For the purposes of explaining the Matlab algorithm, we will be following the data acquired and calculated from the ‘Black Widow’ ride at Kennywood, however this method applies, and in some cases is dependent on, the other rides that were recorded. 

Phyphox provides acceleration data in the x, y, and z directions, dependent on the placement of the smartphone, along with absolute acceleration, which can then be fed into Matlab as data points. Absolute acceleration is used for this algorithm, as the position of the smartphone across members of the team was not consistent, and thus the effects of x,y, and z accelerations are all equally important to rate intensity.

We then derive an plot of jerk versus time by subtracting a point of acceleration from the one after it, divided by its time interval (da/dt). The maximum and average values of this plot will be used to influence the rating of the given ride.

Curve smoothing is then applied to the absolute acceleration plot to simplify the data and allows it to be manipulated more easily. The equation for curve smoothing is an exponential moving average. 

An exponential moving average is a rolling average dependant upon a smoothing factor. A high smoothing factor results in less smoothing and thus high responsiveness to variations in the data. We used a smoothing factor of 0.8 which got rid of the majority of the noise but still allowed us to determine acceleration peaks corresponding to drops and loops on coasters. A time step of 200 was also chosen through trial and error – a smaller timestep results in a less smooth, but more accurate plot. 

A smoothed graph provides a preferred data set for further calculations and gives an overall better concept of the state and intensity of the ride, removing large outliers like spikes in the data that may occur through an error in recording. From this plot, we can find the average and maximum acceleration, as well as specific points of interest within the ride such as drops and loops. 

We also calculate the root mean squared of the data to represent a given ride’s ‘shakiness’. For example, a wooden, bumpy roller coaster will have many more vibrations than a smoother, steel roller coaster.

Finally, we normalize each variable in relation to every ride’s value of that variable. A vector exists for each variable, and a relative scale is created from 0 to 1, being the minimum and maximum of that variable for all rides in the set. This allows the accurate representation of the weighting of each term in our final score equation, so as to not let a less influential term of greater magnitude influence the final score more than it should.

Score = ((Jerkavg * 0.3) + (Jerkmax * 0.2) + (aavg*0.7) + (amax * 0.5) + (section*0.2) + (Vibrationavg * 0.2)) / 0.21 (2)

Each variable is assigned a factor of relevance based on how important its magnitude is to the overall intensity of a roller coaster from our personal experience. For example, the average acceleration is the most relevant variable in intensity, thereby receiving a factor of 0.7, whereas vibrations and sections are not as relevant but still important, receiving a factor of 0.2. These values, along with the dividing factor, were tuned on trial and error based on the data we received, working towards a scale of 1-10 for each ride.