover in paces per hour. The also record their height, and they record their inseam. The students all get a record of this and upload to a common database. The student then go inside - there is a blackboard prepared with a range of angles from 1/2 degree to 25 degrees marked - also in radians. The students stand at a marked point on the floor and then use the angular scale to measure the angles subtended by various combinations of their fingers at end of the outstretched arm. They record these readings (e.g. my index finger subtends 1.5 degrees). The students then enter information on their paces and biometrics into a database. Once all the information is published, the students then use the database to find the mean number of paces per mile (should be close to 1000 since the name comes from latin 'mille pacem') for the class as a whole, also the uncertainty in the mean, and the standard deviation. They do this exercise for a few other quantities, like walking speed. The students also look at the correlation between number of paces per mile and pace turnover, and correlation with inseam length.

There are two attachments for this activity: a handout detailing the assignment, as well as the accompanying worksheet.

handout.pdf84 KB
worksheet.pdf68 KB