In my last post (“Rowing Data…”) I discussed the steps associated with downloading the Garmin Vivoactive HR data from Garmin Connect to an Excel spreadsheet. In this post, I’m going to take the reader through the analysis of the data as a tutorial and guide for assessing certain elements of these data.
Raw data in Excel format are shown in Figure 1. I am going to focus on distance (column M), speed (column N), and heart rate (column O).
I normally like to study discrete, time-based data by translating the time component from the Zulu time (column L) into a relative time from the start of the workout. Furthermore, I like to translate these into units of seconds as the base unit.
To do so, we can take advantage of some powerful capabilities contained within formulas inside of Microsoft Excel. For example, the start time listed in column L begins with the entry:
The next entry is:
These are “Zulu” time or absolute time references. We wish all future times to be keyed or made in reference to the first time. In order to do so, we need to translate this entry into a time in seconds. We can do so by parsing each element of the entry. These entries are listed sequentially in column L2 and L3, respectively.
Each element is translated into seconds by parsing the hours, minutes and seconds using the following formula:
The first component extracts the time in hours and translates into seconds. The second component extracts the “minutes” and translates into seconds. The third component extracts the “seconds” element by itself. The total time is the superposition of all three individual components.
Thus, what I normally do is to copy the contents of the initial spreadsheet into a new sheet adjacent to the original and then begin working on the data. Presently, I am in the process of developing an application that will perform this function automatically. Yet, here I am “walking the track” associated with analyzing the data in order to chronicle the mathematics surrounding the process.
The hour, minute and second can be extracted as separate columns. Let us copy the contents of column L in the original spreadsheet into a new sheet within the existing workbook and place the time in column A of that new sheet. Thus, the entries in this sheet would appear as follows:
|ns1:Time||Absolute Time (seconds)||Relative Time (seconds)|
The Absolute time in the middle column is the time in seconds represented by the left-hand column relative to Midnight Zulu time. The right-hand column is the time relative to the first cell entry in the middle column. Thus, zero corresponds to 50971-50971. The entry for three seconds corresponds to the difference between 50974 (second entry) and 50971 (first entry), and so on.
I also created some columns to validate parameter entries. For instance, the reported total distance and speed (in units of meters and meters per second, respectively), in column M and N and the heart rate, in column O, are referred to next. I created a new column O in the new spreadsheet to provide a derived estimate of total distance, which I computed as the integral of speed over time. The incremental distance, dS, is equal to the speed at that time, dV, multiplied by the time differential between the current time and the previous time stamp, dt. Then, the total distance is the integral, or the summation of this incremental distance and all prior distances. I reflect this as column G in the new worksheet, shown in Figure 2.
What follows now are plots of the raw and derived data. First, the heart rate measurement over time is shown in Figure 3. Note that the resting rate is shown at first. Once the workout intensifies, heart rate increases and remains relatively high throughout the duration of the workout.
The total distance covered over time is shown in Figure 4. This tends to imply a relatively constant speed during the workout due to the linear behavior over the 8700+ meters.
The reported speed, as measured via GPS, shows variability but is typically centered about 1.85 meters per second. The speed over time is shown in Figure 5.
The GPS coordinates are also available through the Excel data. I have subtracted out the starting location in order to provide a relative longitude-latitude plot of the workout, shown in Figure 6.
In my next post I will focus on the athletic aspects of the workout related to training.