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Measuring Breakaway Gaps

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Mar 7, 2011
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Master50 said:
Take a very simple and easy method of measuring gaps and make it so complicated that to explain it to the general public we need a math degree and finite element analysis. Try explaining any of this to the TV audience and people just change the channel. Your standing at the edge of the road watching the racers go by. You have a watch on your wrist and now we have to go out on the road to measure distance between gaps? Or you watch the ;eager go by and time the gaps. At that point on the road everyone has exactly the same climbing, decending and distance covered. How do you get their speed to calculate their distance apart? Ask? He andy how fast are you going? Time is the only objective method of knowing the gap. If the break and the chase maintain the same time gap the distance between them will change according to their speed and that is often changing by terrain.

BTW a timed crit is still a distance race unless the time ends exactly at the line. The winner is the fist guy to travel the next full lap and all riders are judged at a specific distance.

This thread while interesting has been an absurd exercise and I challenge anyone to make distance work as an easy tool to show TV audiences the gap. On a climb he is 200 meters ahead and on the decent he is 1000 meters with exactly the same time gap. IT is time we use and it is time we will always use. Distance is the length of the course.

Granted, much of the complicated math has, I think, been just for fun.
I don't think, however, that anyone (with the possible exception of Bavarianrider) has argued for distance since early in the thread -- certainly not any of the people doing any of the complicated math. All the complicated math has been designed to provide the exact same simple quantity as broadcasts already do, i.e. a time gap in minutes and seconds. The hard work would be for the producers to do behind the scenes -- the whole purpose (if any of it were actually implemented) would be to make things easier on the viewer by providing a gap which had fewer strange behaviors in edge cases. For example, when the leader crashes, the standard method-A gap remains exactly the same while the leader is off the bike, then later when the chasers pass the point where the leader had crashed, suddenly plummets. A gap using Magnus's correction, on the other hand, would tick down steadily at close to one second per second while the leader was off the bike, and wouldn't have a sharp discontinuity when the chasers later passed that point. I think that as a new viewer -- and even as an experienced one! -- I would find the latter easier to understand. (This is similar to the situation in countless industries where the producer accepts difficult and tricky work to make the consumer's life easier. All the coordination hotel employees have to do behind the scenes to make my stay pleasant doesn't require me to have a degree in hotel management.)
 
rokopt said:
Granted, much of the complicated math has, I think, been just for fun.
I don't think, however, that anyone (with the possible exception of Bavarianrider) has argued for distance since early in the thread -- certainly not any of the people doing any of the complicated math. All the complicated math has been designed to provide the exact same simple quantity as broadcasts already do, i.e. a time gap in minutes and seconds. The hard work would be for the producers to do behind the scenes -- the whole purpose (if any of it were actually implemented) would be to make things easier on the viewer by providing a gap which had fewer strange behaviors in edge cases. For example, when the leader crashes, the standard method-A gap remains exactly the same while the leader is off the bike, then later when the chasers pass the point where the leader had crashed, suddenly plummets. A gap using Magnus's correction, on the other hand, would tick down steadily at close to one second per second while the leader was off the bike, and wouldn't have a sharp discontinuity when the chasers later passed that point. I think that as a new viewer -- and even as an experienced one! -- I would find the latter easier to understand. (This is similar to the situation in countless industries where the producer accepts difficult and tricky work to make the consumer's life easier. All the coordination hotel employees have to do behind the scenes to make my stay pleasant doesn't require me to have a degree in hotel management.)
So does it mean the the Flux Capacitor will not be built? :(

ps: it was an interesting thread
 
Jun 1, 2011
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Any reasonably seasoned rider in a break can take the time gap and account for the parcours and "estimate" the "real" gap they have. 20 seconds on a 10% climb is what, at least 60 seconds on the flat. Something like that. Since time difference has been the easiest to measure from the sport's onset, it is still used.

Once a break is established and is working well together, they usally put in the maxium effort in realation to the the distance to the finish and not the closing speed of the peloton until the closing Ks. The later can effect a rider deciding to go forward or give up and drop back.
 
Mar 13, 2009
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Hilarious thread, completely ridiculous.
Would it help if instead of saying the break is 1 minute up or the peloton is 1 minute down, if we said the break passed through the point where the peloton is now 1 minute ago?
Anything other than elapsed time is ridiculously complex and not much (if any at all) extra use.

I now feel dumber for having contributed :(
 
Mar 7, 2011
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karlboss said:
Hilarious thread, completely ridiculous.
Would it help if instead of saying the break is 1 minute up or the peloton is 1 minute down, if we said the break passed through the point where the peloton is now 1 minute ago?
Anything other than elapsed time is ridiculously complex and not much (if any at all) extra use.

I now feel dumber for having contributed :(

No, that'll never do, because I had another idea. The duality between the functions I called A and D had been bothering me -- considering the derivatives D' = F' - 1 and A' = 1 - P', it is clear that while D cannot suddenly plummet in an instant the way A can, it can, unlike A, suddenly skyrocket. Perhaps D is no more true than A?

Returning to earlier principles, E, the time gap as a function of location, is easy (T2 - T1), but time gap as a function of time is hard because there are two different locations involved at any one time, the location of the breakaway and the location of the chase. The question is how to combine two different places into one time -- a kind of cycling theory of relativity. One way of looking at that question is how much of the total time difference made at a given location to count when the leader passes. We could call that a weight function, Wlead, from location to [0,1]. Then we must count the rest when the chase passes: Wchase = 1 - Wlead. So for some weight function we could express the rate of change of the gap as a function of time as

G' = (Wlead o L1)(E o L1)' + (Wchase o L2)(E o L2)'

meaning amount the time gap changes in a unit of time is the fraction of the difference that we've chosen to account to the leader at the location where the leader is plus the fraction of the difference that we've chosen to account to the chaser at the location where the chaser is. Note that (E o L1)' is D' and (E o L2)' is A'. Any gap function generated from any Wlead could be considered valid, and the degree to which W differs from 1/2 could be viewed as the degree to which one ascribes the difference made at a particular spot more to the leader or more to the chaser. This mathematically formalizes the arguments that cycling fans have after the race over who was soft-pedaling and who was on the limit and so forth. (Wherever V1 > V2, for example, choosing Wlead > 1/2 is like saying that the difference was more a matter of the leaders gaining time, whereas Wlead < 1/2 is like saying it was more a matter of the chasers losing time.)

So even in retrospect after the race, there is an infinite number of functions, each generated by a different Wlead, which could be considered valid time gaps. (In particular, a constant Wlead = 0 gives G' = A', and a constant Wlead = 1 gives G' = D'.) Is any one preferable to the others? Doing some computation on the above gives

G' = (Wlead o L1)(S1 - S2 o F)/(S2 o F) + (Wchase o L2)(S1 o P - S2)/(S1 o P)

I was hoping to find a smooth function that didn't change instantly, so I wanted to try to "control" the S1 term in the lead component of the above and the S2 term in the chase component. That suggests the possibility of

Wlead = V2 / (V1 + V2)
Wchase = 1 - Wlead = V1 / (V1 + V2)

A certain amount of algebra later, we obtain

G' = (S1 - S2 o F)/(S1 + S2 o F) + (S1 o P - S2)/(S1 o P + S2)

This derivative has many wonderful properties. In all the edge cases I can think of that we've examined so far, when one gap measurement has been reasonable and another has not, this one's derivative reduces to the derivative of the reasonable choice. For example, when the lead group is crashed (S1 = 0), the first term becomes -1 -- the gap ticks down second-by-second, as in the correction that Magnus thought of, instead of remaining the same and later plummeting, like the method-A gap. It thus generalizes all the specific-case corrections we have made thus far. This derivative is bounded everywhere by -2 <= G <= 2 -- the gap can never rise nor drop more than two seconds per second (the extremes occur when one group is crashed and the other group is riding through another location where the crashed group also crashed or will crash). Hence, G itself is Lipschitz continuous. (That G might even be the only one that is Lipschitz continuous that can be generated by some suitable choice of W, but I am too ignorant to prove or disprove that.)

There's only one problem with this derivative: I can't integrate it. :D I'm not sure anyone can -- I don't think it has a closed-form integral. But that doesn't have to stop us. I still say we switch our post-race analyses to using this new, improved One True Gap which can only be approximated by numerical integration. And anyone who disagrees does not get to use my flux capacitor.
 
This thread is great! Next time I'm in the front comm's car at one of our local chippers I'm going to need my laptop and some serious macros running. Just now we yell out "passing red house on the left about.... now" and the guy driving with the bunch runs a stopwatch until he gets there. Things need to change!
 
Oct 30, 2011
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BillytheKid said:
Any reasonably seasoned rider in a break can take the time gap and account for the parcours and "estimate" the "real" gap they have. 20 seconds on a 10% climb is what, at least 60 seconds on the flat. Something like that. Since time difference has been the easiest to measure from the sport's onset, it is still used.

Once a break is established and is working well together, they usally put in the maxium effort in realation to the the distance to the finish and not the closing speed of the peloton until the closing Ks. The later can effect a rider deciding to go forward or give up and drop back.

Are you for real?
 
Mar 7, 2011
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VO2 Max said:
This thread is great! Next time I'm in the front comm's car at one of our local chippers I'm going to need my laptop and some serious macros running. Just now we yell out "passing red house on the left about.... now" and the guy driving with the bunch runs a stopwatch until he gets there. Things need to change!

Fantastic! I can't wait to hear the results. ;) ("Okay, the lead is now... hang on, I'm still feeding the output of my multivariable future-chase-speed-prediction analysis into the numeric integration to make the gap Lipschitz continuous... the lead is... does anyone have a faster laptop?")
 
Jun 1, 2011
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Caruut said:
Are you for real?

Very. Of course, you do account for the distance to the chase, but also the time and distance to the finish. Say you've got roughly 2 hours to the finish (a long- shot break), that distance will factor into the effort your can or are willing to expend. If it it's ten minutes to the line, you should be able to ride full trottle and focus more on your effort than the chase, solo or not.

You usually see someone go out of the long break for a final effort, often to fail, but it also sometimes win.

If your riding in the last Ks and your trying calculate the closing speed of the chase, that's ridiculous. You may be aware of it, but if your not focused on your body and the distance to the line, how to take the next corner, avoid that whole in the road, etc.. then your likely not going to be able hit your top mark or even worse go anaerobic and blow up.

All I am saying is your always aware of the distance to the chase, but it's all relative and your better off estimating things quickly, unless your a professional and have the director telling you what to do.

And even then, your mind and body is going to govern you anyway. So what if you have the data, the chase is closing and you need to increase you speed, but are unable to lift it much?

What has so many here laughing is that a good break can suceed more on belief than on data.

Data geeks are too busy calculating and not riding with both head and heart.
 

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