Different riders at constant power

[F1_Fan]

Cool. So how are "you" doing then?

Relatively well thanks

I am returning racing after a 12 year absence (during which time I barely touched a bike), lost 80 lbs and I herniated a disc twice in 2003 and 2004 so it's been a slow return to form.

Season best times (climb: 2.2 km 5.5%):
1991 - 6:30
[...]
2003 - 10:12
2004 - 9:45
2005 - 7:43 (in July)

I expect to go under 7 minutes this winter (and back into the 6:30 range by spring) as this hill and my PowerTap SL are being integrated into my winter training... I'm shooting for a really early season peak to match a May crit I want to do well in.

 

[kmavm]

Actually, I wouldn't anticipate "wildly" different splits. Assuming two riders of different weight (and power) are equally adept at deploying a variable power pacing strategy for fastest total time, they will be using more power in the same places (uphill, upwind) and less power in the same places (downhill, downwind) and in similar proportional amounts (e.g., 110%FT or 90%FT). So, while the actual speeds will be somewhat different as a result of the power/weight ratio (uphill) or power/frontal area ratio (flats, downhill), they won't be as different as they would be if the two cyclists were deploying completely different pacing strategies.

So, I'm such a pig-headed idiot that I actually spent a chunk of a perfectly good Saturday messing around with analyticcycling.com and Excel. Long story short: you guys are right, I'm wrong.

I put together a fantasy "harder than rolling" time trial course, and raced a 280W, 60Kg rider against a 300W, 70Kg rider. For both constant power, and a somewhat aggressive (+5% uphill, -10% down) VPP strategy, the two riders finish within a couple seconds of each other, with a total time in the 1600s range (around 26:40). I put "time checks" at all the changes in grade, and the furthest the two riders ever got from one another was approximately 10 seconds at the top of a climb. As RDO and others predicted, hardly "radical." If you're curious I can drop the spreadsheet on you, but there's not much of use in it; all the cool stuff is just numbers I copy/pasted out of analyticcycling.com.

It's amazing what a difference VPP makes; 20-22 seconds, with the more powerful rider benefitting more. I'm not sure how realistic +5% is; 315W sure is a lot more than 300W. In my fantasy course, the climb lasts about 5 minutes, followed by about two minutes of rest.

 

[RapDaddyo]

It's amazing what a difference VPP makes; 20-22 seconds, with the more powerful rider benefitting more. I'm not sure how realistic +5% is; 315W sure is a lot more than 300W. In my fantasy course, the climb lasts about 5 minutes, followed by about two minutes of rest.

Yep, sounds about right. Now, imagine the advantage one would have with an "optimal" VP pacing strategy on a 40K TT, taking into account both grade and wind. Would probably beat most aero wheels or frames or maybe even both wheels and frames.

 

[palewin]

Yep, sounds about right. Now, imagine the advantage one would have with an "optimal" VP pacing strategy on a 40K TT, taking into account both grade and wind. Would probably beat most aero wheels or frames or maybe even both wheels and frames.

Foolish question: Isn't VPP intuitive? I think every one of us who trains with a power meter has noticed that it is very, very difficult to put out anywhere near max sustainable power on downhills, while it is surprisingly easy to generate relatively large power numbers (granted for relatively short periods of time) on even gradual climbs. So it would seem to me that even without thinking about it, if we look at our power outputs on rolling courses, we will see relative decreases of power on the descents, and increases on the climbs. Factor in the fact that we are going at "max perceived effort" in a TT, and the +/- 5 or 10% changes would seem to occur even without consciously "adopting a VPP strategy." In fact, maintaining a constant power level on a rolling course would seem to me to be almost impossible, given my difficulty in laying down large (for me) power numbers as soon as the road points down! Thoughts?

 

[RapDaddyo]

Foolish question: Isn't VPP intuitive? I think every one of us who trains with a power meter has noticed that it is very, very difficult to put out anywhere near max sustainable power on downhills, while it is surprisingly easy to generate relatively large power numbers (granted for relatively short periods of time) on even gradual climbs. So it would seem to me that even without thinking about it, if we look at our power outputs on rolling courses, we will see relative decreases of power on the descents, and increases on the climbs. Factor in the fact that we are going at "max perceived effort" in a TT, and the +/- 5 or 10% changes would seem to occur even without consciously "adopting a VPP strategy." In fact, maintaining a constant power level on a rolling course would seem to me to be almost impossible, given my difficulty in laying down large (for me) power numbers as soon as the road points down! Thoughts?

Well, I think what you're saying is that VP pacing is virtually assured, at least with respect to downhill or downwind course segments because of the difficulty of maintaining higher powers at those times. I don't agree as to the uphill and upwind segments. It may be natural to increase power in those segments, but it is by no means mandatory. I can ride an uphill or upwind segment at low power levels if I choose to (even if it requires intense concentration). And, yes, it is very difficult to ride at a constant power even if I try very hard to do so. But, as to the question of what is an optimal pacing strategy on a given course with consideration of both terrain (grade), conditions (wind direction and velocity) and sustainable power (FT), I don't think it is at all obvious or simple. Actually, it is very complex because it requires the integration of two complex sciences that affect the cyclist -- physiology and physics. Fundamentally, it is a linear programming problem in which one is optimizing elapsed time under the dual constraints of physiology (NP=FT) and physics (which determines bike speed under different assumptions). Even if one has an "optimal" pacing plan (which is only valid under the wind conditions under which it was computed), it is no simple matter to execute. I know because I have tried, for durations ranging from 5 minutes to 2 hours. The gold ring is definitely out there, but it is not a simple matter to grab it. Too bad Roger Bannister wasn't a cyclist. I think he would have solved this issue a long time ago.

 

[asgelle]

Too bad Roger Bannister wasn't a cyclist. I think he would have solved this issue a long time ago.

Do you mean Eric Bannister of TRIMP? Roger Bannister (4 min. mile) is a neurologist.

 

[RapDaddyo]

Do you mean Eric Bannister of TRIMP? Roger Bannister (4 min. mile) is a neurologist.

No, I meant Roger. He took a more scientific approach to training and pacing than anyone before him. If he had been a cyclist, I think he would have applied his scientific approach to the sciences affecting the cyclist and it would have been interesting to see what he would have come up with. One of the reasons we know what we know now is because of scientist-cyclists such as Andy Coggan, who set out to understand the scientific principles affecting the cyclist. Pacing is all about science.

 

[palewin]

Actually, it is very complex because it requires the integration of two complex sciences that affect the cyclist -- physiology and physics. Fundamentally, it is a linear programming problem in which one is optimizing elapsed time under the dual constraints of physiology (NP=FT) and physics (which determines bike speed under different assumptions).

RDO: I think you have hit on what causes me the greatest problem with the discussions of VPP: it is an LP, and the vast majority of cyclists haven't studied linear programming, let alone learned how to apply it. I'm tempted to reply with Occam's Razor, that the simplest solution is usually best, and an LP isn't it. Let's digress for a second to your Roger Bannister comment. I believe that for running, the constant speed solution always yields the optimum theoretical result - the "ideal mile" given the constraint of energy and physics, is four even quarters. But Bannister, and I think virtually every mile record since, ran negative splits, at least for the final quarter. So reality and theory diverge, at least in the application. Back to cycling TTs. I would suggest that most of us, at some subconscious level, are trying to hold our speed constant (or as close to that as we can). In this scenario, ramping up the power in a climb is natural, to maintain speed; as we've agreed, cutting back power on the downhill is almost inevitable given the difficulty of generating full power on a descent. Hence the cyclist with no knowledge of VPP is likely to end up with a result that mimics VPP. This seems consistent with Andy's comment somewhere in the thread that most experienced cyclists will end up riding a TT course using very similar strategies. I guess I'm repeating my earlier thought in different words, that while VPP strategy can be best "calculated" mathematically (and does yield better results than constant power), it is the strategy that most cyclists will adopt automatically without ever having heard the term, and that by trying to actually calculate out the LP, you're overworking the problem. The way to "prove" that VPP differs from intuition would be to show that the power increases and decreases would be greater than the variations an experienced cyclist performs automatically. (As an aside, I seem to remember Michael Rogers saying that his strategy at the World's was to save some energy in the 1st half, and let it all out over the 2nd half, which sounds suspiciously like a runner running negative splits...)

 

[acoggan]

The way to "prove" that VPP differs from intuition would be to show that the power increases and decreases would be greater than the variations an experienced cyclist performs automatically.

This is, in fact, a scientific study that I'd like to do (if I had the spare time): calculate the theoretically optimal variable power pacing strategy for a non-flat course, and then compare that to the power distributions for a number of experienced riders. To the extent that you found agreement, this would provide evidence of significant self-optimization, as you've described and has been observed in other situations (e.g., stride length selection in runners). OTOH, to the extent that you found disagreement you've provided fodder for further investigation to determine why even experienced cyclists may "get it wrong", as well as illustrated the degree to which performance may theoretically be improved by more careful attention to pacing.

In considering this idea, I concluded that the ideal course to use would be the TT course used at master/elite nationals in Salt Lake City the last couple of years. That way there should be no shortage of volunteers, and the pacing strategy derived via the calculations would be of considerable practical interest.

 

[RapDaddyo]

RDO: I think you have hit on what causes me the greatest problem with the discussions of VPP: it is an LP, and the vast majority of cyclists haven't studied linear programming, let alone learned how to apply it.

I never said it was easy, I just said that was how one would come up with the optimal pacing strategy. Practical implementation with today's technology is a formidable task. I know because I have taken VP pacing to its logical limits with today's technology. My most recent exercise was to put markers on the side of the road for pacing triggers and to use an armband for the power levels (sort of like the cheat sheet that Matt Leinart uses). That doesn't work so well because if there are many power changes it gets hard to keep up with where you are in the sequence. So, I plan to try loading an audio file on an Apple iPod and then it would be sequenced. It's just a pain to hit the play/stop buttons while riding >=FT. Then there's the small matter that an optimal pacing plan is only valid until you take the first pedal stroke. The actual optimal pacing plan is a continuous LP solution, taking into account what you have actually done to that point on the course as well as what lies ahead.

I'm tempted to reply with Occam's Razor, that the simplest solution is usually best, and an LP isn't it.

Today.

Let's digress for a second to your Roger Bannister comment. I believe that for running, the constant speed solution always yields the optimum theoretical result - the "ideal mile" given the constraint of energy and physics, is four even quarters.

Actually, not true if there is wind.

But Bannister, and I think virtually every mile record since, ran negative splits, at least for the final quarter. So reality and theory diverge, at least in the application.

That isn't proof that this is the fastest pacing strategy.

Back to cycling TTs. I would suggest that most of us, at some subconscious level, are trying to hold our speed constant (or as close to that as we can).

This isn't necessarily the fastest pacing strategy. In fact, the speed differences could be huge. Let's look at two simple out/back 40K courses. Course #1 is a steady 2% grade on the outbound leg (and obviously -2% on the return leg). Course #2 is a steady 4% grade. At my FT, weight, frontal area, etc., etc., and assuming no wind, my optimal pacing strategy for course #1 would be 295w/230w, with speeds of 19.46mph/29.06mph. For course #2, the optimal pacing strategy is 295w/180w, with speeds of 14.76mph and 33.78mph. Note that optimal pacing strategy has been rounded to the nearest 5w. I would say that riding either of these courses at a constant speed would be a slow strategy. BTW, the VP pacing strategy on course #2 beats CP by >2%, in excess of most aero equipment (wheels, frames, etc.).

In this scenario, ramping up the power in a climb is natural, to maintain speed; as we've agreed, cutting back power on the downhill is almost inevitable given the difficulty of generating full power on a descent. Hence the cyclist with no knowledge of VPP is likely to end up with a result that mimics VPP.

It sort of depends on what you mean by mimic. If you mean nothing more than more power uphill and upwind and less power downhill and downwind, I agree. If you mean closely approximates an optimal VPP strategy, I disagree.

This seems consistent with Andy's comment somewhere in the thread that most experienced cyclists will end up riding a TT course using very similar strategies.

I know what Andy says. I think it remains to be seen how close these experienced riders are to "optimal." Most cyclists (me included) go out too hard in the first 1/3 to 1/2 of the course, fall off the pace and then go hard at the end.

I guess I'm repeating my earlier thought in different words, that while VPP strategy can be best "calculated" mathematically (and does yield better results than constant power), it is the strategy that most cyclists will adopt automatically without ever having heard the term, and that by trying to actually calculate out the LP, you're overworking the problem.

Well, clearly I'm working the problem. Whether I'm "overworking" the problem remains to be seen. Very little empirical data exist on pacing strategies on courses with both grade and wind changes (i.e., 99% of all TT courses).

The way to "prove" that VPP differs from intuition would be to show that the power increases and decreases would be greater than the variations an experienced cyclist performs automatically. (As an aside, I seem to remember Michael Rogers saying that his strategy at the World's was to save some energy in the 1st half, and let it all out over the 2nd half, which sounds suspiciously like a runner running negative splits...)

No, the way to prove that an optimal VPP strategy is superior to an intuitive VPP pacing strategy would be to have the same rider ride a course using his intuitive VPP approach and then to ride it (under the same conditions) using an optimal VPP approach (e.g., having a support vehicle following behind giving power levels through a 2-way radio at every point in the course). Anyway, I'm not one of these mythical cyclists that Andy talks about. I'm a mere mortal and I'm lousy at pacing intuitively. I know because I've tested myself.

 

[RapDaddyo]

The way to "prove" that VPP differs from intuition would be to show that the power increases and decreases would be greater than the variations an experienced cyclist performs automatically. (As an aside, I seem to remember Michael Rogers saying that his strategy at the World's was to save some energy in the 1st half, and let it all out over the 2nd half, which sounds suspiciously like a runner running negative splits...)

Let me correct my earlier comment. If you have a certain type of course "map" and if you knew all of the relevant data about the rider and the conditions of the ride, yes, you could do an analysis of his ride against the optimal pacing plan, including the overall time difference. The problem lies in taking the analysis further, to specifically where on the course the rider "lost" time because if he used too much power in a segment of the course, that has consequences for the remainder of his ride (less power available, but where to apply it) and if he used too little power in a segment of the course, that also has consequences for the remainder of his ride (more power available, but again where to apply it). I suppose you could apply power (increases and decreases) pro-rata. Anyway, yes, you could do a post-ride analysis against an optimal pacing strategy.

 

[RapDaddyo]

I believe that for running, the constant speed solution always yields the optimum theoretical result - the "ideal mile" given the constraint of energy and physics, is four even quarters.

One more correction. This is true as stated. I was subconsciously thinking about whether an optimal pacing strategy would be constant speed throughout the course and it would be constant only if there were no wind. If there were wind, especially with a headwind/tailwind on the long sides of the track, the optimal pacing strategy would not be constant speed.

 

[palewin]

the optimal pacing strategy would not be constant speed.

RDO: I'm afraid my "constant speed" comment was due to my imprecise use of language. I was trying to express the thought that I suspect most cyclists will automatically increase their power output on a climb in order to avoid losing too much speed. In statistics one says that events "regress towards the mean" and in some imprecise way, during a TT, one "regresses towards their average speed." I was never arguing against the VPP model, merely wondering how far it differs from intuition. I think we (you, myself, Andy, and probably most readers) agree that the interesting study would be one which indicated whether an experienced rider intuitively self-optimizes (in which case we go back to simply concentrating on maximizing our sustainable power) or whether there is a better, non-intuitive strategy (in which case we have to work both on power and on application of the strategy). What intrigues me (and I mentioned it earlier as the possible difference between a theory and the application of that theory) is whether "reality" and "theory" are divorced or not. It has been pointed out that as a sport, running has one of the best statistical data bases of all sports, because it is practiced in almost every country, and records have been kept for at least a century. If, for example, mile records are always set with negative splits (a hunch, but I certainly have not done the research), does that suggest that the "even paced" theory is incorrect, or too difficult to apply? If reality seems to differ with the model, does that mean the model is missing a variable? To be a bit more of a philosopher than a mathematician, perhaps human "drive" (for results, achievement) is non-linear, and thus doesn't fit a linear programming model. I have these two mental images, one of the current director sportif shouting at his TT rider "good, go, go, go..." (see 'Armstrong's War' for the full transcript...) vs. the mathematical director sportif suggested in your earlier post shouting "400 watts for the next 10 seconds, then 425 for 30 seconds..." (much like the navigators in World Rally Car telecasts...). Which one is the correct image? Only time will tell, since new innovations (both technology as in LeMond's aero bars, and technique/strategy as Armstrong's cadence) constantly evolve. Anyway, this is my last post on this thread, it's time for me to let others have the [virtual] floor...

 

[RapDaddyo]

...What intrigues me (and I mentioned it earlier as the possible difference between a theory and the application of that theory) is whether "reality" and "theory" are divorced or not. ... If reality seems to differ with the model, does that mean the model is missing a variable? To be a bit more of a philosopher than a mathematician, perhaps human "drive" (for results, achievement) is non-linear, and thus doesn't fit a linear programming model. I have these two mental images, one of the current director sportif shouting at his TT rider "good, go, go, go..." (see 'Armstrong's War' for the full transcript...) vs. the mathematical director sportif suggested in your earlier post shouting "400 watts for the next 10 seconds, then 425 for 30 seconds..." (much like the navigators in World Rally Car telecasts...). Which one is the correct image? Only time will tell, since new innovations (both technology as in LeMond's aero bars, and technique/strategy as Armstrong's cadence) constantly evolve. Anyway, this is my last post on this thread, it's time for me to let others have the [virtual] floor...

Well, you've posed some interesting questions. Not that I have all the answers, but I have given this subject a lot of thought so I'll give you a few quick takes on the issues you raise. First, Andy has repeatedly suggested that highly experienced TTers intuitively ride something approximating an optimal pacing strategy. That may or may not be, but the TTer of greatest interest to me is me. And, I can tell you categorically that I do not intuitively follow anything close to an optimal pacing strategy. Now, am I just lousy or am I just the only one to admit it or do most people simply not have the foggiest idea how close to optimal their pacing strategy is? I have no idea. Second, whether the physiological and physics relationships are linear or non-linear is irrelevant. It just complicates the computations. Even if the relationships had some randomness, it wouldn't matter. We deal with random variables all the time. And, as to which type of director sportif (cheerleader shouting encouragement or university mathematician giving watts targets) would produce the best results, I have never had either type and don't expect I will (ever), so that issue is someone else's concern but not mine. I have two goals: (1) pull up to the start line with as much sustainable power as I can on that day; and (2) use that sustainable power to my maximum advantage for the lowest elapsed time. These are not mutually exclusive. At the moment, I have all the tools necessary to achieve (1) and I have only my PM to achieve (2). I am not satisfied with that state of affairs and plan to do do something about it.

 

[frenchyge]

This is an interesting topic, as always. Here's a couple cents worth:
1) Cyclists certainly have more on-board data available to them than runners do, so there is probably room for a more sophisticated strategy than "take it easy at the start, then give it all you have at the finish (ie, run a negative split)."
2) Even if pros can approximate an optimal pacing strategy through years of experience, preparation specific to the course, and coaching/training staff efforts and feedback, I think most of us could use some help in the matter.
3) Optimal pacing is more than just "push harder up the hills and rest on the downhills." There are certainly different levels of effort available for those early hills, and the amount of effort plays a big role in whether the overall pacing is successful or not.
4) I like encouragement and motivation, but having a pacing plan based on past performance (eg, 60-min power from past training rides) gives me confidence that I can achieve the plan regardless of what my body tells me. That's valuable too.