Yo-Yo TT Pacing Strategy

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The more I have explored variable power TT pacing strategy, the more interested I have become in its potential. There are two clear reasons to employ a VP pacing strategy: (1) top cyclists do it; and (2) analytically it's easy to prove that it works. For me personally, that has raised the question of my personal limits in deploying such a strategy. Originally, I was thinking about power variations of maybe +/-100w. Then, I started doing some experimentation on my bike and have recently re-defined my own personal realistic power variation options. I was shocked by the results. I now believe I can vary my power by 600w! That's basically from 100w (no point in totally coasting) to 700w (e.g., climbing off the saddle, high cadence, medium gear). I'm not bragging -- I think anybody can do this. My question is, now that I know what kind of power I have under the hood, how do I manage the gas pedal? I'm calling this a Highly Variable Pacing strategy, or affectionately a "Yo-Yo Pacing Strategy." Do you employ a variable power pacing strategy in TTs? Do you do it based on experience and "feel" or do you approach it scientifically and analytically? What's your power range in a typical TT (rolling terrain, some wind)? I'm planning to do some full tests of this HVP pacing strategy in the near future and will report the results (unless, of course, they are spectacular).

You might want to read about normalized power here:
http://www.cyclingpeakssoftware.com/defined.html

and variable pacing strategies here:
http://www.biketechreview.com/power/supercomputers.htm

among possible articles

You might want to read about normalized power here:
http://www.cyclingpeakssoftware.com/defined.html

and variable pacing strategies here:
http://www.biketechreview.com/power/supercomputers.htm

among possible articlesThanks for those links. I have actually seen both of those documents and, in fact, the Kraig Willett article is one of the things that piqued my interest in a structured approach to variable power pacing strategies. I am presently using the normalized power algorithm to model recovery duration/power combinations, but some of the recovery penalties are quite severe. For example, by my calculations, if your 40K MP is 275 and you employ a 1 min @ 400w push, you need to recover for 5 1/2 minutes at 150w. My reading of the NP algorithm is that it is basically driven by the blood lactate curve just above and below LT. But, this may be steady state lactate levels. I'm looking for some data on actual acidosis (or lactate as a proxy) recovery rates, driven by clearance rates. Barring that, I'll have to turn myself into a lab rat for some testing.

For example, by my calculations, if your 40K MP is 275 and you employ a 1 min @ 400w push, you need to recover for 5 1/2 minutes at 150w. My reading of the NP algorithm is that it is basically driven by the blood lactate curve just above and below LT. But, this may be steady state lactate levels. I'm looking for some data on actual acidosis (or lactate as a proxy) recovery rates, driven by clearance rates. Barring that, I'll have to turn myself into a lab rat for some testing.

would you mind explaining the calculation a little? That sounds like way more recovery (int a TT!) than I would expect given 1-minute at ~135-140% FT.

FWIW, on Sunday I did a training TT on a 23k variable loop with everything from 100m bumps, to a 5k nearly flat tailwind section, to a 2km ~5% cilmb into a headwind ... etc. Power varied from 0 to 650W but averaged only 278.

rmur

would you mind explaining the calculation a little? That sounds like way more recovery (int a TT!) than I would expect given 1-minute at ~135-140% FT.

FWIW, on Sunday I did a training TT on a 23k variable loop with everything from 100m bumps, to a 5k nearly flat tailwind section, to a 2km ~5% cilmb into a headwind ... etc. Power varied from 0 to 650W but averaged only 278.

rmurSure. It's derived from Andy Coggan's Training Stress Score (raw), which is based on the normalized power algorithm. And, of course, the TSS is similar to the TRIMPS score of Dr. Eric Bannister. The TSS (raw) score is duration * average power * (average power/power at LT)^3.9. The last part of this computation is referred to as the Intensity Factor. It places an increasing "penalty" on durations at power >LT power. The IF at LT power is, of course, 1.0, whereas the IF at 145% of LT power (e.g., 400/275) is 4.31. All of this is based on the famous blood lactate as a function of power curve, which slopes upward exponentially after LT power. I derived a computation of recovery duration on the assumption of a symmetric power/variable time pacing strategy. In other words, if my LT power is 275w and I push it to 300w for 60 seconds then I want to recover at 250w for the required number of seconds. I'm approaching it this way so that I can do the computations in my head during a ride. At most, I would have a little cheat sheet on my arm. Of course, this breaks down a bit if I do a push >550w, but that'll be the exception. The derivation starts with the assumption that the TSS scores (push + recovery) should be equal to the TSS for the same combined duration at steady-state LT power. Here's the derivation. Maybe you can spot an error in my math.
TSSLT = TSSQ + TSSR
TSSR = TSSLT – TSSQ
[DR * PR * (PR/PLT)^3.9] = [(DQ + DR) * PLT * 1] – [DQ * PQ * (PQ/PLT)^3.9]
Solve for DR:
DR = ([(DQ + DR) * PLT * 1] – [DQ * PQ * (PQ/PLT)^3.9])/ ([PR * (PR/PLT)^3.9])
Set DQ = 1 and simplify:
DR = ([PLT + DR * PLT] – [PQ * (PQ/PLT)^3.9])/([PR * (PR/PLT)^3.9])
Substitute Q = [PQ * (PQ/PLT)^3.9] and R = [PR * (PR/PLT)^3.9]:
DR = ([PLT + DR * PLT] – Q)/R
DR = (PLT * DR + PLT – Q)/R
DR = (PLT * DR + PLT – Q)/R
R * DR = PLT * DR + PLT – Q
PLT * DR – R * DR = Q – PLT
DR * (PLT – R) = Q – PLT
DR = (Q – PLT) / (PLT – R)
Substitute [PQ * (PQ/PLT)^3.9] = Q and [PR * (PR/PLT)^3.9] = R:
DR = ([PQ * (PQ/PLT)^3.9] – PLT) / (PLT – [PR * (PR/PLT)^3.9])

Where:
TSS = Training Stress Score (raw)
LT = Lactate Threshold
Q = Push
R = Recovery
D = Duration
P = Power

this might work for hilly course or during some windy sections. But on a flat course, if you vary your power from 100-700watts, you will be a lot slower, because all your energy will go in to accelerating. On a flat course, there is no shortcut, you must be as steady as possible to have the best average speed. It's all about efficiency.

Think about how car will get better gas mileage on the highway with no stops. It's a lot more efficient to keep a constant speed/power output.

this might work for hilly course or during some windy sections. But on a flat course, if you vary your power from 100-700watts, you will be a lot slower, because all your energy will go in to accelerating. On a flat course, there is no shortcut, you must be as steady as possible to have the best average speed. It's all about efficiency.

Think about how car will get better gas mileage on the highway with no stops. It's a lot more efficient to keep a constant speed/power output.

That's true, but how many perfectly flat, windless courses are there....probably zero, even in CT. The trainer is about the only place where resistance is constant.

this might work for hilly course or during some windy sections. But on a flat course, if you vary your power from 100-700watts, you will be a lot slower, because all your energy will go in to accelerating. On a flat course, there is no shortcut, you must be as steady as possible to have the best average speed. It's all about efficiency.

Think about how car will get better gas mileage on the highway with no stops. It's a lot more efficient to keep a constant speed/power output.No argument from me. Even analytically one can prove that on a flat course with no wind direction change it is fastest to ride at a rock-steady power equal to one's maximum power for that duration. No question about it. But, that's not real world, unless you want to limit your TTs to indoor tracks. The real world is variable topography and wind direction changes. Under those circumstances, there is absolutely no doubt that a variable power pacing strategy is faster.

Sure. It's derived from Andy Coggan's Training Stress Score (raw), which is based on the normalized power algorithm. And, of course, the TSS is similar to the TRIMPS score of Dr. Eric Bannister. The TSS (raw) score is duration * average power * (average power/power at LT)^3.9. The last part of this computation is referred to as the Intensity Factor. It places an increasing "penalty" on durations at power >LT power. The IF at LT power is, of course, 1.0, whereas the IF at 145% of LT power (e.g., 400/275) is 4.31. All of this is based on the famous blood lactate as a function of power curve, which slopes upward exponentially after LT power. I derived a computation of recovery duration on the assumption of a symmetric power/variable time pacing strategy. In other words, if my LT power is 275w and I push it to 300w for 60 seconds then I want to recover at 250w for the required number of seconds. I'm approaching it this way so that I can do the computations in my head during a ride. At most, I would have a little cheat sheet on my arm. Of course, this breaks down a bit if I do a push >550w, but that'll be the exception. The derivation starts with the assumption that the TSS scores (push + recovery) should be equal to the TSS for the same combined duration at steady-state LT power. Here's the derivation. Maybe you can spot an error in my math.
TSSLT = TSSQ + TSSR
TSSR = TSSLT – TSSQ
[DR * PR * (PR/PLT)^3.9] = [(DQ + DR) * PLT * 1] – [DQ * PQ * (PQ/PLT)^3.9]
Solve for DR:
DR = ([(DQ + DR) * PLT * 1] – [DQ * PQ * (PQ/PLT)^3.9])/ ([PR * (PR/PLT)^3.9])
Set DQ = 1 and simplify:
DR = ([PLT + DR * PLT] – [PQ * (PQ/PLT)^3.9])/([PR * (PR/PLT)^3.9])
Substitute Q = [PQ * (PQ/PLT)^3.9] and R = [PR * (PR/PLT)^3.9]:
DR = ([PLT + DR * PLT] – Q)/R
DR = (PLT * DR + PLT – Q)/R
DR = (PLT * DR + PLT – Q)/R
R * DR = PLT * DR + PLT – Q
PLT * DR – R * DR = Q – PLT
DR * (PLT – R) = Q – PLT
DR = (Q – PLT) / (PLT – R)
Substitute [PQ * (PQ/PLT)^3.9] = Q and [PR * (PR/PLT)^3.9] = R:
DR = ([PQ * (PQ/PLT)^3.9] – PLT) / (PLT – [PR * (PR/PLT)^3.9])

Where:
TSS = Training Stress Score (raw)
LT = Lactate Threshold
Q = Push
R = Recovery
D = Duration
P = Powerwhew too much math for me today but I can offer some comments:
1. I would not use TSS for this but consider just NP over the Dq+Dr. Now perhaps that's what your calc boils down to?

2. You omitted the 30-second rolling average which really flattens a 'square-wave' or step in power from FT to ~135% FT lasting one minute.

3. Ignoring the 30sec myself ;) , and assuming Dq=1, defining IFq= Pq/LT and IFr =Pr/Lt, I get the formula:

IFr = ((1-Ifq^4+Dr)/Dr)^0.25

If IFq=1.35 and Dq=1 then looking at Dr I get:
1.0 min undefined (not possible to recover in that time)
2.0 min undefined ... ditto

2.5 min 0.52
3.0 min 0.69
3.5 min 0.76
4.0 min 0.80
5.0 min 0.86

That's a push of ~371W for 1-min and targetting an IF of 1.0 over the push + recovery interval .. which believe is a good approach. That push should ideally be followed by about 3min at 200W if I've done the math correctly.

** Note that the 'in-use' NP, TSS factors are exponent 4.0 rather than 3.9 to simplify things.

Personally, I'd never try to figure this sort of thing during a TT but it's an interesting exercise ... maybe compare to how one actually rode and improve next time 'round?

regards,
rmur

1. I would not use TSS for this but consider just NP over the Dq+Dr. Now perhaps that's what your calc boils down to?
Yes, that is what his equations boil down to. He uses the original exponent of 3.9 instead of 4, but other than that his equations yield the same results as if you set NP=1 and solved for one of the other variables in:

{[DQ*(PQ/PLT)^4 + DR*(PR/PLT)^4]/(DQ+DR) }^.25 = 1

Personally, I'd never try to figure this sort of thing during a TT but it's an interesting exercise ... Sure, but what if your cycling computer did it automatically for you? Rap/Andy - you guys should look into it and send me a freebie gift of the first power sensor and cycling computer that integrates an "IF/TSS-based dynamic power output management system"!

:)

On a more serious note, I have the same "concern" that rmur raised in point 2. That is, isn't normalized power, and therefore TSS, computed based on 30-second rolling average power raised to the 4th power (or 3.9 per your calculations) and averaged? You say:

"The TSS (raw) score is duration * average power * (average power/power at LT)^3.9."

But isn't it really "duration * NORMALIZED power * (NORMALIZED power / power at LT)^3.9".

Rap - I know I've made a similar point in a different thread before. I'm not trying to be an ass. Just let me know if I'm misinterpreting something, either in your framework or Andy's paper. I haven't had a chance to pay a lot of close attention to your calculations, but you certainly seem to be putting a lot of thought and effort into it and probably understand this better than I do.

Although, I did recently incorporate IF/TSS calculations into the Perl script that creates my training log online:

http://www.employees.org/~bozceri/training/20050731T073157.32297.srd.html (http://www.employees.org/%7Ebozceri/training/20050731T073157.32297.srd.html)

That's from the bike leg of a Half Ironman tri I did this past weekend. Please don't laugh at my average power. :)

Berend

2. You omitted the 30-second rolling average which really flattens a 'square-wave' or step in power from FT to ~135% FT lasting one minute.
On a more serious note, I have the same "concern" that rmur raised in point 2. That is, isn't normalized power, and therefore TSS, computed based on 30-second rolling average power raised to the 4th power (or 3.9 per your calculations) and averaged?
The 30-second averaging serves to flatten all the jagged-ness out of the curve for ease of calculation. The averaging simplifies the calculations and also mimics the physiological responses better for short fluctuations. It doesn't change the longer pushes except to make them 'round-ier.' :)

As far as the averaging flattening out a 1 min push to 135%, no it really doesn't. The avg'd curve will build from 100% up to 135% over the course of 30 seconds, remain at 135% for 30 seconds, and then decay back to 100% in 30 seconds after the push ends. The height of the avg'd push is still 135%, and the area under the curve remains the same.

What gets flattened are all the little blips lasting *less that 30 seconds.* Rap would need to consider that effect in his Highly Variable Pacing approach since it's unlikely that he can hold a +400W push for more than 30 seconds. Maybe that's the recovery piece of his model that he's been missing for those short pushes.

1. I would not use TSS for this but consider just NP over the Dq+Dr. Now perhaps that's what your calc boils down to?Well, until I think about it a little more I won't put forward a strong argument one way or the other about that, in part because both approaches are, in my view, based on the wrong relationship. NP and TSS are built upon the blood lactate levels at steady-state power, the famous ski-slope curve of lactate as a function of power. What I want to model is lactate recovery rates. After 1 min at 371w, how long does it take my body to get my lactate level down to where it would be at 275w steady-state (assume 200w recovery power)? And, is there a cumulative fatigue effect? IOW, does it take my body longer to get my lactate level down from a 1 min x 371w push to 275w steady-state after 1 hr at 275w? I'm looking for data on this. But, I am skeptical about both of our numbers (you get 3.0, I get 4.22). I think they're both too high, based on my own interval training rides. If I do a 371w push for 1 min, I "feel" recovered after ~2 mins at 200w. But, maybe I'll feel differently after I go to a lab and get tested.

2. You omitted the 30-second rolling average which really flattens a 'square-wave' or step in power from FT to ~135% FT lasting one minute.Yes, I've ignored the 30-sec rolling average in NP. But, I'm not ignoring the <30 sec pushes, which are basically free bites from the apple. I'm ignoring those because in theory recovery is not required.

Personally, I'd never try to figure this sort of thing during a TTActually, I think if one works out the numbers in advance, it is pretty simple to implement. That's in part why I am approaching it as a symmetric power/variable time strategy. I envision a simple table of time ratios associated with power levels in 10w increments beginning at 40K MP +10w. So, let's say that my table shows +50w = 2x time ratio. If I've studied or ridden the course, I have a pretty good idea where I want to push and about how long the push is going to be (e.g., a hill followed by a descent). I'd try to estimate the duration of the push and the average push power (e.g., 1 min at +50w). Since I ride at a pretty consistent cadence ~100, I can usually just count my pedal strokes. Once I start the descent and get my speed up, I'd do the recovery calculation (2 min at -50w). Again, I usually just count my pedal strokes rather than looking at my watch. Remember, I don't need to do any calculations during the push; I just need to be able to estimate the duration and average power of the push. I do the math after I've gotten my speed up and started the recovery segment. That's a boring time anyway -- may as well do some thinking.

Is this approach anal? Some will think so, but I look at it this way. I've got a bunch of resources at my disposal in a TT, one of which is my brain. Why not use all the resources at my disposal to ride the fastest time my body and training can produce at that point in time? My first choice would be to have a 40K MP of 500w and just go out for a nice little ride in the park at ~450w, maybe get a cup of coffee along the way. But, I'll have to do a bit more training before I can deploy that pacing strategy.

What gets flattened are all the little blips lasting *less that 30 seconds.* Rap would need to consider that effect in his Highly Variable Pacing approach since it's unlikely that he can hold a +400W push for more than 30 seconds. Maybe that's the recovery piece of his model that he's been missing for those short pushes.Yes, I'm ignoring these <30 sec pushes, hoping Andy is right when he says that these pushes are "free" bites from the apple, due to the 1/2 life of metabolic responses. Based on my own intervals, I think that's true so long as the <30 sec pushes are followed by >2 mins at 40K MP or less. And, yes, I envision in real-life limiting the >400w pushes to <30 sec (e.g., a short hill < 1/4 mile). I would also use these short high-power blips to keep speed up on descents, even when I am in recovery mode, because I have found that with a little downgrade it takes very little time to push the bike speed up (e.g., 5-10 secs) and then it stays up there a pretty long time even at a steady-state recovery power (e.g., 150w).

Sure, but what if your cycling computer did it automatically for you? Rap/Andy - you guys should look into it and send me a freebie gift of the first power sensor and cycling computer that integrates an "IF/TSS-based dynamic power output management system"!:)I'm on it. But, you may have to get a new PM -- mine. I envision a user-definable sustainable power level (e.g., 40K MP) and recovery algorithm and a "green light" icon that means you've fully recovered from a push > your sustainable power level. So, after a push of any duration and any power, you can start a recovery at any recovery power and just wait for the "green light."

I think they're both too high, based on my own interval training rides. If I do a 371w push for 1 min, I "feel" recovered after ~2 mins at 200w. But, maybe I'll feel differently after I go to a lab and get tested.
They're too high if you use the NP model for a "1-min, 371W push." However, that's not the case when you're using the 30-sec averaging, and that's why I say that might be the missing piece in your puzzle (modelling the physiological delay/recovery). Using 30s averaging you're only at 371W for 30s, even though you're above 275W for 90s. The 371W square wave becomes a trapezoid 90sec long with an avg power of 323W. Try that value and duration in your TSS model and see if you feel better about the result.

They're too high if you use the NP model for a "1-min, 371W push." However, that's not the case when you're using the 30-sec averaging, and that's why I say that might be the missing piece in your puzzle (modelling the physiological delay/recovery). Using 30s averaging you're only at 371W for 30s, even though you're above 275W for 90s. The 371W square wave becomes a trapezoid 90sec long with an avg power of 323W. Try that value and duration in your TSS model and see if you feel better about the result.Yes, averaging brings down the average power over the 90 secs, which in turn shortens the required recovery, because of the high penalty paid by higher power levels (due to the 3.9 exponent). And, it may be even better if the 30 sec averaging is one-sided. What if there is a lag in acidosis (measured by lactate) production when you increase power into the non-sustainable levels but there is no lag in shutting down acidosis production when you cut the power?

Yes, averaging brings down the average power over the 90 secs, which in turn shortens the required recovery, because of the high penalty paid by higher power levels (due to the 3.9 exponent). And, it may be even better if the 30 sec averaging is one-sided. What if there is a lag in acidosis (measured by lactate) production when you increase power into the non-sustainable levels but there is no lag in shutting down acidosis production when you cut the power?
Even if acid production drops immediately, there will still be a 'decay' in acidosis because of the time it takes for the transport and removal processes to bring the acid-ity (oh screw it! -- lactate :D ) levels back down to the steady state value where production and removal rates are equal. I'd think you still need to count the lagging side of the trapezoid.

Even if acid production drops immediately, there will still be a 'decay' in acidosis because of the time it takes for the transport and removal processes to bring the acid-ity (oh screw it! -- lactate :D ) levels back down to the steady state value where production and removal rates are equal. I'd think you still need to count the lagging side of the trapezoid.Careful, we'll be lectured by Lindsay on terminology (which is not all bad). I agree that there is a lag in the level of acid-ity, driven by the clearance rate. But including both sides of the trapezoid implies that the high production rates lag as well. What if production stops immediately and then the level drops gradually due to clearance rate?

Careful, we'll be lectured by Lindsay on terminology (which is not all bad). I agree that there is a lag in the level of acid-ity, driven by the clearance rate. But including both sides of the trapezoid implies that the high production rates lag as well. What if production stops immediately and then the level drops gradually due to clearance rate?
ah the body is analogue, not digital, so none of these processes start/stop instantaneously IMHO.

You guys are digging beyond the trees, into the root network now!

But the big picture is that NP provides an excellent model to think about, analyze and, yes, even plan variable pacing for a well-known course.

If you go over threshold power for a significant period, you WILL pay the piper. Well, unless the you've crossed the finish line ;)

TT's are perfect for NP as we hardly ever really 'recover' during the event. There's no opportunity to recharge anaerobic stores to any degree.

regards,
rmur