A range is good enough.
How is it wasted?
I assume we’re picturing an artificial environment with no trees and a bunch of CO2 scrubbers?
That’s easy. None. It’s all being used efficiently.
Are you sure you meant to ask “for an hour” instead of “for a mile” or some other distance?
Perhaps someone here will suggest that more oxygen is being consumed per hour than walking. Let’s assume that there is such a number for the exercise period. However, a well conditioned person will tend to have a slower heartbeat and reduced respiration rate. My heartbeat is about 50 and my resting breath rate is about 3-3.5. So during the balance of the day my breathing is less and the oxygen uptake is more efficient. Any useful equation should take the global calculation in mind.
You will consume far more oxygen running vs. walking for an hour. By the mile, it’s roughly the same.
I’m still unsure what the OP means by wasted.
Your supposed to use more energy if you run than walk for a given amount of time. How much more oxygen will this burn up for the same person?
From a quick skim, it looks like at normal walking speed, you use less but when you start forcing the pace you reach a point where running is more efficient.