Distance on each leg of a 4x1

[texas_speed]

I'm almost embarrassed to ask but what is the standard distance covered on each leg of the 4x1?

I know the 2nd is the "longest leg" but numerically, how long is each leg of the entire relay?

[paulthefan]

you are kidding, right? you almost had me there! But seriously one could consider 4 random distances, the sum of which always equals 400m with the most random scenario looking like: L1~100+uniform(-10,10). L2|L1~uniform(210,190)-L1 ... so on until L4~Uniform(-10,10)+100.

[Marlow]

you are kidding, right? you almost had me there!

The nominal answer is 100m, but yes, traditionally one puts the fastest straightaway runners on the 2nd and 4th legs and try to get them the stick early in their zones (and 2nd runner late in the zone to the 3rd runner), so you optimize the team's time.

[texas_speed]

I really am being serious.

I was just sitting here thinking about why the 2nd leg is always referred to as being the longest leg and if that is the case then what is the actual distance of that leg vs the others.

I fully understand the rationale behind why you would run any given runner on a particular leg.

Again, the question almost sounds too stupid to ask but I figured here would be as good as place as any to ask.

[paulthefan]

you are kidding, right? you almost had me there! But seriously one could consider 4 random distances, the sum of which always equals 400m with the most random scenario looking like: L1~100+uniform(-10,10). L2|L1~uniform(210,190)-L1 ... so on until L4~Uniform(-10,10)+100..

you could consider other distributions with nonzero probability only over the 20m interval (if this is going to be a legal race). These could even be different for each of the legs. Perhaps a scaled and translated beta but we should probably get some empirical data and a kinematic model and see what fits.

[texas_speed]

Uh...so...in laymen's terms....

[gh]

Ignore the smarmouth: Marlow's answer is correct. Let me try to put this into the simplest of terms:

Each of the three exchange zones is 20 meters long. From the start line to the middle of the first exchange is 100m, and the middle of each subsequent zone is another 100m away, so the final one is 100m from the finish.

You can exchange the baton anywhere within that 20-meter zone. So if the second runner took the baton at the beginning, the first runner would have covered only 90 meters. And if the third runner doesn't take the baton until the very end of his zone, the second runner will have covered 120m.

10m that "belonged" to the first runner, his own center-to-center 100m, then another 10m of the third runner.

You could accomplish the same thing with the third runner, but since he is mainly running on the curve, you'd tend not to do that.

Some teams try to put their fastest guy (or guy who is able to sustain top-end speed the longest) on the second leg and stretch it out that way.

If you use a reductio ad absurdum in positing hypothetical times,you see what teh advantage is: if you have three guys who can only run 13-flat and one guy who can run 9-flat, you want the 9-flat guy running as much of the race as possible, so you aim for a "120."

Obviously, your chances of incurring a DQ go up astronomically the closer you get to the end of the zone, front or back.

[paulthefan]

you already knew the obvious, so masters of it you didn't need, just stick with what I wrote and you will learn something.

[Marlow]

Uh...so...in laymen's terms....

you already knew the obvious, so masters of it you didn't need, just stick with what I wrote and you will learn something.

This makes me sad. Sometimes we all assume something that literally makes no sense, e.g., 'The road to hell is paved with good intentions.'

t_s had a legit question, given the fact that all legs are nominally 100m, but many people DO say that some legs are longer than others. The TOE says it definitely was NOT a stupid question and thank you, gh, for elaborating.

[paulthefan]

Uh...so...in laymen's terms....

you already knew the obvious, so masters of it you didn't need, just stick with what I wrote and you will learn something.

This makes me sad. Sometimes we all assume something that literally makes no sense, e.g., 'The road to hell is paved with good intentions.'

t_s had a legit question, given the fact that all legs are nominally 100m, but many people DO say that some legs are longer than others. The TOE says it definitely was NOT a stupid question and thank you, gh, for elaborating.

I thought that my answer was of value and I thought yours was too.

[texas_speed]

Thanks gh and Marlow.

Sometimes the most obvious answers just need to written out or discussed for one to understand it better...in this case myself.

I just couldn't find the proper wording when trying to figure it out in my mind.

Thank you both.

[Marlow]

I thought that my answer was of value

you could consider other distributions with nonzero probability . . . a scaled and translated beta but we should probably get some empirical data and a kinematic model and see what fits.

To whom? Eldrick and JRM? I took a year of math after differential equations and also college statistics, and that is gibberish to me.

[paulthefan]

To whom? Eldrick and JRM? I took a year of math after differential equations and also college statistics, and that is gibberish to me.

Sorry, I was just trying to help.

[Marlow]

Sorry, I was just trying to help.

Now we're back to my paradoxical adage from above.

[TrackDaddy]

I really am being serious.

I was just sitting here thinking about why the 2nd leg is always referred to as being the longest leg and if that is the case then what is the actual distance of that leg vs the others.

I fully understand the rationale behind why you would run any given runner on a particular leg.

Again, the question almost sounds too stupid to ask but I figured here would be as good as place as any to ask.