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.