Live : Tramway acceleration in Grenoble

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:


and the one in cartesian 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
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