Tuesday, August 28, 2012

More on Matched Filters and Cycling

My group lunch ride got me thinking about how applicable the engineering concept of matched filtering is to cycling again. There are subtleties in group riding dynamics that may be non-intuitive to some riders. Maybe I can explain some of these subtleties with a story. The names of the characters have been changed to protect the innocent.

A tri guy, a scull boy and a climber freak went for a ride one day on their lunch break. It was agreed that intervals would not be the theme of the day, but rather go more for steady pace, maybe a team time-trial type of effort.

Tri guy was on a TT bike, which generally raises all kinds of warning flags in group rides, but scull boy and climber freak had him dialed. No worries. Tri guy posts some impressive results in Olympic distance tri's and can hold a pretty hard pace for hours at a time, but doesn't fare so well in sprinting or on sustained climbs. His aero position on the TT bike makes him a rocket on descents.

Scull boy is a fast twitch specialist and has done well on the velodrome track in the past, but spends most of his days on the water now. One day per week on the bike, peak fitness maintains not.

Climber freak tends to be biased towards fast twitch and sucks least on terrain that goes up. He can also put out some pretty mad anaerobic Watts for his age too, at least for anything longer than a sprint.

It was never discussed, but after a while, the ride gravitated towards maintaining average speed at all cost.  Mid ride, the trio began hitting variable terrain. Some flats, climbs, descents, headwind, tail wind, bit of everything. This got the climber freak to thinking, "if we're trying to optimize our average speed, is there an optimal way to stage riders in the paceline rotation relative to terrain?" Climber freak posed a suggestion to the other two. Neither liked it. What do you think climber freak suggested?

A term needs to be defined before we can begin analyzing this scenario. The term is "work." Cyclists use this term a lot. The term is frequently used correctly, but too often it is misused. What does it mean to do "work" in a peloton? And how is "work" quantified?

I define work as the difference, in Watts (real time) or kiloJoules (over period of time) between a rider pulling at the front of the pack and the average of the riders not at the front of the pack. For those who ride with power meters, you know that your power drops substantially when pulling off the front and you slip back into the pack. The difference in Watts is the work riders at the front are doing to keep the pace up. It is not their total power.

A numerical example may help explain. On flat terrain, an average size rider on regular bike may have to generate 400W to hold 28mph. A rider tucked close in behind him may need to produce only 300W to go the same speed. Thus the rider pulling at the front is doing 100W of work, which is 100W more than the rider drafting him needs to produce to go the same speed. This is substantial. The rider pulling is likely going deeply anaerobic, while the drafter is sub-threshold. This is why a rotating paceline can maintain a much high speed than a single rider can. Riders recover in the pack and then go anaerobic briefly at the front.

So what happens when you go uphill? The work the rider up front drops dramatically. On a 12% grade, the speed may drop to 8mph at 400W. There is almost no drafting benefit at this speed, thus the rider behind him will be producing upwards of 390W. Even though the rider up front in working really hard, just as hard in the 28mph flat case, he is doing almost no work, maybe only 10W. The power differential is very small. Riders hanging onto his wheel are getting almost no benefit by staying there, and unless they are of similar fitness, will soon find themselves separated from this rider.

Then there are downhills. What happens to our definition of work there? Turns out on a moderately steep downhill, the pulling rider can hammer at 400W while everybody in tow behind him are coasting or even hitting the brakes. In this case, the rider up front is doing 400W of work, which is a huge amount, as those in the draft are doing nothing.

So far, this should be pretty obvious to everybody. The range of work one can do is almost nothing going uphill to almost all of it going downhill. Now it is time for a quiz. Can you match the type of terrain each of the three riders in our story should pull on? Remember, the goal was to keep the 3-man team time-trail together and complete the course as fast as possible:

1. Tri guy (on TT bike)   a. climbs
2. Scull boy                     b. flats
3. Climber freak              c. descents

It may not seem intuitive, but the rider that can least handle the climbs (scull boy) should pull on the climbs. Why? Because he will do the least work there, even though it feels like you work like hell setting pace on a climb. But whatever Watts he generates, so too will the others. Then when the terrain flattens out, the next rider can do actual work, where scull boy's power will drop. This is especially true on the descents. Scull boy should never work on the descents, as he most needs the recovery, even though he could potentially just coast on the front and go almost as fast as working. But this does not optimize the group's speed.

The tri guy with his TT bike slips through air much easier than scull boy and climber freak on non-aero bikes. This becomes very important as the speeds go up. Tri guy can go fastest on the descents, doing disproportionate amount of work, and because of this speed, forces the other two to put in some effort too to stay with him.

The climber freak gets all the terrain in between, namely the long, flat boring parts that just need to be hammered out. The other two can tuck in behind him and recover there. You do not want to put climber freak up front on a climb, as the rider that pulled to the climb will promptly get popped off, then the group has to slow down to let him get back on. Let climber freak kill himself on the flats, where it is relatively easy for the other two to stay in his draft and recover.

So you see, there is a strategy that can optimize a circuit time with differing abilities and equipment among the riders. Understanding the definition of work and matching riders to the terrain, and thus work they can contribute, will net a fastest time around a varying circuit.


Mookie said...

The lower the variability and higher the average power, the faster you will go and the less matches you will burn.

Hill Junkie said...

Yeah but, the matched filter approach increases the variability for some of the riders. This is why Tri-guy bulked, like if he has to drill the downhills, and he has to work just as hard as scull-guy on the uphills, where does he get to rest? Remember, the goal was to keep group together, keep a rotation going, and finish as fast as possible. Thus we had to make sure the weakest rider did the least amount of work. This can increase the variability and work done by others. As a TTT group though, or as a solo rider, you are totally correct.

Mookie said...

If the 3rd guy is considerably weaker than the other 2, you might have him NEVER pull. I know it discounts ups/downs but interesting study here:


DaveP said...

Yeah, but why are you even bothering riding with a tri guy and scull boy? Stick with the folk that actually know how to ride a bike and apply your optimization logic there and you'll go faster even still.

the bully said...

Sending this to my road buddies. Poor fitness boy climbs and then hangs on for dear life!