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

Based on energy expenditure uphill vs downhill, the uphill costs more per meter incline than what is gained from a meter of decline. 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. Strava have collected a lot of running data from runners based on HR, pace and elevation and my formula follows that quite well.

The distance addition of 2xtotal incline relies on that you are equally good at uphill as downhill running

Yes, as long as the mild rolling hills work out to net downhill

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.

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.

Exactly correct

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.

What about a 5k loop course when the first 400-500m is a step uphill followed by a flat smooth decline of the the 4500m?

I think footing makes more of a difference than anything. One year I finished 4th in my Power 5 conference in XC - 10K back in the day - and it most of the race was on a rock hard trail that was like a track (I was a miler). Run that race in the mud and I would have been 20th. Conditions matter in XC, except to truly great XC runners (why I was so impressed by Connor Mantz's performance this year).

I think Jamin is right and all of you citing "physics" don't really know what your talking about, this is a complex system, it's not as easy as energy in = energy out.

I say that it greatly depends on where the hills are placed along the course - a mildly hilly portion in the middle of a course might be slight benefit, a mildly hilly portion at the beginning or end might push one over the edge (either before the body has adapted to the effort level or after it has passed a threshold). Flat courses probably lead to people gassing out too early and hilly courses let one mete out effort at a more reasonable rate.

Renato Canova and Kevin Hanson both say yes. See the third to last paragraph

https://www.letsrun.com/forum/flat_read.php?thread=5276018#5276640

They are incorrect.

maybe a marathon/ half with a moderately hilly first few miles, then a long gentle descent at the end ?

Since the race is so long, it helps to slow you down slightly at the beginning, then at the end you'll still moving fast with the downhill

idk though never ran a long road race, just guessing

jamin wrote:

I say maybe. The seconds you lose on the uphill could be regained on the downhill, plus a bonus second when it flattens out and you have that little boost from the downhill speed. I stress the word mild.

Of course, so many factors.

-you are feeling better on any particular day

-you gain momentum on downhills. Some runners are better navigating the dips on courses

Generally though, flat courses will produce faster times.

Carlsbad has this.

It's called flat, but even Steve Scott himself said to both frontload the first mile and run the tangents.

In my PR in 2014 19:35...I was able to go 5:52 my first mile, 6:31 my second (a bit uphill) and 7:12 my final 1.107 ( because of the final descent (all downhill)

I mean slight elevation like 20 ft is not a hill but in race comparison..sure.

Jon Arne Glomsrud wrote:

Based on energy expenditure uphill vs downhill, the uphill costs more per meter incline than what is gained from a meter of decline. 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. Strava have collected a lot of running data from runners based on HR, pace and elevation and my formula follows that quite well.

The distance addition of 2xtotal incline relies on that you are equally good at uphill as downhill running

Wrong. Using Pythagoras’ Theorem, the extra distance travelled by there being an incline or decline will vary depending on the original distance. This will decrease the further the original distance is.

Example: (excuse the lack of proper symbols, as using an iPhone)

100 metres of incline over the course of a 10k =

10000^2 + 100^2 = 100,010,000 (Square Root of which is 10,000.49999 metres)

100 metres of incline over the course of a 5k =

5000^2 + 100^2 = 25,010,000 (Square Root of which is 5000.9999 metres)

It’s not something that I’d even thought about until now, but I do wonder if fitness watches etc. take this into account?

Mr. Grumpy wrote:

Wrong. Using Pythagoras’ Theorem, the extra distance travelled by there being an incline or decline will vary depending on the original distance.

You don't run any "extra distance" going up or downhill and that's not what his formula is implying

Hardloper wrote:

Mr. Grumpy wrote:

Wrong. Using Pythagoras’ Theorem, the extra distance travelled by there being an incline or decline will vary depending on the original distance.

You don't run any "extra distance" going up or downhill and that's not what his formula is implying

My bad. I misread what he was getting at. However, if a GPS device doesn’t take the elevation change into account, then the distance WILL be slightly short. This will increase more if running steep hills or in the mountains etc.

Do you guys really think it's a coincidence that the marathon WR is always set/lowered on a course that is extremely flat? Don't you think that pretty much closes this discussion?

jamin wrote:

I say maybe. The seconds you lose on the uphill could be regained on the downhill, plus a bonus second when it flattens out and you have that little boost from the downhill speed. I stress the word mild.

Less potential for high wind?

So maybe not hill...hills, but a little bit of undulations/false flat type stuff could alter motor recruitment patterns a bit and might be helpful from a fatigue standpoint in longer efforts. Michael Joyner mentions this in his Wired interview about Kipchoge Sub 2 performance.

Of course it's possible, are you daft?