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Introduction:
As Chritopher Brochu once noted in his osteological study on Tyrannosaurus: "Nothing evokes prehistory more than Tyrannosaurus rex. Nearly any five-year-old in the industrialized world knows what it is, and to many, Tyrannosaurus is the quintessential predatory dinosaur-as Paul (1988:344) stated, "this is the theropod." It is the only nonavian dinosaur (and one of the few organisms) popularly known by the specific rather than generic name-"T. rex" is as common in the popular media as "Tyrannosaurus."
As well as:
“Tyrannosaurids are no more relevant to phylogenetics or comparative biology than any other group of organisms, but they are extremely popular. When we do science with Tyrannosaurus, we do it with a broader audience than if it were done with almost any other animal.”
Along with the biggest fame, come the greatest hyperboles, and the highest numbers of fanatics, as well as the most intense of them. However so do the most harsh minusvalorations, and the highest ammount of detractors, as well of the most insistent of them.
Despite the subjective appreciations of each individual, Tyrannosaurus is still just an extint animal which can be anylized by scientific methodology just as any other, nothing more, and nothing less. On the basis of theese premises and without further dilation; the results of this mass estimation on FMNH PR 2081 and the multiview restoration used are ofered.
Results:
Restoration analyzed:
Discussion of the methodology:
The totality of the animal has been reconstructed from several views based on it's osteological description (Brochu 2003) and LIDAR scans (Hutchinson 2011), as well as those of other Tyrannosaurid specimens, in order to produce the mass estimation, and each body section has been analyzed and weighted by a high fidelity MATLAB script, made by my partner and me (a big thank you to her for always being my greatest support) .
For those unfamiliarized with the method, the program analyzes two views of the same section of the body, for example the torso seen from top and from the side, and then constructs a three-dimensional model of it based on a lot of eliptical sections put together, with one of the elypsis' axis based on one view, and the other one on the other.
The program makes this Graphical Double Integration method ( svpow.com/2011/01/20/tutorial-… ) as exact as it can be, doing one slice per pixel in order to produce the pixel wide elypsis that will be put together. Being one meter equal to 490 pixels in my restorations, the program produces thousends of eliptical sections in order to weight the animal, much more than the 50-100 ish that can be done with a paper and a pencil or with excel.
In order to produce the torso, all the ribs were attached to the dorsal vertebrae in anterior view, and then projected to the dorsal view and angled from above in order to give the torso of the animal a shape.
Example of the methodology used to reconstruct the trunk sections:
The torso has been produced in a somewhat conservative manner.
Hutchinson (2011) assests "that the torso of the mount is inflated in width due to a dorsal displacement of the transverse processes on the trunk vertebrae, which forced a dorsal displacement of the tubercular articulations and a lateral expansion of the rib cage as a whole."
Therefore the distortion of the transverse processes in the vertebrae was corrected in order to avoid the artificial expansion of some of the ribs. Hutchinson's main concern about their mass estimation is then fixed.
Example of de-crushing applied to all of the vertebrae:
The ribs are more angled from above than those of the mount of FMNH PR 2081 in the Field museum of Chicago, and therefore mounted more similarly to how the BHI articulates the Tyrannosaurus mounts they prepare.
Considering both modifications, it is not surprising that the results of this estimation are moderately lower than those of Hutchinson et al 2011 (8830 kg compared to 9500 for the minimal model).
It is, however slightly larger than the estimation Scott Hartman came up with, and that has adquired a significant amount of fame in the internet due to being compared to that of Giganotosaurus.
Discussion of the result and conclusions:
The estimation of FMNH PR 2081 that I have produced is moderately to substantially higher than the masses that I have calculated using this same methodology for the other largest theropod dinosaur specimens.
The mass of 8830 kg of Tyrannosaurus (FMNH PR 2081) is ofered in contrast to that of 7560 kg of Spinosaurus (MNSM v 4047) , 6840 kg in Giganotosaurus (Mucpv Ch1), 6400 kg in Tyrannotitan (MPEF pv 1157), 6325 kg in Carcharodontosaurus (SGM din 1) and 6110 kg in Acrocanthosaurus (NCSM 14345). Therefore according to theese the largest theropod specimen would belong to Tyrannosaurus rex.
The results compare well with those obtained with other volumetric estimations, falling between the estimations of
(8400 kg static1.squarespace.com/static… ) and Hutchison et al 2011 (9500 kg journals.plos.org/plosone/arti…). Considering that Scott showed concerns regarding the mass probably being on the low end, and Hutchinson showed concerns about their mass estimation potentially being too high, I find the results satisfactory and probable.
Here you can see the mass calculations made on the other animals:
Mathematical analysis on Carcharodontosaurus mass
A mathematical analysis on Tyrannotitan mass.
A mathematical analysis on Giganotosaurus mass.
A mathematical analysis on Spinosaurus mass.
Acrocanthosaurus GDI:
AcroGDIhump
References:
Christopher A. Brochu (2003): Osteology of Tyrannosaurus Rex: Insights from a nearly complete Skeleton and High-Resolution Computed Tomographic Analysis of the Skull, Journal of Vertebrate Paleontology, 22:sup4, 1-138
Hutchinson JR, Bates KT, Molnar J, Allen V, Makovicky PJ (2014) Correction: A Computational Analysis of Limb and Body Dimensions in Tyrannosaurus rex with Implications for Locomotion, Ontogeny, and Growth. PLOS ONE 9(5): e97055.
Bates KT, Manning PL, Hodgetts D, Sellers WI (2009) Estimating Mass Properties of Dinosaurs Using Laser Imaging and 3D Computer Modelling. PLoS ONE 4(2): e4532.
www.skeletaldrawing.com/home/m…
svpow.com/2011/01/20/tutorial-…
As Chritopher Brochu once noted in his osteological study on Tyrannosaurus: "Nothing evokes prehistory more than Tyrannosaurus rex. Nearly any five-year-old in the industrialized world knows what it is, and to many, Tyrannosaurus is the quintessential predatory dinosaur-as Paul (1988:344) stated, "this is the theropod." It is the only nonavian dinosaur (and one of the few organisms) popularly known by the specific rather than generic name-"T. rex" is as common in the popular media as "Tyrannosaurus."
As well as:
“Tyrannosaurids are no more relevant to phylogenetics or comparative biology than any other group of organisms, but they are extremely popular. When we do science with Tyrannosaurus, we do it with a broader audience than if it were done with almost any other animal.”
Along with the biggest fame, come the greatest hyperboles, and the highest numbers of fanatics, as well as the most intense of them. However so do the most harsh minusvalorations, and the highest ammount of detractors, as well of the most insistent of them.
Despite the subjective appreciations of each individual, Tyrannosaurus is still just an extint animal which can be anylized by scientific methodology just as any other, nothing more, and nothing less. On the basis of theese premises and without further dilation; the results of this mass estimation on FMNH PR 2081 and the multiview restoration used are ofered.
Results:
Restoration analyzed:
Discussion of the methodology:
The totality of the animal has been reconstructed from several views based on it's osteological description (Brochu 2003) and LIDAR scans (Hutchinson 2011), as well as those of other Tyrannosaurid specimens, in order to produce the mass estimation, and each body section has been analyzed and weighted by a high fidelity MATLAB script, made by my partner and me (a big thank you to her for always being my greatest support) .
For those unfamiliarized with the method, the program analyzes two views of the same section of the body, for example the torso seen from top and from the side, and then constructs a three-dimensional model of it based on a lot of eliptical sections put together, with one of the elypsis' axis based on one view, and the other one on the other.
The program makes this Graphical Double Integration method ( svpow.com/2011/01/20/tutorial-… ) as exact as it can be, doing one slice per pixel in order to produce the pixel wide elypsis that will be put together. Being one meter equal to 490 pixels in my restorations, the program produces thousends of eliptical sections in order to weight the animal, much more than the 50-100 ish that can be done with a paper and a pencil or with excel.
In order to produce the torso, all the ribs were attached to the dorsal vertebrae in anterior view, and then projected to the dorsal view and angled from above in order to give the torso of the animal a shape.
Example of the methodology used to reconstruct the trunk sections:
The torso has been produced in a somewhat conservative manner.
Hutchinson (2011) assests "that the torso of the mount is inflated in width due to a dorsal displacement of the transverse processes on the trunk vertebrae, which forced a dorsal displacement of the tubercular articulations and a lateral expansion of the rib cage as a whole."
Therefore the distortion of the transverse processes in the vertebrae was corrected in order to avoid the artificial expansion of some of the ribs. Hutchinson's main concern about their mass estimation is then fixed.
Example of de-crushing applied to all of the vertebrae:
The ribs are more angled from above than those of the mount of FMNH PR 2081 in the Field museum of Chicago, and therefore mounted more similarly to how the BHI articulates the Tyrannosaurus mounts they prepare.
Considering both modifications, it is not surprising that the results of this estimation are moderately lower than those of Hutchinson et al 2011 (8830 kg compared to 9500 for the minimal model).
It is, however slightly larger than the estimation Scott Hartman came up with, and that has adquired a significant amount of fame in the internet due to being compared to that of Giganotosaurus.
Discussion of the result and conclusions:
The estimation of FMNH PR 2081 that I have produced is moderately to substantially higher than the masses that I have calculated using this same methodology for the other largest theropod dinosaur specimens.
The mass of 8830 kg of Tyrannosaurus (FMNH PR 2081) is ofered in contrast to that of 7560 kg of Spinosaurus (MNSM v 4047) , 6840 kg in Giganotosaurus (Mucpv Ch1), 6400 kg in Tyrannotitan (MPEF pv 1157), 6325 kg in Carcharodontosaurus (SGM din 1) and 6110 kg in Acrocanthosaurus (NCSM 14345). Therefore according to theese the largest theropod specimen would belong to Tyrannosaurus rex.
The results compare well with those obtained with other volumetric estimations, falling between the estimations of
(8400 kg static1.squarespace.com/static… ) and Hutchison et al 2011 (9500 kg journals.plos.org/plosone/arti…). Considering that Scott showed concerns regarding the mass probably being on the low end, and Hutchinson showed concerns about their mass estimation potentially being too high, I find the results satisfactory and probable.Here you can see the mass calculations made on the other animals:
Mathematical analysis on Carcharodontosaurus mass
A mathematical analysis on Tyrannotitan mass.
A mathematical analysis on Giganotosaurus mass.
A mathematical analysis on Spinosaurus mass.
Acrocanthosaurus GDI:
AcroGDIhump
References:
Christopher A. Brochu (2003): Osteology of Tyrannosaurus Rex: Insights from a nearly complete Skeleton and High-Resolution Computed Tomographic Analysis of the Skull, Journal of Vertebrate Paleontology, 22:sup4, 1-138
Hutchinson JR, Bates KT, Molnar J, Allen V, Makovicky PJ (2014) Correction: A Computational Analysis of Limb and Body Dimensions in Tyrannosaurus rex with Implications for Locomotion, Ontogeny, and Growth. PLOS ONE 9(5): e97055.
Bates KT, Manning PL, Hodgetts D, Sellers WI (2009) Estimating Mass Properties of Dinosaurs Using Laser Imaging and 3D Computer Modelling. PLoS ONE 4(2): e4532.
www.skeletaldrawing.com/home/m…
svpow.com/2011/01/20/tutorial-…
Amphicoelias fragillimus redescribed
Just as predicted six years ago by Andcrea Cau in his blog, and four years ago by user ~palaeozoologist (https://www.deviantart.com/palaeozoologist) , "Amphicoelias fragilimus" is now redescribed as a new rebbachisaurid taxon; Maraapunisaurus fragillimus by no less than the renowned doctor in paleontology Kenneth Carpenter, the same sciencist that catapulted the 60 meters diplodocid version to fame in 2006.
The publication suggests that the morphological characters of AMNH 5777 show shared apomorphies (defining characters) with rebbachisauridae, and that thus should be considered to be part of said group. Going by this, Maraapunisaurus fragillimus would be the largest and oldest
Mathematical analysis on Carcharodontosaurus mass
As always, the results first:
Here you have the previous calculations made with the method used; graphical double integration, a type of vollumetric estimation:
A mathematical analysis on Tyrannotitan mass.
A mathematical analysis on Giganotosaurus mass.
A mathematical analysis on Spinosaurus mass.
The method consists in constructing a simplified 3D model of the animal mathematically, by building eliptical cross sections and adding them up, given two views of each of it's body sections. The analysis is performed by a matlab mathematical script with pixel accuracy. More information about the method itselft here:
http://www..com/users/out
A mathematical analysis on Tyrannotitan mass.
The results first:
Here you have the previous calculations made with the method used; graphical double integration, a type of vollumetric estimation.
The method consists in constructing a simplified 3D model of the animal mathematically, by building eliptical cross sections and adding them up, given two views of each of it's body sections. The analysis is performed by a matlab mathematical script with pixel accuracy. More information about the method itselft here:
https://svpow.com/2011/01/20/tutorial-11-graphic-double-integration-or-weighing-dinosaurs-on-the-cheap/
Some discussing about Tyrannotitan size and overall proportions:
The ske
A mathematical analysis on Giganotosaurus mass.
First of all, the results:
Conclussions , methodology, and anatomical references:
For those who don't know which method was used, I recommend reading the previous journal entry, about a mathematical anaylsis on Spinosaurus mass , another legendary carnivorous dinosaur; and this excelent post by SVPOW. https://svpow.com/2011/01/20/tutorial-11-graphic-double-integration-or-weighing-dinosaurs-on-the-cheap/
Overall the method intends to construct a simplified 3D model of the animal by building eliptical cross sections and adding them up, given two views of each of it's body sections. The analysis is performed by a matlab mathematical script wi
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Hi Franoys!
Awesome skeletals as always, i got a little question, How does Sue compare to Scotty?