Following the previous example for the case of measuring street defects, the X-axis is considered when we turn the handle swiftly left or right or on shocks. A sudden shift in lateral direction implies a lack of fluidity of the bike-lane, and affects the overall quality of the bike ride. It is therefore within relevant to include abrupt shocks in the X axis.
The Y axis considers the direction of the bike's velocity. A sudden application of the brakes will cause an abrupt shock to the Y axis. This could include a sudden brake due to a pothole, an obstacle , or a cause related to the fluidity of the bike-lane. In all of these cases, is it important to measure the particular braking event. However, the event could also be due to a cyclist braking at a red light. To avoid this, the Y-axis measurement can be weighed. A sudden acceleration will return the same abrupt shock measurement but this type of activity is not expected with bikes due to limited speed capabilities. Precisely measuring ride quality involves registering measurements that are related to abrupt shocks or swift changes in direction as opposed to slight changes over elongated periods of time.
Our objective is to develop a robust measurements using all 3 axis of the accelerometer that adequately describes abrupt shocks and changes as a method to infer the fluidity of bike ride.
The Ride Quality (V) statistic
A key objective is to allow for a single measure of overall ride quality. The difference between the measurements along 3 axes at time t (\(V_t\)), against the measurement on the same axes for the previous time period (\(Vt-1\)) is considered. To this end, the vector magnitude of these 3 values give us our Ride Quality statistic.
Another way to look at this is to think the problem as an
euclidean distance in a n-dimensional space \cite{lab_n-dimensional_nodate}. So our final vector is compounded of the square difference in all of the three axis:
\(V\ =\ \sqrt{\left(x_{t\ }-x_{t-1}\right)^2+\left(y_{t\ }-y_{t-1}\right)^2+\left(z_{t\ }-z_{t-1}\right)^2}\\)