220 Curve Running

[bambam]

Since we're talking about the 220/200 straightaway, let me ask about 200 curve running. This one is mostly for eldrick, who I think will delight in the calculations.

What is the theoretic advantage of running in lane 8 vs. lane 1, at speeds of around 20 seconds? I'm sure eldy will throw some mv^2/r formulae in here to amaze us all.

And then we can use this for more adjusted times in the 200, adding it to altitude and wind, and really tick off malmo.

[Texas]

There is a time that has always intriqued me. A 20.6 in 1926 by Roland Locke. What is a slightly curved track?

[imaginative]

It is relatively easy to calculate how much extra force the runner
must use to combat the centrifugal effect (basically your formula);
however, there are several other factors that would complicate a
calculation so much that we would probably be better off with some
kind of statistical analysis (or an ad hoc experiment). Consider e.g.
whether the effect is mainly through a speed-loss through the curve or
through making the runner more tired; whether the effect can be
lessened by entering the curve close to the inner line, and drifting
slightly outwards through-out the curve, entering the straight close
to the outer line; or whether a slighly different set of muscle groups
are used running the curve.

(As for Eldrick: He went MIA roughly at the same time that the AOY
thread was axed. I suspect that he is on a two week vacation.)

[dukehjsteve]

There is a time that has always intriqued me. A 20.6 in 1926 by Roland Locke. What is a slightly curved track?

It's a track with a slight curve.

[paulthefan]

it would seem that the curve had a greater negative impact on the runners in the dirt/cinder age as they would have been unable to lean as much since traction/grip would have been a larger factor for them. The modern 200m runner gets a tremendous amount of grab with little or no loss to pay. The only cost is more stress on the ankles but shoes can help a bit there too.

[bambam]

it would seem that the curve had a greater negative impact on the runners in the dirt/cinder age as they would have been unable to lean as much since traction/grip would have been a larger factor for them. The modern 200m runner gets a tremendous amount of grab with little or no loss to pay. The only cost is more stress on the ankles but shoes can help a bit there too.

How can shoes help with ankle stress when running spikes don't come up above the ankle?

[imaginative]

it would seem that the curve had a greater negative impact on the runners in the dirt/cinder age as they would have been unable to lean as much since traction/grip would have been a larger factor for them. The modern 200m runner gets a tremendous amount of grab with little or no loss to pay. The only cost is more stress on the ankles but shoes can help a bit there too.

By the nature of curve running and basic mechanics the runners have to
constantly accelerate through-out the curve, which is a much larger
factor than stress on ankles. From context, I am not sure whether you
just simplified your statement or actually oversaw this, but I mention
it anyway to be on the safe side.

(The point about traction and greater losses in the cinder era is
excellent, however.)

[tc]

Locke's 20.6 (all three watches had 20.5, and the time was rounded up), run at the Nebraska-Missouri collegiate dual meet, was on a course (not on a 440y track) that was reported as a 96-yard curve and a 124-yard straight. Mathematician and sprint statistician extraordinaire Don Potts determined that this constituted a quarter turn.

[malmo]

Re: 220 Curve Running

And then we can use this for more adjusted times in the 200, adding it to altitude and wind, and really tick off malmo.

Really tick me off? You're projecting. Take a chill pill hothead.

[Texas]

There is a time that has always intriqued me. A 20.6 in 1926 by Roland Locke. What is a slightly curved track?

It's a track with a slight curve.

\

Zoooommmmmmmmmmm....right over your head as usual.

[tandfman]

No, I don't think so. I think his response went right over yours.

[dukehjsteve]

No, I don't think so. I think his response went right over yours.

Thank you tandfman. Ole Tex does not appreciate my humor I guess.

[bambam]

Alright, I'll try a little bit since eldy doesn't seem to be piping in.

Assume 42 inch lanes, assume a 100 metre length curve, therefore radius = 31.83 metres, assume an 80 kg. runner (176 lbs.), assume time is about 20 seconds or 10 m/s - I know there's an acceleration phase at the start but I'm not going to get into the calculus of figuring the acceleration and speed for the first 50 metres - I'll assume constant speed. (I also assumed running in the middle of the lane and I know there's a difference in lane 1 than outer lanes because the curb but I neglected that - it would be a relatively minor difference.)

Given all that the force used to overcome the centripetal force of running the curve is as follows:

Lane 1 247.22 m-kg/s^2 (newtons)
Lane 8 200.85 m-kg/s^2 (newtons)

That's a pretty significant difference. You have to use 23% more force to overcome the centripetal force of running the curve in lane 1 than in lane 8. But I don't know exactly how that would correlate mathematically into a time difference for the race.

However, let's assume that both sprinters can generate 225 newtons force to overcome the curve (near mean of the above). Using the above assumptions, this would mean that, given the same force generated, the velocities on the curve would be as follows:

Lane 1 9.54 m/s
Lane 8 10.58 m/s

Again, the acceleration phase, when one is running is slower, would mitigate this difference somewhat. But if one further assumes that the last 50 metres of the curve is run at top-end speed, then this would make a difference of up to 0.5 seconds over 200 metres.

That seems large - probably too many assumptions here.

Eldrick?

[tandfman]

Someone suggested a few days ago that eldrick might be on "vacation." Wouldn't surprise me.

[Kevin Richardson]

There are differing degrees of curve on tracks, particularly from that era. The track I ran on in college was laid out about that same time, and the curves were quite tight, very unlike the current ones. Not as tight as the ones on the 1896 Athens track, but something like it. I would imagine that the slightly curved track in question is closer to what we have today.