Here comes Mars with the math!
The average male penis when erect is approximately 6 inches long and (I'm guesstimating) about 1 inch in diameter. So that's 6 cubic inches, assuming a constant diameter along the entire length (which obviously isn't true). There are approximately 16 millilitres in a cubic inch, so the entire penis, were it a constant diameter and completely hollow so that the entire internal volume were filled with blood, would contain approximately 96 millilitres of blood.
The average adult male human body contains approximately 5 litres of blood, which means that 96 millilitres is about 1/50th of the amount of blood in your entire system. Even during vigorous exercise, I'm quite certain that the body could spare that much without great difficulty and that's using a very high number (I would make a rough estimate at the actual amount of blood in the penis during an erection being half that, maybe less). To put in in context, they take a pint of blood when you donate, which is roughly equal to half a litre. So even if we use our ridiculously high number it's still only a fifth of what you donate, which a lot of people can give without suffering any real negative consequences.
So is it possible? Physically, yeah it is. If that's where your hindbrain is going to go, then that's where it's going to go. But let's take brain chemistry into account. When you run, your brain releases endorphins and adrenaline, which leads to the so-called 'runner's high'. It also activates the fight-or-flight mechanism, which has several physiological side effects. As has been noted, your digestive tract nearly shuts down, as do many other parts of your body in order to conserve the much-needed oxygen for the bits that are crucial to your survival - namely your brain, your heart and your leg muscles. Given that, sex is more or less pushed out of your head. Your instinctive brain says 'survive now, fuck later.'
So, yeah. Is it possible to get an erection while running? Certainly it is. Is it possible to get aroused? I'm going to say probably not.
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I wake up in the morning more tired than before I slept
I get through cryin' and I'm sadder than before I wept
I get through thinkin' now, and the thoughts have left my head
I get through speakin' and I can't remember, not a word that I said
- Ben Harper, Show Me A Little Shame
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