1532 lines
147 KiB
XML
1532 lines
147 KiB
XML
<document ID-DOI="http://doi.org/10.5281/zenodo.3728372" ID-GBIF-Dataset="5a771e17-dcab-482b-b758-ce2c83a9c7a2" ID-GBIF-Taxon="162716714" ID-ISSN="1476-4687" ID-Zenodo-Dep="3728372" checkinTime="1584980053655" checkinUser="jeremy" docAuthor="Hutchinson, John R. & Garcia, Mariano" docDate="2002" docId="F42287A9FFD4D97A3B41A42C6573FE32" docLanguage="en" docName="HutchinsonGarcia2002.pdf.imd" docOrigin="Nature 415 (28)" docStyle="DocumentStyle{}" docTitle="Tyrannosaurus" docType="treatment" docVersion="11" lastPageId="4" lastPageNumber="1021" masterDocId="081BFFD1FFD5D97E3879A773606CFFC9" masterDocTitle="Tyrannosaurus was not a fast runner" masterLastPageNumber="1021" masterPageNumber="1018" pageId="1" pageNumber="1018" updateTime="1635470440257" updateUser="ExternalLinkService">
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<mods:mods xmlns:mods="http://www.loc.gov/mods/v3">
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<mods:titleInfo>
|
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<mods:title>Tyrannosaurus was not a fast runner</mods:title>
|
||
</mods:titleInfo>
|
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<mods:name type="personal">
|
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<mods:role>
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<mods:roleTerm>Author</mods:roleTerm>
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</mods:role>
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<mods:namePart>Hutchinson, John R.</mods:namePart>
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</mods:name>
|
||
<mods:name type="personal">
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<mods:role>
|
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<mods:roleTerm>Author</mods:roleTerm>
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</mods:role>
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<mods:namePart>Garcia, Mariano</mods:namePart>
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</mods:name>
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<mods:typeOfResource>text</mods:typeOfResource>
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<mods:relatedItem type="host">
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<mods:titleInfo>
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<mods:title>Nature</mods:title>
|
||
</mods:titleInfo>
|
||
<mods:part>
|
||
<mods:date>2002</mods:date>
|
||
<mods:detail type="pubDate">
|
||
<mods:number>2002-03-31</mods:number>
|
||
</mods:detail>
|
||
<mods:detail type="volume">
|
||
<mods:number>415</mods:number>
|
||
</mods:detail>
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||
<mods:detail type="issue">
|
||
<mods:number>28</mods:number>
|
||
</mods:detail>
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<mods:extent unit="page">
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<mods:start>1018</mods:start>
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<mods:end>1021</mods:end>
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</mods:extent>
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</mods:part>
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</mods:relatedItem>
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<mods:classification>journal article</mods:classification>
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<mods:identifier type="DOI">10.1038/4151018a</mods:identifier>
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<mods:identifier type="GBIF-Dataset">5a771e17-dcab-482b-b758-ce2c83a9c7a2</mods:identifier>
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<mods:identifier type="ISSN">1476-4687</mods:identifier>
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<mods:identifier type="Zenodo-Dep">3724611</mods:identifier>
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</mods:mods>
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<treatment ID-DOI="http://doi.org/10.5281/zenodo.3728372" ID-GBIF-Taxon="162716714" ID-Zenodo-Dep="3728372" LSID="urn:lsid:plazi:treatment:F42287A9FFD4D97A3B41A42C6573FE32" httpUri="http://treatment.plazi.org/id/F42287A9FFD4D97A3B41A42C6573FE32" lastPageId="4" lastPageNumber="1021" pageId="1" pageNumber="1018">
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<subSubSection lastPageId="2" lastPageNumber="1019" pageId="1" pageNumber="1018" type="nomenclature">
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<paragraph blockId="1.[800,1462,286,1107]" lastBlockId="2.[122,784,136,803]" lastPageId="2" lastPageNumber="1019" pageId="1" pageNumber="1018">
|
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Most assessments of running ability in large theropods are qualitative, based on analogies to walking elephants or running birds and hoofed mammals
|
||
<superScript attach="left" box="[1074,1108,914,927]" fontSize="6" pageId="1" pageNumber="1018">3,5–7</superScript>
|
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. Earlier quantitative assessments of the biomechanics of
|
||
<taxonomicName authority="Osborn, 1905" box="[1015,1158,946,967]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="1" pageNumber="1021" phylum="Chordata" rank="genus">
|
||
<emphasis box="[1015,1158,946,967]" italics="true" pageId="1" pageNumber="1018">Tyrannosaurus</emphasis>
|
||
</taxonomicName>
|
||
suggested that it had limited locomotor performance
|
||
<superScript attach="left" box="[1038,1087,970,983]" fontSize="6" pageId="1" pageNumber="1018">
|
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<bibRefCitation author="Alexander, R. McN" box="[1038,1043,970,983]" journalOrPublisher="Zool. J. Linn. Soc." pageId="1" pageNumber="1018" pagination="1 - 25" part="83" refId="ref3839" refString="1. Alexander, R. McN. Mechanics of posture and gait of some large dinosaurs. Zool. J. Linn. Soc. 83, 1 - 25 (1985)." title="Mechanics of posture and gait of some large dinosaurs" type="journal article" year="1985">1</bibRefCitation>
|
||
,
|
||
<bibRefCitation author="Alexander, R. McN" box="[1046,1055,970,983]" journalOrPublisher="Columbia Univ. Press, New York" pageId="1" pageNumber="1018" refId="ref3874" refString="2. Alexander, R. McN. Dynamics of Dinosaurs and Other Extinct Giants (Columbia Univ. Press, New York, 1989)." title="Dynamics of Dinosaurs and Other Extinct Giants" type="book" year="1989">2</bibRefCitation>
|
||
,
|
||
<bibRefCitation author="Farlow, J. O. & Smith, M. B. & Robinson, J. M." box="[1058,1067,970,983]" journalOrPublisher="J. Vert. Paleont." pageId="1" pageNumber="1018" pagination="713 - 725" part="15" refId="ref4108" refString="4. Farlow, J. O., Smith, M. B. & Robinson, J. M. Body mass, '' strength indicator' ', and cursorial potential of Tyrannosaurus rex. J. Vert. Paleont. 15, 713 - 725 (1995)." title="Body mass, '' strength indicator' ', and cursorial potential of Tyrannosaurus rex" type="journal article" year="1995">4</bibRefCitation>
|
||
,
|
||
<bibRefCitation author="Christiansen, P." box="[1069,1077,970,983]" journalOrPublisher="Gaia" pageId="1" pageNumber="1018" pagination="241 - 255" part="15" refId="ref4234" refString="8. Christiansen, P. Strength indicator values of theropod long bones, with comments on limb proportions and cursorial potential. Gaia 15, 241 - 255 (2000)" title="Strength indicator values of theropod long bones, with comments on limb proportions and cursorial potential" type="journal article" year="2000">8</bibRefCitation>
|
||
,
|
||
<bibRefCitation author="Farlow, J. O. & Gatesy, S. M. & Holtz, T. R. Jr & Hutchinson, J. R. & Robinson, J. M." box="[1079,1087,970,983]" journalOrPublisher="Am. Zool." pageId="1" pageNumber="1018" pagination="640 - 663" part="40" refId="ref4267" refString="9. Farlow, J. O., Gatesy, S. M., Holtz, T. R. Jr, Hutchinson, J. R. & Robinson, J. M. Theropod locomotion. Am. Zool. 40, 640 - 663 (2000)." title="Theropod locomotion" type="journal article" year="2000">9</bibRefCitation>
|
||
</superScript>
|
||
, but uncertainties about tyrannosaur anatomy, physiology, and behaviour have impeded resolution of this debate
|
||
<superScript attach="left" box="[907,930,1026,1039]" fontSize="6" pageId="1" pageNumber="1018">
|
||
<bibRefCitation author="Alexander, R. McN" box="[907,912,1026,1039]" journalOrPublisher="Zool. J. Linn. Soc." pageId="1" pageNumber="1018" pagination="1 - 25" part="83" refId="ref3839" refString="1. Alexander, R. McN. Mechanics of posture and gait of some large dinosaurs. Zool. J. Linn. Soc. 83, 1 - 25 (1985)." title="Mechanics of posture and gait of some large dinosaurs" type="journal article" year="1985">1</bibRefCitation>
|
||
–
|
||
<bibRefCitation author="Farlow, J. O. & Gatesy, S. M. & Holtz, T. R. Jr & Hutchinson, J. R. & Robinson, J. M." box="[922,930,1026,1039]" journalOrPublisher="Am. Zool." pageId="1" pageNumber="1018" pagination="640 - 663" part="40" refId="ref4267" refString="9. Farlow, J. O., Gatesy, S. M., Holtz, T. R. Jr, Hutchinson, J. R. & Robinson, J. M. Theropod locomotion. Am. Zool. 40, 640 - 663 (2000)." title="Theropod locomotion" type="journal article" year="2000">9</bibRefCitation>
|
||
</superScript>
|
||
. Fossilized footprints demonstrate that smaller theropod dinosaurs could run
|
||
<bibRefCitation author="Irby, G. V." box="[1042,1056,1054,1067]" journalOrPublisher="Mus. N. Arizona Bull." pageId="1" pageNumber="1018" pagination="109 - 112" part="60" refId="ref4335" refString="10. Irby, G. V. Paleoichnological evidence for running dinosaurs worldwide. Mus. N. Arizona Bull. 60, 109 - 112 (1999)." title="Paleoichnological evidence for running dinosaurs worldwide" type="journal article" year="1999">
|
||
<superScript attach="left" box="[1042,1056,1054,1067]" fontSize="6" pageId="1" pageNumber="1018">10</superScript>
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||
</bibRefCitation>
|
||
, but running tracks from large theropods are unknown
|
||
<superScript attach="left" box="[935,953,1082,1095]" fontSize="6" pageId="1" pageNumber="1018">
|
||
<bibRefCitation author="Paul, G. S." box="[935,943,1082,1095]" journalOrPublisher="Gaia" pageId="1" pageNumber="1018" pagination="257 - 270" part="15" refId="ref4204" refString="7. Paul, G. S. Limb design, function and running performance in ostrich-mimics and tyrannosaurs. Gaia 15, 257 - 270 (2000)." title="Limb design, function and running performance in ostrich-mimics and tyrannosaurs" type="journal article" year="2000">7</bibRefCitation>
|
||
,
|
||
<bibRefCitation author="Farlow, J. O. & Gatesy, S. M. & Holtz, T. R. Jr & Hutchinson, J. R. & Robinson, J. M." box="[945,953,1082,1095]" journalOrPublisher="Am. Zool." pageId="1" pageNumber="1018" pagination="640 - 663" part="40" refId="ref4267" refString="9. Farlow, J. O., Gatesy, S. M., Holtz, T. R. Jr, Hutchinson, J. R. & Robinson, J. M. Theropod locomotion. Am. Zool. 40, 640 - 663 (2000)." title="Theropod locomotion" type="journal article" year="2000">9</bibRefCitation>
|
||
</superScript>
|
||
. Bulky limbs and other analogies with elephants provide evidence that the enormous sauropod dinosaurs did not run
|
||
<superScript attach="left" box="[158,203,161,174]" fontSize="6" pageId="2" pageNumber="1019">
|
||
<bibRefCitation author="Alexander, R. McN" box="[158,164,161,174]" journalOrPublisher="Zool. J. Linn. Soc." pageId="2" pageNumber="1019" pagination="1 - 25" part="83" refId="ref3839" refString="1. Alexander, R. McN. Mechanics of posture and gait of some large dinosaurs. Zool. J. Linn. Soc. 83, 1 - 25 (1985)." title="Mechanics of posture and gait of some large dinosaurs" type="journal article" year="1985">1</bibRefCitation>
|
||
,
|
||
<bibRefCitation author="Alexander, R. McN" box="[166,175,161,174]" journalOrPublisher="Columbia Univ. Press, New York" pageId="2" pageNumber="1019" refId="ref3874" refString="2. Alexander, R. McN. Dynamics of Dinosaurs and Other Extinct Giants (Columbia Univ. Press, New York, 1989)." title="Dynamics of Dinosaurs and Other Extinct Giants" type="book" year="1989">2</bibRefCitation>
|
||
,
|
||
<bibRefCitation author="Bakker, R. T." box="[177,185,161,174]" journalOrPublisher="William Morrow, New York" pageId="2" pageNumber="1019" refId="ref4160" refString="5. Bakker, R. T. Dinosaur Heresies (William Morrow, New York, 1986)." title="Dinosaur Heresies" type="book" year="1986">5</bibRefCitation>
|
||
,
|
||
<bibRefCitation author="Coombs, W. P. Jr." box="[188,203,161,174]" journalOrPublisher="Palaeogeogr. Palaeoclimatol. Palaeoecol." pageId="2" pageNumber="1019" pagination="1 - 33" part="17" refId="ref4391" refString="11. Coombs, W. P. Jr. Sauropod habits and habitats. Palaeogeogr. Palaeoclimatol. Palaeoecol. 17, 1 - 33 (1975)." title="Sauropod habits and habitats" type="journal article" year="1975">11</bibRefCitation>
|
||
</superScript>
|
||
.
|
||
</paragraph>
|
||
</subSubSection>
|
||
<caption ID-DOI="http://doi.org/10.5281/zenodo.3961016" ID-Zenodo-Dep="3961016" httpUri="https://zenodo.org/record/3961016/files/figure.png" pageId="1" pageNumber="1018" startId="1.[800,853,1702,1721]" targetBox="[801,1455,1164,1662]" targetPageId="1">
|
||
<paragraph blockId="1.[800,1464,1702,2002]" pageId="1" pageNumber="1018">
|
||
Figure 1 Explanation of freebody diagram analysis of body segments.Skeletal illustration modified from ref. 6. The initial
|
||
<taxonomicName box="[1042,1153,1730,1749]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="1" pageNumber="1021" phylum="Chordata" rank="genus">Tyrannosaurus</taxonomicName>
|
||
model (
|
||
<taxonomicName authority="Osborn, 1905" box="[1214,1252,1730,1749]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="1" pageNumber="1021" phylum="Chordata" rank="species" species="rex">Trex</taxonomicName>
|
||
_1) is shown in right lateral view and (x, y)coordinate space,with the origin located at the toe joint. Pelvic pitch,hip, knee, ankle and toe joint angle definitions are shown (see Supplementary Information). One of the angles is redundant (four angles suffice). The ground reaction force (GRF) is vertical (typical for midstance
|
||
<superScript attach="left" box="[1024,1060,1837,1850]" fontSize="5" pageId="1" pageNumber="1018">
|
||
<bibRefCitation author="Roberts, T. J." box="[1024,1039,1837,1850]" journalOrPublisher="Bull. Mus. Comp. Zool." pageId="1" pageNumber="1018" pagination="283 - 295" part="156" refId="ref4421" refString="12. Roberts, T. J. Muscle force and stress during running in dogs and wild turkeys. Bull. Mus. Comp. Zool. 156, 283 - 295 (2001)." title="Muscle force and stress during running in dogs and wild turkeys" type="journal article" year="2001">12</bibRefCitation>
|
||
–
|
||
<bibRefCitation author="Roberts, T. R. & Chen, M. S. & Taylor, C. R." box="[1045,1060,1837,1850]" journalOrPublisher="J. Exp. Biol." pageId="1" pageNumber="1018" pagination="2753 - 2762" part="201" refId="ref4624" refString="14. Roberts, T. R., Chen, M. S. & Taylor, C. R. Energetics of bipedal running. II. Limb design and running mechanics. J. Exp. Biol. 201, 2753 - 2762 (1998)." title="Energetics of bipedal running. II. Limb design and running mechanics" type="journal article" year="1998">14</bibRefCitation>
|
||
</superScript>
|
||
) and acts at a distance R from the toe joints.The body segment weights (
|
||
<subScript attach="left" box="[951,957,1878,1891]" fontSize="5" pageId="1" pageNumber="1018">Wb</subScript>
|
||
,
|
||
<subScript attach="left" box="[982,986,1878,1891]" fontSize="5" pageId="1" pageNumber="1018">Wt</subScript>
|
||
,
|
||
<subScript attach="left" box="[1010,1016,1878,1891]" fontSize="5" pageId="1" pageNumber="1018">Ws</subScript>
|
||
and
|
||
<subScript attach="left" box="[1068,1078,1878,1891]" fontSize="5" pageId="1" pageNumber="1018">Wm</subScript>
|
||
for the trunk,thigh,shank and metatarsus) are also shown.A freebody diagram was used to calculate the internal moments about each joint. For example, about the knee joint (see inset), the moment that knee extensor muscles must generate (
|
||
<subScript attach="left" box="[934,940,1961,1974]" fontSize="5" pageId="1" pageNumber="1018">Mk</subScript>
|
||
) is equal to the ankle contact force (
|
||
<subScript attach="left" box="[1235,1241,1961,1974]" fontSize="5" pageId="1" pageNumber="1018">Fa</subScript>
|
||
) times its respective moment arm, plus the gravitational moment of the shank segment and the ankle moment (
|
||
<subScript attach="left" box="[1446,1452,1989,2002]" fontSize="5" pageId="1" pageNumber="1018">Ma</subScript>
|
||
).
|
||
</paragraph>
|
||
</caption>
|
||
<subSubSection lastPageId="4" lastPageNumber="1021" pageId="2" pageNumber="1019" type="description">
|
||
<paragraph blockId="2.[122,784,136,803]" pageId="2" pageNumber="1019">
|
||
For extant animals, our results (
|
||
<tableCitation box="[464,538,192,214]" captionStart="Table 1" captionStartId="2.[122,172,873,889]" captionTargetBox="[122,784,909,1793]" captionTargetPageId="2" captionText="Table 1 Muscle anatomical data entered in equation (1) to estimate T" httpUri="http://table.plazi.org/id/28F46637FFD7D97C3803A41A62B2FCB0" pageId="2" pageNumber="1019" tableUuid="28F46637FFD7D97C3803A41A62B2FCB0">Table 1</tableCitation>
|
||
) matched reality: alligators cannot run bipedally, whereas chickens are adept runners. Our dissected
|
||
<taxonomicName box="[220,304,248,270]" class="Reptilia" family="Alligatoridae" genus="Alligator" kingdom="Animalia" order="Crocodylia" pageId="2" pageNumber="1019" phylum="Chordata" rank="genus">
|
||
<emphasis box="[220,304,248,270]" italics="true" pageId="2" pageNumber="1019">Alligator</emphasis>
|
||
</taxonomicName>
|
||
only had about 3.6%
|
||
<emphasis box="[531,550,249,270]" italics="true" pageId="2" pageNumber="1019">m</emphasis>
|
||
<subScript attach="left" box="[550,583,258,273]" fontSize="6" pageId="2" pageNumber="1019">body</subScript>
|
||
per leg as extensor muscles, but we estimated that it would need about 7.7%
|
||
<emphasis box="[692,711,277,298]" italics="true" pageId="2" pageNumber="1019">m</emphasis>
|
||
<subScript attach="left" box="[711,744,286,301]" fontSize="6" pageId="2" pageNumber="1019">body</subScript>
|
||
per leg to run quickly on its hindlimbs. In contrast, our
|
||
<taxonomicName box="[624,686,304,326]" class="Aves" family="Phasianidae" genus="Gallus" kingdom="Animalia" order="Galliformes" pageId="2" pageNumber="1019" phylum="Chordata" rank="genus">
|
||
<emphasis box="[624,686,304,326]" italics="true" pageId="2" pageNumber="1019">Gallus</emphasis>
|
||
</taxonomicName>
|
||
specimen had about 8.8%
|
||
<emphasis box="[280,299,333,354]" italics="true" pageId="2" pageNumber="1019">m</emphasis>
|
||
<subScript attach="left" box="[300,333,341,356]" fontSize="6" pageId="2" pageNumber="1019">body</subScript>
|
||
per leg as extensor muscles, but it should only need about 4.7%
|
||
<emphasis box="[291,310,361,382]" italics="true" pageId="2" pageNumber="1019">m</emphasis>
|
||
<subScript attach="left" box="[311,344,369,384]" fontSize="6" pageId="2" pageNumber="1019">body</subScript>
|
||
per leg for fast running. Thus alligators have less than half the extensor muscle they would need to run fast, whereas chickens have almost twice the required amount of extensor muscle.
|
||
</paragraph>
|
||
<paragraph blockId="2.[122,784,136,803]" pageId="2" pageNumber="1019">
|
||
Well known scaling principles
|
||
<superScript attach="left" box="[445,484,468,481]" fontSize="6" pageId="2" pageNumber="1019">
|
||
<bibRefCitation author="Roberts, T. J." box="[445,460,468,481]" journalOrPublisher="Bull. Mus. Comp. Zool." pageId="2" pageNumber="1019" pagination="283 - 295" part="156" refId="ref4421" refString="12. Roberts, T. J. Muscle force and stress during running in dogs and wild turkeys. Bull. Mus. Comp. Zool. 156, 283 - 295 (2001)." title="Muscle force and stress during running in dogs and wild turkeys" type="journal article" year="2001">12</bibRefCitation>
|
||
–
|
||
<bibRefCitation author="Roberts, T. R. & Chen, M. S. & Taylor, C. R." box="[469,484,468,481]" journalOrPublisher="J. Exp. Biol." pageId="2" pageNumber="1019" pagination="2753 - 2762" part="201" refId="ref4624" refString="14. Roberts, T. R., Chen, M. S. & Taylor, C. R. Energetics of bipedal running. II. Limb design and running mechanics. J. Exp. Biol. 201, 2753 - 2762 (1998)." title="Energetics of bipedal running. II. Limb design and running mechanics" type="journal article" year="1998">14</bibRefCitation>
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||
</superScript>
|
||
predict that animals of larger body mass (
|
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<emphasis box="[250,269,500,521]" italics="true" pageId="2" pageNumber="1019">m</emphasis>
|
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<subScript attach="left" box="[269,302,509,524]" fontSize="6" pageId="2" pageNumber="1019">body</subScript>
|
||
) have more restricted locomotor performance because muscle force scales as (
|
||
<emphasis box="[457,476,528,549]" italics="true" pageId="2" pageNumber="1019">m</emphasis>
|
||
<subScript attach="left" box="[476,509,537,552]" fontSize="6" pageId="2" pageNumber="1019">body</subScript>
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)
|
||
<superScript attach="none" box="[519,547,522,537]" fontSize="6" pageId="2" pageNumber="1019">0.67</superScript>
|
||
, whereas muscle mass scales as (
|
||
<emphasis box="[217,236,556,577]" italics="true" pageId="2" pageNumber="1019">m</emphasis>
|
||
<subScript attach="left" box="[236,269,564,579]" fontSize="6" pageId="2" pageNumber="1019">body</subScript>
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)
|
||
<superScript attach="none" box="[279,299,549,564]" fontSize="6" pageId="2" pageNumber="1019">1.0</superScript>
|
||
. To be a fast runner, a
|
||
<taxonomicName authority="Osborn, 1905" box="[522,665,556,577]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="2" pageNumber="1019" phylum="Chordata" rank="genus">
|
||
<emphasis box="[522,665,556,577]" italics="true" pageId="2" pageNumber="1019">Tyrannosaurus</emphasis>
|
||
</taxonomicName>
|
||
would have needed enough extensor muscle mass to support itself. We calculated (
|
||
<figureCitation box="[184,241,611,633]" captionStart="Figure 1" captionStartId="1.[800,853,1702,1721]" captionTargetBox="[801,1455,1164,1662]" captionTargetId="graphics@1.[858,1251,1165,1428]" captionTargetPageId="1" captionText="Figure 1 Explanation of freebody diagram analysis of body segments.Skeletal illustration modified from ref. 6. The initial Tyrannosaurus model (Trex_1) is shown in right lateral view and (x, y)coordinate space,with the origin located at the toe joint. Pelvic pitch,hip, knee, ankle and toe joint angle definitions are shown (see Supplementary Information). One of the angles is redundant (four angles suffice). The ground reaction force (GRF) is vertical (typical for midstance12–14) and acts at a distance R from the toe joints.The body segment weights (Wb, Wt, Ws and Wm for the trunk,thigh,shank and metatarsus) are also shown.A freebody diagram was used to calculate the internal moments about each joint. For example, about the knee joint (see inset), the moment that knee extensor muscles must generate (Mk) is equal to the ankle contact force (Fa) times its respective moment arm, plus the gravitational moment of the shank segment and the ankle moment (Ma)." figureDoi="http://doi.org/10.5281/zenodo.3961016" httpUri="https://zenodo.org/record/3961016/files/figure.png" pageId="2" pageNumber="1019">Fig. 1</figureCitation>
|
||
; Methods) this mass for various animals to determine whether running would require too much muscle mass.
|
||
</paragraph>
|
||
<paragraph blockId="2.[122,784,136,803]" lastBlockId="2.[815,1477,136,1137]" pageId="2" pageNumber="1019">
|
||
Smaller theropods had lower estimates of minimum extensor muscle mass per leg (
|
||
<emphasis box="[333,348,696,717]" italics="true" pageId="2" pageNumber="1019">T</emphasis>
|
||
) than
|
||
<taxonomicName authority="Osborn, 1905" box="[414,557,696,717]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="2" pageNumber="1019" phylum="Chordata" rank="genus">
|
||
<emphasis box="[414,557,696,717]" italics="true" pageId="2" pageNumber="1019">Tyrannosaurus</emphasis>
|
||
</taxonomicName>
|
||
(
|
||
<tableCitation box="[570,642,694,716]" captionStart="Table 1" captionStartId="2.[122,172,873,889]" captionTargetBox="[122,784,909,1793]" captionTargetPageId="2" captionText="Table 1 Muscle anatomical data entered in equation (1) to estimate T" httpUri="http://table.plazi.org/id/28F46637FFD7D97C3803A41A62B2FCB0" pageId="2" pageNumber="1019" tableUuid="28F46637FFD7D97C3803A41A62B2FCB0">Table 1</tableCitation>
|
||
), and thus we expect they had a broader range of running performance. We initially calculated (
|
||
<figureCitation box="[319,380,750,772]" captionStart="Figure 2" captionStartId="2.[815,868,1870,1889]" captionTargetBox="[949,1333,1188,1833]" captionTargetId="figure@2.[949,1333,1188,1833]" captionTargetPageId="2" captionText="Figure 2 Limb orientation used for model Trex_1. The values of mi, the percentage of body mass as extensor muscle acting about each joint (muscle moment action shown as a red arrow) required to maintain static equilibrium at midstance during fast running are shown in red. Actual hindlimb bones were digitized from Tyrannosaurus specimen MOR 555 (Museum of the Rockies; Boseman, Montana)." figureDoi="http://doi.org/10.5281/zenodo.3961018" httpUri="https://zenodo.org/record/3961018/files/figure.png" pageId="2" pageNumber="1019">Fig. 2</figureCitation>
|
||
) that
|
||
<taxonomicName authority="Osborn, 1905" box="[443,586,751,772]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="2" pageNumber="1019" phylum="Chordata" rank="genus">
|
||
<emphasis box="[443,586,751,772]" italics="true" pageId="2" pageNumber="1019">Tyrannosaurus</emphasis>
|
||
</taxonomicName>
|
||
needed about 43% of its body mass as extensor muscles in each leg (86%
|
||
<emphasis box="[645,664,779,800]" italics="true" pageId="2" pageNumber="1019">m</emphasis>
|
||
<subScript attach="left" box="[664,697,788,803]" fontSize="6" pageId="2" pageNumber="1019">body</subScript>
|
||
for both legs) in order to run quickly. This high estimate of
|
||
<emphasis box="[1332,1347,138,159]" italics="true" pageId="2" pageNumber="1019">T</emphasis>
|
||
is surprising because our input parameter values were generously weighted towards a low
|
||
<emphasis box="[964,977,193,214]" italics="true" pageId="2" pageNumber="1019">T</emphasis>
|
||
. These findings suggest that
|
||
<taxonomicName authority="Osborn, 1905" box="[1270,1413,193,214]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="2" pageNumber="1019" phylum="Chordata" rank="genus">
|
||
<emphasis box="[1270,1413,193,214]" italics="true" pageId="2" pageNumber="1019">Tyrannosaurus</emphasis>
|
||
</taxonomicName>
|
||
could not run quickly.
|
||
</paragraph>
|
||
<paragraph blockId="2.[815,1477,136,1137]" pageId="2" pageNumber="1019">
|
||
A parameter study was then performed to assess the sensitivity of these findings to the values of the assumed parameters. Many of the parameters needed to model the limb mechanics of extinct dinosaurs are uncertain. To test how
|
||
<emphasis box="[1175,1190,333,354]" italics="true" pageId="2" pageNumber="1019">T</emphasis>
|
||
was affected by the initial parameters, we entered a range of values and observed how
|
||
<emphasis box="[1462,1477,361,382]" italics="true" pageId="2" pageNumber="1019">T</emphasis>
|
||
changed (
|
||
<tableCitation box="[910,988,387,409]" captionStart="Table 2" captionStartId="3.[107,157,791,807]" captionTargetBox="[107,768,827,1867]" captionTargetPageId="3" captionText="Table 2 Parameter sensitivity in Tyrannosaurus models" httpUri="http://table.plazi.org/id/28F46637FFD6D97D3812A464623AFCEE" pageId="2" pageNumber="1019" tableUuid="28F46637FFD6D97D3812A464623AFCEE">Table 2</tableCitation>
|
||
). Some unknown parameters, such as the muscle fibre pennation angle (v), were relatively unimportant: within a reasonable range of values (compared to extant taxa) they had little or no effect. Likewise, our approximations of the muscle moment arms (
|
||
<emphasis box="[879,888,500,521]" italics="true" pageId="2" pageNumber="1019">r</emphasis>
|
||
) were presumably reliable because we used rigorous muscle reconstructions that minimize speculation
|
||
<superScript attach="left" box="[1246,1278,524,537]" fontSize="6" pageId="2" pageNumber="1019">
|
||
<bibRefCitation author="Hutchinson, J. R. The" box="[1246,1260,524,537]" journalOrPublisher="Univ. California" pageId="2" pageNumber="1019" refId="ref4674" refString="15. Hutchinson, J. R. The Evolution of Hindlimb Anatomy and Function in Theropod Dinosaurs. PhD thesis, Univ. California (2001)." title="Evolution of Hindlimb Anatomy and Function in Theropod Dinosaurs" type="book" year="2001">15</bibRefCitation>
|
||
,
|
||
<bibRefCitation author="Carrano, M. T. & Hutchinson, J. R." box="[1263,1278,524,537]" journalOrPublisher="J. Morphol. (in the press)" pageId="2" pageNumber="1019" refId="ref4703" refString="16. Carrano, M. T. & Hutchinson, J. R. The pelvic and hind limb musculature of Tyrannosaurus rex (Dinosauria: Theropoda). J. Morphol. (in the press)" title="The pelvic and hind limb musculature of Tyrannosaurus rex (Dinosauria: Theropoda)" type="book" year="2001">16</bibRefCitation>
|
||
</superScript>
|
||
. Although
|
||
<emphasis box="[1398,1417,528,549]" italics="true" pageId="2" pageNumber="1019">m</emphasis>
|
||
<subScript attach="left" box="[1417,1450,537,552]" fontSize="6" pageId="2" pageNumber="1019">body</subScript>
|
||
is unknown for extinct taxa, our calculation expressed the required extensor muscle mass as a percentage of body mass (
|
||
<emphasis box="[1349,1364,584,605]" italics="true" pageId="2" pageNumber="1019">T</emphasis>
|
||
), factoring out
|
||
<emphasis box="[856,875,612,633]" italics="true" pageId="2" pageNumber="1019">m</emphasis>
|
||
<subScript attach="left" box="[875,908,620,635]" fontSize="6" pageId="2" pageNumber="1019">body</subScript>
|
||
(see Methods).
|
||
</paragraph>
|
||
<paragraph blockId="2.[815,1477,136,1137]" pageId="2" pageNumber="1019">
|
||
In contrast, uncertainty about other parameter values was quite important. The limb orientation used (
|
||
<figureCitation box="[1207,1268,666,688]" captionStart="Figure 1" captionStartId="1.[800,853,1702,1721]" captionTargetBox="[801,1455,1164,1662]" captionTargetId="graphics@1.[858,1251,1165,1428]" captionTargetPageId="1" captionText="Figure 1 Explanation of freebody diagram analysis of body segments.Skeletal illustration modified from ref. 6. The initial Tyrannosaurus model (Trex_1) is shown in right lateral view and (x, y)coordinate space,with the origin located at the toe joint. Pelvic pitch,hip, knee, ankle and toe joint angle definitions are shown (see Supplementary Information). One of the angles is redundant (four angles suffice). The ground reaction force (GRF) is vertical (typical for midstance12–14) and acts at a distance R from the toe joints.The body segment weights (Wb, Wt, Ws and Wm for the trunk,thigh,shank and metatarsus) are also shown.A freebody diagram was used to calculate the internal moments about each joint. For example, about the knee joint (see inset), the moment that knee extensor muscles must generate (Mk) is equal to the ankle contact force (Fa) times its respective moment arm, plus the gravitational moment of the shank segment and the ankle moment (Ma)." figureDoi="http://doi.org/10.5281/zenodo.3961016" httpUri="https://zenodo.org/record/3961016/files/figure.png" pageId="2" pageNumber="1019">Figs 1</figureCitation>
|
||
and
|
||
<figureCitation box="[1319,1332,666,688]" captionStart="Figure 2" captionStartId="2.[815,868,1870,1889]" captionTargetBox="[949,1333,1188,1833]" captionTargetId="figure@2.[949,1333,1188,1833]" captionTargetPageId="2" captionText="Figure 2 Limb orientation used for model Trex_1. The values of mi, the percentage of body mass as extensor muscle acting about each joint (muscle moment action shown as a red arrow) required to maintain static equilibrium at midstance during fast running are shown in red. Actual hindlimb bones were digitized from Tyrannosaurus specimen MOR 555 (Museum of the Rockies; Boseman, Montana)." figureDoi="http://doi.org/10.5281/zenodo.3961018" httpUri="https://zenodo.org/record/3961018/files/figure.png" pageId="2" pageNumber="1019">2</figureCitation>
|
||
) was a critical assumption because a more columnar (straightlegged) orientation (
|
||
<tableCitation box="[822,898,722,744]" captionStart="Table 2" captionStartId="3.[107,157,791,807]" captionTargetBox="[107,768,827,1867]" captionTargetPageId="3" captionText="Table 2 Parameter sensitivity in Tyrannosaurus models" httpUri="http://table.plazi.org/id/28F46637FFD6D97D3812A464623AFCEE" pageId="2" pageNumber="1019" tableUuid="28F46637FFD6D97D3812A464623AFCEE">Table 2</tableCitation>
|
||
) decreased the moment arms (
|
||
<emphasis box="[1216,1231,723,744]" italics="true" pageId="2" pageNumber="1019">R</emphasis>
|
||
) of the ground reaction force (GRF) and hence decreased
|
||
<emphasis box="[1152,1167,751,772]" italics="true" pageId="2" pageNumber="1019">T</emphasis>
|
||
compared to a more crouched (bentlegged) limb orientation. A more posterior position of the trunk centre of mass, shorter extensor muscle fibre lengths (
|
||
<emphasis box="[1449,1462,807,828]" italics="true" pageId="2" pageNumber="1019">L</emphasis>
|
||
), greater extensor muscle moment arms (
|
||
<emphasis box="[1205,1214,835,856]" italics="true" pageId="2" pageNumber="1019">r</emphasis>
|
||
), or a lower multiplier (
|
||
<emphasis box="[1451,1468,835,856]" italics="true" pageId="2" pageNumber="1019">G</emphasis>
|
||
) of the GRF would also decrease our estimated values of
|
||
<emphasis box="[1361,1376,863,884]" italics="true" pageId="2" pageNumber="1019">T</emphasis>
|
||
(
|
||
<tableCitation box="[1388,1465,862,884]" captionStart="Table 2" captionStartId="3.[107,157,791,807]" captionTargetBox="[107,768,827,1867]" captionTargetPageId="3" captionText="Table 2 Parameter sensitivity in Tyrannosaurus models" httpUri="http://table.plazi.org/id/28F46637FFD6D97D3812A464623AFCEE" pageId="2" pageNumber="1019" tableUuid="28F46637FFD6D97D3812A464623AFCEE">Table 2</tableCitation>
|
||
). The relative lengths of muscle fibres (
|
||
<collectionCode box="[1219,1232,891,912]" country="Netherlands" lsid="urn:lsid:biocol.org:col:15678" name="Nationaal Herbarium Nederland, Leiden University branch" pageId="2" pageNumber="1019" type="Herbarium">
|
||
<emphasis box="[1219,1232,891,912]" italics="true" pageId="2" pageNumber="1019">L</emphasis>
|
||
</collectionCode>
|
||
) vary widely in extant taxa
|
||
<superScript attach="left" box="[856,888,914,927]" fontSize="6" pageId="2" pageNumber="1019">
|
||
<bibRefCitation author="Alexander, R. McN. & Jayes, A. S. & Maloiy, G. M. O. & Wathuta, E. M." box="[856,871,914,927]" journalOrPublisher="J. Zool." pageId="2" pageNumber="1019" pagination="539 - 552" part="194" refId="ref4790" refString="17. Alexander, R. McN., Jayes, A. S., Maloiy, G. M. O. & Wathuta, E. M. Allometry of the leg muscles of mammals. J. Zool. 194, 539 - 552 (1981)." title="Allometry of the leg muscles of mammals" type="journal article" year="1981">17</bibRefCitation>
|
||
,
|
||
<bibRefCitation author="Bennett, M. B." box="[873,888,914,927]" journalOrPublisher="J. Zool." pageId="2" pageNumber="1019" pagination="435 - 443" part="238" refId="ref4842" refString="18. Bennett, M. B. Allometry of the leg muscles of birds. J. Zool. 238, 435 - 443 (1996)." title="Allometry of the leg muscles of birds" type="journal article" year="1996">18</bibRefCitation>
|
||
</superScript>
|
||
, so this parameter deserves more study. Admittedly, our calculations omitted other parameters that a more realistic model could include (Supplementary Information). However, most of these assumptions were conservative, leading to an underestimate of
|
||
<collectionCode box="[842,855,1030,1051]" name="Tavera, Department of Geology and Geophysics" pageId="2" pageNumber="1019">
|
||
<emphasis box="[842,855,1030,1051]" italics="true" pageId="2" pageNumber="1019">T</emphasis>
|
||
</collectionCode>
|
||
.
|
||
</paragraph>
|
||
<caption ID-Table-UUID="28F46637FFD7D97C3803A41A62B2FCB0" box="[122,734,873,889]" httpUri="http://table.plazi.org/id/28F46637FFD7D97C3803A41A62B2FCB0" pageId="2" pageNumber="1019" startId="2.[122,172,873,889]" targetBox="[122,784,909,1793]" targetIsTable="true" targetPageId="2">
|
||
<paragraph blockId="2.[122,734,873,889]" box="[122,734,873,889]" pageId="2" pageNumber="1019">Table 1 Muscle anatomical data entered in equation (1) to estimate T</paragraph>
|
||
</caption>
|
||
<paragraph pageId="2" pageNumber="1019">
|
||
<table box="[122,784,909,1793]" gridcols="4" gridrows="36" pageId="2" pageNumber="1019">
|
||
<tr box="[122,784,909,937]" gridrow="0" pageId="2" pageNumber="1019">
|
||
<th box="[122,784,909,937]" colspan="4" colspanRight="3" gridcol="0" gridrow="0" pageId="2" pageNumber="1019">Hip Knee Ankle Toe .............................................................................................................................................................................</th>
|
||
</tr>
|
||
<tr box="[122,784,944,958]" gridrow="1" pageId="2" pageNumber="1019" rowspan-1="1" rowspan-2="1" rowspan-3="1">
|
||
<th box="[122,384,944,958]" gridcol="0" gridrow="1" pageId="2" pageNumber="1019">
|
||
<taxonomicName box="[122,181,944,958]" class="Reptilia" family="Alligatoridae" genus="Alligator" kingdom="Animalia" order="Crocodylia" pageId="2" pageNumber="1019" phylum="Chordata" rank="genus">Alligator</taxonomicName>
|
||
</th>
|
||
</tr>
|
||
<tr box="[122,784,972,989]" gridrow="2" pageId="2" pageNumber="1019">
|
||
<th box="[122,384,972,989]" gridcol="0" gridrow="2" pageId="2" pageNumber="1019">
|
||
<subScript attach="left" box="[137,165,979,989]" fontSize="4" pageId="2" pageNumber="1019">Mmusc</subScript>
|
||
(N m) 16
|
||
</th>
|
||
<td box="[461,523,972,989]" gridcol="1" gridrow="2" pageId="2" pageNumber="1019">12</td>
|
||
<td box="[601,654,972,989]" gridcol="2" gridrow="2" pageId="2" pageNumber="1019">12</td>
|
||
<td box="[730,784,972,989]" gridcol="3" gridrow="2" pageId="2" pageNumber="1019">4.7</td>
|
||
</tr>
|
||
<tr box="[122,784,992,1008]" gridrow="3" pageId="2" pageNumber="1019">
|
||
<th box="[122,384,992,1008]" gridcol="0" gridrow="3" pageId="2" pageNumber="1019">L (m) 0.092</th>
|
||
<td box="[461,523,992,1008]" gridcol="1" gridrow="3" pageId="2" pageNumber="1019">–</td>
|
||
<td box="[601,654,992,1008]" gridcol="2" gridrow="3" pageId="2" pageNumber="1019">0.037</td>
|
||
<td box="[730,784,992,1008]" gridcol="3" gridrow="3" pageId="2" pageNumber="1019">0.0020</td>
|
||
</tr>
|
||
<tr box="[122,784,1013,1029]" gridrow="4" pageId="2" pageNumber="1019">
|
||
<th box="[122,384,1013,1029]" gridcol="0" gridrow="4" pageId="2" pageNumber="1019">v (8) 18</th>
|
||
<td box="[461,523,1013,1029]" gridcol="1" gridrow="4" pageId="2" pageNumber="1019">–</td>
|
||
<td box="[601,654,1013,1029]" gridcol="2" gridrow="4" pageId="2" pageNumber="1019">21</td>
|
||
<td box="[730,784,1013,1029]" gridcol="3" gridrow="4" pageId="2" pageNumber="1019">19</td>
|
||
</tr>
|
||
<tr box="[122,784,1034,1050]" gridrow="5" pageId="2" pageNumber="1019">
|
||
<th box="[122,384,1034,1050]" gridcol="0" gridrow="5" pageId="2" pageNumber="1019">r (m) 0.019</th>
|
||
<td box="[461,523,1034,1050]" gridcol="1" gridrow="5" pageId="2" pageNumber="1019">–</td>
|
||
<td box="[601,654,1034,1050]" gridcol="2" gridrow="5" pageId="2" pageNumber="1019">0.017</td>
|
||
<td box="[730,784,1034,1050]" gridcol="3" gridrow="5" pageId="2" pageNumber="1019">0.0050</td>
|
||
</tr>
|
||
<tr box="[122,784,1054,1071]" gridrow="6" pageId="2" pageNumber="1019">
|
||
<th box="[122,384,1054,1071]" gridcol="0" gridrow="6" pageId="2" pageNumber="1019">
|
||
<subScript attach="left" box="[136,140,1061,1071]" fontSize="4" pageId="2" pageNumber="1019">mi</subScript>
|
||
(%
|
||
<subScript attach="right" box="[180,205,1061,1071]" fontSize="4" pageId="2" pageNumber="1019">mbody</subScript>
|
||
) 4.9
|
||
</th>
|
||
<td box="[461,523,1054,1071]" gridcol="1" gridrow="6" pageId="2" pageNumber="1019">0</td>
|
||
<td box="[601,654,1054,1071]" gridcol="2" gridrow="6" pageId="2" pageNumber="1019">1.7</td>
|
||
<td box="[730,784,1054,1071]" gridcol="3" gridrow="6" pageId="2" pageNumber="1019">1.1</td>
|
||
</tr>
|
||
<tr box="[122,784,1075,1092]" gridrow="7" pageId="2" pageNumber="1019" rowspan-1="1" rowspan-2="1">
|
||
<th box="[122,384,1075,1092]" gridcol="0" gridrow="7" pageId="2" pageNumber="1019">T (% mbody)</th>
|
||
<td box="[730,784,1075,1092]" gridcol="3" gridrow="7" pageId="2" pageNumber="1019">7.7</td>
|
||
</tr>
|
||
<tr box="[122,784,1117,1131]" gridrow="8" pageId="2" pageNumber="1019">
|
||
<th box="[122,784,1117,1131]" colspan="4" colspanRight="3" gridcol="0" gridrow="8" pageId="2" pageNumber="1019">
|
||
<taxonomicName box="[122,168,1117,1131]" class="Aves" family="Phasianidae" genus="Gallus" kingdom="Animalia" order="Galliformes" pageId="2" pageNumber="1019" phylum="Chordata" rank="genus">Gallus</taxonomicName>
|
||
</th>
|
||
</tr>
|
||
<tr box="[122,784,1144,1161]" gridrow="9" pageId="2" pageNumber="1019">
|
||
<th box="[122,384,1144,1161]" gridcol="0" gridrow="9" pageId="2" pageNumber="1019">Mmusc (N m) 4.0</th>
|
||
<td box="[461,523,1144,1161]" gridcol="1" gridrow="9" pageId="2" pageNumber="1019">0.30</td>
|
||
<td box="[601,654,1144,1161]" gridcol="2" gridrow="9" pageId="2" pageNumber="1019">4.7</td>
|
||
<td box="[730,784,1144,1161]" gridcol="3" gridrow="9" pageId="2" pageNumber="1019">2.2</td>
|
||
</tr>
|
||
<tr box="[122,784,1165,1181]" gridrow="10" pageId="2" pageNumber="1019">
|
||
<th box="[122,384,1165,1181]" gridcol="0" gridrow="10" pageId="2" pageNumber="1019">L (m) 0.085</th>
|
||
<td box="[461,523,1165,1181]" gridcol="1" gridrow="10" pageId="2" pageNumber="1019">0.051</td>
|
||
<td box="[601,654,1165,1181]" gridcol="2" gridrow="10" pageId="2" pageNumber="1019">0.026</td>
|
||
<td box="[730,784,1165,1181]" gridcol="3" gridrow="10" pageId="2" pageNumber="1019">0.026</td>
|
||
</tr>
|
||
<tr box="[122,784,1186,1202]" gridrow="11" pageId="2" pageNumber="1019">
|
||
<th box="[122,384,1186,1202]" gridcol="0" gridrow="11" pageId="2" pageNumber="1019">v (8) 0</th>
|
||
<td box="[461,523,1186,1202]" gridcol="1" gridrow="11" pageId="2" pageNumber="1019">25</td>
|
||
<td box="[601,654,1186,1202]" gridcol="2" gridrow="11" pageId="2" pageNumber="1019">23</td>
|
||
<td box="[730,784,1186,1202]" gridcol="3" gridrow="11" pageId="2" pageNumber="1019">22</td>
|
||
</tr>
|
||
<tr box="[122,784,1206,1222]" gridrow="12" pageId="2" pageNumber="1019">
|
||
<th box="[122,384,1206,1222]" gridcol="0" gridrow="12" pageId="2" pageNumber="1019">r (m) 0.038</th>
|
||
<td box="[461,523,1206,1222]" gridcol="1" gridrow="12" pageId="2" pageNumber="1019">0.026</td>
|
||
<td box="[601,654,1206,1222]" gridcol="2" gridrow="12" pageId="2" pageNumber="1019">0.010</td>
|
||
<td box="[730,784,1206,1222]" gridcol="3" gridrow="12" pageId="2" pageNumber="1019">0.0050</td>
|
||
</tr>
|
||
<tr box="[122,784,1227,1244]" gridrow="13" pageId="2" pageNumber="1019" rowspan-3="1">
|
||
<th box="[122,384,1227,1244]" gridcol="0" gridrow="13" pageId="2" pageNumber="1019">mi (% mbody) 0.08</th>
|
||
<td box="[461,523,1227,1244]" gridcol="1" gridrow="13" pageId="2" pageNumber="1019">2.0</td>
|
||
<td box="[601,654,1227,1244]" gridcol="2" gridrow="13" pageId="2" pageNumber="1019">2.0</td>
|
||
</tr>
|
||
<tr box="[122,784,1247,1264]" gridrow="14" pageId="2" pageNumber="1019" rowspan-1="1" rowspan-2="1">
|
||
<th box="[122,384,1247,1264]" gridcol="0" gridrow="14" pageId="2" pageNumber="1019">T (% mbody)</th>
|
||
<td box="[730,784,1247,1264]" gridcol="3" gridrow="14" pageId="2" pageNumber="1019">4.7</td>
|
||
</tr>
|
||
<tr box="[122,784,1289,1303]" gridrow="15" pageId="2" pageNumber="1019">
|
||
<th box="[122,784,1289,1303]" colspan="4" colspanRight="3" gridcol="0" gridrow="15" pageId="2" pageNumber="1019">
|
||
<taxonomicName authority="Cope, 1889" box="[122,212,1289,1303]" class="Reptilia" family="Coelophysidae" genus="Coelophysis" kingdom="Animalia" order="Dinosauria" pageId="2" pageNumber="1019" phylum="Chordata" rank="genus">Coelophysis</taxonomicName>
|
||
</th>
|
||
</tr>
|
||
<tr box="[122,784,1317,1334]" gridrow="16" pageId="2" pageNumber="1019">
|
||
<th box="[122,384,1317,1334]" gridcol="0" gridrow="16" pageId="2" pageNumber="1019">
|
||
<subScript attach="left" box="[137,165,1324,1334]" fontSize="4" pageId="2" pageNumber="1019">Mmusc</subScript>
|
||
(N m) 45
|
||
</th>
|
||
<td box="[461,523,1317,1334]" gridcol="1" gridrow="16" pageId="2" pageNumber="1019">14</td>
|
||
<td box="[601,654,1317,1334]" gridcol="2" gridrow="16" pageId="2" pageNumber="1019">56</td>
|
||
<td box="[730,784,1317,1334]" gridcol="3" gridrow="16" pageId="2" pageNumber="1019">44</td>
|
||
</tr>
|
||
<tr box="[122,784,1338,1354]" gridrow="17" pageId="2" pageNumber="1019">
|
||
<th box="[122,384,1338,1354]" gridcol="0" gridrow="17" pageId="2" pageNumber="1019">L (m) 0.17</th>
|
||
<td box="[461,523,1338,1354]" gridcol="1" gridrow="17" pageId="2" pageNumber="1019">0.097</td>
|
||
<td box="[601,654,1338,1354]" gridcol="2" gridrow="17" pageId="2" pageNumber="1019">0.065</td>
|
||
<td box="[730,784,1338,1354]" gridcol="3" gridrow="17" pageId="2" pageNumber="1019">0.037</td>
|
||
</tr>
|
||
<tr box="[122,784,1358,1374]" gridrow="18" pageId="2" pageNumber="1019">
|
||
<th box="[122,384,1358,1374]" gridcol="0" gridrow="18" pageId="2" pageNumber="1019">v (8) 9.0</th>
|
||
<td box="[461,523,1358,1374]" gridcol="1" gridrow="18" pageId="2" pageNumber="1019">21</td>
|
||
<td box="[601,654,1358,1374]" gridcol="2" gridrow="18" pageId="2" pageNumber="1019">22</td>
|
||
<td box="[730,784,1358,1374]" gridcol="3" gridrow="18" pageId="2" pageNumber="1019">21</td>
|
||
</tr>
|
||
<tr box="[122,784,1379,1395]" gridrow="19" pageId="2" pageNumber="1019">
|
||
<th box="[122,384,1379,1395]" gridcol="0" gridrow="19" pageId="2" pageNumber="1019">r (m) 0.080</th>
|
||
<td box="[461,523,1379,1395]" gridcol="1" gridrow="19" pageId="2" pageNumber="1019">0.028</td>
|
||
<td box="[601,654,1379,1395]" gridcol="2" gridrow="19" pageId="2" pageNumber="1019">0.014</td>
|
||
<td box="[730,784,1379,1395]" gridcol="3" gridrow="19" pageId="2" pageNumber="1019">0.0060</td>
|
||
</tr>
|
||
<tr box="[122,784,1400,1416]" gridrow="20" pageId="2" pageNumber="1019">
|
||
<th box="[122,384,1400,1416]" gridcol="0" gridrow="20" pageId="2" pageNumber="1019">mi (% mbody) 1.4</th>
|
||
<td box="[461,523,1400,1416]" gridcol="1" gridrow="20" pageId="2" pageNumber="1019">0.73</td>
|
||
<td box="[601,654,1400,1416]" gridcol="2" gridrow="20" pageId="2" pageNumber="1019">4.0</td>
|
||
<td box="[730,784,1400,1416]" gridcol="3" gridrow="20" pageId="2" pageNumber="1019">4.1</td>
|
||
</tr>
|
||
<tr box="[122,784,1420,1437]" gridrow="21" pageId="2" pageNumber="1019" rowspan-1="1" rowspan-2="1">
|
||
<th box="[122,384,1420,1437]" gridcol="0" gridrow="21" pageId="2" pageNumber="1019">T (% mbody)</th>
|
||
<td box="[730,784,1420,1437]" gridcol="3" gridrow="21" pageId="2" pageNumber="1019">10</td>
|
||
</tr>
|
||
<tr box="[122,784,1461,1477]" gridrow="22" pageId="2" pageNumber="1019">
|
||
<th box="[122,784,1461,1477]" colspan="4" colspanRight="3" gridcol="0" gridrow="22" pageId="2" pageNumber="1019">
|
||
Small
|
||
<taxonomicName box="[167,255,1461,1477]" class="Reptilia" family="Tyrannosauridae" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="2" pageNumber="1021" phylum="Chordata" rank="family">tyrannosaur</taxonomicName>
|
||
</th>
|
||
</tr>
|
||
<tr box="[122,784,1490,1507]" gridrow="23" pageId="2" pageNumber="1019">
|
||
<th box="[122,384,1490,1507]" gridcol="0" gridrow="23" pageId="2" pageNumber="1019">
|
||
<subScript attach="left" box="[137,165,1497,1507]" fontSize="4" pageId="2" pageNumber="1019">Mmusc</subScript>
|
||
(N m) 570
|
||
</th>
|
||
<td box="[461,523,1490,1507]" gridcol="1" gridrow="23" pageId="2" pageNumber="1019">180</td>
|
||
<td box="[601,654,1490,1507]" gridcol="2" gridrow="23" pageId="2" pageNumber="1019">580</td>
|
||
<td box="[730,784,1490,1507]" gridcol="3" gridrow="23" pageId="2" pageNumber="1019">390</td>
|
||
</tr>
|
||
<tr box="[122,784,1510,1526]" gridrow="24" pageId="2" pageNumber="1019">
|
||
<th box="[122,384,1510,1526]" gridcol="0" gridrow="24" pageId="2" pageNumber="1019">L (m) 0.40</th>
|
||
<td box="[461,523,1510,1526]" gridcol="1" gridrow="24" pageId="2" pageNumber="1019">0.19</td>
|
||
<td box="[601,654,1510,1526]" gridcol="2" gridrow="24" pageId="2" pageNumber="1019">0.18</td>
|
||
<td box="[730,784,1510,1526]" gridcol="3" gridrow="24" pageId="2" pageNumber="1019">0.062</td>
|
||
</tr>
|
||
<tr box="[122,784,1531,1547]" gridrow="25" pageId="2" pageNumber="1019">
|
||
<th box="[122,384,1531,1547]" gridcol="0" gridrow="25" pageId="2" pageNumber="1019">v (8) 9.0</th>
|
||
<td box="[461,523,1531,1547]" gridcol="1" gridrow="25" pageId="2" pageNumber="1019">21</td>
|
||
<td box="[601,654,1531,1547]" gridcol="2" gridrow="25" pageId="2" pageNumber="1019">22</td>
|
||
<td box="[730,784,1531,1547]" gridcol="3" gridrow="25" pageId="2" pageNumber="1019">21</td>
|
||
</tr>
|
||
<tr box="[122,784,1552,1568]" gridrow="26" pageId="2" pageNumber="1019">
|
||
<th box="[122,384,1552,1568]" gridcol="0" gridrow="26" pageId="2" pageNumber="1019">r (m) 0.14</th>
|
||
<td box="[461,523,1552,1568]" gridcol="1" gridrow="26" pageId="2" pageNumber="1019">0.057</td>
|
||
<td box="[601,654,1552,1568]" gridcol="2" gridrow="26" pageId="2" pageNumber="1019">0.025</td>
|
||
<td box="[730,784,1552,1568]" gridcol="3" gridrow="26" pageId="2" pageNumber="1019">0.020</td>
|
||
</tr>
|
||
<tr box="[122,784,1572,1589]" gridrow="27" pageId="2" pageNumber="1019">
|
||
<th box="[122,384,1572,1589]" gridcol="0" gridrow="27" pageId="2" pageNumber="1019">mi (% mbody) 4.2</th>
|
||
<td box="[461,523,1572,1589]" gridcol="1" gridrow="27" pageId="2" pageNumber="1019">1.6</td>
|
||
<td box="[601,654,1572,1589]" gridcol="2" gridrow="27" pageId="2" pageNumber="1019">11.4</td>
|
||
<td box="[730,784,1572,1589]" gridcol="3" gridrow="27" pageId="2" pageNumber="1019">3.3</td>
|
||
</tr>
|
||
<tr box="[122,784,1593,1610]" gridrow="28" pageId="2" pageNumber="1019" rowspan-1="1" rowspan-2="1">
|
||
<th box="[122,384,1593,1610]" gridcol="0" gridrow="28" pageId="2" pageNumber="1019">T (% mbody)</th>
|
||
<td box="[730,784,1593,1610]" gridcol="3" gridrow="28" pageId="2" pageNumber="1019">21</td>
|
||
</tr>
|
||
<tr box="[122,784,1634,1650]" gridrow="29" pageId="2" pageNumber="1019">
|
||
<th box="[122,784,1634,1650]" colspan="4" colspanRight="3" gridcol="0" gridrow="29" pageId="2" pageNumber="1019">
|
||
<taxonomicName box="[122,232,1635,1649]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="2" pageNumber="1021" phylum="Chordata" rank="genus">Tyrannosaurus</taxonomicName>
|
||
(
|
||
<taxonomicName authority="Osborn, 1905" box="[240,275,1634,1650]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="2" pageNumber="1021" phylum="Chordata" rank="species" species="rex">Trex</taxonomicName>
|
||
_1 best guess)
|
||
</th>
|
||
</tr>
|
||
<tr box="[122,784,1663,1679]" gridrow="30" pageId="2" pageNumber="1019">
|
||
<th box="[122,384,1663,1679]" gridcol="0" gridrow="30" pageId="2" pageNumber="1019">
|
||
<subScript attach="left" box="[137,165,1669,1679]" fontSize="4" pageId="2" pageNumber="1019">Mmusc</subScript>
|
||
(N m) 75,000
|
||
</th>
|
||
<td box="[461,523,1663,1679]" gridcol="1" gridrow="30" pageId="2" pageNumber="1019">24,000</td>
|
||
<td box="[601,654,1663,1679]" gridcol="2" gridrow="30" pageId="2" pageNumber="1019">66,000</td>
|
||
<td box="[730,784,1663,1679]" gridcol="3" gridrow="30" pageId="2" pageNumber="1019">49,000</td>
|
||
</tr>
|
||
<tr box="[122,784,1683,1699]" gridrow="31" pageId="2" pageNumber="1019">
|
||
<th box="[122,384,1683,1699]" gridcol="0" gridrow="31" pageId="2" pageNumber="1019">L (m) 1.2</th>
|
||
<td box="[461,523,1683,1699]" gridcol="1" gridrow="31" pageId="2" pageNumber="1019">0.52</td>
|
||
<td box="[601,654,1683,1699]" gridcol="2" gridrow="31" pageId="2" pageNumber="1019">0.39</td>
|
||
<td box="[730,784,1683,1699]" gridcol="3" gridrow="31" pageId="2" pageNumber="1019">0.19</td>
|
||
</tr>
|
||
<tr box="[122,784,1704,1720]" gridrow="32" pageId="2" pageNumber="1019">
|
||
<th box="[122,384,1704,1720]" gridcol="0" gridrow="32" pageId="2" pageNumber="1019">v (8) 9.0</th>
|
||
<td box="[461,523,1704,1720]" gridcol="1" gridrow="32" pageId="2" pageNumber="1019">21</td>
|
||
<td box="[601,654,1704,1720]" gridcol="2" gridrow="32" pageId="2" pageNumber="1019">22</td>
|
||
<td box="[730,784,1704,1720]" gridcol="3" gridrow="32" pageId="2" pageNumber="1019">21</td>
|
||
</tr>
|
||
<tr box="[122,784,1724,1740]" gridrow="33" pageId="2" pageNumber="1019">
|
||
<th box="[122,384,1724,1740]" gridcol="0" gridrow="33" pageId="2" pageNumber="1019">r (m) 0.37</th>
|
||
<td box="[461,523,1724,1740]" gridcol="1" gridrow="33" pageId="2" pageNumber="1019">0.22</td>
|
||
<td box="[601,654,1724,1740]" gridcol="2" gridrow="33" pageId="2" pageNumber="1019">0.11</td>
|
||
<td box="[730,784,1724,1740]" gridcol="3" gridrow="33" pageId="2" pageNumber="1019">0.065</td>
|
||
</tr>
|
||
<tr box="[122,784,1745,1762]" gridrow="34" pageId="2" pageNumber="1019">
|
||
<th box="[122,384,1745,1762]" gridcol="0" gridrow="34" pageId="2" pageNumber="1019">
|
||
<subScript attach="left" box="[136,140,1752,1762]" fontSize="4" pageId="2" pageNumber="1019">mi</subScript>
|
||
(%
|
||
<subScript attach="right" box="[180,205,1752,1762]" fontSize="4" pageId="2" pageNumber="1019">mbody</subScript>
|
||
) 15
|
||
</th>
|
||
<td box="[461,523,1745,1762]" gridcol="1" gridrow="34" pageId="2" pageNumber="1019">3.6</td>
|
||
<td box="[601,654,1745,1762]" gridcol="2" gridrow="34" pageId="2" pageNumber="1019">15</td>
|
||
<td box="[730,784,1745,1762]" gridcol="3" gridrow="34" pageId="2" pageNumber="1019">9.0</td>
|
||
</tr>
|
||
<tr box="[122,784,1766,1793]" gridrow="35" pageId="2" pageNumber="1019">
|
||
<th box="[122,784,1766,1793]" colspan="4" colspanRight="3" gridcol="0" gridrow="35" pageId="2" pageNumber="1019">
|
||
T (%
|
||
<subScript attach="left" box="[172,197,1772,1782]" fontSize="4" pageId="2" pageNumber="1019">mbody</subScript>
|
||
) 43 .............................................................................................................................................................................
|
||
</th>
|
||
</tr>
|
||
</table>
|
||
</paragraph>
|
||
<paragraph blockId="2.[815,1477,136,1137]" lastBlockId="3.[107,769,136,717]" lastPageId="3" lastPageNumber="1020" pageId="2" pageNumber="1019">
|
||
We asked how much hindlimb muscle mass would be unreasonable for an extinct theropod dinosaur: in extant tetrapods, 50% or less of
|
||
<emphasis box="[884,903,1114,1135]" italics="true" pageId="2" pageNumber="1019">m</emphasis>
|
||
<subScript attach="left" box="[904,937,1122,1137]" fontSize="6" pageId="2" pageNumber="1019">body</subScript>
|
||
is typically composed of muscle
|
||
<bibRefCitation author="Grand, T. I." box="[1264,1278,1110,1123]" journalOrPublisher="Am. J. Phys. Anthropol." pageId="2" pageNumber="1019" pagination="211 - 240" part="47" refId="ref4871" refString="19. Grand, T. I. Body weight: its relation to tissue composition, segment distribution, and motor function. II. Interspecific comparisons. Am. J. Phys. Anthropol. 47, 211 - 240 (1977)." title="Body weight: its relation to tissue composition, segment distribution, and motor function. II. Interspecific comparisons" type="journal article" year="1977">
|
||
<superScript attach="left" box="[1264,1278,1110,1123]" fontSize="6" pageId="2" pageNumber="1019">19</superScript>
|
||
</bibRefCitation>
|
||
. This proportion is independent of
|
||
<emphasis box="[268,287,138,159]" italics="true" pageId="3" pageNumber="1020">m</emphasis>
|
||
<subScript attach="left" box="[288,321,146,161]" fontSize="6" pageId="3" pageNumber="1020">body</subScript>
|
||
(ref. 20). Of that 50%, a total of 5–40% of
|
||
<emphasis box="[107,126,165,186]" italics="true" pageId="3" pageNumber="1020">m</emphasis>
|
||
<subScript attach="left" box="[126,159,174,189]" fontSize="6" pageId="3" pageNumber="1020">body</subScript>
|
||
is allocated to limb extensor muscles
|
||
<superScript attach="left" box="[524,580,161,174]" fontSize="6" pageId="3" pageNumber="1020">15,17–19</superScript>
|
||
. Considering these data, the simplest inference is that if
|
||
<collectionCode box="[464,479,193,214]" name="Tavera, Department of Geology and Geophysics" pageId="3" pageNumber="1020">
|
||
<emphasis box="[464,479,193,214]" italics="true" pageId="3" pageNumber="1020">T</emphasis>
|
||
</collectionCode>
|
||
is greater than 25%
|
||
<emphasis box="[677,696,193,214]" italics="true" pageId="3" pageNumber="1020">m</emphasis>
|
||
<subScript attach="left" box="[697,730,202,217]" fontSize="6" pageId="3" pageNumber="1020">body</subScript>
|
||
per leg as limb extensors (that is, more than 50%
|
||
<emphasis box="[559,578,221,242]" italics="true" pageId="3" pageNumber="1020">m</emphasis>
|
||
<subScript attach="left" box="[578,611,230,245]" fontSize="6" pageId="3" pageNumber="1020">body</subScript>
|
||
), a biped could not run quickly (if at all), because it would not have enough muscle to exert the necessary forces.
|
||
</paragraph>
|
||
<tableNote pageId="2" pageNumber="1019" targetBox="[122,784,909,1793]" targetPageId="2">
|
||
<paragraph blockId="2.[122,785,1799,1999]" pageId="2" pageNumber="1019">
|
||
Values given are for all four limb joints (hip,knee,ankle,toe).
|
||
<subScript attach="both" box="[533,559,1805,1815]" fontSize="4" pageId="2" pageNumber="1019">Mmusc</subScript>
|
||
is the muscle moment required to maintain static equilibrium during single limb support at midstance of fast running (with G 2:5); L is mean muscle fibre length; v is mean extensor muscle fibre pennation angle; r is mean extensor muscle moment arm (means were weighted by physiological crosssectional area as in refs 12–14);
|
||
<subScript attach="both" box="[135,139,1880,1890]" fontSize="4" pageId="2" pageNumber="1019">mi</subScript>
|
||
is the percentage of
|
||
<subScript attach="left" box="[290,313,1880,1890]" fontSize="4" pageId="2" pageNumber="1019">mbody</subScript>
|
||
needed as extensor muscles about one joint; T is the total percentage of
|
||
<subScript attach="left" box="[152,175,1898,1908]" fontSize="4" pageId="2" pageNumber="1019">mbody</subScript>
|
||
per leg needed as extensor muscle (sum of all four
|
||
<subScript attach="both" box="[541,545,1898,1908]" fontSize="4" pageId="2" pageNumber="1019">mi</subScript>
|
||
values).
|
||
</paragraph>
|
||
<caption ID-DOI="http://doi.org/10.5281/zenodo.3961018" ID-Zenodo-Dep="3961018" httpUri="https://zenodo.org/record/3961018/files/figure.png" pageId="2" pageNumber="1019" startId="2.[815,868,1870,1889]" targetBox="[949,1333,1188,1833]" targetPageId="2">
|
||
<paragraph blockId="2.[815,1477,1870,2000]" pageId="2" pageNumber="1019">
|
||
Figure 2 Limb orientation used for model
|
||
<taxonomicName authority="Osborn, 1905" box="[1137,1176,1870,1889]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="2" pageNumber="1021" phylum="Chordata" rank="species" species="rex">Trex</taxonomicName>
|
||
_1. The values of
|
||
<subScript attach="left" box="[1323,1327,1878,1891]" fontSize="5" pageId="2" pageNumber="1019">mi</subScript>
|
||
, the percentage of body mass as extensor muscle acting about each joint (muscle moment action shown as a red arrow) required to maintain static equilibrium at midstance during fast running are shown in red. Actual hindlimb bones were digitized from
|
||
<taxonomicName box="[1246,1357,1953,1972]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="2" pageNumber="1021" phylum="Chordata" rank="genus">Tyrannosaurus</taxonomicName>
|
||
specimen
|
||
<materialsCitation ID-GBIF-Occurrence="2579591225" collectionCode="MOR" pageId="2" pageNumber="1019" specimenCode="MOR 555">MOR 555</materialsCitation>
|
||
(Museum of the Rockies; Boseman, Montana).
|
||
</paragraph>
|
||
</caption>
|
||
<paragraph blockId="2.[122,785,1799,1999]" pageId="2" pageNumber="1019">
|
||
The
|
||
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|
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shown is an extensor moment if it is positive, flexor if negative; except at the knee where the converse is true. In the
|
||
<taxonomicName box="[352,406,1929,1943]" class="Reptilia" family="Alligatoridae" genus="Alligator" kingdom="Animalia" order="Crocodylia" pageId="2" pageNumber="1019" phylum="Chordata" rank="genus">Alligator</taxonomicName>
|
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model, the knee joint
|
||
<subScript attach="both" box="[569,573,1935,1945]" fontSize="4" pageId="2" pageNumber="1019">mi</subScript>
|
||
was set at 0 because the knee
|
||
<subScript attach="left" box="[135,161,1954,1964]" fontSize="4" pageId="2" pageNumber="1019">Mmusc</subScript>
|
||
was a flexor moment and we conservatively assumed that twojoint hip extensors and knee flexors (for example M. caudofemoralis longus) could stabilize both joints. See Supplementary Information for more details.
|
||
</paragraph>
|
||
</tableNote>
|
||
<paragraph blockId="3.[107,769,136,717]" pageId="3" pageNumber="1020">
|
||
Judging from extant taxa, values of
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|
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</collectionCode>
|
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from 5–25% per leg indicate that an animal may or may not be a fast runner, depending on the ratio of the actual percentage of
|
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|
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|
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that is extensor muscle to
|
||
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|
||
<emphasis box="[749,762,361,382]" italics="true" pageId="3" pageNumber="1020">T</emphasis>
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</collectionCode>
|
||
, the estimated percentage of extensor muscle required. Values of
|
||
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|
||
<emphasis box="[753,768,389,410]" italics="true" pageId="3" pageNumber="1020">T</emphasis>
|
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</collectionCode>
|
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closer to 25% probably indicate poor running ability (if any) because the ratio of actual extensor muscle percentage to
|
||
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|
||
<emphasis box="[686,701,444,465]" italics="true" pageId="3" pageNumber="1020">T</emphasis>
|
||
</collectionCode>
|
||
would be perilously close to 1. Adept runners (such as ground birds
|
||
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<bibRefCitation author="Roberts, T. J." box="[727,742,468,481]" journalOrPublisher="Bull. Mus. Comp. Zool." pageId="3" pageNumber="1020" pagination="283 - 295" part="156" refId="ref4421" refString="12. Roberts, T. J. Muscle force and stress during running in dogs and wild turkeys. Bull. Mus. Comp. Zool. 156, 283 - 295 (2001)." title="Muscle force and stress during running in dogs and wild turkeys" type="journal article" year="2001">12</bibRefCitation>
|
||
,
|
||
<bibRefCitation author="Gatesy, S. M." box="[744,759,468,481]" journalOrPublisher="J. Morphol." pageId="3" pageNumber="1020" pagination="115 - 125" part="240" refId="ref5078" refString="21. Gatesy, S. M. Guineafowl hind limb function. I: Cineradiographic analysis and speed effects. J. Morphol. 240, 115 - 125 (1999)." title="Guineafowl hind limb function. I: Cineradiographic analysis and speed effects" type="journal article" year="1999">21</bibRefCitation>
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||
</superScript>
|
||
) have
|
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|
||
<emphasis box="[157,172,500,521]" italics="true" pageId="3" pageNumber="1020">T</emphasis>
|
||
</collectionCode>
|
||
values below 5%, maintaining a high ratio of actual extensor muscle mass to
|
||
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|
||
<emphasis box="[266,281,528,549]" italics="true" pageId="3" pageNumber="1020">T</emphasis>
|
||
</collectionCode>
|
||
(almost 2.0 in
|
||
<taxonomicName box="[434,496,527,549]" class="Aves" family="Phasianidae" genus="Gallus" kingdom="Animalia" order="Galliformes" pageId="3" pageNumber="1020" phylum="Chordata" rank="genus">
|
||
<emphasis box="[434,496,527,549]" italics="true" pageId="3" pageNumber="1020">Gallus</emphasis>
|
||
</taxonomicName>
|
||
). This allows the musculoskeletal system to operate with a generous margin of safety
|
||
<superScript attach="left" box="[702,740,552,565]" fontSize="6" pageId="3" pageNumber="1020">
|
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<bibRefCitation author="Roberts, T. J." box="[702,717,552,565]" journalOrPublisher="Bull. Mus. Comp. Zool." pageId="3" pageNumber="1020" pagination="283 - 295" part="156" refId="ref4421" refString="12. Roberts, T. J. Muscle force and stress during running in dogs and wild turkeys. Bull. Mus. Comp. Zool. 156, 283 - 295 (2001)." title="Muscle force and stress during running in dogs and wild turkeys" type="journal article" year="2001">12</bibRefCitation>
|
||
–
|
||
<bibRefCitation author="Roberts, T. R. & Chen, M. S. & Taylor, C. R." box="[725,740,552,565]" journalOrPublisher="J. Exp. Biol." pageId="3" pageNumber="1020" pagination="2753 - 2762" part="201" refId="ref4624" refString="14. Roberts, T. R., Chen, M. S. & Taylor, C. R. Energetics of bipedal running. II. Limb design and running mechanics. J. Exp. Biol. 201, 2753 - 2762 (1998)." title="Energetics of bipedal running. II. Limb design and running mechanics" type="journal article" year="1998">14</bibRefCitation>
|
||
</superScript>
|
||
to accommodate unexpected increases of joint moments.
|
||
</paragraph>
|
||
<paragraph blockId="3.[107,769,136,717]" lastBlockId="3.[800,1463,136,1218]" pageId="3" pageNumber="1020">
|
||
Some robust conclusions are possible despite the uncertainties about parameter values. Our findings agree with data from fossilized footprints (fastest estimated speeds are,
|
||
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|
||
s
|
||
<superScript attach="left" box="[633,650,661,676]" fontSize="6" pageId="3" pageNumber="1020">1</superScript>
|
||
)
|
||
<superScript attach="left" box="[659,684,663,676]" fontSize="6" pageId="3" pageNumber="1020">
|
||
<bibRefCitation author="Farlow, J. O. & Gatesy, S. M. & Holtz, T. R. Jr & Hutchinson, J. R. & Robinson, J. M." box="[659,666,663,676]" journalOrPublisher="Am. Zool." pageId="3" pageNumber="1020" pagination="640 - 663" part="40" refId="ref4267" refString="9. Farlow, J. O., Gatesy, S. M., Holtz, T. R. Jr, Hutchinson, J. R. & Robinson, J. M. Theropod locomotion. Am. Zool. 40, 640 - 663 (2000)." title="Theropod locomotion" type="journal article" year="2000">9</bibRefCitation>
|
||
,
|
||
<bibRefCitation author="Irby, G. V." box="[669,684,663,676]" journalOrPublisher="Mus. N. Arizona Bull." pageId="3" pageNumber="1020" pagination="109 - 112" part="60" refId="ref4335" refString="10. Irby, G. V. Paleoichnological evidence for running dinosaurs worldwide. Mus. N. Arizona Bull. 60, 109 - 112 (1999)." title="Paleoichnological evidence for running dinosaurs worldwide" type="journal article" year="1999">10</bibRefCitation>
|
||
</superScript>
|
||
indicating that smaller theropods could run quickly. Although our
|
||
<collectionCode box="[753,768,696,717]" name="Tavera, Department of Geology and Geophysics" pageId="3" pageNumber="1020">
|
||
<emphasis box="[753,768,696,717]" italics="true" pageId="3" pageNumber="1020">
|
||
<collectionCodeEnum box="[753,768,696,717]" pageId="3" pageNumber="1020">T</collectionCodeEnum>
|
||
</emphasis>
|
||
</collectionCode>
|
||
estimates are somewhat high (10–21%
|
||
<emphasis box="[1217,1236,138,159]" italics="true" pageId="3" pageNumber="1020">m</emphasis>
|
||
<subScript attach="left" box="[1236,1269,146,161]" fontSize="6" pageId="3" pageNumber="1020">body</subScript>
|
||
per leg), a more columnar limb orientation could easily have reduced
|
||
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|
||
<collectionCodeEnum box="[1339,1354,165,186]" pageId="3" pageNumber="1020">
|
||
<emphasis box="[1339,1354,165,186]" italics="true" pageId="3" pageNumber="1020">T</emphasis>
|
||
</collectionCodeEnum>
|
||
</collectionCode>
|
||
enough to enable fast running (,5%
|
||
<emphasis box="[1065,1084,193,214]" italics="true" pageId="3" pageNumber="1020">m</emphasis>
|
||
<subScript attach="right" box="[1085,1118,202,217]" fontSize="6" pageId="3" pageNumber="1020">body</subScript>
|
||
).
|
||
</paragraph>
|
||
<paragraph blockId="3.[800,1463,136,1218]" pageId="3" pageNumber="1020">
|
||
Yet our estimates of
|
||
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|
||
<collectionCodeEnum box="[1032,1047,221,242]" pageId="3" pageNumber="1020">
|
||
<emphasis box="[1032,1047,221,242]" italics="true" pageId="3" pageNumber="1020">T</emphasis>
|
||
</collectionCodeEnum>
|
||
</collectionCode>
|
||
for an adult
|
||
<taxonomicName box="[1183,1326,221,242]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="3" pageNumber="1020" phylum="Chordata" rank="genus">
|
||
<emphasis box="[1183,1326,221,242]" italics="true" pageId="3" pageNumber="1020">Tyrannosaurus</emphasis>
|
||
</taxonomicName>
|
||
were so high that it is difficult to justify the reconstruction of
|
||
<taxonomicName box="[1277,1420,249,270]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="3" pageNumber="1020" phylum="Chordata" rank="genus">
|
||
<emphasis box="[1277,1420,249,270]" italics="true" pageId="3" pageNumber="1020">Tyrannosaurus</emphasis>
|
||
</taxonomicName>
|
||
as a fast runner. Even with generous assumptions we were unable to reduce the estimates of
|
||
<collectionCode box="[1030,1045,305,326]" name="Tavera, Department of Geology and Geophysics" pageId="3" pageNumber="1020">
|
||
<collectionCodeEnum box="[1030,1045,305,326]" pageId="3" pageNumber="1020">
|
||
<emphasis box="[1030,1045,305,326]" italics="true" pageId="3" pageNumber="1020">T</emphasis>
|
||
</collectionCodeEnum>
|
||
</collectionCode>
|
||
to 5%
|
||
<emphasis box="[1113,1132,305,326]" italics="true" pageId="3" pageNumber="1020">m</emphasis>
|
||
<subScript attach="left" box="[1132,1165,314,329]" fontSize="6" pageId="3" pageNumber="1020">body</subScript>
|
||
per leg or less. Indeed, scaling data
|
||
<superScript attach="left" box="[843,875,329,342]" fontSize="6" pageId="3" pageNumber="1020">
|
||
<bibRefCitation author="Alexander, R. McN. & Jayes, A. S. & Maloiy, G. M. O. & Wathuta, E. M." box="[843,858,329,342]" journalOrPublisher="J. Zool." pageId="3" pageNumber="1020" pagination="539 - 552" part="194" refId="ref4790" refString="17. Alexander, R. McN., Jayes, A. S., Maloiy, G. M. O. & Wathuta, E. M. Allometry of the leg muscles of mammals. J. Zool. 194, 539 - 552 (1981)." title="Allometry of the leg muscles of mammals" type="journal article" year="1981">17</bibRefCitation>
|
||
,
|
||
<bibRefCitation author="Bennett, M. B." box="[860,875,329,342]" journalOrPublisher="J. Zool." pageId="3" pageNumber="1020" pagination="435 - 443" part="238" refId="ref4842" refString="18. Bennett, M. B. Allometry of the leg muscles of birds. J. Zool. 238, 435 - 443 (1996)." title="Allometry of the leg muscles of birds" type="journal article" year="1996">18</bibRefCitation>
|
||
</superScript>
|
||
suggest that a
|
||
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|
||
<taxonomicName box="[1133,1276,333,354]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="3" pageNumber="1020" phylum="Chordata" rank="genus">
|
||
<emphasis box="[1133,1276,333,354]" italics="true" pageId="3" pageNumber="1020">Tyrannosaurus</emphasis>
|
||
</taxonomicName>
|
||
had only 7–10%
|
||
<emphasis box="[800,819,361,382]" italics="true" pageId="3" pageNumber="1020">m</emphasis>
|
||
<subScript attach="left" box="[819,852,369,384]" fontSize="6" pageId="3" pageNumber="1020">body</subScript>
|
||
per leg as extensors. Therefore we conclude that an adult
|
||
<taxonomicName box="[800,943,389,410]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="3" pageNumber="1020" phylum="Chordata" rank="genus">
|
||
<emphasis box="[800,943,389,410]" italics="true" pageId="3" pageNumber="1020">Tyrannosaurus</emphasis>
|
||
</taxonomicName>
|
||
had very limited, if any, running ability. Our best estimates indicate that an adult
|
||
<taxonomicName box="[1171,1314,417,438]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="3" pageNumber="1020" phylum="Chordata" rank="genus">
|
||
<emphasis box="[1171,1314,417,438]" italics="true" pageId="3" pageNumber="1020">Tyrannosaurus</emphasis>
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||
</taxonomicName>
|
||
needed over 40%
|
||
<emphasis box="[849,868,444,465]" italics="true" pageId="3" pageNumber="1020">m</emphasis>
|
||
<subScript attach="left" box="[868,901,453,468]" fontSize="6" pageId="3" pageNumber="1020">body</subScript>
|
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per leg as extensor muscle. If this is correct, then such animals were unable to run at all. If
|
||
<taxonomicName box="[1169,1312,472,493]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="3" pageNumber="1020" phylum="Chordata" rank="genus">
|
||
<emphasis box="[1169,1312,472,493]" italics="true" pageId="3" pageNumber="1020">Tyrannosaurus</emphasis>
|
||
</taxonomicName>
|
||
was indeed an adept runner, then it must have had many musculoskeletal specializations that available data do not suggest.
|
||
</paragraph>
|
||
<paragraph blockId="3.[800,1463,136,1218]" pageId="3" pageNumber="1020">
|
||
<collectionCode box="[824,840,555,576]" country="USA" httpUri="http://biocol.org/urn:lsid:biocol.org:col:15406" lsid="urn:lsid:biocol.org:col:15406" name="Harvard University - Arnold Arboretum" pageId="3" pageNumber="1020" type="Herbarium">A</collectionCode>
|
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final model is illustrative. We isometrically scaledup our chicken model to
|
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|
||
to simulate a
|
||
<taxonomicName box="[1261,1404,584,605]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="3" pageNumber="1020" phylum="Chordata" rank="genus">
|
||
<emphasis box="[1261,1404,584,605]" italics="true" pageId="3" pageNumber="1020">Tyrannosaurus</emphasis>
|
||
</taxonomicName>
|
||
sized chicken. Our model shows that a gigantic chicken, using the same limb orientation as an extant galliform
|
||
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|
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<superScript attach="left" box="[1178,1192,635,648]" fontSize="6" pageId="3" pageNumber="1020">21</superScript>
|
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</bibRefCitation>
|
||
, would need 99%
|
||
<emphasis box="[1371,1390,640,661]" italics="true" pageId="3" pageNumber="1020">m</emphasis>
|
||
<subScript attach="left" box="[1390,1423,648,663]" fontSize="6" pageId="3" pageNumber="1020">body</subScript>
|
||
per leg as extensor muscles to run quickly, which is clearly impossible and is much higher than for a typical chicken (4.7%
|
||
<emphasis box="[1321,1340,696,717]" italics="true" pageId="3" pageNumber="1020">m</emphasis>
|
||
<subScript attach="left" box="[1340,1373,704,719]" fontSize="6" pageId="3" pageNumber="1020">body</subScript>
|
||
per leg). Features such as the more posterior position of the trunk centre of mass of
|
||
<taxonomicName box="[877,1020,751,772]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="3" pageNumber="1020" phylum="Chordata" rank="genus">
|
||
<emphasis box="[877,1020,751,772]" italics="true" pageId="3" pageNumber="1020">Tyrannosaurus</emphasis>
|
||
</taxonomicName>
|
||
explain why we obtained lower estimates of
|
||
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|
||
<emphasis box="[1447,1462,751,772]" italics="true" pageId="3" pageNumber="1020">
|
||
<collectionCodeEnum box="[1447,1462,751,772]" pageId="3" pageNumber="1020">T</collectionCodeEnum>
|
||
</emphasis>
|
||
</collectionCode>
|
||
for
|
||
<taxonomicName box="[834,977,779,800]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="3" pageNumber="1020" phylum="Chordata" rank="genus">
|
||
<emphasis box="[834,977,779,800]" italics="true" pageId="3" pageNumber="1020">Tyrannosaurus</emphasis>
|
||
</taxonomicName>
|
||
(43%
|
||
<emphasis box="[1039,1058,779,800]" italics="true" pageId="3" pageNumber="1020">m</emphasis>
|
||
<subScript attach="left" box="[1058,1091,788,803]" fontSize="6" pageId="3" pageNumber="1020">body</subScript>
|
||
per leg) than for the
|
||
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|
||
chicken. Nonetheless, the high estimated values of
|
||
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|
||
<emphasis box="[1222,1237,807,828]" italics="true" pageId="3" pageNumber="1020">
|
||
<collectionCodeEnum box="[1222,1237,807,828]" pageId="3" pageNumber="1020">T</collectionCodeEnum>
|
||
</emphasis>
|
||
</collectionCode>
|
||
in both models reveal how giant terrestrial animals become restricted from extreme locomotor performance
|
||
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||
<bibRefCitation author="Farlow, J. O. & Gatesy, S. M. & Holtz, T. R. Jr & Hutchinson, J. R. & Robinson, J. M." box="[1038,1046,858,871]" journalOrPublisher="Am. Zool." pageId="3" pageNumber="1020" pagination="640 - 663" part="40" refId="ref4267" refString="9. Farlow, J. O., Gatesy, S. M., Holtz, T. R. Jr, Hutchinson, J. R. & Robinson, J. M. Theropod locomotion. Am. Zool. 40, 640 - 663 (2000)." title="Theropod locomotion" type="journal article" year="2000">9</bibRefCitation>
|
||
,
|
||
<bibRefCitation author="Biewener, A. A." box="[1048,1063,858,871]" journalOrPublisher="Science" pageId="3" pageNumber="1020" pagination="45 - 48" part="245" refId="ref4463" refString="13. Biewener, A. A. Scaling body support in mammals: limb posture and muscle mechanics. Science 245, 45 - 48 (1989)." title="Scaling body support in mammals: limb posture and muscle mechanics" type="journal article" year="1989">13</bibRefCitation>
|
||
</superScript>
|
||
.
|
||
</paragraph>
|
||
<caption ID-Table-UUID="28F46637FFD6D97D3812A464623AFCEE" box="[107,598,791,807]" httpUri="http://table.plazi.org/id/28F46637FFD6D97D3812A464623AFCEE" pageId="3" pageNumber="1020" startId="3.[107,157,791,807]" targetBox="[107,768,827,1867]" targetIsTable="true" targetPageId="3">
|
||
<paragraph blockId="3.[107,598,791,807]" box="[107,598,791,807]" pageId="3" pageNumber="1020">
|
||
Table 2 Parameter sensitivity in
|
||
<taxonomicName authority="Osborn, 1905" box="[394,527,791,807]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="3" pageNumber="1021" phylum="Chordata" rank="genus">Tyrannosaurus</taxonomicName>
|
||
models
|
||
</paragraph>
|
||
</caption>
|
||
<paragraph pageId="3" pageNumber="1020">
|
||
<table box="[107,768,827,1867]" gridcols="5" gridrows="43" pageId="3" pageNumber="1020">
|
||
<tr box="[107,768,827,854]" gridrow="0" pageId="3" pageNumber="1020">
|
||
<th box="[107,768,827,854]" colspan="5" colspanRight="4" gridcol="0" gridrow="0" pageId="3" pageNumber="1020">Hip Knee Ankle Toe .............................................................................................................................................................................</th>
|
||
</tr>
|
||
<tr box="[107,768,861,877]" gridrow="1" pageId="3" pageNumber="1020" rowspan-1="1" rowspan-2="1" rowspan-3="1" rowspan-4="1">
|
||
<th box="[107,196,861,877]" gridcol="0" gridrow="1" pageId="3" pageNumber="1020">Trex_2</th>
|
||
</tr>
|
||
<tr box="[107,768,889,906]" gridrow="2" pageId="3" pageNumber="1020">
|
||
<th box="[107,196,889,906]" gridcol="0" gridrow="2" pageId="3" pageNumber="1020">
|
||
<subScript attach="left" box="[121,149,896,906]" fontSize="4" pageId="3" pageNumber="1020">Mmusc</subScript>
|
||
(N m)
|
||
</th>
|
||
<td box="[316,369,889,906]" gridcol="1" gridrow="2" pageId="3" pageNumber="1020">53,000</td>
|
||
<td box="[445,508,889,906]" gridcol="2" gridrow="2" pageId="3" pageNumber="1020">56,000</td>
|
||
<td box="[586,639,889,906]" gridcol="3" gridrow="2" pageId="3" pageNumber="1020">72,000</td>
|
||
<td box="[715,768,889,906]" gridcol="4" gridrow="2" pageId="3" pageNumber="1020">45,000</td>
|
||
</tr>
|
||
<tr box="[107,768,910,926]" gridrow="3" pageId="3" pageNumber="1020">
|
||
<th box="[107,196,910,926]" gridcol="0" gridrow="3" pageId="3" pageNumber="1020">L (m)</th>
|
||
<td box="[316,369,910,926]" gridcol="1" gridrow="3" pageId="3" pageNumber="1020">1.2</td>
|
||
<td box="[445,508,910,926]" gridcol="2" gridrow="3" pageId="3" pageNumber="1020">0.52</td>
|
||
<td box="[586,639,910,926]" gridcol="3" gridrow="3" pageId="3" pageNumber="1020">0.39</td>
|
||
<td box="[715,768,910,926]" gridcol="4" gridrow="3" pageId="3" pageNumber="1020">0.19</td>
|
||
</tr>
|
||
<tr box="[107,768,931,947]" gridrow="4" pageId="3" pageNumber="1020">
|
||
<th box="[107,196,931,947]" gridcol="0" gridrow="4" pageId="3" pageNumber="1020">v (8)</th>
|
||
<td box="[316,369,931,947]" gridcol="1" gridrow="4" pageId="3" pageNumber="1020">9.0</td>
|
||
<td box="[445,508,931,947]" gridcol="2" gridrow="4" pageId="3" pageNumber="1020">21</td>
|
||
<td box="[586,639,931,947]" gridcol="3" gridrow="4" pageId="3" pageNumber="1020">22</td>
|
||
<td box="[715,768,931,947]" gridcol="4" gridrow="4" pageId="3" pageNumber="1020">21</td>
|
||
</tr>
|
||
<tr box="[107,768,951,967]" gridrow="5" pageId="3" pageNumber="1020">
|
||
<th box="[107,196,951,967]" gridcol="0" gridrow="5" pageId="3" pageNumber="1020">r (m)</th>
|
||
<td box="[316,369,951,967]" gridcol="1" gridrow="5" pageId="3" pageNumber="1020">0.37</td>
|
||
<td box="[445,508,951,967]" gridcol="2" gridrow="5" pageId="3" pageNumber="1020">0.22</td>
|
||
<td box="[586,639,951,967]" gridcol="3" gridrow="5" pageId="3" pageNumber="1020">0.11</td>
|
||
<td box="[715,768,951,967]" gridcol="4" gridrow="5" pageId="3" pageNumber="1020">0.065</td>
|
||
</tr>
|
||
<tr box="[107,768,972,989]" gridrow="6" pageId="3" pageNumber="1020">
|
||
<th box="[107,196,972,989]" gridcol="0" gridrow="6" pageId="3" pageNumber="1020">
|
||
<subScript attach="left" box="[121,125,979,989]" fontSize="4" pageId="3" pageNumber="1020">mi</subScript>
|
||
(%
|
||
<subScript attach="left" box="[164,189,979,989]" fontSize="4" pageId="3" pageNumber="1020">mbody</subScript>
|
||
)
|
||
</th>
|
||
<td box="[316,369,972,989]" gridcol="1" gridrow="6" pageId="3" pageNumber="1020">10</td>
|
||
<td box="[445,508,972,989]" gridcol="2" gridrow="6" pageId="3" pageNumber="1020">8.3</td>
|
||
<td box="[586,639,972,989]" gridcol="3" gridrow="6" pageId="3" pageNumber="1020">16</td>
|
||
<td box="[715,768,972,989]" gridcol="4" gridrow="6" pageId="3" pageNumber="1020">8.3</td>
|
||
</tr>
|
||
<tr box="[107,768,992,1009]" gridrow="7" pageId="3" pageNumber="1020" rowspan-1="1" rowspan-2="1" rowspan-3="1">
|
||
<th box="[107,196,992,1009]" gridcol="0" gridrow="7" pageId="3" pageNumber="1020">T (% mbody)</th>
|
||
<td box="[715,768,992,1009]" gridcol="4" gridrow="7" pageId="3" pageNumber="1020">43</td>
|
||
</tr>
|
||
<tr box="[107,768,1034,1050]" gridrow="8" pageId="3" pageNumber="1020">
|
||
<th box="[107,768,1034,1050]" colspan="5" colspanRight="4" gridcol="0" gridrow="8" pageId="3" pageNumber="1020">Trex_3</th>
|
||
</tr>
|
||
<tr box="[107,768,1062,1079]" gridrow="9" pageId="3" pageNumber="1020">
|
||
<th box="[107,196,1062,1079]" gridcol="0" gridrow="9" pageId="3" pageNumber="1020">
|
||
<subScript attach="left" box="[121,149,1069,1079]" fontSize="4" pageId="3" pageNumber="1020">Mmusc</subScript>
|
||
(N m)
|
||
</th>
|
||
<td box="[316,369,1062,1079]" gridcol="1" gridrow="9" pageId="3" pageNumber="1020">75,000</td>
|
||
<td box="[445,508,1062,1079]" gridcol="2" gridrow="9" pageId="3" pageNumber="1020">49,000</td>
|
||
<td box="[586,639,1062,1079]" gridcol="3" gridrow="9" pageId="3" pageNumber="1020">80,000</td>
|
||
<td box="[715,768,1062,1079]" gridcol="4" gridrow="9" pageId="3" pageNumber="1020">29,000</td>
|
||
</tr>
|
||
<tr box="[107,768,1083,1099]" gridrow="10" pageId="3" pageNumber="1020">
|
||
<th box="[107,196,1083,1099]" gridcol="0" gridrow="10" pageId="3" pageNumber="1020">L (m)</th>
|
||
<td box="[316,369,1083,1099]" gridcol="1" gridrow="10" pageId="3" pageNumber="1020">1.2</td>
|
||
<td box="[445,508,1083,1099]" gridcol="2" gridrow="10" pageId="3" pageNumber="1020">–</td>
|
||
<td box="[586,639,1083,1099]" gridcol="3" gridrow="10" pageId="3" pageNumber="1020">0.39</td>
|
||
<td box="[715,768,1083,1099]" gridcol="4" gridrow="10" pageId="3" pageNumber="1020">0.19</td>
|
||
</tr>
|
||
<tr box="[107,768,1103,1119]" gridrow="11" pageId="3" pageNumber="1020">
|
||
<th box="[107,196,1103,1119]" gridcol="0" gridrow="11" pageId="3" pageNumber="1020">v (8)</th>
|
||
<td box="[316,369,1103,1119]" gridcol="1" gridrow="11" pageId="3" pageNumber="1020">9.0</td>
|
||
<td box="[445,508,1103,1119]" gridcol="2" gridrow="11" pageId="3" pageNumber="1020">–</td>
|
||
<td box="[586,639,1103,1119]" gridcol="3" gridrow="11" pageId="3" pageNumber="1020">22</td>
|
||
<td box="[715,768,1103,1119]" gridcol="4" gridrow="11" pageId="3" pageNumber="1020">21</td>
|
||
</tr>
|
||
<tr box="[107,768,1124,1140]" gridrow="12" pageId="3" pageNumber="1020">
|
||
<th box="[107,196,1124,1140]" gridcol="0" gridrow="12" pageId="3" pageNumber="1020">r (m)</th>
|
||
<td box="[316,369,1124,1140]" gridcol="1" gridrow="12" pageId="3" pageNumber="1020">0.37</td>
|
||
<td box="[445,508,1124,1140]" gridcol="2" gridrow="12" pageId="3" pageNumber="1020">–</td>
|
||
<td box="[586,639,1124,1140]" gridcol="3" gridrow="12" pageId="3" pageNumber="1020">0.11</td>
|
||
<td box="[715,768,1124,1140]" gridcol="4" gridrow="12" pageId="3" pageNumber="1020">0.065</td>
|
||
</tr>
|
||
<tr box="[107,768,1144,1161]" gridrow="13" pageId="3" pageNumber="1020">
|
||
<th box="[107,196,1144,1161]" gridcol="0" gridrow="13" pageId="3" pageNumber="1020">mi (% mbody)</th>
|
||
<td box="[316,369,1144,1161]" gridcol="1" gridrow="13" pageId="3" pageNumber="1020">15</td>
|
||
<td box="[445,508,1144,1161]" gridcol="2" gridrow="13" pageId="3" pageNumber="1020">0</td>
|
||
<td box="[586,639,1144,1161]" gridcol="3" gridrow="13" pageId="3" pageNumber="1020">18</td>
|
||
<td box="[715,768,1144,1161]" gridcol="4" gridrow="13" pageId="3" pageNumber="1020">5.3</td>
|
||
</tr>
|
||
<tr box="[107,768,1165,1182]" gridrow="14" pageId="3" pageNumber="1020" rowspan-1="1" rowspan-2="1" rowspan-3="1">
|
||
<th box="[107,196,1165,1182]" gridcol="0" gridrow="14" pageId="3" pageNumber="1020">T (% mbody)</th>
|
||
<td box="[715,768,1165,1182]" gridcol="4" gridrow="14" pageId="3" pageNumber="1020">38</td>
|
||
</tr>
|
||
<tr box="[107,768,1206,1222]" gridrow="15" pageId="3" pageNumber="1020">
|
||
<th box="[107,768,1206,1222]" colspan="5" colspanRight="4" gridcol="0" gridrow="15" pageId="3" pageNumber="1020">Trex_4</th>
|
||
</tr>
|
||
<tr box="[107,768,1235,1252]" gridrow="16" pageId="3" pageNumber="1020">
|
||
<th box="[107,196,1235,1252]" gridcol="0" gridrow="16" pageId="3" pageNumber="1020">
|
||
<subScript attach="left" box="[121,149,1242,1252]" fontSize="4" pageId="3" pageNumber="1020">Mmusc</subScript>
|
||
(N m)
|
||
</th>
|
||
<td box="[316,369,1235,1252]" gridcol="1" gridrow="16" pageId="3" pageNumber="1020">75,000</td>
|
||
<td box="[445,508,1235,1252]" gridcol="2" gridrow="16" pageId="3" pageNumber="1020">6,500</td>
|
||
<td box="[586,639,1235,1252]" gridcol="3" gridrow="16" pageId="3" pageNumber="1020">4,400</td>
|
||
<td box="[715,768,1235,1252]" gridcol="4" gridrow="16" pageId="3" pageNumber="1020">4,100</td>
|
||
</tr>
|
||
<tr box="[107,768,1255,1271]" gridrow="17" pageId="3" pageNumber="1020">
|
||
<th box="[107,196,1255,1271]" gridcol="0" gridrow="17" pageId="3" pageNumber="1020">L (m)</th>
|
||
<td box="[316,369,1255,1271]" gridcol="1" gridrow="17" pageId="3" pageNumber="1020">1.2</td>
|
||
<td box="[445,508,1255,1271]" gridcol="2" gridrow="17" pageId="3" pageNumber="1020">–</td>
|
||
<td box="[586,639,1255,1271]" gridcol="3" gridrow="17" pageId="3" pageNumber="1020">0.39</td>
|
||
<td box="[715,768,1255,1271]" gridcol="4" gridrow="17" pageId="3" pageNumber="1020">0.19</td>
|
||
</tr>
|
||
<tr box="[107,768,1276,1292]" gridrow="18" pageId="3" pageNumber="1020">
|
||
<th box="[107,196,1276,1292]" gridcol="0" gridrow="18" pageId="3" pageNumber="1020">v (8)</th>
|
||
<td box="[316,369,1276,1292]" gridcol="1" gridrow="18" pageId="3" pageNumber="1020">9.0</td>
|
||
<td box="[445,508,1276,1292]" gridcol="2" gridrow="18" pageId="3" pageNumber="1020">–</td>
|
||
<td box="[586,639,1276,1292]" gridcol="3" gridrow="18" pageId="3" pageNumber="1020">22</td>
|
||
<td box="[715,768,1276,1292]" gridcol="4" gridrow="18" pageId="3" pageNumber="1020">21</td>
|
||
</tr>
|
||
<tr box="[107,768,1297,1313]" gridrow="19" pageId="3" pageNumber="1020">
|
||
<th box="[107,196,1297,1313]" gridcol="0" gridrow="19" pageId="3" pageNumber="1020">r (m)</th>
|
||
<td box="[316,369,1297,1313]" gridcol="1" gridrow="19" pageId="3" pageNumber="1020">0.37</td>
|
||
<td box="[445,508,1297,1313]" gridcol="2" gridrow="19" pageId="3" pageNumber="1020">–</td>
|
||
<td box="[586,639,1297,1313]" gridcol="3" gridrow="19" pageId="3" pageNumber="1020">0.11</td>
|
||
<td box="[715,768,1297,1313]" gridcol="4" gridrow="19" pageId="3" pageNumber="1020">0.065</td>
|
||
</tr>
|
||
<tr box="[107,768,1317,1334]" gridrow="20" pageId="3" pageNumber="1020">
|
||
<th box="[107,196,1317,1334]" gridcol="0" gridrow="20" pageId="3" pageNumber="1020">mi (% mbody)</th>
|
||
<td box="[316,369,1317,1334]" gridcol="1" gridrow="20" pageId="3" pageNumber="1020">15</td>
|
||
<td box="[445,508,1317,1334]" gridcol="2" gridrow="20" pageId="3" pageNumber="1020">0</td>
|
||
<td box="[586,639,1317,1334]" gridcol="3" gridrow="20" pageId="3" pageNumber="1020">0.99</td>
|
||
<td box="[715,768,1317,1334]" gridcol="4" gridrow="20" pageId="3" pageNumber="1020">0.75</td>
|
||
</tr>
|
||
<tr box="[107,768,1338,1355]" gridrow="21" pageId="3" pageNumber="1020" rowspan-1="1" rowspan-2="1" rowspan-3="1">
|
||
<th box="[107,196,1338,1355]" gridcol="0" gridrow="21" pageId="3" pageNumber="1020">T (% mbody)</th>
|
||
<td box="[715,768,1338,1355]" gridcol="4" gridrow="21" pageId="3" pageNumber="1020">17</td>
|
||
</tr>
|
||
<tr box="[107,768,1379,1395]" gridrow="22" pageId="3" pageNumber="1020" rowspan-1="1" rowspan-2="1" rowspan-3="1" rowspan-4="1">
|
||
<th box="[107,196,1379,1395]" gridcol="0" gridrow="22" pageId="3" pageNumber="1020">Trex_Lgator</th>
|
||
</tr>
|
||
<tr box="[107,768,1400,1416]" gridrow="23" pageId="3" pageNumber="1020">
|
||
<th box="[107,196,1400,1416]" gridcol="0" gridrow="23" pageId="3" pageNumber="1020">
|
||
<subScript attach="left" box="[121,149,1406,1416]" fontSize="4" pageId="3" pageNumber="1020">Mmusc</subScript>
|
||
(N m)
|
||
</th>
|
||
<td box="[316,369,1400,1416]" gridcol="1" gridrow="23" pageId="3" pageNumber="1020">75,000</td>
|
||
<td box="[445,508,1400,1416]" gridcol="2" gridrow="23" pageId="3" pageNumber="1020">24,000</td>
|
||
<td box="[586,639,1400,1416]" gridcol="3" gridrow="23" pageId="3" pageNumber="1020">66,000</td>
|
||
<td box="[715,768,1400,1416]" gridcol="4" gridrow="23" pageId="3" pageNumber="1020">49,000</td>
|
||
</tr>
|
||
<tr box="[107,768,1420,1436]" gridrow="24" pageId="3" pageNumber="1020">
|
||
<th box="[107,196,1420,1436]" gridcol="0" gridrow="24" pageId="3" pageNumber="1020">L (m)</th>
|
||
<td box="[316,369,1420,1436]" gridcol="1" gridrow="24" pageId="3" pageNumber="1020">0.93</td>
|
||
<td box="[445,508,1420,1436]" gridcol="2" gridrow="24" pageId="3" pageNumber="1020">0.39</td>
|
||
<td box="[586,639,1420,1436]" gridcol="3" gridrow="24" pageId="3" pageNumber="1020">0.37</td>
|
||
<td box="[715,768,1420,1436]" gridcol="4" gridrow="24" pageId="3" pageNumber="1020">0.19</td>
|
||
</tr>
|
||
<tr box="[107,768,1441,1457]" gridrow="25" pageId="3" pageNumber="1020">
|
||
<th box="[107,196,1441,1457]" gridcol="0" gridrow="25" pageId="3" pageNumber="1020">v (8)</th>
|
||
<td box="[316,369,1441,1457]" gridcol="1" gridrow="25" pageId="3" pageNumber="1020">18</td>
|
||
<td box="[445,508,1441,1457]" gridcol="2" gridrow="25" pageId="3" pageNumber="1020">16</td>
|
||
<td box="[586,639,1441,1457]" gridcol="3" gridrow="25" pageId="3" pageNumber="1020">21</td>
|
||
<td box="[715,768,1441,1457]" gridcol="4" gridrow="25" pageId="3" pageNumber="1020">19</td>
|
||
</tr>
|
||
<tr box="[107,768,1461,1477]" gridrow="26" pageId="3" pageNumber="1020">
|
||
<th box="[107,196,1461,1477]" gridcol="0" gridrow="26" pageId="3" pageNumber="1020">r (m)</th>
|
||
<td box="[316,369,1461,1477]" gridcol="1" gridrow="26" pageId="3" pageNumber="1020">0.37</td>
|
||
<td box="[445,508,1461,1477]" gridcol="2" gridrow="26" pageId="3" pageNumber="1020">0.22</td>
|
||
<td box="[586,639,1461,1477]" gridcol="3" gridrow="26" pageId="3" pageNumber="1020">0.11</td>
|
||
<td box="[715,768,1461,1477]" gridcol="4" gridrow="26" pageId="3" pageNumber="1020">0.065</td>
|
||
</tr>
|
||
<tr box="[107,768,1482,1499]" gridrow="27" pageId="3" pageNumber="1020">
|
||
<th box="[107,196,1482,1499]" gridcol="0" gridrow="27" pageId="3" pageNumber="1020">mi (% mbody)</th>
|
||
<td box="[316,369,1482,1499]" gridcol="1" gridrow="27" pageId="3" pageNumber="1020">12</td>
|
||
<td box="[445,508,1482,1499]" gridcol="2" gridrow="27" pageId="3" pageNumber="1020">2.6</td>
|
||
<td box="[586,639,1482,1499]" gridcol="3" gridrow="27" pageId="3" pageNumber="1020">14</td>
|
||
<td box="[715,768,1482,1499]" gridcol="4" gridrow="27" pageId="3" pageNumber="1020">9.0</td>
|
||
</tr>
|
||
<tr box="[107,768,1502,1519]" gridrow="28" pageId="3" pageNumber="1020" rowspan-1="1" rowspan-2="1" rowspan-3="1">
|
||
<th box="[107,196,1502,1519]" gridcol="0" gridrow="28" pageId="3" pageNumber="1020">T (% mbody)</th>
|
||
<td box="[715,768,1502,1519]" gridcol="4" gridrow="28" pageId="3" pageNumber="1020">38</td>
|
||
</tr>
|
||
<tr box="[107,768,1544,1560]" gridrow="29" pageId="3" pageNumber="1020" rowspan-1="1" rowspan-2="1" rowspan-3="1" rowspan-4="1">
|
||
<th box="[107,196,1544,1560]" gridcol="0" gridrow="29" pageId="3" pageNumber="1020">Trex_Lchick</th>
|
||
</tr>
|
||
<tr box="[107,768,1564,1581]" gridrow="30" pageId="3" pageNumber="1020">
|
||
<th box="[107,196,1564,1581]" gridcol="0" gridrow="30" pageId="3" pageNumber="1020">
|
||
<subScript attach="left" box="[121,149,1571,1581]" fontSize="4" pageId="3" pageNumber="1020">Mmusc</subScript>
|
||
(N m)
|
||
</th>
|
||
<td box="[316,369,1564,1581]" gridcol="1" gridrow="30" pageId="3" pageNumber="1020">75,000</td>
|
||
<td box="[445,508,1564,1581]" gridcol="2" gridrow="30" pageId="3" pageNumber="1020">24,000</td>
|
||
<td box="[586,639,1564,1581]" gridcol="3" gridrow="30" pageId="3" pageNumber="1020">66,000</td>
|
||
<td box="[715,768,1564,1581]" gridcol="4" gridrow="30" pageId="3" pageNumber="1020">49,000</td>
|
||
</tr>
|
||
<tr box="[107,768,1585,1601]" gridrow="31" pageId="3" pageNumber="1020">
|
||
<th box="[107,196,1585,1601]" gridcol="0" gridrow="31" pageId="3" pageNumber="1020">L (m)</th>
|
||
<td box="[316,369,1585,1601]" gridcol="1" gridrow="31" pageId="3" pageNumber="1020">1.1</td>
|
||
<td box="[445,508,1585,1601]" gridcol="2" gridrow="31" pageId="3" pageNumber="1020">0.65</td>
|
||
<td box="[586,639,1585,1601]" gridcol="3" gridrow="31" pageId="3" pageNumber="1020">0.41</td>
|
||
<td box="[715,768,1585,1601]" gridcol="4" gridrow="31" pageId="3" pageNumber="1020">0.33</td>
|
||
</tr>
|
||
<tr box="[107,768,1605,1621]" gridrow="32" pageId="3" pageNumber="1020">
|
||
<th box="[107,196,1605,1621]" gridcol="0" gridrow="32" pageId="3" pageNumber="1020">v (8)</th>
|
||
<td box="[316,369,1605,1621]" gridcol="1" gridrow="32" pageId="3" pageNumber="1020">0</td>
|
||
<td box="[445,508,1605,1621]" gridcol="2" gridrow="32" pageId="3" pageNumber="1020">25</td>
|
||
<td box="[586,639,1605,1621]" gridcol="3" gridrow="32" pageId="3" pageNumber="1020">23</td>
|
||
<td box="[715,768,1605,1621]" gridcol="4" gridrow="32" pageId="3" pageNumber="1020">22</td>
|
||
</tr>
|
||
<tr box="[107,768,1626,1642]" gridrow="33" pageId="3" pageNumber="1020">
|
||
<th box="[107,196,1626,1642]" gridcol="0" gridrow="33" pageId="3" pageNumber="1020">r (m)</th>
|
||
<td box="[316,369,1626,1642]" gridcol="1" gridrow="33" pageId="3" pageNumber="1020">0.37</td>
|
||
<td box="[445,508,1626,1642]" gridcol="2" gridrow="33" pageId="3" pageNumber="1020">0.22</td>
|
||
<td box="[586,639,1626,1642]" gridcol="3" gridrow="33" pageId="3" pageNumber="1020">0.11</td>
|
||
<td box="[715,768,1626,1642]" gridcol="4" gridrow="33" pageId="3" pageNumber="1020">0.065</td>
|
||
</tr>
|
||
<tr box="[107,768,1647,1663]" gridrow="34" pageId="3" pageNumber="1020">
|
||
<th box="[107,196,1647,1663]" gridcol="0" gridrow="34" pageId="3" pageNumber="1020">mi (% mbody)</th>
|
||
<td box="[316,369,1647,1663]" gridcol="1" gridrow="34" pageId="3" pageNumber="1020">13</td>
|
||
<td box="[445,508,1647,1663]" gridcol="2" gridrow="34" pageId="3" pageNumber="1020">4.6</td>
|
||
<td box="[586,639,1647,1663]" gridcol="3" gridrow="34" pageId="3" pageNumber="1020">16</td>
|
||
<td box="[715,768,1647,1663]" gridcol="4" gridrow="34" pageId="3" pageNumber="1020">16</td>
|
||
</tr>
|
||
<tr box="[107,768,1667,1684]" gridrow="35" pageId="3" pageNumber="1020" rowspan-1="1" rowspan-2="1" rowspan-3="1">
|
||
<th box="[107,196,1667,1684]" gridcol="0" gridrow="35" pageId="3" pageNumber="1020">T (% mbody)</th>
|
||
<td box="[715,768,1667,1684]" gridcol="4" gridrow="35" pageId="3" pageNumber="1020">50</td>
|
||
</tr>
|
||
<tr box="[107,768,1708,1724]" gridrow="36" pageId="3" pageNumber="1020">
|
||
<th box="[107,768,1708,1724]" colspan="5" colspanRight="4" gridcol="0" gridrow="36" pageId="3" pageNumber="1020">Trex_lowest</th>
|
||
</tr>
|
||
<tr box="[107,768,1737,1754]" gridrow="37" pageId="3" pageNumber="1020">
|
||
<th box="[107,196,1737,1754]" gridcol="0" gridrow="37" pageId="3" pageNumber="1020">
|
||
<subScript attach="left" box="[121,149,1744,1754]" fontSize="4" pageId="3" pageNumber="1020">Mmusc</subScript>
|
||
(N m)
|
||
</th>
|
||
<td box="[316,369,1737,1754]" gridcol="1" gridrow="37" pageId="3" pageNumber="1020">75,000</td>
|
||
<td box="[445,508,1737,1754]" gridcol="2" gridrow="37" pageId="3" pageNumber="1020">6,500</td>
|
||
<td box="[586,639,1737,1754]" gridcol="3" gridrow="37" pageId="3" pageNumber="1020">4,400</td>
|
||
<td box="[715,768,1737,1754]" gridcol="4" gridrow="37" pageId="3" pageNumber="1020">4,100</td>
|
||
</tr>
|
||
<tr box="[107,768,1758,1774]" gridrow="38" pageId="3" pageNumber="1020">
|
||
<th box="[107,196,1758,1774]" gridcol="0" gridrow="38" pageId="3" pageNumber="1020">L (m)</th>
|
||
<td box="[316,369,1758,1774]" gridcol="1" gridrow="38" pageId="3" pageNumber="1020">0.93</td>
|
||
<td box="[445,508,1758,1774]" gridcol="2" gridrow="38" pageId="3" pageNumber="1020">–</td>
|
||
<td box="[586,639,1758,1774]" gridcol="3" gridrow="38" pageId="3" pageNumber="1020">0.37</td>
|
||
<td box="[715,768,1758,1774]" gridcol="4" gridrow="38" pageId="3" pageNumber="1020">0.19</td>
|
||
</tr>
|
||
<tr box="[107,768,1778,1794]" gridrow="39" pageId="3" pageNumber="1020">
|
||
<th box="[107,196,1778,1794]" gridcol="0" gridrow="39" pageId="3" pageNumber="1020">v (8)</th>
|
||
<td box="[316,369,1778,1794]" gridcol="1" gridrow="39" pageId="3" pageNumber="1020">0</td>
|
||
<td box="[445,508,1778,1794]" gridcol="2" gridrow="39" pageId="3" pageNumber="1020">–</td>
|
||
<td box="[586,639,1778,1794]" gridcol="3" gridrow="39" pageId="3" pageNumber="1020">0</td>
|
||
<td box="[715,768,1778,1794]" gridcol="4" gridrow="39" pageId="3" pageNumber="1020">0</td>
|
||
</tr>
|
||
<tr box="[107,768,1799,1815]" gridrow="40" pageId="3" pageNumber="1020">
|
||
<th box="[107,196,1799,1815]" gridcol="0" gridrow="40" pageId="3" pageNumber="1020">r (m)</th>
|
||
<td box="[316,369,1799,1815]" gridcol="1" gridrow="40" pageId="3" pageNumber="1020">0.37</td>
|
||
<td box="[445,508,1799,1815]" gridcol="2" gridrow="40" pageId="3" pageNumber="1020">–</td>
|
||
<td box="[586,639,1799,1815]" gridcol="3" gridrow="40" pageId="3" pageNumber="1020">0.11</td>
|
||
<td box="[715,768,1799,1815]" gridcol="4" gridrow="40" pageId="3" pageNumber="1020">0.065</td>
|
||
</tr>
|
||
<tr box="[107,768,1819,1836]" gridrow="41" pageId="3" pageNumber="1020">
|
||
<th box="[107,196,1819,1836]" gridcol="0" gridrow="41" pageId="3" pageNumber="1020">
|
||
<subScript attach="left" box="[121,125,1826,1836]" fontSize="4" pageId="3" pageNumber="1020">mi</subScript>
|
||
(%
|
||
<subScript attach="left" box="[164,189,1826,1836]" fontSize="4" pageId="3" pageNumber="1020">mbody</subScript>
|
||
)
|
||
</th>
|
||
<td box="[316,369,1819,1836]" gridcol="1" gridrow="41" pageId="3" pageNumber="1020">11</td>
|
||
<td box="[445,508,1819,1836]" gridcol="2" gridrow="41" pageId="3" pageNumber="1020">0</td>
|
||
<td box="[586,639,1819,1836]" gridcol="3" gridrow="41" pageId="3" pageNumber="1020">0.87</td>
|
||
<td box="[715,768,1819,1836]" gridcol="4" gridrow="41" pageId="3" pageNumber="1020">0.71</td>
|
||
</tr>
|
||
<tr box="[107,768,1840,1867]" gridrow="42" pageId="3" pageNumber="1020">
|
||
<th box="[107,768,1840,1867]" colspan="5" colspanRight="4" gridcol="0" gridrow="42" pageId="3" pageNumber="1020">
|
||
T (%
|
||
<subScript attach="left" box="[157,182,1847,1857]" fontSize="4" pageId="3" pageNumber="1020">mbody</subScript>
|
||
) 13 .............................................................................................................................................................................
|
||
</th>
|
||
</tr>
|
||
</table>
|
||
</paragraph>
|
||
<paragraph blockId="3.[800,1463,136,1218]" pageId="3" pageNumber="1020">
|
||
The ‘giant chicken’ example naturally prompts one to look at equation (1) in terms of scaling. Assuming isometric scaling, and that muscle pennation (v) and stress (j) are independent of body mass
|
||
<superScript attach="left" box="[849,917,970,983]" fontSize="6" pageId="3" pageNumber="1020">
|
||
<bibRefCitation author="Biewener, A. A." box="[849,863,970,983]" journalOrPublisher="Science" pageId="3" pageNumber="1020" pagination="45 - 48" part="245" refId="ref4463" refString="13. Biewener, A. A. Scaling body support in mammals: limb posture and muscle mechanics. Science 245, 45 - 48 (1989)." title="Scaling body support in mammals: limb posture and muscle mechanics" type="journal article" year="1989">13</bibRefCitation>
|
||
,
|
||
<bibRefCitation author="Alexander, R. McN. & Jayes, A. S. & Maloiy, G. M. O. & Wathuta, E. M." box="[866,881,970,983]" journalOrPublisher="J. Zool." pageId="3" pageNumber="1020" pagination="539 - 552" part="194" refId="ref4790" refString="17. Alexander, R. McN., Jayes, A. S., Maloiy, G. M. O. & Wathuta, E. M. Allometry of the leg muscles of mammals. J. Zool. 194, 539 - 552 (1981)." title="Allometry of the leg muscles of mammals" type="journal article" year="1981">17</bibRefCitation>
|
||
,
|
||
<bibRefCitation author="Bennett, M. B." box="[883,898,970,983]" journalOrPublisher="J. Zool." pageId="3" pageNumber="1020" pagination="435 - 443" part="238" refId="ref4842" refString="18. Bennett, M. B. Allometry of the leg muscles of birds. J. Zool. 238, 435 - 443 (1996)." title="Allometry of the leg muscles of birds" type="journal article" year="1996">18</bibRefCitation>
|
||
,
|
||
<bibRefCitation author="Johnston, I. A." box="[900,917,970,983]" journalOrPublisher="J. Exp. Biol." pageId="3" pageNumber="1020" pagination="239 - 251" part="115" refId="ref5112" refString="22. Johnston, I. A. Sustained force development: specializations and variation among the vertebrates. J. Exp. Biol. 115, 239 - 251 (1985)." title="Sustained force development: specializations and variation among the vertebrates" type="journal article" year="1985">22</bibRefCitation>
|
||
</superScript>
|
||
, we predict that
|
||
<collectionCode box="[1079,1094,974,995]" country="0" httpUri="http://grbio.org/cool/ey0i-ifzt" name="Tavera, Department of Geology and Geophysics" pageId="3" pageNumber="1020">
|
||
<emphasis box="[1079,1094,974,995]" italics="true" pageId="3" pageNumber="1020">
|
||
<collectionCodeEnum box="[1079,1094,974,995]" pageId="3" pageNumber="1020">T</collectionCodeEnum>
|
||
</emphasis>
|
||
</collectionCode>
|
||
increases linearly with increasing size (
|
||
<figureCitation box="[807,867,1001,1023]" captionStart="Figure 3" captionStartId="3.[800,853,1730,1749]" captionTargetBox="[821,1443,1275,1698]" captionTargetId="graphics@3.[894,1360,1285,1653]" captionTargetPageId="3" captionText="Figure 3 Estimated extensor muscle mass (T, as a percentage of body mass per leg) required to run quickly. Data are from various models and extant species plotted against log(mbody) to illustrate the scaling of T. Larger runners need a larger fraction of their body allocated to extensor muscle mass.Three shades of grey indicate the likelihood of running ability, based on estimated T. Very low estimated T implies a good chance of being a capable runner. Very high estimated T signals little chance of being a capable runner. Intermediate values of estimated T are inconclusive, and running ability in this case depends on the ratio of actual extensor muscle mass to T. Values of T greater than 50% per leg,or greater than 100% in total,are impossible.The solid line represents the case of scaling a chicken isometrically up to 6,000 kg." figureDoi="http://doi.org/10.5281/zenodo.3961020" httpUri="https://zenodo.org/record/3961020/files/figure.png" pageId="3" pageNumber="1020">Fig. 3</figureCitation>
|
||
). We expect
|
||
<collectionCode box="[995,1010,1002,1023]" country="0" httpUri="http://grbio.org/cool/ey0i-ifzt" name="Tavera, Department of Geology and Geophysics" pageId="3" pageNumber="1020">
|
||
<emphasis box="[995,1010,1002,1023]" italics="true" pageId="3" pageNumber="1020">
|
||
<collectionCodeEnum box="[995,1010,1002,1023]" pageId="3" pageNumber="1020">T</collectionCodeEnum>
|
||
</emphasis>
|
||
</collectionCode>
|
||
to increase with mass roughly in the manner shown by the dashed curve in
|
||
<figureCitation box="[1106,1163,1029,1051]" captionStart="Figure 3" captionStartId="3.[800,853,1730,1749]" captionTargetBox="[821,1443,1275,1698]" captionTargetId="graphics@3.[894,1360,1285,1653]" captionTargetPageId="3" captionText="Figure 3 Estimated extensor muscle mass (T, as a percentage of body mass per leg) required to run quickly. Data are from various models and extant species plotted against log(mbody) to illustrate the scaling of T. Larger runners need a larger fraction of their body allocated to extensor muscle mass.Three shades of grey indicate the likelihood of running ability, based on estimated T. Very low estimated T implies a good chance of being a capable runner. Very high estimated T signals little chance of being a capable runner. Intermediate values of estimated T are inconclusive, and running ability in this case depends on the ratio of actual extensor muscle mass to T. Values of T greater than 50% per leg,or greater than 100% in total,are impossible.The solid line represents the case of scaling a chicken isometrically up to 6,000 kg." figureDoi="http://doi.org/10.5281/zenodo.3961020" httpUri="https://zenodo.org/record/3961020/files/figure.png" pageId="3" pageNumber="1020">Fig. 3</figureCitation>
|
||
, especially if limb orientation remains quite flexed.
|
||
</paragraph>
|
||
<paragraph blockId="3.[800,1463,136,1218]" lastBlockId="4.[122,785,136,605]" lastPageId="4" lastPageNumber="1021" pageId="3" pageNumber="1020">
|
||
Our conclusions lead us to question the reconstructions of
|
||
<taxonomicName box="[800,943,1114,1135]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="3" pageNumber="1020" phylum="Chordata" rank="genus">
|
||
<emphasis box="[800,943,1114,1135]" italics="true" pageId="3" pageNumber="1020">Tyrannosaurus</emphasis>
|
||
</taxonomicName>
|
||
running at
|
||
<quantity box="[1066,1153,1113,1135]" metricMagnitude="1" metricUnit="m" metricValue="1.55" metricValueMax="2.0" metricValueMin="1.1" pageId="3" pageNumber="1020" unit="m" value="15.5" valueMax="20.0" valueMin="11.0">11–20 m</quantity>
|
||
s
|
||
<superScript attach="left" box="[1166,1183,1107,1122]" fontSize="6" pageId="3" pageNumber="1020">1</superScript>
|
||
(refs 3–8). Even at a lower running speed of
|
||
<quantity box="[987,1035,1141,1163]" metricMagnitude="1" metricUnit="m" metricValue="1.1" pageId="3" pageNumber="1020" unit="m" value="11.0">11 m</quantity>
|
||
s
|
||
<superScript attach="left" box="[1048,1065,1135,1150]" fontSize="6" pageId="3" pageNumber="1020">1</superScript>
|
||
(refs 3, 4, 8), an adult
|
||
<taxonomicName box="[1319,1462,1142,1163]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="3" pageNumber="1020" phylum="Chordata" rank="genus">
|
||
<emphasis box="[1319,1462,1142,1163]" italics="true" pageId="3" pageNumber="1020">Tyrannosaurus</emphasis>
|
||
</taxonomicName>
|
||
would have been near or above its maximum muscular capacity.
|
||
<collectionCode box="[1446,1462,1169,1190]" country="USA" httpUri="http://biocol.org/urn:lsid:biocol.org:col:15406" name="Harvard University - Arnold Arboretum" pageId="3" pageNumber="1020" type="Herbarium">A</collectionCode>
|
||
walking tyrannosaur could have adopted more extended limb joints to lower the GRF moment arms (
|
||
<emphasis box="[453,468,138,159]" italics="true" pageId="4" pageNumber="1021">
|
||
<collectionCode box="[453,468,138,159]" country="Chile" httpUri="http://grbio.org/cool/az7k-p4g9" name="Departamento de Geologia, Universidad de Chile" pageId="4" pageNumber="1021">
|
||
<collectionCodeEnum box="[453,468,138,159]" pageId="4" pageNumber="1021">R</collectionCodeEnum>
|
||
</collectionCode>
|
||
</emphasis>
|
||
) and used double limb support to reduce the GRF, decreasing the
|
||
<emphasis box="[479,494,165,186]" italics="true" pageId="4" pageNumber="1021">
|
||
<collectionCode box="[479,494,165,186]" country="0" httpUri="http://grbio.org/cool/ey0i-ifzt" name="Tavera, Department of Geology and Geophysics" pageId="4" pageNumber="1021">
|
||
<collectionCodeEnum box="[479,494,165,186]" pageId="4" pageNumber="1021">T</collectionCodeEnum>
|
||
</collectionCode>
|
||
</emphasis>
|
||
required for walking within reasonable bounds (
|
||
<tableCitation box="[334,417,192,214]" captionStart="Table 2" captionStartId="3.[107,157,791,807]" captionTargetBox="[107,768,827,1867]" captionTargetPageId="3" captionText="Table 2 Parameter sensitivity in Tyrannosaurus models" httpUri="http://table.plazi.org/id/28F46637FFD6D97D3812A464623AFCEE" pageId="4" pageNumber="1021" tableUuid="28F46637FFD6D97D3812A464623AFCEE">Table 2</tableCitation>
|
||
: models Trex_4 and Trex_lowest). However, our calculations suggest that even a walking tyrannosaur required activation of a large fraction of its extensor muscle volume, at considerable metabolic expense.
|
||
</paragraph>
|
||
<caption ID-DOI="http://doi.org/10.5281/zenodo.3961020" ID-Zenodo-Dep="3961020" httpUri="https://zenodo.org/record/3961020/files/figure.png" pageId="3" pageNumber="1020" startId="3.[800,853,1730,1749]" targetBox="[821,1443,1275,1698]" targetPageId="3">
|
||
<paragraph blockId="3.[800,1462,1730,2000]" pageId="3" pageNumber="1020">
|
||
Figure 3 Estimated extensor muscle mass (T, as a percentage of body mass per leg) required to run quickly. Data are from various models and extant species plotted against log(
|
||
<subScript attach="left" box="[842,866,1794,1807]" fontSize="5" pageId="3" pageNumber="1020">mbody</subScript>
|
||
) to illustrate the scaling of T. Larger runners need a larger fraction of their body allocated to extensor muscle mass.Three shades of grey indicate the likelihood of running ability, based on estimated T. Very low estimated T implies a good chance of being a capable runner. Very high estimated T signals little chance of being a capable runner. Intermediate values of estimated T are inconclusive, and running ability in this case depends on the ratio of actual extensor muscle mass to T. Values of T greater than 50% per leg,or greater than 100% in total,are impossible.The solid line represents the case of scaling a chicken isometrically up to 6,000 kg.
|
||
</paragraph>
|
||
</caption>
|
||
<paragraph blockId="3.[107,771,1873,1999]" pageId="3" pageNumber="1020">
|
||
<tableNote pageId="3" pageNumber="1020" targetBox="[107,768,827,1867]" targetPageId="3">
|
||
This shows the effect on the estimate of T (relative to model Trex_1) when we changed limb orientation (models Trex_24) or musclefibre lengths (model Trex_Lgator and Trex_Lchick, isometrically scaling up L from
|
||
<taxonomicName box="[350,404,1910,1924]" class="Reptilia" family="Alligatoridae" genus="Alligator" kingdom="Animalia" order="Crocodylia" pageId="3" pageNumber="1019" phylum="Chordata" rank="genus">Alligator</taxonomicName>
|
||
(5.91 kg) and
|
||
<taxonomicName box="[521,563,1910,1924]" class="Aves" family="Phasianidae" genus="Gallus" kingdom="Animalia" order="Galliformes" pageId="3" pageNumber="1020" phylum="Chordata" rank="genus">Gallus</taxonomicName>
|
||
(2.89 kg) to
|
||
<taxonomicName box="[667,768,1910,1924]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="3" pageNumber="1021" phylum="Chordata" rank="genus">Tyrannosaurus</taxonomicName>
|
||
(6,000 kg). As with
|
||
<taxonomicName box="[237,291,1929,1943]" class="Reptilia" family="Alligatoridae" genus="Alligator" kingdom="Animalia" order="Crocodylia" pageId="3" pageNumber="1019" phylum="Chordata" rank="genus">Alligator</taxonomicName>
|
||
(
|
||
<tableCitation box="[299,348,1929,1943]" captionStart="Table 1" captionStartId="2.[122,172,873,889]" captionTargetBox="[122,784,909,1793]" captionTargetPageId="2" captionText="Table 1 Muscle anatomical data entered in equation (1) to estimate T" httpUri="http://table.plazi.org/id/28F46637FFD7D97C3803A41A62B2FCB0" pageId="3" pageNumber="1020" tableUuid="28F46637FFD7D97C3803A41A62B2FCB0">Table 1</tableCitation>
|
||
), models Trex_3, Trex_4, and Trex_lowest had a flexor
|
||
<subScript attach="left" box="[743,769,1935,1945]" fontSize="4" pageId="3" pageNumber="1020">Mmusc</subScript>
|
||
about the knee joint, so the knee
|
||
<subScript attach="left" box="[362,366,1954,1964]" fontSize="4" pageId="3" pageNumber="1020">mi</subScript>
|
||
was conservatively set at 0. Model Trex_lowest shows a combination of parameter values (L from model Trex_Lgator, limb orientation from model Trex_4, and v set at 08) that brought T to its lowest estimated value (see Supplementary Information).
|
||
</tableNote>
|
||
</paragraph>
|
||
<paragraph blockId="4.[122,785,136,605]" lastBlockId="4.[122,784,637,868]" pageId="4" pageNumber="1021">
|
||
These conclusions should apply to all larger dinosaurs, invalidating arguments that tyrannosaurs were too slow to prey on large contemporaries
|
||
<bibRefCitation author="Horner, J. R. & Lessem, D." box="[277,284,356,369]" journalOrPublisher="Simon & Schuster, New York" pageId="4" pageNumber="1021" refId="ref3902" refString="3. Horner, J. R. & Lessem, D. The Complete T. rex (Simon & Schuster, New York, 1993)." title="The Complete T. rex" type="book" year="1993">
|
||
<superScript attach="left" box="[277,284,356,369]" fontSize="6" pageId="4" pageNumber="1021">3</superScript>
|
||
</bibRefCitation>
|
||
such as
|
||
<taxonomicName authorityName="Marsh" authorityYear="1889" box="[366,472,361,382]" class="Reptilia" family="Ceratopsidae" genus="Triceratops" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="4" pageNumber="1021" phylum="Chordata" rank="genus">
|
||
<emphasis box="[366,472,361,382]" italics="true" pageId="4" pageNumber="1021">Triceratops</emphasis>
|
||
</taxonomicName>
|
||
.
|
||
<taxonomicName box="[483,626,361,382]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="4" pageNumber="1021" phylum="Chordata" rank="genus">
|
||
<emphasis box="[483,626,361,382]" italics="true" pageId="4" pageNumber="1021">Tyrannosaurus</emphasis>
|
||
</taxonomicName>
|
||
shows the most extreme cursorial (that is, locomotionrelated) specializations of larger theropods
|
||
<superScript attach="left" box="[285,309,412,425]" fontSize="6" pageId="4" pageNumber="1021">
|
||
<bibRefCitation author="Bakker, R. T." box="[285,292,412,425]" journalOrPublisher="William Morrow, New York" pageId="4" pageNumber="1021" refId="ref4160" refString="5. Bakker, R. T. Dinosaur Heresies (William Morrow, New York, 1986)." title="Dinosaur Heresies" type="book" year="1986">5</bibRefCitation>
|
||
–
|
||
<bibRefCitation author="Farlow, J. O. & Gatesy, S. M. & Holtz, T. R. Jr & Hutchinson, J. R. & Robinson, J. M." box="[301,309,412,425]" journalOrPublisher="Am. Zool." pageId="4" pageNumber="1021" pagination="640 - 663" part="40" refId="ref4267" refString="9. Farlow, J. O., Gatesy, S. M., Holtz, T. R. Jr, Hutchinson, J. R. & Robinson, J. M. Theropod locomotion. Am. Zool. 40, 640 - 663 (2000)." title="Theropod locomotion" type="journal article" year="2000">9</bibRefCitation>
|
||
</superScript>
|
||
, but even it was probably a slow runner, at best. Therefore we infer that the numerous lineages of theropod dinosaurs that evolved enormous sizes
|
||
<bibRefCitation author="Farlow, J. O. & Gatesy, S. M. & Holtz, T. R. Jr & Hutchinson, J. R. & Robinson, J. M." box="[475,482,468,481]" journalOrPublisher="Am. Zool." pageId="4" pageNumber="1021" pagination="640 - 663" part="40" refId="ref4267" refString="9. Farlow, J. O., Gatesy, S. M., Holtz, T. R. Jr, Hutchinson, J. R. & Robinson, J. M. Theropod locomotion. Am. Zool. 40, 640 - 663 (2000)." title="Theropod locomotion" type="journal article" year="2000">
|
||
<superScript attach="left" box="[475,482,468,481]" fontSize="6" pageId="4" pageNumber="1021">9</superScript>
|
||
</bibRefCitation>
|
||
independently reduced their running ability. Conversely, reduction of body size and relative increases of extensor muscle sizes and moment arms probably increased running ability in maniraptoran theropods, especially birds
|
||
<superScript attach="left" box="[172,204,580,593]" fontSize="6" pageId="4" pageNumber="1021">
|
||
<bibRefCitation author="Hutchinson, J. R. The" box="[172,186,580,593]" journalOrPublisher="Univ. California" pageId="4" pageNumber="1021" refId="ref4674" refString="15. Hutchinson, J. R. The Evolution of Hindlimb Anatomy and Function in Theropod Dinosaurs. PhD thesis, Univ. California (2001)." title="Evolution of Hindlimb Anatomy and Function in Theropod Dinosaurs" type="book" year="2001">15</bibRefCitation>
|
||
,
|
||
<bibRefCitation author="Carrano, M. T. & Hutchinson, J. R." box="[189,204,580,593]" journalOrPublisher="J. Morphol. (in the press)" pageId="4" pageNumber="1021" refId="ref4703" refString="16. Carrano, M. T. & Hutchinson, J. R. The pelvic and hind limb musculature of Tyrannosaurus rex (Dinosauria: Theropoda). J. Morphol. (in the press)" title="The pelvic and hind limb musculature of Tyrannosaurus rex (Dinosauria: Theropoda)" type="book" year="2001">16</bibRefCitation>
|
||
</superScript>
|
||
.
|
||
<heading box="[122,213,637,661]" fontSize="10" level="1" pageId="4" pageNumber="1021" reason="1">Methods</heading>
|
||
</paragraph>
|
||
<paragraph blockId="4.[122,784,637,868]" pageId="4" pageNumber="1021">
|
||
The minimum mass of muscle (
|
||
<emphasis box="[363,378,669,686]" italics="true" pageId="4" pageNumber="1021">
|
||
<emphasis box="[377,381,677,688]" italics="true" pageId="4" pageNumber="1021">
|
||
<subScript attach="left" box="[377,381,677,688]" fontSize="5" pageId="4" pageNumber="1021">mi</subScript>
|
||
</emphasis>
|
||
</emphasis>
|
||
) required to produce the joint moment
|
||
<emphasis box="[686,702,669,686]" italics="true" pageId="4" pageNumber="1021">
|
||
<collectionCode box="[686,702,669,686]" country="Germany" httpUri="http://biocol.org/urn:lsid:biocol.org:col:15637" name="Botanische Staatssammlung M<>nchen" pageId="4" pageNumber="1021" type="Herbarium">M</collectionCode>
|
||
</emphasis>
|
||
<subScript attach="left" box="[703,730,677,688]" fontSize="5" pageId="4" pageNumber="1021">musc</subScript>
|
||
to maintain static equilibrium about any joint
|
||
<emphasis box="[452,457,692,709]" italics="true" pageId="4" pageNumber="1021">i</emphasis>
|
||
is a function of the muscle density (
|
||
<emphasis box="[733,742,692,709]" italics="true" pageId="4" pageNumber="1021">d</emphasis>
|
||
), multiplied by the volume (
|
||
<emphasis box="[325,337,714,731]" italics="true" pageId="4" pageNumber="1021">
|
||
<collectionCodeEnum box="[325,337,714,731]" pageId="4" pageNumber="1021">
|
||
<collectionCode box="[325,337,714,731]" country="Canada" httpUri="http://biocol.org/urn:lsid:biocol.org:col:13946" name="Royal British Columbia Museum - Herbarium" pageId="4" pageNumber="1021" type="Museum">V</collectionCode>
|
||
</collectionCodeEnum>
|
||
</emphasis>
|
||
), divided by the fraction of active muscle volume (
|
||
<emphasis box="[723,730,714,731]" italics="true" pageId="4" pageNumber="1021">c</emphasis>
|
||
).
|
||
<emphasis box="[746,758,714,731]" italics="true" pageId="4" pageNumber="1021">
|
||
<collectionCode box="[746,758,714,731]" country="Canada" httpUri="http://biocol.org/urn:lsid:biocol.org:col:13946" lsid="urn:lsid:biocol.org:col:13946" name="Royal British Columbia Museum - Herbarium" pageId="4" pageNumber="1021" type="Museum">
|
||
<collectionCodeEnum box="[746,758,714,731]" pageId="4" pageNumber="1021">V</collectionCodeEnum>
|
||
</collectionCode>
|
||
</emphasis>
|
||
is equal to the muscle fibre length (
|
||
<emphasis box="[371,381,737,754]" italics="true" pageId="4" pageNumber="1021">
|
||
<collectionCode box="[371,381,737,754]" country="Netherlands" httpUri="http://biocol.org/urn:lsid:biocol.org:col:15678" lsid="urn:lsid:biocol.org:col:15678" name="Nationaal Herbarium Nederland, Leiden University branch" pageId="4" pageNumber="1021" type="Herbarium">L</collectionCode>
|
||
</emphasis>
|
||
), times the crosssectional area (
|
||
<emphasis box="[629,641,737,754]" italics="true" pageId="4" pageNumber="1021">
|
||
<collectionCode box="[629,641,737,754]" country="USA" httpUri="http://biocol.org/urn:lsid:biocol.org:col:15406" lsid="urn:lsid:biocol.org:col:15406" name="Harvard University - Arnold Arboretum" pageId="4" pageNumber="1021" type="Herbarium">A</collectionCode>
|
||
</emphasis>
|
||
), divided by the cosine of the pennation angle of the muscle fibres (cosv)
|
||
<superScript attach="none" box="[546,574,757,767]" fontSize="4" pageId="4" pageNumber="1021">12–14</superScript>
|
||
. Furthermore,
|
||
<emphasis box="[689,701,760,777]" italics="true" pageId="4" pageNumber="1021">
|
||
<collectionCode box="[689,701,760,777]" country="USA" httpUri="http://biocol.org/urn:lsid:biocol.org:col:15406" lsid="urn:lsid:biocol.org:col:15406" name="Harvard University - Arnold Arboretum" pageId="4" pageNumber="1021" type="Herbarium">A</collectionCode>
|
||
</emphasis>
|
||
is equal to the muscle force (
|
||
<emphasis box="[257,267,782,799]" italics="true" pageId="4" pageNumber="1021">
|
||
<collectionCode box="[257,267,782,799]" country="USA" httpUri="http://biocol.org/urn:lsid:biocol.org:col:15707" lsid="urn:lsid:biocol.org:col:15707" name="Field Museum of Natural History, Botany Department" pageId="4" pageNumber="1021" type="Herbarium">F</collectionCode>
|
||
</emphasis>
|
||
) divided by the stress (j). Finally,
|
||
<emphasis box="[528,538,782,799]" italics="true" pageId="4" pageNumber="1021">
|
||
<collectionCode box="[528,538,782,799]" country="USA" httpUri="http://biocol.org/urn:lsid:biocol.org:col:15707" lsid="urn:lsid:biocol.org:col:15707" name="Field Museum of Natural History, Botany Department" pageId="4" pageNumber="1021" type="Herbarium">F</collectionCode>
|
||
</emphasis>
|
||
must be the
|
||
<emphasis box="[636,652,782,799]" italics="true" pageId="4" pageNumber="1021">
|
||
<collectionCode box="[636,652,782,799]" country="Germany" httpUri="http://biocol.org/urn:lsid:biocol.org:col:15637" lsid="urn:lsid:biocol.org:col:15637" name="Botanische Staatssammlung München" pageId="4" pageNumber="1021" type="Herbarium">M</collectionCode>
|
||
</emphasis>
|
||
<subScript attach="left" box="[652,679,790,801]" fontSize="5" pageId="4" pageNumber="1021">musc</subScript>
|
||
required to stabilize each joint,divided by the mean extensor muscle moment arm (
|
||
<emphasis box="[648,655,805,822]" italics="true" pageId="4" pageNumber="1021">r</emphasis>
|
||
)
|
||
<superScript attach="none" box="[662,690,802,812]" fontSize="4" pageId="4" pageNumber="1021">12–14</superScript>
|
||
. Combining these expressions to solve for the extensor muscle mass required to act about a particular joint
|
||
<emphasis box="[162,167,850,867]" italics="true" pageId="4" pageNumber="1021">i</emphasis>
|
||
(
|
||
<emphasis box="[179,194,850,867]" italics="true" pageId="4" pageNumber="1021">
|
||
<emphasis box="[194,198,857,868]" italics="true" pageId="4" pageNumber="1021">
|
||
<subScript attach="left" box="[194,198,857,868]" fontSize="5" pageId="4" pageNumber="1021">mi</subScript>
|
||
</emphasis>
|
||
</emphasis>
|
||
; expressed as a percentage of body mass,
|
||
<emphasis box="[510,525,850,867]" italics="true" pageId="4" pageNumber="1021">m</emphasis>
|
||
<subScript attach="left" box="[525,550,857,868]" fontSize="5" pageId="4" pageNumber="1021">body</subScript>
|
||
) produces:
|
||
</paragraph>
|
||
<paragraph blockId="4.[321,584,888,907]" box="[321,783,888,907]" lastBlockId="4.[762,783,888,905]" pageId="4" pageNumber="1021">
|
||
<emphasis box="[321,336,888,905]" italics="true" pageId="4" pageNumber="1021">m</emphasis>
|
||
<emphasis box="[336,340,897,907]" italics="true" pageId="4" pageNumber="1021">i</emphasis>
|
||
100
|
||
<emphasis box="[401,417,888,905]" italics="true" pageId="4" pageNumber="1021">
|
||
<collectionCode box="[401,417,888,905]" country="Germany" httpUri="http://biocol.org/urn:lsid:biocol.org:col:15637" lsid="urn:lsid:biocol.org:col:15637" name="Botanische Staatssammlung München" pageId="4" pageNumber="1021" type="Herbarium">M</collectionCode>
|
||
</emphasis>
|
||
musc
|
||
<emphasis box="[443,462,888,905]" italics="true" pageId="4" pageNumber="1021">Ld</emphasis>
|
||
=
j
|
||
<emphasis box="[490,518,888,905]" italics="true" pageId="4" pageNumber="1021">crm</emphasis>
|
||
body cosv
1
|
||
|
||
</paragraph>
|
||
<paragraph blockId="4.[122,783,933,975]" pageId="4" pageNumber="1021">
|
||
These parameters do not depend greatly on the physiology of the animal
|
||
<superScript attach="left" box="[651,662,933,943]" fontSize="4" pageId="4" pageNumber="1021">22</superScript>
|
||
, so the equation holds for both warm and coldblooded animals.
|
||
</paragraph>
|
||
<subSection pageId="4" pageNumber="1021" type="multiple">
|
||
<paragraph blockId="4.[122,785,1009,1262]" box="[122,413,1009,1030]" pageId="4" pageNumber="1021">
|
||
<heading box="[122,413,1009,1030]" fontSize="8" level="2" pageId="4" pageNumber="1021" reason="1">
|
||
Estimating the joint moment
|
||
<subScript attach="left" box="[382,413,1018,1030]" fontSize="5" pageId="4" pageNumber="1021">Mmusc</subScript>
|
||
</heading>
|
||
</paragraph>
|
||
<paragraph blockId="4.[122,785,1009,1262]" pageId="4" pageNumber="1021">
|
||
In order to estimate
|
||
<emphasis box="[275,291,1040,1057]" italics="true" pageId="4" pageNumber="1021">
|
||
<collectionCode box="[275,291,1040,1057]" country="Germany" httpUri="http://biocol.org/urn:lsid:biocol.org:col:15637" lsid="urn:lsid:biocol.org:col:15637" name="Botanische Staatssammlung München" pageId="4" pageNumber="1021" type="Herbarium">M</collectionCode>
|
||
</emphasis>
|
||
<subScript attach="left" box="[291,318,1048,1059]" fontSize="5" pageId="4" pageNumber="1021">musc</subScript>
|
||
(and hence
|
||
<emphasis box="[410,425,1040,1057]" italics="true" pageId="4" pageNumber="1021">
|
||
<emphasis box="[425,429,1048,1059]" italics="true" pageId="4" pageNumber="1021">
|
||
<subScript attach="left" box="[425,429,1048,1059]" fontSize="5" pageId="4" pageNumber="1021">mi</subScript>
|
||
</emphasis>
|
||
</emphasis>
|
||
), we used MATLAB (The Mathworks) software to compute the joint moments needed to maintain static equilibrium in a particular limb orientation. To maintain equilibrium, muscles must exert net muscle moments about joints that balance equal and opposite moments incurred by external and internal forces, such as the ground reaction force (GRF) and segment weights (
|
||
<emphasis box="[599,616,1131,1148]" italics="true" pageId="4" pageNumber="1021">
|
||
<collectionCode box="[599,616,1131,1148]" country="Austria" httpUri="http://biocol.org/urn:lsid:biocol.org:col:15588" lsid="urn:lsid:biocol.org:col:15588" name="Naturhistorisches Museum Wien" pageId="4" pageNumber="1021" type="Herbarium">W</collectionCode>
|
||
</emphasis>
|
||
<subScript attach="left" box="[616,622,1138,1149]" fontSize="5" pageId="4" pageNumber="1021">b</subScript>
|
||
,
|
||
<emphasis box="[632,648,1131,1148]" italics="true" pageId="4" pageNumber="1021">
|
||
<collectionCode box="[632,648,1131,1148]" country="Austria" httpUri="http://biocol.org/urn:lsid:biocol.org:col:15588" lsid="urn:lsid:biocol.org:col:15588" name="Naturhistorisches Museum Wien" pageId="4" pageNumber="1021" type="Herbarium">W</collectionCode>
|
||
</emphasis>
|
||
<subScript attach="left" box="[648,652,1138,1149]" fontSize="5" pageId="4" pageNumber="1021">t</subScript>
|
||
,
|
||
<emphasis box="[662,679,1131,1148]" italics="true" pageId="4" pageNumber="1021">
|
||
<collectionCode box="[662,679,1131,1148]" country="Austria" httpUri="http://biocol.org/urn:lsid:biocol.org:col:15588" lsid="urn:lsid:biocol.org:col:15588" name="Naturhistorisches Museum Wien" pageId="4" pageNumber="1021" type="Herbarium">W</collectionCode>
|
||
</emphasis>
|
||
<subScript attach="left" box="[678,682,1138,1149]" fontSize="5" pageId="4" pageNumber="1021">s</subScript>
|
||
and
|
||
<emphasis box="[721,737,1131,1148]" italics="true" pageId="4" pageNumber="1021">
|
||
<collectionCode box="[721,737,1131,1148]" country="Austria" httpUri="http://biocol.org/urn:lsid:biocol.org:col:15588" lsid="urn:lsid:biocol.org:col:15588" name="Naturhistorisches Museum Wien" pageId="4" pageNumber="1021" type="Herbarium">W</collectionCode>
|
||
</emphasis>
|
||
<subScript attach="left" box="[737,747,1138,1149]" fontSize="5" pageId="4" pageNumber="1021">m</subScript>
|
||
in
|
||
<figureCitation box="[122,162,1153,1170]" captionStart="Figure 1" captionStartId="1.[800,853,1702,1721]" captionTargetBox="[801,1455,1164,1662]" captionTargetId="graphics@1.[858,1251,1165,1428]" captionTargetPageId="1" captionText="Figure 1 Explanation of freebody diagram analysis of body segments.Skeletal illustration modified from ref. 6. The initial Tyrannosaurus model (Trex_1) is shown in right lateral view and (x, y)coordinate space,with the origin located at the toe joint. Pelvic pitch,hip, knee, ankle and toe joint angle definitions are shown (see Supplementary Information). One of the angles is redundant (four angles suffice). The ground reaction force (GRF) is vertical (typical for midstance12–14) and acts at a distance R from the toe joints.The body segment weights (Wb, Wt, Ws and Wm for the trunk,thigh,shank and metatarsus) are also shown.A freebody diagram was used to calculate the internal moments about each joint. For example, about the knee joint (see inset), the moment that knee extensor muscles must generate (Mk) is equal to the ankle contact force (Fa) times its respective moment arm, plus the gravitational moment of the shank segment and the ankle moment (Ma)." figureDoi="http://doi.org/10.5281/zenodo.3961016" httpUri="https://zenodo.org/record/3961016/files/figure.png" pageId="4" pageNumber="1021">Fig.1</figureCitation>
|
||
). These moments can be calculated in two dimensions by drawing a set of freebody diagrams and applying the three equilibrium equations (
|
||
<collectionCode box="[548,559,1176,1193]" country="Sweden" httpUri="http://biocol.org/urn:lsid:biocol.org:col:15668" lsid="urn:lsid:biocol.org:col:15668" name="Department of Botany, Swedish Museum of Natural History" pageId="4" pageNumber="1021" type="Herbarium">S</collectionCode>
|
||
<emphasis box="[560,570,1176,1193]" italics="true" pageId="4" pageNumber="1021">
|
||
<collectionCode box="[560,570,1176,1193]" country="USA" httpUri="http://biocol.org/urn:lsid:biocol.org:col:15707" lsid="urn:lsid:biocol.org:col:15707" name="Field Museum of Natural History, Botany Department" pageId="4" pageNumber="1021" type="Herbarium">F</collectionCode>
|
||
</emphasis>
|
||
<emphasis box="[570,575,1184,1194]" italics="true" pageId="4" pageNumber="1021">
|
||
<subScript attach="left" box="[570,575,1184,1194]" fontSize="4" pageId="4" pageNumber="1021">x</subScript>
|
||
</emphasis>
|
||
0,
|
||
<collectionCode box="[620,631,1176,1193]" country="Sweden" httpUri="http://biocol.org/urn:lsid:biocol.org:col:15668" lsid="urn:lsid:biocol.org:col:15668" name="Department of Botany, Swedish Museum of Natural History" pageId="4" pageNumber="1021" type="Herbarium">S</collectionCode>
|
||
<emphasis box="[631,641,1176,1193]" italics="true" pageId="4" pageNumber="1021">
|
||
<collectionCode box="[631,641,1176,1193]" country="USA" httpUri="http://biocol.org/urn:lsid:biocol.org:col:15707" lsid="urn:lsid:biocol.org:col:15707" name="Field Museum of Natural History, Botany Department" pageId="4" pageNumber="1021" type="Herbarium">F</collectionCode>
|
||
</emphasis>
|
||
<emphasis box="[642,647,1184,1194]" italics="true" pageId="4" pageNumber="1021">
|
||
<subScript attach="left" box="[642,647,1184,1194]" fontSize="4" pageId="4" pageNumber="1021">y</subScript>
|
||
</emphasis>
|
||
0,
|
||
<collectionCode box="[692,703,1176,1193]" country="Sweden" httpUri="http://biocol.org/urn:lsid:biocol.org:col:15668" lsid="urn:lsid:biocol.org:col:15668" name="Department of Botany, Swedish Museum of Natural History" pageId="4" pageNumber="1021" type="Herbarium">S</collectionCode>
|
||
<emphasis box="[703,719,1176,1193]" italics="true" pageId="4" pageNumber="1021">
|
||
<collectionCode box="[703,719,1176,1193]" country="Germany" httpUri="http://biocol.org/urn:lsid:biocol.org:col:15637" lsid="urn:lsid:biocol.org:col:15637" name="Botanische Staatssammlung München" pageId="4" pageNumber="1021" type="Herbarium">M</collectionCode>
|
||
</emphasis>
|
||
0).
|
||
</paragraph>
|
||
<paragraph blockId="4.[122,785,1009,1262]" pageId="4" pageNumber="1021">
|
||
This procedure is appropriate for standing, and we explain below how it can be applied to running. We summed
|
||
<emphasis box="[291,306,1221,1238]" italics="true" pageId="4" pageNumber="1021">
|
||
<emphasis box="[305,309,1228,1239]" italics="true" pageId="4" pageNumber="1021">
|
||
<subScript attach="left" box="[305,309,1228,1239]" fontSize="5" pageId="4" pageNumber="1021">mi</subScript>
|
||
</emphasis>
|
||
</emphasis>
|
||
for all four limb joints to estimate
|
||
<emphasis box="[575,585,1221,1238]" italics="true" pageId="4" pageNumber="1021">
|
||
<collectionCode box="[575,585,1221,1238]" country="0" httpUri="http://grbio.org/cool/ey0i-ifzt" name="Tavera, Department of Geology and Geophysics" pageId="4" pageNumber="1021">
|
||
<collectionCodeEnum box="[575,585,1221,1238]" pageId="4" pageNumber="1021">T</collectionCodeEnum>
|
||
</collectionCode>
|
||
</emphasis>
|
||
, the total extensor muscle mass required per leg, as a percentage of
|
||
<emphasis box="[430,445,1244,1261]" italics="true" pageId="4" pageNumber="1021">m</emphasis>
|
||
<subScript attach="left" box="[444,468,1251,1262]" fontSize="5" pageId="4" pageNumber="1021">body</subScript>
|
||
.
|
||
</paragraph>
|
||
</subSection>
|
||
<paragraph blockId="4.[122,784,1295,1478]" box="[122,218,1295,1314]" pageId="4" pageNumber="1021">
|
||
<heading box="[122,218,1295,1314]" fontSize="8" level="2" pageId="4" pageNumber="1021" reason="1">
|
||
Choosing
|
||
<collectionCode box="[206,218,1295,1314]" country="Switzerland" httpUri="http://biocol.org/urn:lsid:biocol.org:col:15706" lsid="urn:lsid:biocol.org:col:15706" name="Conservatoire et Jardin botaniques de la Ville de Genève" pageId="4" pageNumber="1021" type="Herbarium">G</collectionCode>
|
||
</heading>
|
||
</paragraph>
|
||
<paragraph blockId="4.[122,784,1295,1478]" pageId="4" pageNumber="1021">
|
||
We multiplied the
|
||
<potCollectionCode box="[262,296,1326,1343]" pageId="4" pageNumber="1021">GRF</potCollectionCode>
|
||
magnitude in the freebody diagram analysis by a factor
|
||
<emphasis box="[726,739,1326,1343]" italics="true" pageId="4" pageNumber="1021">
|
||
<collectionCode box="[726,739,1326,1343]" country="Switzerland" httpUri="http://biocol.org/urn:lsid:biocol.org:col:15706" lsid="urn:lsid:biocol.org:col:15706" name="Conservatoire et Jardin botaniques de la Ville de Genève" pageId="4" pageNumber="1021" type="Herbarium">G</collectionCode>
|
||
</emphasis>
|
||
, the ratio of the
|
||
<potCollectionCode box="[211,245,1348,1365]" pageId="4" pageNumber="1021">GRF</potCollectionCode>
|
||
to body weight (
|
||
<emphasis box="[375,390,1348,1365]" italics="true" pageId="4" pageNumber="1021">m</emphasis>
|
||
<subScript attach="both" box="[390,415,1356,1367]" fontSize="5" pageId="4" pageNumber="1021">body</subScript>
|
||
<emphasis box="[415,423,1348,1365]" italics="true" pageId="4" pageNumber="1021">g</emphasis>
|
||
, with
|
||
<emphasis box="[471,479,1348,1365]" italics="true" pageId="4" pageNumber="1021">g</emphasis>
|
||
9:
|
||
<quantity box="[518,554,1348,1365]" metricMagnitude="1" metricUnit="m" metricValue="8.1" pageId="4" pageNumber="1021" unit="m" value="81.0">81 m</quantity>
|
||
s
|
||
<superScript attach="left" box="[564,579,1346,1356]" fontSize="4" pageId="4" pageNumber="1021">22</superScript>
|
||
), to estimate the
|
||
<emphasis box="[713,729,1348,1365]" italics="true" pageId="4" pageNumber="1021">
|
||
<collectionCode box="[713,729,1348,1365]" country="Germany" httpUri="http://biocol.org/urn:lsid:biocol.org:col:15637" lsid="urn:lsid:biocol.org:col:15637" name="Botanische Staatssammlung München" pageId="4" pageNumber="1021" type="Herbarium">M</collectionCode>
|
||
</emphasis>
|
||
<subScript attach="left" box="[729,756,1356,1367]" fontSize="5" pageId="4" pageNumber="1021">musc</subScript>
|
||
needed to support the body on one leg at midstance of fast running. At midstance of running, the body centre of mass is at its lowest point accelerating upwards, but inertial moments are miniscule relative to the moments of the
|
||
<potCollectionCode box="[518,552,1416,1433]" pageId="4" pageNumber="1021">GRF</potCollectionCode>
|
||
,so midstance is approximated as quasistatic
|
||
<superScript attach="left" box="[227,269,1436,1446]" fontSize="4" pageId="4" pageNumber="1021">12–14,23</superScript>
|
||
. The value of
|
||
<emphasis box="[376,389,1439,1456]" italics="true" pageId="4" pageNumber="1021">
|
||
<collectionCode box="[376,389,1439,1456]" country="Switzerland" httpUri="http://biocol.org/urn:lsid:biocol.org:col:15706" lsid="urn:lsid:biocol.org:col:15706" name="Conservatoire et Jardin botaniques de la Ville de Genève" pageId="4" pageNumber="1021" type="Herbarium">G</collectionCode>
|
||
</emphasis>
|
||
was set at 2.5, which is a reasonable value for fast running or hopping bipeds
|
||
<superScript attach="left" box="[326,381,1459,1469]" fontSize="4" pageId="4" pageNumber="1021">12–14,24,25</superScript>
|
||
.
|
||
</paragraph>
|
||
<paragraph blockId="4.[122,784,1510,1784]" box="[122,367,1510,1529]" pageId="4" pageNumber="1021">
|
||
<heading box="[122,367,1510,1529]" fontSize="8" level="2" pageId="4" pageNumber="1021" reason="1">Determining forward velocity</heading>
|
||
</paragraph>
|
||
<paragraph blockId="4.[122,784,1510,1784]" pageId="4" pageNumber="1021">
|
||
To determine an approximate forward velocity that would be consistent with
|
||
<emphasis box="[697,710,1541,1558]" italics="true" pageId="4" pageNumber="1021">
|
||
<collectionCode box="[697,710,1541,1558]" country="Switzerland" httpUri="http://biocol.org/urn:lsid:biocol.org:col:15706" lsid="urn:lsid:biocol.org:col:15706" name="Conservatoire et Jardin botaniques de la Ville de Genève" pageId="4" pageNumber="1021" type="Herbarium">G</collectionCode>
|
||
</emphasis>
|
||
2:5 for
|
||
<taxonomicName box="[122,230,1564,1581]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="4" pageNumber="1021" phylum="Chordata" rank="genus">
|
||
<emphasis box="[122,230,1564,1581]" italics="true" pageId="4" pageNumber="1021">Tyrannosaurus</emphasis>
|
||
</taxonomicName>
|
||
, we can use the notion of dynamic similarity, such as the Froude number (Fr), the ratio of centripetal to gravitational forces
|
||
<superScript attach="left" box="[499,510,1584,1594]" fontSize="4" pageId="4" pageNumber="1021">26</superScript>
|
||
, calculated as Fr
|
||
</paragraph>
|
||
<paragraph blockId="4.[122,784,1510,1784]" pageId="4" pageNumber="1021">
|
||
velocity
|
||
<superScript attach="none" box="[192,197,1606,1616]" fontSize="4" pageId="4" pageNumber="1021">2</superScript>
|
||
=
hip height
|
||
<quantity box="[293,320,1609,1626]" metricMagnitude="-3" metricUnit="kg" metricValue="3.0" pageId="4" pageNumber="1021" unit="g" value="3.0">
|
||
3
|
||
<emphasis box="[312,320,1609,1626]" italics="true" pageId="4" pageNumber="1021">g</emphasis>
|
||
</quantity>
|
||
. Our value of
|
||
<emphasis box="[434,447,1609,1626]" italics="true" pageId="4" pageNumber="1021">
|
||
<collectionCode box="[434,447,1609,1626]" country="Switzerland" httpUri="http://biocol.org/urn:lsid:biocol.org:col:15706" lsid="urn:lsid:biocol.org:col:15706" name="Conservatoire et Jardin botaniques de la Ville de Genève" pageId="4" pageNumber="1021" type="Herbarium">G</collectionCode>
|
||
</emphasis>
|
||
2:5 for
|
||
<taxonomicName box="[524,631,1609,1626]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="4" pageNumber="1021" phylum="Chordata" rank="genus">
|
||
<emphasis box="[524,631,1609,1626]" italics="true" pageId="4" pageNumber="1021">Tyrannosaurus</emphasis>
|
||
</taxonomicName>
|
||
highspeed running is comparable to the value (
|
||
<emphasis box="[331,344,1631,1648]" italics="true" pageId="4" pageNumber="1021">
|
||
<collectionCode box="[331,344,1631,1648]" country="Switzerland" lsid="urn:lsid:biocol.org:col:15706" name="Conservatoire et Jardin botaniques de la Ville de Genève" pageId="4" pageNumber="1021" type="Herbarium">G</collectionCode>
|
||
</emphasis>
|
||
2:7) estimated for an ostrich
|
||
<superScript attach="left" box="[582,593,1629,1639]" fontSize="4" pageId="4" pageNumber="1021">27</superScript>
|
||
running at
|
||
<quantity box="[683,719,1631,1648]" metricMagnitude="1" metricUnit="m" metricValue="1.2" pageId="4" pageNumber="1021" unit="m" value="12.0">12 m</quantity>
|
||
s
|
||
<superScript attach="left" box="[729,741,1627,1638]" fontSize="5" pageId="4" pageNumber="1021">1</superScript>
|
||
with Fr 16. For
|
||
<taxonomicName box="[221,328,1654,1671]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="4" pageNumber="1021" phylum="Chordata" rank="genus">
|
||
<emphasis box="[221,328,1654,1671]" italics="true" pageId="4" pageNumber="1021">Tyrannosaurus</emphasis>
|
||
</taxonomicName>
|
||
(hip height is roughly 2.5 m), Fr 16 implies an average forward speed of almost
|
||
<quantity box="[309,344,1676,1693]" metricMagnitude="1" metricUnit="m" metricValue="2.0" pageId="4" pageNumber="1021" unit="m" value="20.0">20m</quantity>
|
||
s
|
||
<superScript attach="left" box="[355,367,1673,1684]" fontSize="5" pageId="4" pageNumber="1021">1</superScript>
|
||
. Therefore our model assumes a GRF magnitude consistent with the faster estimates of
|
||
<taxonomicName box="[408,516,1699,1716]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="4" pageNumber="1021" phylum="Chordata" rank="genus">
|
||
<emphasis box="[408,516,1699,1716]" italics="true" pageId="4" pageNumber="1021">Tyrannosaurus</emphasis>
|
||
</taxonomicName>
|
||
running speed
|
||
<superScript attach="left" box="[629,647,1697,1707]" fontSize="4" pageId="4" pageNumber="1021">5–7</superScript>
|
||
. In theory, at
|
||
</paragraph>
|
||
<paragraph blockId="4.[122,784,1510,1784]" pageId="4" pageNumber="1021">
|
||
Fr. 1, an animal should switch from a walk to a run
|
||
<superScript attach="left" box="[524,535,1719,1729]" fontSize="4" pageId="4" pageNumber="1021">26</superScript>
|
||
. Consequently the maximum walking speed that an adult tyrannosaur might have used was roughly
|
||
<quantity box="[642,669,1744,1761]" metricMagnitude="0" metricUnit="m" metricValue="5.0" pageId="4" pageNumber="1021" unit="m" value="5.0">5 m</quantity>
|
||
s
|
||
<superScript attach="left" box="[679,692,1740,1751]" fontSize="5" pageId="4" pageNumber="1021">1</superScript>
|
||
(
|
||
<specimenCount box="[702,746,1744,1761]" pageId="4" pageNumber="1021" type="generic">
|
||
<quantity box="[702,743,1744,1761]" metricMagnitude="1" metricUnit="m" metricValue="1.1" pageId="4" pageNumber="1021" unit="m" value="11.0">11 m</quantity>
|
||
.
|
||
</specimenCount>
|
||
p.h.), which is still faster than speed estimates from known tracks of large theropods
|
||
<superScript attach="left" box="[711,716,1765,1775]" fontSize="4" pageId="4" pageNumber="1021">9</superScript>
|
||
.
|
||
</paragraph>
|
||
<paragraph blockId="4.[122,783,1816,2000]" box="[122,275,1816,1835]" pageId="4" pageNumber="1021">
|
||
<heading box="[122,275,1816,1835]" fontSize="8" level="2" pageId="4" pageNumber="1021" reason="1">Model parameters</heading>
|
||
</paragraph>
|
||
<paragraph blockId="4.[122,783,1816,2000]" pageId="4" pageNumber="1021">
|
||
To reconstruct running mechanics in extinct dinosaurs, we modelled a small adult theropod (
|
||
<emphasis box="[203,286,1869,1886]" italics="true" pageId="4" pageNumber="1021">Coelophysis</emphasis>
|
||
), a small juvenile tyrannosaur, and an adult
|
||
<taxonomicName authority="(Supplementary Information)" baseAuthorityName="Supplementary Information" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="4" pageNumber="1021" phylum="Chordata" rank="genus">
|
||
<emphasis box="[623,731,1869,1886]" italics="true" pageId="4" pageNumber="1021">Tyrannosaurus</emphasis>
|
||
(Supplementary Information)
|
||
</taxonomicName>
|
||
. Functional segment lengths (distances between centres of joint rotation), masses,and centres of mass were measured from dissections for the extant taxa, or approximated for the extinct taxa.Hip, knee, ankle and toe joints connected these segments and were given joint angles.These parameters (see Supplementary Information) were used in a freebody diagram analysis (
|
||
<figureCitation box="[446,488,1982,1999]" captionStart="Figure 1" captionStartId="1.[800,853,1702,1721]" captionTargetBox="[801,1455,1164,1662]" captionTargetId="graphics@1.[858,1251,1165,1428]" captionTargetPageId="1" captionText="Figure 1 Explanation of freebody diagram analysis of body segments.Skeletal illustration modified from ref. 6. The initial Tyrannosaurus model (Trex_1) is shown in right lateral view and (x, y)coordinate space,with the origin located at the toe joint. Pelvic pitch,hip, knee, ankle and toe joint angle definitions are shown (see Supplementary Information). One of the angles is redundant (four angles suffice). The ground reaction force (GRF) is vertical (typical for midstance12–14) and acts at a distance R from the toe joints.The body segment weights (Wb, Wt, Ws and Wm for the trunk,thigh,shank and metatarsus) are also shown.A freebody diagram was used to calculate the internal moments about each joint. For example, about the knee joint (see inset), the moment that knee extensor muscles must generate (Mk) is equal to the ankle contact force (Fa) times its respective moment arm, plus the gravitational moment of the shank segment and the ankle moment (Ma)." figureDoi="http://doi.org/10.5281/zenodo.3961016" httpUri="https://zenodo.org/record/3961016/files/figure.png" pageId="4" pageNumber="1021">Fig. 1</figureCitation>
|
||
) to calculate
|
||
<emphasis box="[591,607,1982,1999]" italics="true" pageId="4" pageNumber="1021">
|
||
<collectionCode box="[591,607,1982,1999]" country="Germany" lsid="urn:lsid:biocol.org:col:15637" name="Botanische Staatssammlung München" pageId="4" pageNumber="1021" type="Herbarium">M</collectionCode>
|
||
</emphasis>
|
||
<subScript attach="left" box="[608,635,1989,2000]" fontSize="5" pageId="4" pageNumber="1021">musc</subScript>
|
||
for equation (1).
|
||
</paragraph>
|
||
<paragraph pageId="4" pageNumber="1021">
|
||
We entered other parameter values (
|
||
<tableCitation box="[1099,1153,136,153]" captionStart="Table 1" captionStartId="2.[122,172,873,889]" captionTargetBox="[122,784,909,1793]" captionTargetPageId="2" captionText="Table 1 Muscle anatomical data entered in equation (1) to estimate T" httpUri="http://table.plazi.org/id/28F46637FFD7D97C3803A41A62B2FCB0" pageId="4" pageNumber="1021" tableUuid="28F46637FFD7D97C3803A41A62B2FCB0">Table 1</tableCitation>
|
||
) into equation (1) to estimate
|
||
<emphasis box="[1380,1390,136,153]" italics="true" pageId="4" pageNumber="1021">T</emphasis>
|
||
. The values of
|
||
<emphasis box="[835,845,159,176]" italics="true" pageId="4" pageNumber="1021">L</emphasis>
|
||
, v and
|
||
<emphasis box="[898,905,159,176]" italics="true" pageId="4" pageNumber="1021">r</emphasis>
|
||
were measured from dissections for the extant taxa, or approximated for the extinct taxa. The muscle density (
|
||
<emphasis box="[1068,1077,181,198]" italics="true" pageId="4" pageNumber="1021">d</emphasis>
|
||
) was set at 1:06 3 10
|
||
<quantity box="[1239,1267,179,198]" metricMagnitude="0" metricUnit="kg" metricValue="3.0" pageId="4" pageNumber="1021" unit="kg" value="3.0">3 kg</quantity>
|
||
m23 as in typical skeletal muscle
|
||
<bibRefCitation author="Mendez, J. & Keys, A." box="[867,878,202,212]" journalOrPublisher="Metabolism" pageId="4" pageNumber="1021" pagination="184 - 188" part="9" refId="ref5500" refString="28. Mendez, J. & Keys, A. Density and composition of mammalian muscle. Metabolism 9, 184 - 188 (1960)." title="Density and composition of mammalian muscle" type="journal article" year="1960">28</bibRefCitation>
|
||
, and the muscle stress (j) was entered as 3:00
|
||
<geoCoordinate box="[1228,1289,202,221]" degrees="3" direction="north" minutes="10" orientation="latitude" pageId="4" pageNumber="1021" precision="15" seconds="5" value="3.1680555">3 10 5 N</geoCoordinate>
|
||
m22, the maximum isometric stress frequently measured
|
||
<bibRefCitation author="Johnston, I. A." box="[1085,1096,224,234]" journalOrPublisher="J. Exp. Biol." pageId="4" pageNumber="1021" pagination="239 - 251" part="115" refId="ref5112" refString="22. Johnston, I. A. Sustained force development: specializations and variation among the vertebrates. J. Exp. Biol. 115, 239 - 251 (1985)." title="Sustained force development: specializations and variation among the vertebrates" type="journal article" year="1985">22</bibRefCitation>
|
||
. Because we were estimating the minimum mass of muscle required to produce
|
||
<emphasis box="[1028,1044,249,266]" italics="true" pageId="4" pageNumber="1021">M</emphasis>
|
||
musc, we set the fraction of active muscle volume (
|
||
<emphasis box="[1416,1423,249,266]" italics="true" pageId="4" pageNumber="1021">c</emphasis>
|
||
) at 1. Muscle moment arms (
|
||
<emphasis box="[991,998,272,289]" italics="true" pageId="4" pageNumber="1021">r</emphasis>
|
||
) were estimated for extinct taxa by applying muscle reconstructions
|
||
<bibRefCitation author="Hutchinson, J. R. The" box="[931,942,292,302]" journalOrPublisher="Univ. California" pageId="4" pageNumber="1021" refId="ref4674" refString="15. Hutchinson, J. R. The Evolution of Hindlimb Anatomy and Function in Theropod Dinosaurs. PhD thesis, Univ. California (2001)." title="Evolution of Hindlimb Anatomy and Function in Theropod Dinosaurs" type="book" year="2001">15</bibRefCitation>
|
||
,
|
||
<bibRefCitation author="Carrano, M. T. & Hutchinson, J. R." box="[944,955,292,302]" journalOrPublisher="J. Morphol. (in the press)" pageId="4" pageNumber="1021" refId="ref4703" refString="16. Carrano, M. T. & Hutchinson, J. R. The pelvic and hind limb musculature of Tyrannosaurus rex (Dinosauria: Theropoda). J. Morphol. (in the press)" title="The pelvic and hind limb musculature of Tyrannosaurus rex (Dinosauria: Theropoda)" type="book" year="2001">16</bibRefCitation>
|
||
to skeletal material, at appropriate joint angles.
|
||
</paragraph>
|
||
<paragraph box="[815,926,346,365]" pageId="4" pageNumber="1021">T constraints</paragraph>
|
||
<paragraph pageId="4" pageNumber="1021">
|
||
The ratio of actual extensor muscle mass to
|
||
<emphasis box="[1147,1157,377,394]" italics="true" pageId="4" pageNumber="1021">T</emphasis>
|
||
, the required mass (both terms as a percentage of
|
||
<emphasis box="[920,935,399,416]" italics="true" pageId="4" pageNumber="1021">m</emphasis>
|
||
body) must be at least 1 for a bipedal animal to be able to run quickly; otherwise the actual muscles would be unable to generate the required forces. For extinct animals, we cannot measure the actual muscle masses, but as the estimated
|
||
<emphasis box="[1384,1395,445,462]" italics="true" pageId="4" pageNumber="1021">T</emphasis>
|
||
increases, good running performance becomes increasingly unlikely.If
|
||
<emphasis box="[1262,1273,467,484]" italics="true" pageId="4" pageNumber="1021">T</emphasis>
|
||
is more than 50%
|
||
<emphasis box="[1409,1424,467,484]" italics="true" pageId="4" pageNumber="1021">m</emphasis>
|
||
body per leg (100%
|
||
<emphasis box="[894,909,490,507]" italics="true" pageId="4" pageNumber="1021">m</emphasis>
|
||
body total), running at Fr 16 is certainly impossible.
|
||
</paragraph>
|
||
</subSubSection>
|
||
</treatment>
|
||
</document> |