But I understand running pace is a function of power. Does this mean a 10% increase in pace requires 10% more power?
If this is the case I can see Dr Coggan's point of view.
This is pretty much the case especially at the speeds triathletes typically run which I believe has been Andy's main point all along.
I suspect it's far from linear. In particular when you become more fatigued. Also at certain paces or uphill vs. downhill.
It is true over a range of paces on relatively flat ground.
But I don't have hard data, it's what I've come to believe looking at me own data and some of my clients. Below a certain pace, their run mechanics change and the ratio of pace to energy output changes.
I also know one athlete that has a very narrow range between aerobic threshold and lactate threshold. Very narrow. I suspect it's a main reason he performs much better in 70.3 compared to IM. You can cross that line frequently without penalty. You cannot in IM.
On a constant grade, the metabolic cost of running is directly proportional to speed from ~4 mph up to as fast as you can run for several minutes (hard to say beyond that point, as a steady-state in VO2 won't be achieved, and biomechanical estimates of power output are just that, i.e., estimates).
There is some drift over time/effect of fatigue, but it's really only large at supra-threshold intensities (same is true for cycling). One study in J Appl Physiol that I recall, for example, had ultra marathoners running on a treadmill for ~5 h, allowing them to adjust the pace as they desire. VO2 stayed essentially constant over time, as they slowed down by (IIRC) 8% (implying that if they hadn't slowed down, VO2 would have risen by about the same amount).
A 1% increase in grade typically results in a 4% increase in metabolic demand. As I mentioned before, though, there is also a significant shift in muscle use (e.g., see Costill's classic study of glycogen utilization in the gastroc vs. v. laterals), something that wouldn't be captured by a running pwoermeter.