Is it possible for a course with mild rolling hills to be faster than a perfectly flat course?

How about just some anecdotal stories...for myself, Chicago..which is pretty much flat as can be..I ran a pretty fast time, but felt pretty beat up. Flat like that is using the same muscle group the entire race. Fast forward, next year tried Indy instead...finally broke 3 (was better trained for sure) and felt much better after. Indy is "flat" for sure, but at least has some small rollers to help break it up...and I think that helped with muscle fatigue. Not scientific at all, but I like a few changes in elevation to break up a marathon...same reason you hear people complain about soreness after one of those crazy downhill races...too much of the same is tough on the body

A point to point course could "Roll" from the top of a mountain to the sea level. But that is extreme. Every runner is different. In my youth, when I was in racing shape I had little natural speed. But I had big upper legs & lived in a very hill area of central MA. Some of my best races were hilly. Much of that is the fact that I sought them out, peaked for them & knew I would have a better chance of beating the competition on hillier courses. If I concentrated on flat & fast courses I am sure I would have had better PR's but finished further back in the pack.

Joplin, MO xc course

There’s a course I ran in highschool every year that had a very sharp 300ish meter uphill about half a mile in and then smooth downhill for the next mile with mostly flat terrain for the rest of the course after that.

It’s one of those courses where on athletic.net everyone’s name has SB or PR next to it, and yes we’ve measured the course. It’s a legit 5k

Didn't they make sure Kipchoge ran on a course with ever so slight up and down in his first breaking 2 attempt? The justification being the slight change helps reduce the cumulated fatigue in certain muscle groups?

Yammy wrote:

No. Uphills slow you down more than downhills speed you up. This is well understood both in running and in physics. The fastest course with no net elevation change is one that is perfectly flat.

True, and it's math in addition than Physics.

Anything in series leads to a harmonic mean,

You run 10 mph normally. You go up a hill that makes you go 20% slower (8 mph) and then down a hill that makes you go 20% faster (12 mph). Your average speed is 10 mph and you come out the same, right?

Wrong. 2 miles at 10 mph would be 12 minutes. Your uphill took you 7.5 minutes and your downhill took you 5 minutes for a total of 12.5 minutes, which is an average (harmonic mean) of 9.6 mph.

If you use min/mile, then you're doing a harmonic mean of the velocity.(7.5 min/mile + 5 min/mile)/2 = 6.25 min/mile ==> 9.6 mph. You could argue that you should apply the +/- 20% to the min/mile and then it'd come out even, but that's where you get back to physics. The +/-% on the velocity makes more sense than on the inverse.

Plus, and this was probably pointed out earlier, the fact that some of your energy goes into braking on the downhills shows that hills are always going to be less efficient.

Now maybe for very gradual hills a runner's preference and breaking up the repetition would help some run faster on a course with slight hills, but there's no question that the physics and math strongly favor a flat course.

some modern garmins give you "3D speed and distance"

Yo this guy kinda spitting facts

harmonius wrote:

You run 10 mph normally. You go up a hill that makes you go 20% slower (8 mph) and then down a hill that makes you go 20% faster (12 mph). Your average speed is 10 mph and you come out the same, right?

What's the basis for this premise that downhill speeds you up by an equal percentage that uphill slows you? Looks arbitrary to me.

For most moving objects, the slowing is lower-bounded by zero, and the speeding upper-bounded by infinity. No reason to suppose that the speeding might have a higher magnitude. I believe this is the case in cycling during mountain stages.

joecrunner wrote:

Didn't they make sure Kipchoge ran on a course with ever so slight up and down in his first breaking 2 attempt? The justification being the slight change helps reduce the cumulated fatigue in certain muscle groups?

Yes, I mentioned that course on the Monza car racing track earlier in this thread.

Bad Wigins wrote:

harmonius wrote:

You run 10 mph normally. You go up a hill that makes you go 20% slower (8 mph) and then down a hill that makes you go 20% faster (12 mph). Your average speed is 10 mph and you come out the same, right?

What's the basis for this premise that downhill speeds you up by an equal percentage that uphill slows you? Looks arbitrary to me.

+2600

joecrunner wrote:

Didn't they make sure Kipchoge ran on a course with ever so slight up and down in his first breaking 2 attempt? The justification being the slight change helps reduce the cumulated fatigue in certain muscle groups?

No, it was a coincidence that the course wasn't perfectly flat. At the time it was the best place they could find that was at low altitude. The course wasn't rolling, it was close to flat, a gradual ever so slight incline on one side of the track, reverse on the other.

The course where he did break 2 was flatter, slight down first 200m then flat loops.

I am a hills guy. Hills are my thing. A run isn't a run unless it has some challenge to it for me. Secondly, I'm scary fast downhill. I often have to go with caution on major inclines because I know it's not good for me.

But ... there is the geodesic.

The fastest route will always be the flattest, shortest route.

/End

I think it's possible for a cross country style race. If the slope is so gradual that it doesn't impede your stride, the downhill could be more beneficial than the extra expended energy going uphill.

As an example, if you have a 5 mile cross country course that has a perfect slope of 1 inch per 40 feet in distance, that is a net gain of 11 feet a mile. But if that gain were to really be spread out linearly, I don't think you would be able to feel that and it wouldn't slow you down.. 4 miles of that and than a negative 44 foot drop for mile 5 and I could see a PR for a 5 mile race being set despite it not being a flat course.

I think it's possible so long the slope is below a certain level (I would guess 1%) and the hills are gradual. I'm not sure if that fits the definition of "mild rolling hills" that the OP was asking about though.

pie day wrote:

Bad Wigins wrote:

What's the basis for this premise that downhill speeds you up by an equal percentage that uphill slows you? Looks arbitrary to me.

+2600

Scared to answer?

Cyclists peloton at around 44kph flat. They downhill twice that fast or more. They don't uphill at 0.

Keep admitting I'm right if you think it's funny.

I believe the saying that rolling hills makes you less tired because you are cycling through different muscle groups is a myth.

Jon Arne Glomsrud wrote:

I use a formula that equals every meter of incline of a course that starts and ends at the same elevation to 2 metres extended distance. So if the course have 100m total incline (and obviously 100m decline), it runs 200m longer. A 10k with 100m incline will be like a 10.2km.

this is pretty much true.

an almost inexhaustible amount of data proves that undulating road profiles make you slower. even the most talented runnersslow down. if runners happen to run a pb despite the undulating profile (even when they ran on a completely flat course on other days), it only means that they were in the best shape of their life that day.

For me I have a 2km road I run intervals back and forth on and from maps I have the exact length and inclinen/decline. I use the formula +4.5xIncline and -2.5xDecline. If the elevation is the same at the start/end this equals to +2xIncline (4.5-2.5). The 4.5/2.5 numbers, I have adjusted based on my threshold interval workouts going back and forth the same workout. I used 5/3, but I always run "faster" uphill than downhill so I adjusted and now they get very close.

So for me I have proven these numbers sufficiently. I am equally good at uphill as downhill. These numbers also correspond well to Strava GAP.

Strava GAP is not crap at all. It is based on a massive amount of data from runners using pace, elevation and HR. It is statistically significant as far as I can understand. Of course, as with any statistics, one cannot use it on all individuals, but if you are an average runner it will be very close.

Bad Wigins wrote:

[quote]harmonius wrote:

For most moving objects, the slowing is lower-bounded by zero, and the speeding upper-bounded by infinity.

You can run infinity mph?

The terminal velocity (so-called because you're going to die) of a human falling through the air is about 150 mph. Let's make that the upper bound.

As you said, the lower bound is zero. You could have a cliff with no footholds that cannot be climbed (don't tell Alex Honnold). Okay, let's make the lower bound Alex's speed on his free solo of about 0.125 mph.

Let's go back to our case where 2 miles on flat at 10 mph takes you 12 minutes.

What is your time and average mph or min/mile for going two miles where the first is at 0.125 miles per hour and the second is at 150 mph?

That's too much slowing. How about this? Going uphill the first mile slows you down only by half (5 mph), while you speed downhill the second mile at the terminal velocity of 150 mph. Certainly the huge increase in speed drops your time under 12 minutes, right?