Using VIBRATION on iPhone 4 in the Grenoble Tramway to measure acceleration and to analyse the Tramway displacement (Academic level : Basic Mechanics from freshmen) VIBRATION records the three components of the iPhone 4 acceleration as they are captured by the MEMS accelerometer inserted in the iPhone 4. The iPhone was simply put on a chair inside the tramway before Hubert Dubedout Station and stop close the Halle Sainte Claire (approximate informations) : Recorded acceleration: These snapshot can be analyzed using the acceleration vector in polar coordinates: The Y axis is oriented along the Tram (parallel to the tram displacement). In straight line this is d2r/dt2 (first term in line one) The X axis is perpendicular to the Tram displacement. When the Tram trajectory is curved, at constant speed (km/h), the measured value is : -r(dθ/dt)2 (second term in first line) The complete recording took 102 seconds. Radius of gyration are approximately 70 meters as indicated below. The acceleration is close to a=0.05g=0.5m/sec2 during the curve (see red curve) The above picture shows curve radius of R=70 meters. These numbers are consistent with a speed of V=sqrt(a.R), V= 6m/sec V = 20km/h is a reasonable speed for a Tramway in town. The speed changes as the Tram approaches, stops and leaves the station is shown in the blue curves. This can also be nicely analyzed through a simple numerical integration in excel-like codes. dV/dt = a Vibration provides in an excel file all data and a more comprehensive analysis can be done using iPhone as Pocket Lab |