running km per day: more trend analysis

Yesterday I did a run followed by a hilly hike, each approximately 10.5 km. This put a 21 km point on my trend analysis plot. I then redid the plot, including my least-square regression of an exponential curve. Here's the result, along with two other curves I'll explain in a bit:

plot

This was my longest day so far, but it was just one day. However, the result was a profound change in the exponential trend line.

Small aside: in the plot I did yesterday, I made a small error, which was to assume when you fit a curve K exp(α t) to time-series data, if &alpha is in units 1/week, then this represents a 100×&alpha% per week increase. This is a good approximation only for small values of &alpha. I corrected this error in the text of yesterday's blog (not the plot), and did it correctly in this plot.

Anyway, the problem with the exponential trend line is least-square fits are highly influenced by outliers, especially when they occur at the edge of the data. So yesterday's long day had an exceptional influence on the parameters. This suggests the parameters aren't so good.

So I returned to an established analysis mode: CTS and ATS. These are typically applied to data related to the work done during cycling events, but distance and work in running and hiking are strongly correlated, so applying them directly to distance seems suitable here. ATS (acute training stress) running exponential average with time constant 7 days, while CTS (chronic training stress) is a running exponential average with time constant 42 days. The shorter time constant represents fatigue and responds more rapidly to changes in daily distance, the longer time constant represents fitness and responds slower.

I see ATS spiked at San Diego 3 weeks ago. After that I recovered a but, then ATS ramped up, hitting an even higher spike at the point 0 (yesterday). It's now at 7 km/day. CTS, representing fitness, is only at 3 km/day, however. This implies I'm still ramping up mileage, building endurance. Were I to taper for a marathon, for example, I'd want ATS to dip below CTS by race day.

Comments

Post a Comment

Popular posts from this blog

Marin Avenue (Berkeley)

Image
On Saturday, I got an email from Tim telling letting me know that Murphy's Spring Classics was going to start up Marin Ave. I'd missed that. Murphy announces his courses the day before, and indeed it was already well into the night before when the course announcement went out. I'd skipped over the details, jumping straight to middle and end games. Marin? I laughed at the irony, because not long before when he'd told me he was choosing to repeat the Nifty Twn Fifty which we'd done together last year versus selecting Murphy Mack's Stage Mullett two-day, I responded I didn't think I had it in me to ride Marin Ave two years in succession. Well, so much for that. I was committed, so I went downstairs to swap my 11-26 cassette for my Recon 12-27. The name is easily overlooked: "Marin Ave" fails to strike the same impression as, for example, "Redwood Gulch" or "China Grade". But among those in the know, Marin Ave is infamous i...
Read more

hummingbird feeder physics

Image
I couldn't figure out how the hummingbird feeder worked. Why didn't it overflow? Forces need to balance, of course. Neglecting surface tension, there liquid level is higher in the inner reservoir than in the feeding chamber, so there must be a corresponding pressure difference. Suppose the pressure in the inner chamber were zero. Then the column height difference would need to be atmospheric pressure / (density of liquid × gravity). But this is over 9 meters! Obviously the height difference is only approximately 1% of this. So the pressure difference inside versus outside is only approximately 1%. The inside is only slightly below atmosphere. So air is getting in. How? Does it diffuse through the liquid? If this were the dominant mechanism, it wouldn't take long for the pressure inside to go from 99% to 99.3%, for example, which should be plenty to push the column of liquid down in the inside chamber and thus push liquid out through the holes. It would over...
Read more

Gallium Pro geometry

Image
On Caltrain yesterday, I was surprised to see among the usual set of commuting bikes a SRAM Red-equipped Argon Gallium Pro. The bike immediately stole your attention. The design was one which has been trending: clear-coated carbon with plenty of text detail so the viewer is sure to realize he's gazing upon the result of advanced, proprietary engineering and not at yet another paint job on the same old OEM frames being pumped out of the same old Taiwanese factories. But it worked: the bottom bracket area was huge, the downtube a large-diameter "inverted Kamm tail" design seemingly designed to maximize wind resistance, the top tube a broad, eccentric shape which screamed "vertically compliant yet torsionally stiff". All it lacked were the pencil-think seat stays Cervelo popularized, but this was a machine designed for stiffness over anything else. It seemed dramatic overkill, since the bike was small (the Argon "XS" I suspect). There wasn't muc...
Read more