Question Running vs. Cycling: Energy Required

I brought up this issue many years ago at another biking forum, and it didn’t prompt much of a discussion, but I’m going to try again. In fact, I’ve seen it discussed at a running forum.

How much energy is required for cycling vs. running? The general consensus seems to be that three miles of riding on a flat route is equivalent to about one mile of running. The ratio or relationship is not exact, of course, and depends on other factors, but it’s close enough for the purposes of this discussion. I will note that the energy required for biking depends more on speed than is the case for running. For example, one source I used said a 165 lb. male will consume about 45 calories per mile at 15 mph, vs. 40 at 12 mph, and 38 at 10 mph. The same source that the same man would consume 130 calories running a mile at 7.5 mph, and actually slightly less, 127 calories, running at 12 mph. This reflects the fact that wind resistance is a much bigger factor at the speeds that cyclists normally attain. But again, the variation is not that important.

OK, here’s the problem. When we consider the actual results of cycling vs. running, the 3:1 relationship doesn’t seem nearly correct. Consider that in a Grand Tour, riders complete stages of 100 or more miles every day for three weeks. Even if these stages were pan-flat, riding them should be equivalent to running 30-35 miles. But in fact most of the stages have climbs, and some of them of course have very steep and long climbs. So they’re energetically equivalent to running more than 30-35 miles. In fact, riders of such stages may consume as much as 6000 - 7000 calories per day. This is equivalent to the energy consumption of someone running 50 miles or more.

But very few people can run 50 miles a day, day after day. There are some ultra-marathon events in which a very small number of people might achieve this over a period of weeks. But we're talking about world record holders. Most runners find it difficult just to compete in a marathon two or three times a year. After running one, they need to rest for several weeks even before resuming training, which is likely to be around 20-30 miles a week. An amateur cyclist, given the time, can ride 10-20 times that much per week, throughout the entire season.

Moreover, just anecdotally, most people who have both run and cycled claim that running a marathon is much more difficult than riding one hundred miles. (I welcome some personal observations here; it may not be unanimous, but I’d bet the great majority of posters would agree with this). Running takes much more out of your body—more muscle damage, ofter accompanied by an inflammatory response—and requires much longer periods of recovery. These recovery periods should come with increased energy demands that wouldn’t be reflected in simply measurements of oxygen use or calorie consumption during or immediately after the event.

Is there an energy deficit that’s made up only by maintaining an elevated metabolic rate for weeks or months after running? I've seen some studies that suggest this, but the results are mixed. Where is the missing energy? Or if there is none, how does one explain the much greater impact of running?
 
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I think it is possible for a top class distance runner to train doing up to about 120 miles per week, this is not racing and will be at different pace. The difference between this and a marathon race is that every mile in the race is full gas marathon speed, while the training is at different paces. I don't think it would be possible to do a 10k at race pace every day for a week while it is quite possible to run 10k each day for 7 days if your body is trained for it without any adverse effects at a decent pace.

The difficulty with running is that if you up your training to quickly you are almost certain to pick up an injury.

Also there is no freewheeling in running and downhill running puts massive stresses on your body.
 
Running involves significant skeletal impacts as well as both concentric and eccentric muscle contractions (in contrast to cycling which has little to no impact forces and only involves concentric contractions).

These factors combine to create additional fatigue and differences in efficiency.

The energy cost of running has also been found to rise as distances get longer / fatigue increases.
 

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