Theories are interesting and sometimes real world applications don’t pan out. Each of us is different, with different levels of fitness, etc. There was a recent “tortoise and hare” thread where the general consensus was a steady pace works best.
We can look at cross country racing strategies, where courses are generally 8K to 10K in length, or we can look at ultra marathons where runners run and/or walk. Andrew Skurka has some detailed ultra running plans, training strategies, and post race analysis on his website and has done well in several races. Probably a good read for someone who wants to take a look at the science and the applied and isn’t looking to win some sort of World Championship.
For a general rule in cross country for which I have a lot of experience, a runner wants to go up hills at a steady pace without getting exhausted in the effort. Remember, “What goes up must come down,” so really good cross country runners will pick up speed on the downhills and let gravity assist to the point of not losing control — this is a learned skill. This is how cross country races are often won — stay in contact with the lead pack, maintain a reasonable and steady pace on the uphills, pass competitors on the downhills, and keep enough energy in reserve to pass competitors on the flats or any possible sprints to the finish. It’s all about proper pacing throughout the entire race and the ability to adjust the pace over any given terrain or weather conditions.
For us mere mortals I can only share ancedotal experience. When I am in great shape I can do long stretches of constant elevation gain at a steady pace, such as 8,000 feet elevation gain in 11 miles, which is less than 1,000 feet per mile. Sections that are steeper than this require a slower, but constant pace. But it all comes down to physical condition. When I am in great shape, I move the fastest, at the steadiest speed, and have little or no recovery time needed. When I am not in great shape, I cannot hike long inclines without an occasional rest. Lots of elevation gain means fewer miles per day for me.
But I don’t pick trails based on trail construction methods, number of switch backs, elevation gain, etc. I usually just want to get from point A to point B in a specific amount of time, because I am hiking somewhere that is chosen for specific attributes, other than a particular trail or cross country route.
Today most elite runners get involved with technology and measurements such a heart rate, pulse, VO Max, etc. As a hiker I just want to walk, and all the science takes away or distracts from the fun. If I can learn from experience what pace works best for me on specific terrains, and if I can plan my daily mileage based on the conditions, and hit the distance milestones on time to get from A to B as planned, I am happy. Others want the science to guide them, which is okay if it works for them.
I have a friend who is has extraordinary intellect and is a competent engineer. I took him on some of his first backpacking trips. He would walk behind me on the uphills and analyze my foot placement (mostly toe first he pointed out), length of gait, pace, etc. Mentally he wanted to develop the most efficient method of walking. I finally persuaded him to stop thinking about it and just look at trees, plants, and the world around him. He is now a much happier hiker, enjoys his trips more, and simply walks without thinking about it.
YMMV
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