Shouldn't running a hilly course have the same finishing time of a flat course? What goes up must come down...

You are assuming you are returning to the exact same place, following the same route back. That is not how some courses are set up, though.

The difference of exertion on uphills compared to flats is greater than the difference of exertion on downhills compared to flats. So, no.

I don't have any physics competence but I suspect that not only, assuming you have a looped hill course, that the down hill portions do not even out the uphill exertions, but that there are nonlinear difficulties associated with uphill running

How does " what goes up must come down" relate to a flat course? Am I missing something?

If it was, would it give the same finishing time as flat if the effort was the same the entire time?

In other words, the gains from downhill portions come nowhere near to canceling out the losses from uphill portions, additionally, with those losses being nonlinear, owing to gravity, beyond what you would suspect from simply considering the raw hypotenuse length of the hill portion, or something like that.

Is this why downhill running skills are most important in a hilly course across a field of competitors who all share the same flat racing abilities?

1. going uphill tends to be slower than going downhill is faster. ex. on the flat you run 6:00. uphill is 6:30 but downhill is 5:45

2. its more tiring. uphills increase heart rate a lot. downhills beat up the legs

If you were to run a two mile race on a flat course and average 5 min/mile. This means that you run at 12 mph and finish the race in 10:00.

Now a race with 1 mile uphill and 1 mile down. If an uphill and downhill have the same effect on speed (assume uphill you are 10% slower and downhill 10% faster) you would run 13.2 mph and take 4:33 for the downhill portion. Uphill you would run 10.8 mph and take 5:33 for a sum finish time of 10:06.

Although there are a lot of assumptions in that summary (that the uphill and downhill are symmetrical and have the same effect on speed) it shows roughly that hills are slower than flats. Take a step further and think about the effects of fatigue and it is pretty clear that flat courses are always faster than hilly ones.

If you drive 60 miles at 20 mph and return at 30 mph, your average speed for the 120 miles is 24, not 25 mph. That is because you spend more time at the slower speed. The same would apply to running uphill and downhill, which would have in addition the greater fatigue in working against gravity, which would not be relieved on the downhill, since you would still have to lift your weight off the ground on each step.

ThuMbs_uP wrote:

In other words, the gains from downhill portions come nowhere near to canceling out the losses from uphill portions, additionally, with those losses being nonlinear, owing to gravity, beyond what you would suspect from simply considering the raw hypotenuse length of the hill portion, or something like that.

This ^.

Plus, for any closed course (start and finish at the same place) there will always be more uphill than downhill.