# Power Data Estimates for the climbing stages

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#### CitizenErased

Sophistic said:
Dr.Ferraris formula is crap, at 5,7% a 70kg guy would have a lower watt/kg number than a 55kg guy at the same speed.
Dear friend, your ignorant statement stinks. And quite badly... Are you telling us that a heavier guy will actually produce lower wattages? You must be out of your small mind.
Speed is equal to a precise w/kg on a certain gradient, notwithstanding the weight.
What changes is the wattage, due to different body weights. W/kg remains the same for everyone at that speed.

WAKE UP.

#### kielbasa

CitizenErased said:
Dear friend, your ignorant statement stinks. And quite badly... Are you telling us that a heavier guy will actually produce lower wattages? You must be out of your small mind.
Speed is equal to a precise w/kg on a certain gradient, notwithstanding the weight.
What changes is the wattage, due to different body weights. W/kg remains the same for everyone at that speed.

WAKE UP.
Did you miss LeBreton's post about the bike weight as percentage of total weight being hauled up a hill? You might want to re-read his post before resorting to the use of that vocabulary. Actually, it's best never to use it.

#### Alex Simmons/RST

Le breton said:
I was not refering to the reduced drag, but to the reduced efficiency of the human engine and the correction needed to compare to sea-level efforts ( about 10% at 2200 meters).
Sure but it doesn't change the physics used to determine the actual power requirements to ride at a given speed and grade.

How anyone's power varies with given change in altitude is quite a personal thing and highly variable across athletes.

#### Alex Simmons/RST

CitizenErased said:
Dear friend, your ignorant statement stinks. And quite badly... Are you telling us that a heavier guy will actually produce lower wattages? You must be out of your small mind.
Speed is equal to a precise w/kg on a certain gradient, notwithstanding the weight.
What changes is the wattage, due to different body weights. W/kg remains the same for everyone at that speed.

WAKE UP.
It's not Le breton that needs to wake up. Re-read what he said.

By the way, here's an indication of the proportion of energy required to overcome various resistance forces for solo steady state riding on various gradients:

The actual proportions will vary a little depending on total rider mass and aerodynamics but the shape of the variations and general proportions will show same pattern.

#### halamala

Vuelta a Espana 2011, Stage 8, Last Km [Elevation?]

Joaquim Rodriguez : 3:05 , 19.46 Kph

#### Ferminal

halamala said:
Vuelta a Espana 2011, Stage 8, Last Km [Elevation?]

Joaquim Rodriguez : 3:05 , 19.46 Kph

#### Le breton

Alex Simmons/RST said:
Sure but it doesn't change the physics used to determine the actual power requirements to ride at a given speed and grade.

How anyone's power varies with given change in altitude is quite a personal thing and highly variable across athletes.
I , of course, agree with the first sentence.

Concerning the second one, I have very strong doubts as I have never seen a serious study of that topic relevant for, say, endurance type athletes with a very high level of fitness, say, sea-level VO2 max > 75 ml/mn.kg.

However, if there were very big differences between cyclists it would become apparent as anecdotal evidence.

Let's agree that on average cyclists lose 10% of their "20 min. power" at 2200 meters altitude.
If a subset of a handful of racers only lost, say, 5% while another subset lost, say, 15%, wouldn't you think that those racers and their opponents would eventually notice? They would target their attacks according to the altitude, not just the gradient.

Another remark, in your calculations you take a CdA of 0.3 m^2 for your std ~67 kg cyclist on climbs. This seems to me to be a large underestimate. I am currently just under a bit 60 kg and even on level ground I am above 0.3 m^2 (although my ears stick out less than Pantani's). (I will try to find my 2004 calculation)

I will not go back on your Crr = 0.005, (discussed earlier on this thread I believe) although I prefer 0.004.

#### Le breton

Ferminal said:
20 years ago I once did 105 m. in 2:59, but that was in ~70% staircases, I was fresh and I didn't carry a bike

#### Fergoose

Just a quick post to thank anyone who takes the time to make a constructive contribution to this thread – your efforts are appreciated. I may be hopelessly naïve, but reading some of this gives me some confidence I’m less likely to be watching a complete circus than I was ten years ago (although the context of the climb is key, it doesn’t render comparison worthless). Sure, forms of doping are still ongoing, but its hard to build a case that it is as prevalent and result defining as it was in the a decade ago. This had been my gut feeling before reading this thread and its good to have some reinforcement that I’m not just kidding myself.

Not having great confidence in the international and national federations or in their willingness to cooperate with law enforcement and the judicial process I think threads like this will (unfortunately) be one of the few ways of making any sort of reasoned comparison between cycling over the years. So thanks, carry on and fingers crossed for nothing abnormal on today’s Vuelta stage.

#### Sophistic

CitizenErased said:
Dear friend, your ignorant statement stinks. And quite badly... Are you telling us that a heavier guy will actually produce lower wattages? You must be out of your small mind.
Speed is equal to a precise w/kg on a certain gradient, notwithstanding the weight.
What changes is the wattage, due to different body weights. W/kg remains the same for everyone at that speed.

WAKE UP.
as others have pointed out, you should re-read and rethink.

#### Alex Simmons/RST

Le breton said:
I , of course, agree with the first sentence.

Concerning the second one, I have very strong doubts as I have never seen a serious study of that topic relevant for, say, endurance type athletes with a very high level of fitness, say, sea-level VO2 max > 75 ml/mn.kg.

However, if there were very big differences between cyclists it would become apparent as anecdotal evidence.

Let's agree that on average cyclists lose 10% of their "20 min. power" at 2200 meters altitude.
If a subset of a handful of racers only lost, say, 5% while another subset lost, say, 15%, wouldn't you think that those racers and their opponents would eventually notice? They would target their attacks according to the altitude, not just the gradient.

Another remark, in your calculations you take a CdA of 0.3 m^2 for your std ~67 kg cyclist on climbs. This seems to me to be a large underestimate. I am currently just under a bit 60 kg and even on level ground I am above 0.3 m^2 (although my ears stick out less than Pantani's). (I will try to find my 2004 calculation)

I will not go back on your Crr = 0.005, (discussed earlier on this thread I believe) although I prefer 0.004.

I'll leave the physiological impact of altitude and what riders do to acclimate for now. Suffice to say that there are differences. It may not be as large as for leading contenders in a race but others may struggle and adaptation time for some is longer for than others, so prep and knowledge of one's individual response is key. Randal Wilbur's book on altitude training gives a pretty fair overview of all the studies (up to time of publishing).

As for the chart, sure CdA will likely be much higher (or lower) for some, in particular when climbing steep gradients since we sit up more rather than be in the drops. However since aero is far less of an issue on steeper gradients, then it doesn't change the trend in relative proportions shown in the chart a lot.

But as an example, my CdA as measured on my road bike as a 88-90kg (bike + rider) on non aero (old Ksyrium) wheels and standard road helmet is ~ 0.33m^2. On my old mass start round tubed steel track bike I was 0.28m^2. And I am by no measure aerodynamically gifted.

A Crr of 0.004 is a very good road surface, smooth tarmac with excellent tyres. At one of the fastest wooden velodromes in the world (Sydney's DGV) ridden on Veloflex Record or high end Vittoria track tyres I get a Crr ~ 0.0023.

Anyway, back to the chart, if I change CdA to something significantly higher, say by a third to 0.4m^2, then the relative proportions of the various resistance forces for steady state cycling go as follows (previous CdA proportions in brackets):

Gravity: 73% (75%)
Bearing/drivetrain: 3% (3%)
Rolling resistance: 7% (8%)
Air resistance: 17% (14%)

Gravity: 89% (90%)
Bearing/drivetrain: 3% (3%)
Rolling resistance: 4% (4%)
Air resistance: 4% (3%)

hence the relative proportions change a bit, but that's not really the point of the chart, it's the trends in those relative proportions as the road tilts upwards that I am pointing out.

#### Le breton

Alex Simmons/RST said:
But as an example, my CdA as measured on my road bike as a 88-90kg (bike + rider) on non aero (old Ksyrium) wheels and standard road helmet is ~ 0.33m^2. On my old mass start round tubed steel track bike I was 0.28m^2. And I am by no measure aerodynamically gifted.
Considering how carefully you study the various aspects of cycling energetics, I will not dispute your findings. Still I am surprised that you could have as low a CdA as 0.33 m^2 on a regular road bike, and of course flabbergasted that could go as low as 0.28 m^2 on your track bike.

Imagine how many km Merckx would have covered in one hour in Mexico if he had had a CdA of 0.28 m^2!

#### halamala

halamala said:
La Covatilla @ Vuelta a Espana 2002 , 2004 , 2006

Best times , Last 8.0 Km , Elevation 645 m , Grade 8.06 %

Roberto Heras 20:23 , 2002 [VAM 1900 m/h]
Joseba Beloki 20:35 , 2002
Felix Garcia Casas 20:53 , 2002
Oscar Sevilla 21:00 , 2002
Aitor Gonzalez 21:00 , 2002
Angel Casero 21:10 , 2002
David Plaza 21:15 , 2002
Gilberto Simoni 21:32 , 2002
Santiago Perez 21:35 , 2004 [VAM 1800 m/h]
Danilo Di Luca 21:37 , 2002
Fabian Jeker 21:54 , 2002
Manuel Beltran 22:03 , 2002
Klaus Moller 22:05 , 2002
Roberto Heras 22:07 , 2004
Francisco Mancebo 22:21 , 2004
------------------------------
Danilo Di Luca 24:12 , 2006 [stage winner]
Re-calulation. 2002 times = 53 seconds slower.

La Covatilla @ Vuelta a Espana 2002 , 2004 , 2006 , 2011

Best times , Last 8.0 Km , Elevation 645 m , Grade 8.06 %

Roberto Heras 21:16 , 2002 [VAM 1820 m/h]
Joseba Beloki 21:28 , 2002
Santiago Perez 21:35 , 2004 [VAM 1800 m/h]
Felix Garcia Casas 21:46 , 2002
Oscar Sevilla 21:53 , 2002
Aitor Gonzalez 21:53 , 2002
Angel Casero 22:03 , 2002
Roberto Heras 22:07 , 2004
Francesco Casagrande 22:08 , 2002
David Plaza 22:08 , 2002
Francisco Mancebo 22:21 , 2004
Gilberto Simoni 22:25 , 2002
Danilo Di Luca 22:30 , 2002
Fabian Jeker 22:47 , 2002
Manuel Beltran 22:56 , 2002
Klaus Moller 22:58 , 2002
------------------------------
Daniel Martin 23:46 , 2011 [stage winner]
Danilo Di Luca 24:12 , 2006 [stage winner]

#### Alex Simmons/RST

Le breton said:
Considering how carefully you study the various aspects of cycling energetics, I will not dispute your findings. Still I am surprised that you could have as low a CdA as 0.33 m^2 on a regular road bike, and of course flabbergasted that could go as low as 0.28 m^2 on your track bike.

Imagine how many km Merckx would have covered in one hour in Mexico if he had had a CdA of 0.28 m^2!
Not sure, you tell me. We don't know his power output at that altitude, so who can really say what his CdA actually was.

My CdA on TT bike is ~ 0.26-0.27m^2 and on pursuit bike it's 0.23-0.24m^2.

I have a client who set a master's hour record, his CdA was 0.185m^2. That's why he did over 48.3km in an hour on 300W at sea level.

Little things matter with aero.

#### Le breton

Alex Simmons/RST said:
Not sure, you tell me. We don't know his power output at that altitude, so who can really say what his CdA actually was.

My CdA on TT bike is ~ 0.26-0.27m^2 and on pursuit bike it's 0.23-0.24m^2.

I have a client who set a master's hour record, his CdA was 0.185m^2. That's why he did over 48.3km in an hour on 300W at sea level.

Little things matter with aero.
So, your client is almost as aero as Chris Boardman (0.18 m^2)

Concerning Merckx in Mexico, assuming "merckx power at 2250 m.) = 90% (Merckx power at sea-level in lab in Cologne= 455 watts) = 410 watts.

Assuming this post of mine on a thread related to the hour record is correct
couldn't resist calculating Merckx's power output using the numbers given in the aerodynamics column of the reference
http://www.bikecult.com/bikecultbook...cordsHour.html
i.e
.34 square meters
0.75 cd

For the air density at Mexico's altitude, assuming 20°C, one gets 310 watts against air resistance. (air density 0.94 g/cm^3)

Adding the low rolling resistance of a wooden track, maybe 20-30 watts (it would be 43 watts on asphalt) and making allowance for maybe 10 watts lost due to the curves and another 2% overall for transmission losses, I get a grand total of 347 watts!!!!
But I don't believe that figure either, it just shows that the reference given is self-contradictory.

I get something like CdA ~0.31 m^2

That bikecult ref. seems inaccessible right now.

#### acoggan

Le breton said:
Concerning the second one, I have very strong doubts as I have never seen a serious study of that topic relevant for, say, endurance type athletes with a very high level of fitness, say, sea-level VO2 max > 75 ml/mn.kg.

However, if there were very big differences between cyclists it would become apparent as anecdotal evidence.

Let's agree that on average cyclists lose 10% of their "20 min. power" at 2200 meters altitude.
If a subset of a handful of racers only lost, say, 5% while another subset lost, say, 15%, wouldn't you think that those racers and their opponents would eventually notice? They would target their attacks according to the altitude, not just the gradient.

Another remark, in your calculations you take a CdA of 0.3 m^2 for your std ~67 kg cyclist on climbs. This seems to me to be a large underestimate. I am currently just under a bit 60 kg and even on level ground I am above 0.3 m^2 (although my ears stick out less than Pantani's). (I will try to find my 2004 calculation)

I will not go back on your Crr = 0.005, (discussed earlier on this thread I believe) although I prefer 0.004.

1. Individual variation in the response to hypoxia is well-established, even among elite athletes, e.g., http://www.ncbi.nlm.nih.gov/pubmed/21311361

2. A CdA of 0.3 m^2 for am average-sized/proportioned racing cyclist on a road bike is not at all unreasonable. Even at 1.83 m (but only 67 kg), mine is 0.28 m^2 on a modern bike (aluminum Cervelo Soloist) and 0.30 m^2 on a Merckx-style bike (steel Specialized Allez).

3. Based on the measurements I've made, I'd split the difference and consider 0.0045 the best estimate of "average" Crr (i.e., 0.005 would mean rougher roads/lower quality tires, whereas 0.004 would only be achievable on really smooth road/with rather light tires).

#### Le breton

acoggan said:
1. Individual variation in the response to hypoxia is well-established, even among elite athletes, e.g., http://www.ncbi.nlm.nih.gov/pubmed/21311361
Thanks Andy.
Amazing, I am truly surprised.

This is the first somewhat convincing paper I see supporting your statement.(basically I thought statements to that effect were mostly unsupported cr@p)

#### halamala

Last 5 Km: Wiggins climbed 5.8 W/kg

Vuelta a Espana 2011, Stage 9, Final climb La Covatilla [last 5.0 Km]

Elevation / Höhenmeter [m] : 365 m
Distance / Streckenlänge [Km] : 5.0 Km
Time in seconds / Fahrzeit in Sekunden [sec] : 835 = 13 min 55 sec = 13:55
Weight rider / Gewicht Fahrer [kg] : 72 kg [TeamSky.com]
Weight bicycle, clothes etc. / Gewicht Fahrrad [kg] : 8 kg

Grade / mittlere Seigung : 7.3 %
Average speed / mittlere Geschwindigkeit : 21.5 Km/h
Total weight / Gesamtgewicht : 80.0 kg

Power : 419.4 Watt
Power / kg : 5.8 Watt / kg

Source: [ http://www.rst.mp-all.de/bergauf.htm ]

Note: Strong wind - power output likely higher.

#### acoggan

Le breton said:
Thanks Andy.
Amazing, I am truly surprised.

This is the first somewhat convincing paper I see supporting your statement.(basically I thought statements to that effect were mostly unsupported cr@p)

Such individual variability is often swept up in presenting mean values. There is, however, plenty of evidence that it exists, both in terms of changes in SaO2 and in terms of changes in other factors (e.g., EPO). Here are a few (of many) studies focussing specifically on such issues (although not all in elite athletes, depending on how you choose to define that):

http://www.ncbi.nlm.nih.gov/pubmed/10331884

http://www.ncbi.nlm.nih.gov/pubmed/9760340

http://www.ncbi.nlm.nih.gov/pubmed/20359949

http://www.ncbi.nlm.nih.gov/pubmed/8789578

http://www.ncbi.nlm.nih.gov/pubmed/9502345

Although the precise reasons why some are less or more impacted by altitude than others are still somewhat uncertain, what is clear is that any such difference could have a significant impact on how well one performs in races at altitude.

#### Alex Simmons/RST

Le breton said:
So, your client is almost as aero as Chris Boardman (0.18 m^2)
Well considering my client had to ride using current UCI pursuit position rules, he might in fact be a little better than Boardman would be under the same regs.

Boardman would be ~ 2200 W/m^2 (power to CdA ratio).

At 6.4W/kg and 69.8kg, that's 447W (say), so a CdA ~ 0.20 m^2

#### halamala

Wiggins climbed 5.6 W/kg

Vuelta a Espana 2011, Stage 11, Final climb Estación de Montaña Manzaneda

From 15.0 Km remaining to 6.0 Km remaining [Distance : 9.0 Km]

Elevation / Höhenmeter [m] : 605 m
Distance / Streckenlänge [Km] : 9.0 Km
Time in seconds / Fahrzeit in Sekunden [sec] : 1462 = 24 min 22 sec = 24:22
Weight rider / Gewicht Fahrer [kg] : 72 kg [TeamSky.com]
Weight bicycle, clothes etc. / Gewicht Fahrrad [kg] : 8 kg

Grade / mittlere Seigung : 6.7 %
Average speed / mittlere Geschwindigkeit : 22.1 Km/h
Total weight / Gesamtgewicht : 80.0 kg

Power : 406.3 Watt
Power / kg : 5.6 Watt / kg

From 4.0 Km remaining to the finish line [Distance : 4.0 Km]

Elevation / Höhenmeter [m] : 271 m
Distance / Streckenlänge [Km] : 4.0 Km
Time in seconds / Fahrzeit in Sekunden [sec] : 656 = 10 min 56 sec = 10:56
Weight rider / Gewicht Fahrer [kg] : 72 kg [TeamSky.com]
Weight bicycle, clothes etc. / Gewicht Fahrrad [kg] : 8 kg

Grade / mittlere Seigung : 6.7 %
Average speed / mittlere Geschwindigkeit : 21.9 Km/h
Total weight / Gesamtgewicht : 80.0 kg

Power : 403.9 Watt
Power / kg : 5.6 Watt / kg

Source: [ http://www.rst.mp-all.de/bergauf.htm ]

halamala said:
Vuelta a Espana 2011, Stage 9, Final climb La Covatilla [last 5.0 Km]

Power : 419.4 Watt
Power / kg : 5.8 Watt / kg

Note: Strong wind - power output likely higher.
Bradley Wiggins: Wiggins insisted that his performance on the climb of La Covatilla on Sunday, in which he came to the front of a small leading group in the final kilometres of a stage eventually won by Garmin-Cervelo’s Dan Martin, proved his climbing credentials.

“Everyone was at his max,” he stated. “When I push 450 watts like I did on Sunday in such a difficult climb, who in the world can do more? Only Alberto Contador and Andy Schleck but they aren’t here. I’ve seen some guys attacking but they couldn’t maintain their speed and stay away. They even paid for their efforts.

“When I took the lead of the front group three kilometres away from the top, I rode fast despite the head wind. I’m pretty good at guessing when my adversaries aren’t well. For three kilometres, I’ve ridden like Miguel Indurain! I had never done that before. I’ve done it after the great work done by Chris [Froome]. It’s fantastic for him to be in the lead. He deserves it and it takes some pressure from me.”

#### Le breton

acoggan said:
1. Individual variation in the response to hypoxia is well-established, even among elite athletes, e.g., http://www.ncbi.nlm.nih.gov/pubmed/21311361
It seems unfortunate cyclists were not used as subjects as the correlation between VO2 and performance would have been much stronger.

Out of 27 athletes a subgroup of 7 might (we don't know if that subgroup had a an average VO2 max of ~72) have experienced a 13% drop in VO2 max at 2100m (compared to sea-level) while slowing down possibly by ~9%. (I am assuming 20 km/h)

Another 7 of our sample only lost about 5% in VO2 max, yet slowed down by as much as ~7%.

Presumably the other 13 fell in between.

The groups were established according to oxygen saturation during exercise at sea-level.

In a sample of GT top contenders we might expect a very good correlation between VO2 max and sustainable VO2 during a 9 minutes effort (not exactly what was tested in this treadmill test), it could even be argued that a 9 minutes uphill race would be practically a "VO2 race".

While in the test :
For all athletes, SaO2 during normoxic race pace running was significantly correlated with both ΔVO2(r = -0.68) and Δ3,000m time (r = -0.38).,

I would tend to believe that for GT contenders in 9 min. uphill races - let's call it 300m uphill race - at sea-level and at 2100m we would have equivalent correlations between (Sa O2 and) ΔVO2 and Δ300m time. If this study were applicable to top GT contenders it would mean that among 27 top cyclists a subgroup of 7 would slow down by about 13% going from 1950m to 2250m, while another subgroup of 7 would only slow down by about 5% (compared with a similar 300m climb from sea-level or 150m below sea-level). The other 13 would fall in between.

My initial claim had been that if among top GT contenders such widespread differences existed w.r.t. response to hypoxia it would be obvious : some of the top performers at the col d'Eze or Mont Faron (near sea-level) would suffer badly on Galibier.

While this study seems to contradict my intuition, I will need more than one study to change my mind.

#### Le breton

http://www.ncbi.nlm.nih.gov/pubmed/10331884

http://www.ncbi.nlm.nih.gov/pubmed/9760340

http://www.ncbi.nlm.nih.gov/pubmed/20359949

http://www.ncbi.nlm.nih.gov/pubmed/8789578

Those references, although relevant are only peripheral, they do not address exactly the question I was raising.

http://www.ncbi.nlm.nih.gov/pubmed/9502345

Impossible to get on this computer.

So we only have one study on 27 subjects to support the claim that there are large variations in response to altitude.

PS : I like the idea of a study at PiO2 = 70 mm Hg!
higher than the Copenhagen study of 1998, done where I lived and occasionnally exercised 30 years earlier!

#### acoggan

Le breton said:
So we only have one study on 27 subjects to support the claim that there are large variations in response to altitude.
No, there are dozens, as well as both animal and human studies that provide insight into possible mechanisms (including genetics). That you refuse to accept this to be true speaks more to your intransigence than the state of the scientific literature.