part 1
Right, now, where were we?
Oh yeah: can physiological knowledge be used to identify “superhuman” performances?
My point in citing Joyner’s theoretical paper was not to criticize it, but simply to help illustrate the magnitude of the uncertainties involved. At the time he wrote the article (in late 1989, early 1990 at the latest), the world record for the marathon was “only” 2:06:50, yet if you combined the highest measured VO2max, lactate threshold (LT), and running economy values reported in various published studies, a time of 1:57:48 was at least theoretically possible. In other words, someone could have broken the record by
~9 min (!) and you
still couldn’t have labeled it a “superhuman” performance based on scientific data.
The >9 W/kg figure for 1 h that I threw out previously was derived using a directly comparable approach. To wit, that is the value you get if you assume:
1) A VO2max of 96 mL/min/kg (i.e., that of Bjorn Dahlie…sorry, no scientific reference, but I’m sure ever one has heard of both him and this figure);
2) A fractional utilization of VO2max of 95% (i.e., that of subject G, a member of the 1988 US Olympic Team, in this study by Coyle et al.:
http://www.ncbi.nlm.nih.gov/pubmed/1997818)
3) A gross efficiency of 28.1% (i.e., that of subject 9, a winner of two UCI professional races, in this study by Lucia et al.:
http://www.ncbi.nlm.nih.gov/pubmed/12471319)
4) An energy yield of 21.13 kJ/L O2 (corresponding to 100% carbohydrate oxidation).
(Specifically: 96 mL/min/kg * 0.95 * .281 * 21.13 kJ/L * 1/60 * 1/1000 = 9.02 W/kg)
Note that the above figure was derived for illustration purposes only, and as I said at the outset I personally don’t really believe it. For example, there is no guarantee that Dahlie did not use EPO or practice blood doping, the VO2max of subject G in the Coyle et al. study may have been underestimated (leading to an overestimate of the percentage of VO2max he maintained), and it has been argued by Jeukendrup, Gore, and Martin (
http://www.ncbi.nlm.nih.gov/pubmed/12840648) as well as others that the data of Lucia et al. are flawed (ironically, Jeukendrup et al. go on to report that the gross efficiency of professional cyclists is only 17-19% while incorrectly claiming that this is completely consistent with the rest of the literature…go figure. Of course, I also find it ironic that Dr. Tucker apparently dismisses Lucia et al.’s data as incorrect yet still cites the paper as evidence that VO2max and efficiency must be inversely related – see below). Consider, however, the value you obtain with slightly more conservative/defensible assumptions:
1) A VO2max of 90 mL/min/kg (i.e., that of Greg Lemond, who is vehement critic of doping in cycling and a proponent of this approach to identifying physiologically-impossible performances…not coincidentally, this is also the value that Peter Keen reported for Chris Boardman’s VO2max at around the time of his 1996 Hour Record – more on this below);
2) A fractional utilization of VO2max of 90% (sustainable by many, including amateur cyclists such as myself – cf. subject 1 of
http://www.ncbi.nlm.nih.gov/pubmed/3403447);
3) A gross efficiency of 24% (again, a value found in a number of highly-efficient cyclists, including myself);
4) An energy yield of 21.13 kJ/L O2, as before.
With these as your starting points, you come up with a value of 6.84 W/kg (I’ll leave it readers to check my math if they wish), which is
still well over the limit of 6.0-6.2 W/kg that Dr. Tucker and others have argued is physiologically impossible. Indeed, Boardman himself was estimated by Peter Keen to have maintained a power of 6.40 W/kg during his record, based on careful measurement of his power vs. speed relationship on the track during his preparation for his attempt. That this figure is likely accurate is supported by fact that you arrive at essentially the same value based on his measured VO2max (i.e., 90 mL/min/kg) and gross efficiency (i.e., 22.6%) and assuming that he maintained 90% of his VO2max for the hour. (As an aside, Keen also estimated that Graham Obree maintained a steady-state VO2 – not VO2max – of 78 mL/min/kg during his prior record ride, which if his efficiency was comparable to Boardman’s means that his power output must also have been over 6.2 W/kg, something that Dr. Tucker has deemed “…simply not physiologically believable, and…strongly suggestive of doping”).
Thus, proponents of the proposed approach must either admit that they consider Boardman’s (and Obree’s) performance to be physiologically impossible without doping*, revise their figures and assumptions, and/or recognize that the approach they advocate is logically flawed. Clearly, to achieve such high, sustained power outputs requires exceptional physiology – however, by definition we are discussing the performance of extreme outliers, not any population norms. Furthermore, when attempting to quantify the upper limit of what is humanly possible any experimental variability in the various input parameters used in such calculations is not just additive, but multiplicative, in nature. Thus, no matter where you choose to “draw a line in the sand”, it is possible to mount a good argument that it should, or at least very well could, be just a little bit higher still.
*BTW, high altitude physiologists once calculated that it was simply impossible to climb Mt. Everest without supplemental O2 – then Reinhold Messner and Peter Habeler did it on May 8, 1978, and a number of other individuals have done it since.
The primary counterargument to the above perspective would seem to be that VO2max and gross efficiency have been reported by Lucia et al. to be inversely related, such that extremely high values of both would never occur in any single individual. As pointed out by others in this thread, however, there is no known physiological mechanism that would preclude some rare athlete from possessing both an extremely high VO2max and an extremely high gross efficiency (indeed, Boardman’s efficiency must be considered at least average, despite his far-above-average VO2max). Furthermore, the hypothesis that such an inverse relationship exists is primarily based upon a single study of only 11 subjects, the findings of which have been questioned by Jeukendrup et al. Even more strikingly, Dr. Tucker himself has previously argued that this inverse relationship is not truly of biological origin, but in essence simply reflects the fact to be a successful endurance athlete you must possess either a high VO2max
or a high movement efficiency or economy (cf.
http://www.ncbi.nlm.nih.gov/pubmed/15179181). At a minimum, then, it seems logically inconsistent to now argue strongly on the basis of this paper that having a high VO2max and a high gross efficiency are mutually exclusive.
Another counterargument that might be raised is that fatigue, either acute or cumulative, will always prevent cyclists from producing as much power in the middle of or at the end of mountainous stages compared to what they could do when “fresh”. While that may (or may not) be true, as far as I know there is no scientific data quantifying the magnitude of any such effect. Furthermore, any such data would merely speak to the typical, i.e., average, impact, whereas the issue at hand is what is possible in the
extreme. Thus, while one might be tempted to speculate on just how much impact fatigue might have (and as I mentioned previously, based on the data I have seen it appears that people routinely overestimate how important this is), speculating is all that one can do – and while such speculation can be interesting and entertaining, it does not qualify as science.