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I think there was a formula for that by Michele Ferrari but I can't find it on the net. I think it can't be bigger than around 6,5 watt per kg for at least an hour or so. Does anybody know the exact number and how it is calculated?

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    I found this info that Bradley Wiggins maintained 440 watts during his hour record and assuming he was 72 kg at that time (he says he is 70 kg during the season but he might have gained a bit more for this attempt I assume), it gives you about 6,10 W/kg and that is on a velodrome. It should be lower in outdoors I think.
    – Ender
    Mar 6, 2022 at 21:09
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    Also - motivation is a key factor. There have been documented cases of people in stressful situations lifting enormously heavy things like cars, safes, boulders and fallen beams. Adrenaline is a helluva performance-enhancing drug. I suggest restricting question to FTP for an hour, and specific to cycling.
    – Criggie
    Mar 6, 2022 at 23:57
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    So if you found that, what did you hope for as an answer? How can this be calculated? Why would the actual power be lower outdoors? The speed may be lower because the road is not as smooth, but that should not limit power output if you measure it properly. Mar 7, 2022 at 3:20
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    Could you clarify what you mean by "sustain?" Even the pace of a one hour record isn't "sustainable" for more than an hour. That said, Peter Keen said Boardman averaged 442w for his 56km record (~6.2 w/kg), Padilla said Indurain did 509w (~6.3 w/kg) for his, and Ferrari hinted that Rominger did ~460w (~7.3 w/kg) for his record. I'm guessing the Indurain and Rominger records weren't done on orange juice.
    – R. Chung
    Mar 7, 2022 at 9:00
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    To put these figures in context, note that running requires ~1 kcal/kg/km. There are 4.2 joules per kcal but if gross metabolic eff is ~23.8% (=1/4.2), then (running speed in m/s)*(body weight in kg) is approximately power in watts; so speed in m/s ~ watts/kg. So to run a marathon in ~2 hours takes ~6 watts/kg. This is just a rule of thumb of course, and running isn't cycling, and one hour isn't two hours, but the rough magnitudes are sometimes useful for back of the envelope comparisons.
    – R. Chung
    Mar 7, 2022 at 9:09

3 Answers 3

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Wilson, in Bicycling Science has a plot that's not quite what you're looking for but very close. Closer than it looks at first, I believe.

Human power graph from Wilson

click for full size

The downside of this is that it isn't normalised to bodyweight. But there are significant error margins - small in the case of ergometer test, but much larger in the case of things like Indurain's TdF climb or even Boardman's hour record. Large enough, I would say, that we can use and average bodyweight. Even between pros, W/kg will vary. Even for a given rider there will be day-to-day variations.

Apparently the average pro cyclist weighs 68kg, so we can get a pretty decent value by dividing that out, or find a specific riders' weight. Taking Boardman's 1996 hour record as an example, that reads off as 420W (give or take about 10W). He's supposed to weigh 70kg (I don't know when that figure applies to) giving 6 W/kg.

To answer the question with a value representative of peak professional performance instead of naming a specific human, I think this precision is probably sensible.

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  • I quickly took a picture of that page before leaving the house this morning. When I have the book in my hand again I might be able to follow up the citations and see if I can get a slightly more precise figure, but I wouldn't read much into it
    – Chris H
    Mar 7, 2022 at 9:44
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    You might find some of the data in table 7 here useful: they give estimated power and mass for several hour records from 1967 to 1996, including Indurain and Rominger. In that table Boardman's 442 watts is reported as measured rather than estimated. pubmed.ncbi.nlm.nih.gov/10589872
    – R. Chung
    Mar 7, 2022 at 10:25
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    @R.Chung the discrepancy between the 2 papers is interesting, and reinforces my point about error margins. Padilla and Basset should be using the same data, but Boardman differs by 3%, Rominger by 6%, and Indurain by over 12% between the 2 papers. The difference in Indurain's power is ~17%. Strangely even the weights don't match, so it's not just an artefact of how they handle the averaging of their power data
    – Chris H
    Mar 7, 2022 at 11:51
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    Indurain was very inexperienced on the track, crashed in practice, and was reportedly skittish during the official attempt so may have backed off from his max sustainable power. Also, he reportedly couldn't hold the black line so certainly went farther than the official distance.
    – R. Chung
    Mar 7, 2022 at 11:51
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    On Ferrari's old 53x12.com site, he talked about Rominger's "prep" for hour, and said that at Indurain's speed, Rominger would have only had to have produced 413 watts. Extrapolating from that to Rominger's actual speed would have produced close to the 462 watt estimate.
    – R. Chung
    Mar 7, 2022 at 12:04
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I think the answers so far are slightly underestimating maximal w/kg FTPs. I've included a table showing FTPs (and maximal powers recorded for shorter periods of time) from the following site. In the table you can see that for men the maximal W/kg FTP is a fair bit over 6 w/kg when fresh.

As an aside, hour record attempts probably won't be the best sources for maximal W/kg since they don't involve climbing and performance instead depends on total watts produced (or more accurately W/CdA). Larger riders tend to have higher FTPs in total watts (and often W/CdA though some small riders can get a really low CdA) while smaller riders tend to have higher W/kg.

Table showing maximal power outputs

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    It’s not clear to me how TrainingPeaks obtained the data for this table and what they even consider FTP (usually it’s the highest average power one can sustain for 1 hour. But sometimes it’s measured for only 20 minutes or 45 minutes or a 95% window within the hour is used. Can’t find any definitive information on TrainingPeaks.).
    – Michael
    Mar 7, 2022 at 12:50
  • @Michael I agree it is unclear exactly how the data is obtained but I believe they are using FTP to refer to power over 1 hour. There is other evidence that the 6 w/kg suggested is an underestimate. e.g. the performances mentioned here lanternerouge.com.au/2022/02/25/… showing climbers doing 6 w/kg for an hour (or very close) at the end of a long day of racing in the middle of a grand tour. Certainly their peak 1 hour power completely rested and fresh would be higher than that.
    – GageMartin
    Mar 7, 2022 at 13:11
  • Also for the numbers from actual races they usually would involve some accelerations/attacks which isn't the most efficient way to maximize average power over an hour (again suggesting that their peak 1 hour power is higher)
    – GageMartin
    Mar 7, 2022 at 13:14
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    @Michael I believe that's a power table produced by Andrew Coggan, an exercise physiologist. I'm not inclined to dig into the history right now, but he may have been compiling this data as early as 2006 - so be aware the very top end might be skewed by doping. I would have guessed that this has to at least be informed by empirical measurements.
    – Weiwen Ng
    Mar 7, 2022 at 16:11
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    @WeiwenNg Yes, that table originally came from Andy Coggan, but it has been modified several times since he first shared it in 2003. I don't think Andy himself uses that table any longer in any serious way--he developed other ways to "profile" riders in later years and I think he thinks his newer ways are superior.
    – R. Chung
    Mar 7, 2022 at 16:44
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Michele Ferrari, the infamous doping doctor for Lance Armstrong and a number of other riders, did make a related statement. In Tyler Hamilton's autobiography, Hamilton reported that Ferrari said the following (around the year 2000, also this is his paraphrase of Ferrari, not a verbatim quote)

He explained that the best measure of ability was in watts per kilogram—the amount of power you produce, divided by your weight. He said that 6.7 watts per kilogram was the magic number, because that was what it took to win the Tour.

I'm not sure what duration that figure refers to. The preceding page says that Ferrari often tested athletes on the Col de la Madone, for which the current men's KOM is held by Richie Porte at 34 minutes 43 seconds. Anyway, Ferrari could have meant functional threshold power over 6.7 W/kg, or 6.7 W/kg up the Madone. Commonly, people understand FTP to be the power you can hold for about one hour, but this isn't correct. Time to exhaustion at FTP varies, and my understanding is that it's commonly around 30-75 minutes, depending on the person.

Ferrari did not state how much power a human "can sustain", which sort of implies the physics-based upper limit to the cycling power we can generate. Nevertheless, because EPO and blood transfusions were commonplace among the elites, people tend to assume that FTPs over 6.7 W/kg are likely not possible without assistance. Corroborating that, Ross Tucker reports here that Bjarne Riis is estimated to have sustained 6.8 W/kg up the Hautacam in 1996, and Lance Armstrong is estimated to have done 6.6 W/kg up the Alpe d'Huez. The Strava segments for each climb are linked. Note that here, weight was presumably based off reported data (which might be incorrectly reported, since athletes don't typically make their weights public), and estimated power data. They weren't racing with any power meters then. The SRM was the only available power meter, and it was very bulky and heavy. There is probably a wide error margin around those estimates.

Later in the post, Tucker said that

I am of the opinion, like Prof Aldo Sassi, that a value above 6.2 W/kg is indicative of doping.

He didn't clearly say what "a value" refers to. Going to the previous paragraphs, he was talking about Armstrong producing the estimated power at 85-90% of his VO2max. I don't know how that output relates to threshold power, because different athletes can sustainably work at a different fraction of their VO2max (that's called fractional utilization). As a side note, if you compare your best 5 min power to your current FTP, that can give you some insight into your fractional utilization. As I write this, my best 5 min power is about 130% of my FTP, so I likely have a low fractional utilization.

Speaking of VO2max, we know that maximum efforts of 3 to 8 minutes put you at VO2max, i.e. your aerobic energy system is at maximum output. I haven't done the math, but if you have someone's time up a short climb, you can estimate their VO2max, keeping mind that wind and drafting could have aided them (biasing your estimate high). You also have to assume a rider's gross mechanical efficiency, or at least plug in a range of plausible values for it. I discuss gross mechanical efficiency here. I cited a paper that found that

... women had an average gross efficiency (GE) of 23.2%, standard deviation 3.5 percentage points. Men had an average GE of 21.2%, standard deviation 1.7 percentage points.

A racer Zwift called Eddy Hoole put out 526W in a 4 min 16 s climb or 8.5 W/kg. Zwift's performance verification board argued that this

requires a VO2max of over 90 mL/min/kg

Or, to nitpick, it's rather that there's a plausible range of VO2maxes this performance implied, and a lot of that range was over 90. Elite athletes have and can succeed with a range of VO2maxes, but 90 is in the range of the highest values ever measured. Never mind Hoole, we could probably estimate an upper bound on power to weight for short efforts this way for men and women.

Last, the original post was made in 2010, and Ferrari is commenting in the late 2000s. We have continued to make advancements in training since then. For example, technology means that indoor training is now much more prevalent and accessible, which aids in structured training, maintenance of form over the winter, and also talent discovery. If you are estimating power from assumptions (e.g. estimate the power a rider would need to complete an ascent given assumptions about their weight, the wind, etc), bikes have become more aero, which may mean that they hit the final climbs fresher. Nutrition has improved. For example, riders now target very high carb intakes to ensure a constant glycogen supply to the muscles. All of this may mean that the ceiling on clean W/kg has grown.

Teams may also have paid more attention to managing rider weight, which is the denominator in W/kg. This can be fine, but it can also be ethically problematic. It might breed eating disorders and relative energy deficiency in sport (RED-S), which women may be more vulnerable to but which men can also experience. Team Sky was suspected to be pushing the rules on corticosteroid therapeutic use exemptions in the early 2010s. If true, one of their reasons may have been to help athletes manage weight from muscle catabolism (although in the short term, they can also cause water retention).

Of note, MyWindSock estimated that Vingegaard did about 7.6 W/kg for 13 mins, 21 secs, up the climb in the stage 16 TT of the 2023 Tour de France. Zach Nehr, writing for Velo (then Velonews) has also produced some estimates up significant climbs in the 2023 Tour. Notably, he thinks that Pogačar and Vingegaard did about 6.1 W/kg up the Alpe d'Huez (nearly 40 minute climb). Sepp Kuss had a maximum 20 minute power of 6.3 W/kg; note that taking 95% of a 20 minute effort can be used to estimate a rider's threshold outside of an FTP test, but that estimate is likely to be biased one way or another. So, these values would indicate possible doping to Tucker, but he's commenting in the early 2010s. We don't know if these represent unassisted values now.

The book citation is: Hamilton, Tyler; Coyle, Daniel. (The Secret Race: Inside the Hidden World of the Tour de France . Random House Publishing Group. Kindle Edition.

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