Not to be too pedantic... But, a pendant is not a pedant.

NOW THE GRAMMER POLICE TOO!

I wanted to bring that up, too, but I didn't want to be the pedant dick

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"What's your claim?" - Ben Gravy
"Your best work is the work you're excited about" - Rick Rubin

Side benefit is by this point the AI system has thrown up its hands on gathering useful information from us, and moved on to saner, more predictable content generators like teens on TikTok.

Noting that coriolis acceleration is proportional to angular velocity at the surface of the earth crossed with the radial velocity into the earth....both of which are many orders of magnitude down. Those are VERY small forces and thus negligible.

A 400m track is roughly 3 arc-seconds of lattitude in length if oriented so the long axis is north-south. So, your angular velocity is 3 arc-seconds per 20 seconds or 1 arc-second per 7 second....or 0.7 uRadians/s.

That's 7 orders of magnitude down.

Yes, but we were in 28:59.999999999.. territory..so this is good enough for the hypothetical runner to have to correct his trajectory one way or another and not break 29 min ;-)

We're all hurtling through space at speeds which are completely variable, depending on where you're measuring against

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"What's your claim?" - Ben Gravy
"Your best work is the work you're excited about" - Rick Rubin

Yeah.
What he said.
I'll just get my 62 year old overweight butt out there and pop off 10 3 minute 1k's.
No problem-o.
On my bike

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I saw this on a white board in a window box at my daughters middle school...
List of what life owes you:
1. __________
2. __________
3. __________

Except that the other velocity is perpendicular to the axis of rotation. This could possibly be measurable at the poles. But, even at the 60* lattitude, that's a 2 m/s radial velocity.

So, 2.1e-6 rad/sec acceleration. The closer to the equator the smaller the effect.

Compare that to the angular acceleration of cornering the ends of the track at 157 mRad. So now the acceleration is 157. 002 mRad.

Also.. Coreliolis is balancing. So, it will bend inward to the track on one half, and outward in the opposite direction. So the net effect... Minus variations in symmetry will be zero.

Finally, coriolis is an effect of motion in two reference frames.... An iniertial frame and a rotating one. Each foot contact reconnects the runner to the rotating reference frame..again negating the bulk of an already minescule, balancing effect.

Presume you are committed to pendant dick status thobut, except when you "bring that up", Coriolis force notwithstanding.

Agreed on everything just not with the last paragraph on the overall Coriolis effect, in theory yes they will cancel but the net effect will be what we feel with a cross wind that we have to constantly apply effort to keep our trajectory, hence, our theoretical runner being a dynamic system will have to use additional power compared to a flat trajectory 4:40.

Uh, no, it just can't be less than 10k.

The length of the course shall not be less than the official distance
for the event. In competitions under Rules 1.1(a), (b), (c) and (f), the
uncertainty in the measurement shall not exceed 0.1% (i.e. 42m for
the Marathon) and the length of the course should have been
certified in advance by an IAAF approved course measurer.

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Excellent calculation on the Coriolis effect. My only issue is when we use reference frames other than the track or the runner to define the distance. On a N/S aligned track very close to the poles you could argue that the Coriolis effect bends the straights of the track (from the astral reference frame) while the runner travels on a straight line from their reference plane. If we allow this then I fear we are running at a 4:40 pace towards 10k records on a moving train.

There is one other fundamental to track running that may fully overcome the CoG distance and other effects. The runner is taking ~50 steps through the turn. By the last of those 50 steps the velocity of the runner must be 180 deg turned from their initial velocity, 3.6 deg per step. I'm not sure how you would even calculate that with discrete footfalls, but you can say at the very least that the necessary downward force on the runners idealized footfall is ~0.5% higher due to the centripetal acceleration.

This is true, however, the discussion was of path distance, not applied power. Provided the runner can apply a lateral force to correct for the 2 uRad/s and maintain their 20cm offset, the distance traveled will be unchanged. In theory (notwithstanding any asymmetry), the entire path of the runner's CG is translated slightly (as with your cross-wind analogy) from the true axis of the track, but not constricted nor expanded (by an increase/decrease in the consistent lean-angle calculated my Mr. Maths).

A vote of thanks to Mr TheTRI for their catalytic (leading-edge) role in the formation of this vortex.
Is one allowed to vote for an enigma (other euphemisms are available) - I guess we'll discover this year.

The actual runner's foot-path is piecewise linear, so, the runner's feet are really following a hectogon and applying a lateral force (in addition to the downward one...or perhaps a rotation, followed by a longitudinal thrust) to impart the 3.6* course change per step. Due to inertial effects and the generally sloppy, human form the CG path will still be mostly round, as the vertices will round off.

I concur with the bold above. Fundamentally, my point with the Coriolis discussion is that even the half-sided effect is several orders of magnitude down (about 5) from these measurable human scale effects, such as you discuss above. With symmetry it is effectively eliminated.

That's a good point about the rounding off of the CoG shape, probably had a sizeable effect on the turning force just by spreading the load over time. There is also the next inferred point that the CoG polygon can legally cross over the inside of the lane freely, so long as the vertices (footfalls) land outside of it.

I was on a lunch run thinking about this and I think there's a simple way to approximate the turning losses.

A runner maintaining an even effort can expect that a uniform step put into the ground (force*time) will yield a uniform stride length. Assume 2m per stride and we can triangulate a simple turning model. Since the force from the previous step is 3.6deg different than the next, we can say the aparrent forward vector (hypotenuse) on the straights is 2 and the vertex angle is 3.6deg, the perpendicular inward motion vector of 0.125m/step must be added. The motion vector has to remain 2 since it's a constant effort, so the actual forward motion vector is 1.996, 99.8% of the apparent. The forward motion is compromised by 0.2% on the turns but not the straights, half the race, leaving the turning loss at ~0.1%, We've shown a track 10k on the measurement line is actually 9,992.4m, 0.076% less, wildly close to the 0.1% above.

I'm not sure if the assumptions going into these calcs are correct, but there's some very smart people on this thread and I'm happy to be corrected. Just fun to nerd out for a minute.

I would probably look at it using force vectors (rather than motion). Perhaps you are mixing the two (it kinda reads that way)? The force vectors would be as you describe, a constant force vector with each stride, but as more of the force is used for cornering, less of the force is available for thrust...therefore, the translational motion will be reduced by the ratios you mention. Reframed that way, I concur with the summary and the overall magnitude of effect.

It would be interesting to know if track runners linear velocity is reduced when cornering within this range (~0.2%), that would be at the limit of measurement errors without some careful thought put into the method of measurement.

This thread is an example of why I read Slowtwitch:)

Actually I tried this at the Canadian Armed Forces Running championships in 1990. There were a bunch of 30 min guys at the front of the field and I was in the sub 34 range, but decided to just run with the "big boys". My "go to pace" in 10 k's was 3:18 per km (target sub 33....never got there)....in any case took it out at the 2:55 that the big boys took it out at...stayed in the lead pack past 1000m and it felt "easy enough" and then 2000m at 6:02 as they backed off the pace....that felt easy enough.....then around 2300m the wheels started falling off. By 3000m, was already "crawling" at just sub 10 min and reset my per km pace to 3:54....finsihed way off the back in just under 37, but it was worth a try!

But I knew the paces by heart once I fell off the pace of the studs like the OP in this thread (3:18, 3;24, 3:30, 3:36, 3:42, 3:48, 3:54, 4:00)

Dev

scenicRoute wrote:

AG 40-44 and my 10K is ~42min, so your 36min seems equally unattainable :-)

And at age age 39 Eliud Kipchoge ran a 2:02:42 at the Berlin Marathon which is 4:41 min/mi pace for four consecutive 29min 10k's in a row.

And at age age 39 Eliud Kipchoge ran a 2:02:42 at the Berlin Marathon//

Well ya, he was still in his 30's, just wait until he turns 40, all hell breaks loose!!!! (-;

By the way, Carlos Lopes won the 1984 marathon, think he was about 38, and set the record the stood for like 25 years I think..We thought that to be so old back then too, guys just weren't in their late 30's still crushing it back then. Different ballgame now of course, and in most endurance sports...

+1

For a failed AI Click-bait attempt this thread got quite entertaining.

Just imagine what could've happened if they'd actually baited the click (= provided the link, or whatever)?

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"What's your claim?" - Ben Gravy
"Your best work is the work you're excited about" - Rick Rubin

Growing up I was taught in my health classes that men peak in strength between about 27-31 years old. My coaches taught me that in endurance sports my peak would be between about 23-26 years old. At age 26 I hadn't seen a PR is years and didn't think I would ever see another PR. I have set PR's in the 10k, 15k, half marathon, and Marathon since I turned 40. Yep, it is a different ballgame now.