Calories/Running

Robert Grumbine said:

In article <[email hidden]>, Dot

dot.h@#att.net said:

Robert Grumbine said:

If I'm lucky, it'll be a lot more elegant than that ugly quintic Dot posted.

Hey, I was just the messenger 😉

I meant to note that as well. You agree, though, that it's ugly, right?

yep! Wouldn't get past me if I were peer reviewer 😉

Quoted message said:

Quoted message said:

Actually, I was surprised they could get something like that published. In my field, I doubt you
could publish with a 5th degree poly with that shaped curve, esp when they acknowledged different
mechanisms. It would probably be broken down piecewise and linear within the pieces. I later lined
the points up with a ruler and the uphill segment of the walking curve is as straight as anything
I've ever seen. The uphill segment of running curve had a slight curvature to it, but so slight I
don't know if the quadratic coefficient would be significant in a regression. Someday when I'm
bored....

The quintic bothers me. As in your field, such a thing would be hard to publish in mine. More to
the point, it would be something that we wouldn't even attempt unless driven to it by the data.
From your description, it's questionable that the higher order terms are actually adding
anything.

Yea. They have 13 (6 positive, 6 negative slopes, 0) data points with multiple observations at each.
Regression 101 teaches us not to try a 5th order there. I wouldn't try a 5th order unless there were
4 changes in direction (real or implied).

I did get partially bored the other night and plugged the eqn in spreadsheet. Then ran a regression
on the +10% and steeper slopes. Walk R2=.988; coef = 33.16 Run R2=.986; coef = 34.97

That's a phenomonally straight line, with surprisingly similar metabolic costs per vertical meter
climbed. The uphill run does have a slight curvature to it, but if you had R2 this high, most likely
you wouldn't try to fit anything higher than 1st order unless you were trying to minimize the error
of prediction. Heck, I get excited with R2=.8 in my stuff 😉

And if I ran the regression across all the numbers (up and down hill), the R2 were .74 for walk and
.78 for run - and standard error changes from a fraction to 3.x 😉 This also is rather meaningless
since there is an obvious turning point around -10%, iirc - at least the way they have drawn the
lines. I didn't play around with the negative numbers or the central part where it curves (about
-10% to +10%, iirc), but the negative portion is also going to be linear, and there's probably a
quadratic or something else with one change in direction that should fit that.

Skimming their methods (I haven't taken the time to sit down and read it in detail to see if there's
something I'm missing), it looks like they did these as a progression - started shallow and
increased steepness, with some recovery time between. They also varied the treadmill speed. If a
person exceeded a certain lactate accumulation (4mM), they stopped the test. IOW, the less efficient
/ conditioned subjects were eliminated from the upper end, but I think they were still included in
the lower end, which may or may not make a difference in curve. At any rate, the protocols seem to
make sense (at my level of ignorance of these types of studies) if you're trying to get empirical
data to develop a theoretical model. However, I suspect if they were to include all the runners in
there - and some non-elites - I'm wondering if the energy costs would go higher. But once they
exceed that point (LT?), are their methods of measuring energy costs valid - not sure, and I suspect
this may be why they capped it. BUT this is totally outside my realm of knowledge. I'm completely
speculating.

Modelling the flatter portions (+-10%) might be interesting since that's where most people run, but
now that I think about it, they have only -10%, 0%, 10% - no points to model in there. But there is
another study that they graph with some points there.

The realities are that it's an interesting academic study, but I'd be curious if they get
different results with "average" runners - or even runners who do hills, but not that steep. And
most likely a person is going to be on a trail, which will likely be tougher than a treadmill
because of the footing issues, scree slopes, etc. And that may become an even more significant
factor at steeper slopes.

Back to reality. I just care about getting *me* and my camelbak up the hill. I was curious about
what point walking becomes more efficient than running, but on this study, it doesn't appear to be
all that much, but I think that might be an artifact of the study. I'll just continue to switch
before body says to (if I wait until then, then it's usually too late).

But I *do* plan on watching the elites when they're here in September.

Dot

--
"Success is different things to different people" -Bernd Heinrich in Racing the Antelope

Dot dot.h@#att.net said:

I did get partially bored the other night and plugged the eqn in spreadsheet. Then ran a regression
on the +10% and steeper slopes. Walk R2=.988; coef = 33.16 Run R2=.986; coef = 34.97

That's a phenomonally straight line, with surprisingly similar metabolic costs per vertical
meter climbed.

Does this mean I was right after all? I got lost in the learned discussion :-

steve common said:

Dot dot.h@#att.net said:

I did get partially bored the other night and plugged the eqn in spreadsheet. Then ran a
regression on the +10% and steeper slopes. Walk R2=.988; coef = 33.16 Run R2=.986; coef = 34.97

That's a phenomonally straight line, with surprisingly similar metabolic costs per vertical meter
climbed.

Does this mean I was right after all? I got lost in the learned discussion :->

Duh? Which statement are you referring to? 😉

This one?

Quoted message said:

This (those values & the monotonic increase) would suggest a "cost" of
1/3 J kg-1 m-1 per degree, right? That's ~10% (of the energy cost on the flat) per degree! So the
10% incline would give more or less DOUBLE the energy expenditure.

If so, the reason I didn't include flat in the regression, is that it does seem to curve noticeably
there, but they don't have any data points between 0 and 10%. The cost of walking (J/(kg m)) on 10%
vs 0% was 4.9 vs 2.5 or about 2, as you say. The cost of running is about 1.66 as costly on 10% vs
0%. Under the protocols of this study, the relative costs of running vs walking were greatest on the
flat and decreased the steeper the hill. The energy costs of the elites running on the flats were
less than that of sedentary subjects from earlier study, but the costs are similar (elite vs
sedentary) in the 10-25% range.

Looking at the incremental cost of running / degree [(Cr on slope - Cr on flat)/ slope (in %)]
varies from 2.36 at 10% to 3.51 at 45%. (unless I set something up wrong 😉

Also looking at the curves, the running curve starts noticeably deviating upward from some
(hypothetical?) efficiency lines - much faster than the walking ones do. Also the error bar at 45%
gets very large compared to the other slopes. This is why I'm not sure it reflects real energy
costs, esp. as it might apply to any of us. Esp. since they didn't use all subjects at the steeper
slopes, because they couldn't maintain submaximal conditions = they removed the ones that would
shoot the curve up even higher. (but I think I see why they did that for the study)

Also, if a runner were on a 45% slope (about 23 deg), there's going to be trail condition issues
(read keeping from wiping out) that will affect costs also. So it's actually a nice study seeing
relative costs, but reality will have more costs.

Dot

--
"Success is different things to different people" -Bernd Heinrich in Racing the Antelope

"Dot" <dot.h@#att.net> wrote in message
"]news:[email hidden]...

Quoted message said:

If so, the reason I didn't include flat in the regression, is that it does seem to curve
noticeably there, but they don't have any data points between 0 and 10%. The cost of walking
(J/(kg m)) on 10% vs 0% was 4.9 vs 2.5 or about 2, as you say. The cost of running is about 1.66
as costly on 10% vs 0%. Under the protocols of this study, the relative costs of running vs
walking were greatest on the flat and decreased the steeper the hill. The energy costs of the
elites running on the flats were less than that of sedentary subjects from earlier study, but the
costs are similar (elite vs sedentary) in the 10-25% range.

<nonsense squared snipped>

Dot, I can see why you have me killfiled. We come from different worlds, live in different worlds,
and will die without ever wishing to understand the other.

Roger.