Evolution of airplanes: a follow-up

I thank Prof. Bejan for graciously replying to my critique of his work in a previous post.  Permit me to follow up briefly here.

Bejan is correct that his earlier publications have cited Tennekes and the others.  He is also right that the earlier writers did not include land and aquatic locomotion in their analyses.  I was aware of Bejan's 2006 paper with Marden (which cites Tennekes only as a data source, not for analysis) but have not seen his 2000 book published by Cambridge U.P.  I thank Prof. Bejan for clarifying these points, although my original post did make many of them already.

Nonetheless, Bejan's 2014 paper makes a specific point about the Concorde case, which Tennekes has discussed at length, as I showed.  A citation in Bejan's 2014 paper in the context of the Concorde discussion would have been pertinent for readers.  As it stands, the 2014 paper makes it seem that the 'outlying' nature of the Concorde on the diagram is a new finding, when it is not.

Bejan's comment also offers a very important distinction, one that I strongly affirm.  A purely empirical analysis of observational data is a wholly different activity to first-principles modeling of such data, especially when the latter is then validated by empirical data.  Many scientists indeed fail to appreciate this distinction.  However, the quantitative predictive modeling in Bejan's 2014 paper seems to be based on basic aerodynamic scaling arguments.  The link with evolution seems at best a metaphor; it is not clear to me that the evolutionary component of Bejan's work is predictive in any quantitative sense.  I stand by my previous comments on interpreting data, particularly the pteranadon case.  Being an outlier on the graph does not prevent the pteranadon for being fit for its ecological niche in its day.  This would seem to limit the scope of the evolutionary metaphor when linked to specific aerodynamic scaling arguments.   My methodological criticisms of correlation analysis also remain valid.

The "evolution" of airplanes: DTLR is not impressed

About three weeks ago, the Journal of Applied Physics published a paper by Adrian Bejan and collaborators, “The evolution of airplanes” (Bejan et al., 2014).  Bejan is a named professor of mechanical engineering and materials science at Duke University, and author of well-known textbooks on heat transfer and thermodynamics.  His co-authors are a Boeing engineer and Duke alum, Jordan Charles, and a French civil engineering professor, Sylvie Lorente, who is also an adjunct Duke professor.  The publisher and Bejan’s university both issued news releases about the paper, and Bejan wrote about his work at The Conversation.  Indeed, the paper has received a lot of online press coverage.  The publisher’s own Inside Science news organ did include some critical comments in its coverage; additional critical comments were also posted at The Conversation in response to Bejan’s post.  The criticisms focus on the overall logic and philosophy of the paper.  I strongly sympathize with these criticisms.  Here, however, I will provide an additional perspective beyond those aired by others thus far.

The paper presents a number of simple analyses including basic aerodynamic scaling arguments, compared favorably with empirical data about aircraft geometry and performance.  A particularly vivid graph in the paper shows empirical data comparing the body mass and velocity of airplanes with those of running, flying, and swimming animals.  The diagram (the paper’s Fig. 2) is reproduced below.

The Ref. 1 in the caption is Bejan and Marden (2006).  The authors make the point that the Concorde is an outlier in this diagram, and further comment as follows.

Looking at the graphs of this paper, we see that there is an outlier, the Concorde, which was perhaps the most radical departure from the traditional swept wing commercial airplane.  The Concorde’s primary goal was to fly fast.  In chasing an “off the charts” speed rating the Concorde deviated from the evolutionary path traced by successful airplanes that preceded it.  It was small, had limited passenger capacity, long fuselage, short wingspan, massive engines, and poor fuel economy relative to the airplanes that preceded it.  Even when it was in service, the Concorde did not sell, and only 20 units were ever produced (whereas successful Boeing and Airbus models were produced by the thousands).  Eventually, due to lack of demand and safety concerns, the Concorde was retired in 2003.  (Bejan, et al., 2014, p. 6.)

Except for the remark about the "evolutionary path", all of this is factual.  However, many of these observations are not original.  In a book published originally in Dutch in 1992, Henk Tennekes (2009) presents the following graph (his Fig. 2) comparing cruise speed and body weight; in the graph he tacitly ties cruise speed to wing loading (weight divided by wing surface area).  Although it does not include running and swimming animals, the graph is otherwise similar in spirit to Bejan et al.’s graph.

Tennekes attributes this sort of analysis to the former DuPont company head, Crawford H. Greenewalt, and later scholars, including Colin J. Pennycuick.  Greenewalt’s original analysis was published in 1962; see Tennekes (2009) for citations and sources of data.  Tennekes also derives a simple scaling formula relating wing loading to cruise speed.  The equation 2 referred to in the caption is a version of this scaling formula.

What does Tennekes have to say about the Concorde?  In Chapter 1, he writes the following.

Wasn’t it supposed to fly at about 1,300 miles per hour?  How come it didn’t have higher wing loading and therefore smaller wings?  The answer is that the Concorde suffered from conflicting design specifications.  Small wings suffice at high speeds, but large wings are needed for taking off and landing at speeds comparable to those of other airliners.  If it could not match the landing speed of other airliners, the Concorde would have needed special, longer runways.  The plane’s predicament was that it has to drag oversize wings along when cruising in the stratosphere at twice the speed of sound.  It could compensate somewhat for that handicap by flying extremely high, at 58,000 feet.  Still, its fuel consumption was outrageous.  (Tennekes, p. 18)

And in the preface, Tennekes writes:

The Concorde went out with a bang.  A fiery crash near Paris on July 25, 2000, signaled the end of its career….In retrospect, the Concorde was a fluke, more so that anyone could have anticipated.  From an evolutionary perspective it was a mutant.  It was a very elegant mutant, but it was only marginally functional.  The fate of the Concorde inspired me to draw parallels between biological evolution and its technological counterpart wherever appropriate.  (Tennekes, p. xii)

Tennekes has more extensive comments on the Concorde in Chapter 6.  At his doctoral thesis defense, he argued “that supersonic airliners would be a step backward in the history of aviation” (p. 165).  He explains that with supersonic flight, the aircraft would have to generate shock waves in the air, which requires “a lot of energy” (p. 166).  On the same page,

Although Concorde passengers didn’t notice anything as their plane penetrated the sound barrier, the economic barrier was real enough.  If you want to exceed March 1, it will cost you 3 times as much as staying below the speed of sound.  For the aircraft industry, supersonic flight was indeed a step in the wrong direction.  Time and again, before aeronautical engineers started dabbling with supersonic flight, they had managed to reach higher speeds and lower costs.  The Concorde broke that trend.

I think it is unfortunate that both Bejan and Tennekes are tempted by the evolutionary metaphor; the critical comments I alluded to in my opening paragraph zero in precisely on this aspect of the work, as well as Bejan’s “constructal law” which he also purports to be at work here.  (I won’t bother to discuss that aspect further.)  Nonetheless the authors are correct that the empirical data and aerodynamic scaling relationships are consistent with each other, and possibly of limited use and interest.  They should not, however, be used to narrow one’s thinking.  For instance, in Tennekes’ plot, a number of animals show up as more severe ‘outliers’ than the Concorde.   Tennekes states that deviations from the trend line may be justified.  The pteranadon, for instance, was a soaring animal.  In prehistoric times there were no polar ice caps, reducing the atmospheric temperature gradient between the poles and equator, compared to today.  As a result there was less wind back then.  He presents other examples, including aircraft.  More generally, just because the bulk of the data fall along a trend line or curve, data away from that trend should not necessarily be deprecated.  Furthermore, correlation should not be confused with causation.  Bejan et al. (2014) offer no such nuances or caveats in their discussion.  Consequently they exaggerate the importance and implications of their findings.

It is also of great concern that Bejan et al. (2014) do not cite, either in the main paper or their supplemental information, Tennekes' work, particularly in the context of the Concorde discussion.  This is unusually poor scholarship.  (Bejan does cite Greenewalt and Pennycuik in an earlier paper, Bejan and Marden, 2006.)  Bejan et al. (2014) also make pointless, tautologous statements such as “Small or large, airplanes are evolving such that they look more and more like airplanes, not like birds” and then in the next paragraph, “Small or large, airplanes are evolving such that they look the same.”  Their abstract ends with the non-sequitur, “The view that emerges is that the evolution phenomenon is broader than biological evolution.  The evolution of technology, river basins, and animal design is one phenomenon, and it belongs in physics.”  Such statements are unjustified, unhelpful, and provide heat rather than light to the discussion.

A technical point should also be made:  at one point, Bejan et al. (2014) comment on their data analysis that “the correlation is statistically meaningful because its P-value is 0.0001, and it is less than 0.05 so that the null hypothesis can be rejected”.  This is a fairly naive and unimpressive statement.  The 0.05 threshold is conventional but totally arbitrary; moreover, the null hypothesis is one of no correlation at all, which is an incredibly low bar to establish a “meaningful” relationship between two variables.  Statistical significance does not necessarily convey practical significance.  For instance, it is possible to make a relationship with a negligibly small slope "statistically significant" if the sample size is large enough.  Reporting any kind of statistical inference (the p-value) on observational, non-randomly sampled data is itself questionable.  Moreover, as Loh (1987) noted, the correlation coefficient does not actually measure the closeness of the data to the best fit line.  The fitted equation and coefficient of determination, which the authors do provide, are more meaningful measures of the strength of the relationship between two variables.  The great statistician John Tukey (1954) stated that "most correlation coefficients should never be calculated."

To conclude, the publication of Bejan et al. (2014) in the Journal of Applied Physics is questionable.  The work should instead have been submitted for review at an aerodynamics or aerospace engineering journal.  I suspect it might not have impressed reviewers in that community.  Moreover, the authors should have cited Tennekes (2009) who provides a more detailed and nuanced discussion of the Concorde case, and they should increase the care with which they interpret correlations in empirical data.  I think the rhetoric about evolution is superfluous and distracting from the authors' primary technical findings, and should have been dispensed with.  Other critics have focused their views on this last point, so I've not dwelt on it here.

References

A. Bejan and J. H. Marden, 2006:  Unifying constructal theory for scale effects in running, swimming, and flying.  Journal of Experimental Biology, 209:  238-248.

A. Bejan, J. D. Charles, and S. Lorente, 2014:  The evolution of airplanes.  Journal of Applied Physics, 116:  044901 (6 pages).

Wei-Yin Loh, 1987:  Does the correlation coefficient really measure the degree of clustering around a line?  Journal of Educational Statistics, 12:  235-239.

Henk Tennekes, 2009:  The Simple Science of Flight:  From Insects to Jumbo Jets.  Revised and expanded edition.  MIT Press (Cambridge, MA).  

John Tukey, 1954:   Causation, regression, and path analysis.  In Statistics and Mathematics in Biology, edited by O. Kempthorne, T. A. Bancroft, J. W. Gowen, and J. L. Lush.  Iowa State College Press (Ames), 35-66.