Data crunching

I bought my treadmill a year ago, in early February. Up until that point, whenever I needed to get a workout done and was unable to do it outside, I used the Precor machine in our gym at work. I did a lot of quality stuff on it -- many threshold workouts and at least one 19-mile marathon-pace session (2 mi easy + 15 mi MP + 2 mi easy). I ran a 1:34:46 half-marathon off training that involved those workouts on that machine, so I feel they were doing a lot of good. Having done so many miles on it (I can almost guarantee no one else at work ran as much on that thing as I did) I had a very good sense of pace and effort on it; 7:30 on the treadmill felt quite a lot like 7:30 on the track, if not a little harder. Whatever the treadmill said I was running more or less felt like the same effort outside, and when I was doing ~7:10/mi T workouts, I felt comfortable and in control at that pace setting on the Precor.

I was very pleased to acquire my own machine for convenience reasons, but I quickly discovered during my first T workout at home that 7:08 on my Landice felt nothing like 7:08 on the Precor at work. I felt like I was flying, and I had to really, really work to maintain the pace. By this time, I had a heart rate monitor with my Garmin and made sure to use it while running on the treadmill as electronic proof that I had actually done the workout as much as for the HR information itself. I did not have the HR monitor for very many workouts on the Precor (approximately 10) as I have had for the Landice (40+), so there isn't a large bucket of data for the work treadmill. Comparing the average pace/average HR data from both treadmills doesn't show a dramatic difference between pace settings. It may be that the Precor data isn't a large enough sample size to be significant against the larger group of data from the Landice; there is quite a bit of scatter, too. Whatever the reason, this comparison did not show unequivocally that I was working harder on the Landice. I'll admit this disappointed me somewhat. I'd wanted to see those Precor data points way offset, but the results say what they say. Regardless of what the data points told, I knew what I was feeling. The Landice felt fast. There had to be a way to show that.

I set up an experiment.¹ I measured the length of the belt and then timed its revolutions at different pace settings. My first experiment averaged 3 trials timing 5 revolutions at a range of pace settings, from 1.5 mph up to 8.6 mph mostly in steps of about 1 mph to cover what I would ever be likely to run on it. I later also did a trial averaging 3 trials of timing 10 revolutions with a similar range in mph but adding a few more steps in the higher range (8-8.7, where I would expect to do my threshold running); it was easier to time 10 revolutions than 5 at faster speeds. From the time per revolution data, I was able to calculate actual mph and convert to actual pace, which I then compared to the theoretical pace based on the machine's setting.

At all settings, there was a significant delta -- the belt was moving faster than what the console claimed. Aha! So I was not mistaken; what felt faster really was faster. I plotted the data; I was expecting some linear dependence where I could calculate some constant I could use to estimate how fast I really ran (e.g., if, based on treadmill settings, I ended up with an 8:15 average mile for my workout, what was my real average pace?), and was confounded when the plot did not show any such dependence. See below (plot from the 5 revolution data set).

The plots for both the 5 and 10 revolution experiments have the same features, so I expect what I see is real. At low mph, there is a very large difference between the setting and calculated pace (more than a minute per mile); the difference jumps up between 1.5 and 2.5 mph, then, as mph increases, the delta decreases -- to a point, where it stabilizes between 5 and 7 mph; a slight increase at 8 mph before suddenly stepping down again at mph greater than 8, where it appears to stabilize again.

Well, this all looked weird. How should I treat this odd relationship? I never, ever run below 5 mph on the treadmill as part of the recorded workout, so in coming up with a correction factor I could ignore that region, which includes the curving part. The great majority of the miles I've put in on the treadmill are below 8 mph (only T workouts go faster, and they are not generally representative of the bulk of the running I do inside), so I could set aside those strangely-offset data points too. I'm left with data points that form a basically straight line with a slight upward slope due to the slight increase in difference at 8 mph.² (See below; plot from the 10 revolution data set, similar obtained for 5 revolutions.)

Using the slope of that line, I calculated adjusted pace for each mph setting; then, I plotted expected pace and adjusted pace for the range of mph settings I typically use to obtain a correction factor (the equation of that line):

Even though the calculations confirmed what I felt to be true, that the treadmill is faster than it says it is, I still thought that somewhere in the heart rate data would be the smoking gun to prove the calculations represented something real. Over the year-plus that I've had the Garmin with the HR monitor, I've racked up about twice the amount of HR data from running on the roads as I have from the treadmill. I've had fun playing with that data too -- correlating HR to altitude, temperature, etc. There is considerable scatter due not only to those factors, but others such also to terrain differences³ -- for example, some times I was in better shape than others or not recovered; some of those workouts are hillier than others, which can skew HR depending on whether I try to run even effort or even pace. Even with all the scatter, there is still a general slope correlating HR with pace. I wanted to compare road HR data (where, assuming reasonably accurate GPS, the reported average pace can be assumed to be actually what I ran) with the treadmill HR data. To cut down a little bit on the scatter, I limited the road data set to runs done in Delaware. The trend is still obvious regardless of the remaining scatter. By plugging in the as-obtained average treadmill place data into the equation from the correction factor plot, I obtained adjusted pace data, which I then plotted with the road data. The treadmill points fall right into the thick of the road points.

The calculated pace of the treadmill looks like it's comparable to the road pace, based on my heart rate. At last: I'm satisfied, and when I'm aiming at a target pace running inside, I can adjust the treadmill mph in good faith.

See anything I missed taking into consideration in my data crunching? Please let me know!

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¹Note: experiments were performed with no one running on the treadmill. It can be expected that the weight of a person running would create some drag on the belt, slowing it relative to no weight on it at all. I cannot judge how significant that would be for me at 110-115 pounds. All data analysis treats this as negligible. Perhaps in the future, in the interest of scientific accuracy, I'll redo the experiment and have someone else do the timing while I'm running those speeds.

²Perhaps someone with experience/knowledge of motors could explain to me why it would work so inconsistently in this fashion.

³I deliberately treat trail workouts separately (due to GPS accuracy issues, mostly).