Nick Willis leads the 2013 TC 1mi |

This week, Twin Cities in Motion announced that
the 2015 edition of the Twin Cities 1 Mile will be run on a new course heading
north on Hennepin Avenue through downtown Minneapolis, instead of the historic course
down Nicollet Mall. The motivation for
this change was construction of a new light rail line that crosses the Mall,
with trains that run every few minutes—far too frequent to be able to get a
full wave of runners across quickly.

The old course was flat and very fast, and with
its very generous prize purse, the elite wave attracted several extremely fast
milers. Because of stormy weather, the
race was canceled at the last minute in 2014, but in 2013, Nick Willis set a
course record of 3:56.1 in 2013 for a cool $10,000 bonus, and

*five*other runners broke four minutes.
A new course, but the same record

In a recent interview with Minnesota running blog Down the Backstretch, TC 1 Mile race director Jeff Decker clarified that, even
though the course has changed, Willis' 3:56 (and Sara Hall's 4:30.8, run in
2011) are still considered the "event records," so to earn the
$10,000 record bonus, these are still the marks a runner would need to
hit.

Which brings us to the new course. The new route up Hennepin Avenue has no turns
to mention, but it

*does*have a noticeable uphill in the first half mile or so. Down the Backstretch provided a handy chart comparing the elevation profile of the old and the new course. Can we use this to predict whether the course will be faster or slower, and what kind of performance would be necessary to break a course record?
In fact, we can, as long as we make a few
simplifications. If we can make an
idealized model of each course, we can compare their relative "fastness." As you can see in the chart above, the old
course fluctuates a bit, but never gains nor loses more than ten feet. Because of this, I'm comfortable treating the
old course as if it were perfectly flat, i.e. no significant differences from
an idealized "fast as possible" course.

The new course gains 30 feet of elevation over the first 0.4 miles, moving from 820 to approximately 850 feet above sea level in the first 640 meters. After this, it's essentially flat. We can make a simplified version of the course that gains 30 feet over 0.4 miles at a consistent incline, and is completely flat thereafter. So, the question then becomes, "How much does a 30 foot gain over 0.4 miles slow down a runner?"

Calculating the losses from uphill running

There are two ways to calculate this, each
forwarded by a prominent coaching figure.

Jack Daniels, of

__Daniels' Running Formula__fame, has stated that research he conducted showed that, for every percent of hill gradient (a unit used to measure hill steepness, expressed in %), you are slowed by 12-15 seconds per mile. A gain of 30 feet over 0.4 miles is a gradient of 1.4%, so crunching the numbers, we get (12 to 15) * 0.4* 1.4 =**6.7 to 8.4 seconds**slower. As the rest of the course is completely flat, the other 0.6 miles of the course have no influence on time.
The other, simpler method comes from internet coaching guru John Kellogg, of LetsRun.com fame. Kellogg, who is reputed to have an uncannily accurate ability to estimate the effects of hills or wind on the speed of a course, states that every ten feet of
vertical gain will result in being slowed by 1.74 seconds, regardless of the
horizontal distance covered. In our
case, we gain 30 vertical feet, so we expect the race to be slowed by 1.74 * 3
=

**5.2 seconds**.
Now, there are some caveats to both of these
estimates. Both Kellogg and Daniels
admit that their calculations are based on data from

*submaximal*running, i.e. speeds slower than VO_{2}max (about 3k-5k pace). This is because these experiments are very simple to do: you can just have a group of runners do several short bouts on a treadmill set at various inclines, and measure the change in oxygen intake as the incline gets steeper. However, as anyone who has done a hill workout knows, running fast up a hill rapidly demands a lot more energy than running on the flat. Once you've hit your VO2 max, it's not possible to measure your energy expenditure through analyzing the gasses in your breath anymore, since any additional increase comes from your body's anaerobic system.
To accurately measure energy expenditure at high
speeds (like, say, four-minute mile pace), it would take a much more
complicated experimental setup. Your best
bet would be to correlate blood lactate levels on a range of inclines and at
various speeds with blood lactate level measurements taken at the same speed,
but with no incline. Another possible
avenue would be a direct estimate of the work done and the power expended at
each joint, which could be done with a 3D gait laboratory. Good luck herding a dozen four-minute milers
into one of those!

Further muddying the picture is the likely fact
that some runners are better at handling inclines than others. There hasn't been any research into this that
I'm aware of, so it's hard to say how big the differences could be. Confidence intervals from Daniels'
experiments could give a rough idea, but I haven't seen the original data.

Considering these restrictions, plus the
assumptions we made in our "idealizing" the courses, how much can we
trust these numbers? That's very much up for debate, but in keeping with the
proud tradition of hand-waving in scientific estimates, I'm willing to
negotiate away to one "sig fig" (significant figure) and use John
Kellogg's rule as a lower bound, and the high end of Jack Daniels' rule as an
upper bound. This leaves us with a
figure of 5 to 8 seconds.

My prediction

After a bit of back-of-the-envelope math, we can state
the following with some confidence:

**The 2015 Twin Cities 1 Mile will be 5-8 seconds slower than previous years, and it is very unlikely that Nick Willis' event record will be broken.**

For Willis' mark of 3:56.1 to be beaten, our
figures suggest it would take a 3:51-3:48 effort to equal that time on the old
course. This would be an incredible (though
not impossible) road mile! Sara Hall's record would require a 4:26-4:23 effort.

Indeed, our numbers suggest that Willis' run last
year would not even be sub-four minutes on the new course. It seems likely that the winner might only
run 4:01 or 4:02 on the new course. This
would be rather disappointing, since being able to see a sub-four mile is still
something pretty special, especially to people who

*aren't*fans of running, and just happen to be walking down Hennepin Avenue on a weekday. A sub-four mile is enough to get anybody excited about running. The six I witnessed at the 2013 TC Mile are still the only sub-four miles I've ever seen in person.
I'd love nothing more than to be proven
wrong. After the race, maybe I'll even
be able to run the numbers and see if a statistical analysis of the results
supports this prediction. But if the
race management is worried about times being too slow, there's an easy
solution. Run the course the other way!
If that's not an option, you can always hope for a tailwind...

*The Twin Cities 1 Mile takes place on May 14th in Minneapolis. I'll update this article, or post a follow-up, afterwards.*

Hi John.

ReplyDeleteEnjoy your blog.

RE: "run the course the other way"

Do Daniels and Kellogg have estimates for downhill?

Also curious, not for this race, but when encountering very steep downhills I am thinking it may be counterproductive as compared with gradual / flat.

Thank you.

Daniels does indeed have an estimate for downhills: he says you gain 8 seconds per mile per % gradient. This makes sense, as you'd expect to not get back as much from a hill as you "put into" it: A hilly loop, with zero net elevation change, is obviously slower than a similar loop that is flat. Kellogg's estimate is more crude because it does not take this into effect: his rule of thumb simply states that every 10 foot difference in elevation is a 1.74 second change in time (regardless if you're going up or down).

ReplyDeleteFor individual hills, Daniels' and Kellogg's rules end up being pretty similar (up or down), but if you are trying to break down a course with lots of ups and downs, you'll want to use Daniels' method.

I do agree with you: A race with very steep downhills is problematic because it fatigues your quads a lot, and it's easier to get more energy out of a gradual downhill than a steep one. Given the choice between a loop that gains elevation very quickly and loses it gradually, and a loop that gains elevation very slowly, then loses it quickly, I think the first option would be a lot faster!

Reference: Twin Cities designers

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