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[sauropod@berkeley.edu: The volume of air in Diplodocus (erratum to Wedel 2005)]

Much goodness from Matt Wedel.  Enjoy!

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From: Matt Wedel <sauropod@berkeley.edu>
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Subject: The volume of air in Diplodocus (erratum to Wedel 2005)
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Could you please forward this to the DML?

Hi all,

You may find this relevant to the wading sauropod discussion.

Table 7.3 in my chapter in The Sauropods: Evolution and Paleobiology was 
misprinted. (To be fair, it was incorrectly formatted in the proofs and 
I didn't catch it.) The table lists all of the air reservoirs in the 
body of a living Diplodocus, their volumes, and how much mass they would 
replace in a volumetric mass estimate. The corrected table is available 
for download at the Padian lab webpage 

I've appended an excerpt from the paper to explain how I arrived at the 
values I used in the table. Please do e-mail me if you find any glaring 
errors, or if you have any questions about my work.



P.S. An excerpt from "Postcranial pneumaticity in sauropods and its 
implications for mass estimates" (Chapter 7 in the The Sauropods).

"...Consider the volume of air present inside a living _Diplodocus_. 
Practically all available mass estimates for _Diplodocus_ (Colbert, 
1962; Alexander, 1985; Paul, 1997; Henderson, 1999) are based on CM 84, 
the nearly complete skeleton described by Hatcher (1901). Uncorrected 
volumetric mass estimatesÂi.e, those that do not include lungs, air 
sacs, or diverticulaÂfor this individual range from 11,700 kg (Colbert, 
1962, as modified by Alexander, 1989:table 2.2) to 18,500 kg (Alexander, 
1985). Paul (1997) calculated a mass of 11,400 kg using the corrected 
SGs cited above, and Henderson (1999) estimated 14,912 kg, or 13,421 kg 
after deducting 10% to represent the lungs. For the purposes of this 
example, the volume of the animal is assumed to have been 15,000 liters. 
The estimated volumes of various air reservoirs and their effects on 
body mass are shown in Table 3.

Estimating the volume of air in the vertebral centra is the most 
straightforward. I used published measurements of centrum length and 
diameter from Hatcher (1901) and Gilmore (1932) and treated the centra 
as cylinders. The caudal series of CM 84 is incomplete, so I substituted 
the measurements for USNM 1065 from Gilmore (1932); comparison of the 
measurements of the elements common to both skeletons indicates that the 
two animals were roughly the same size. I multiplied the volumes 
obtained by 0.60, the mean ASP [air space proportion] of the sauropod 
vertebrae listed in Table 2, to obtain the total volume of air in the 

The volume of air in the neural spines is harder to calculate. The 
neural spines are complex shapes and are not easily approximated with 
simple geometric models. Furthermore, the fossae on the neural arches 
and spines only partially enclosed the diverticula that occupied them. 
Did the diverticula completely fill the space between adjacent laminae, 
did they bulge outward into the surrounding tissues, or did surrounding 
tissues bulge inward? In the complete absence of _in_ _vivo_ 
measurements of diverticulum volume in birds it is impossible to say. 
Based on the size of the neural spine relative to the centrum in most 
sauropods (see Fig. 2), it seems reasonable to assume that in the 
cervical vertebrae, at least as much air was present in the arch and 
spine as in the centrum, if not more. In the high-spined dorsal and 
sacral vertebrae (see Fig. 1), the volume of air in the neural arch and 
spine may have been twice that in the centrum. Finally, proximal caudal 
vertebrae have large neural spines but the size of the spines decreases 
rapidly in successive vertebrae. On average, the caudal neural spines of 
/Diplodocus/ may have contained only half as much air as their 
associated centra. These estimates are admittedly rough, but they are 
probably conservative and so they will suffice for this example.

As they developed, the intraosseous diverticula replaced bony tissue, 
and the density of that tissue must be taken into account in estimating 
how much mass was saved by pneumatization of the skeleton. In apneumatic 
sauropod vertebrae the internal structure is filled with cancellous bone 
and presumably supported red (erythropoeitic) bone marrow (Fig. 7). 
Distal caudal vertebrae of the theropod _Ceratosaurus_ have a large 
central chamber or centrocoel (Madsen and Welles, 2000:fig. 6). This 
cavity lacks large foramina that would connect it to the outside, so it 
cannot be pneumatic in origin. The medullary cavities of apneumatic 
avian and mammalian long bones are filled with adipose tissue that acts 
as lightweight packing material (Currey and Alexander, 1985), and the 
same may have been true of the centrocoels in _Ceratosaurus_ caudals. 
The presence of a similar marrow cavity in sauropod vertebrae prior to 
pneumatization cannot be ruled out, but to my knowledge no such cavities 
have been reported. In birds, the intraosseous diverticula erode the 
inner surfaces of the cortical bone in addition to replacing the 
cancellous bone (Bremer, 1940), so pneumatic bones tend to have thinner 
walls than apneumatic bones (Currey and Alexander, 1985; Cubo and 
Casinos, 2000). The tissues that may have been replaced by intraosseous 
diverticula have SGs that range from 0.9 for some fats and oils to 3.2 
for apatite (Schmidt-Nielsen, 1983:451 and table 11.5). For this 
example, I estimated that the tissue replaced by the intraosseous 
diverticula had an average SG of 1.5 (calculated from data presented in 
Cubo and Casinos, 2000), so air cavities that total 970 liters replace 
1455 kg of tissue. The extraskeletal diverticula, trachea, lungs, and 
air sacs did not replace bony tissue in the body. They are assumed to 
replace soft tissues (density of one gram/cm^3 ) in the solid model.

Extraskeletal diverticula include visceral, intermuscular, and 
subcutaneous diverticula. None of these leave traces that are likely to 
be fossilized. The bony skeleton places only two constraints on the 
extraskeletal diverticula. First, as previously discussed, the 
distribution of pneumatic bones in the skeleton limits the minimum 
extent of the diverticular system. Thus, we can infer that the vertebral 
diverticula in _Diplodocus_ must have extended from the axis to the 
nineteenth caudal vertebra (at least in USNM 1065), but the course and 
diameter of the diverticula are unknown. The second constraint imposed 
by the skeleton is that the canalis intertransversarius, if it existed, 
could not have been larger than the transverse foramina where it passed 
through them, although it may have been smaller or increased in diameter 
on either side. I am unaware of any studies in which the _in_ _vivo_ 
volume of the avian diverticular system is measured. This information 
vacuum prevents me from including a volume estimate for the diverticular 
system in Table 3.

To estimate the volume of the trachea, I used the allometric equations 
presented by Hinds and Calder (1971) for birds. The length equation, L = 
16.77M^0.394 , where L is the length of the trachea in cm and M is the 
mass of the animal in kg, yielded a predicted tracheal length of 6.8 
meters for a 12-ton animal. The cervical series of _Diplodocus_ CM 84 is 
6.7 meters long and the trachea may have been somewhat longer, and I 
judged the correspondence between the neck length and predicted tracheal 
length to be close enough to justify using the equations, especially for 
the coarse level of detail needed in this example. The volume equation, 
V = 3.724M^1.090 , yields a volume of 104 liters.

Finally, the volume of the lungs and air sacs must be taken into 
account. The lungs and air sacs are only constrained by the skeleton in 
that they must fit inside the ribcage and share space with the viscera. 
Based on measurements from caimans and large ungulates, Alexander (1989) 
subtracted eight percent from the volume of each of his models to 
account for lungs. Data presented by King (1966:table 3) indicate that 
the lungs and air sacs of birds may occupy 10-20% of the volume of the 
body. Hazlehurst and Rayner (1992) found an average SG of 0.73 in a 
sample of 25 birds from 12 unspecified species. On this basis, they 
concluded that the lungs and air sacs occupy about a quarter of the 
volume of the body in birds. However, some of the air in their birds 
probably resided in extraskeletal diverticula or pneumatic bones, so the 
volume of the lungs and air sacs may have been somewhat lower. In the 
interests of erring conservatively, I put the volume of the lungs and 
air sacs at 10% of the body volume.

The results of these calculations are necessarily tentative. The lungs 
and air sacs were probably not much smaller than estimated here, but 
they may have been much larger; the trachea could not have been much 
shorter but may have been much longer, or it may have been of different 
or irregular diameter (see McClelland, 1989a for tracheal convolutions 
and bulbous expansions in birds); the neural spines may have contained 
much more or somewhat less air; the ASP of _Diplodocus_ vertebrae may be 
higher or lower; and the tissue replaced by the intraosseous diverticula 
may have been more or less dense. The extraskeletal diverticula have not 
been accounted for at all, although they were certainly extensive in 
linear terms and were probably voluminous as well. Uncertainties aside, 
it seems likely that the vertebrae contained a large volume of air, 
possibly 1000 liters or more if the very tall neural spines are taken 
into account. This air mainly replaced dense bony tissue, so skeletal 
pneumatization may have lightened the animal by up to 10%Âand that does 
not include the extraskeletal diverticula or pulmonary air sacs. In the 
example presented here, the volume of air in the body of _Diplodocus_ is 
calculated to have replaced about 3000 kg of tissue that would have been 
present if the animal were solid. If the total volume of the body was 
15,000 liters and the density of the remaining tissue was one gram per 
cubic centimeter, the body mass would have been about 12 metric tons and 
the SG of the entire body would have been 0.8. This is lower than the 
SGs of squamates and crocodilians (0.81-0.89) found by Colbert (1962), 
higher than the SGs of birds (0.73) found by Hazlehurst and Rayner 
(1992), and about the same as the SGs (0.79-0.82) used by Henderson 
(2004) in his study of sauropod buoyancy. Note that the amount of mass 
saved by skeletal pneumatization is independent of the estimated volume 
of the body, but the proportion of mass saved is not. Thus if we start 
with AlexanderÂs (1985) 18,500 liter estimate for the body volume of 
_Diplodocus_, the mass saved is still 1455 kg, but this is only eight 
percent of the solid mass, not ten percent as in the previous example...."

- -- 
Mathew J. Wedel
University of California
Museum of Paleontology
1101 Valley Life Science Bldg.
Berkeley, CA 94720-4780
lab: (510) 642-1730
fax: (510) 642-1822
"I found that the more seriously you take writing,
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people moan about what a hard life it is being a 
writer.... My attitude is, if you hate it so much,
sod off and do something else!
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