I started to look for a few places --near me--where the grade could be construed as fairly uniform for statistically useful samples, and came across some "gothchas." These two examples are NOT on trails, and both have some feature that prohibits normal walking. The first doesn't require hands, the 2nd does.
The first is the Mummy scree slope as shown below; it averages ~10.6 kfeet in elevation, so the O2 is ~72% of the sea level value; surely that has some effect.
This pretty uniform, obnoxious scree lasts for a little bit over 500-550' vertical. Here's the distance/time plot:
...so this is just one point on a Ze-type plot. The surges reflect periods when I gain ~50 vertical feet, then rest for 20 breaths or so. So one could come up with at least 9 periods when my rate far exceeded the average; but that would be misleading, as I never could have kept up that rate long. The regression line (which averages out all the surges and rests) gives ~0.58 ft/sec for a tangent of ~0.58, as determined from the start and end points of the slope. However, I tend to switchback naturally, and these tiny switchbacks are averaged out in the track recorded by the GPS, so the true grade is hard to define. Here, the average grade is nearly the gradient, as I usually want to get this miserable section over quickly; the scree makes obnoxious footing, with much slipping. What struck me was how uniform was the average. Furthermore, the ft/sec ascent rate on the slope, was roughly the same as my average ascent rate for all 3.8 kfeet of vertical rise to the top, even though most of it was on gentle switchbacked trails (the NLT and Trail Canyon to Charleston Peak).
I looked for a long uniform rock ramp, where I transitioned to scrambling, and the closest I came was this:
The average elevation is ~3.0 kfeet, so altitude has no effect. However, it is a little hard to define the grade. The coarsely averaged gradient is ~1.0, but I generally wander across the ramp a bit to find a path, and there are short, near vertical bands of 3-5'. The rock is very stable and frictional, so you don't slip, but you have to stop and think where the next step should be. Hands are on the rock maybe 20% of the time. For the two trips shown below, the ascent averaged about 0.66 ft/sec (the regression doesn't go through 0, so obviously...) for a grade of ~0.89.
For the pink symbols, I was alone, and the trip from car to summit took me about 60% of the time for the full trip that corresponds to the blue symbols; for the latter, I was with a group of 10 (the last ramp is just about 7% of the total elevation gain to the summit). Yet in both cases I got about the same average rate
on this ramp. For the 1st trip, I was a little spent by the time I hit the ramp, and on the 2nd, I stopped to count the folks below me, to make sure all were in sight.
I guess what this tells me is that 1) the problem is not so easy to define once you are off a trail; and 2) I tend to regulate my own speed, like all sensible people who are not automatons, so my lungs don't burst and my legs don't go anaerobic, yet I am mindful of schedules.
(All point measurements via GPS-calibrated barometric altimeter; relative accuracy for these small times is better than absolute accuracy.)