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The results first:
tttGDIintermediate by Franoys

TyrannotitanGDI by Franoys

Here you have the previous calculations made with the method used; graphical double integration, a type of vollumetric estimation.

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 with pixel accuracy.
The skeletal used is my own bet on the animal. Sadly, and despite more than 22 years having passed since the animal was first (and very briefly) described, most of it's material is not described in detail, specially the axia


A mathematical analysis on Spinosaurus mass.Description of the method:
Graphical double integration performed by Matblab program.
We calculated the mass of the North african theropod dinosaur Spinosaurus aegyptiacus, using a graphical double integration method. We believe GDI is in itself, and without a doubt, one of the best methods to calculatte the mass of extint organisms, and the best that can be used using a multi views silhouette from the animal. The method averages a big amount of eliptical sections to aproximate the volume of a complex 3D object. The more eliptical sections, the more accurate the result will be, when a number of slices made is surpassed the result will be almost real life-like.
This matlab program utilizes digital image processing technology to analize two silhouettes from different views. It counts the number of non white pixels in every pixel-wide column from the image, and produces one slice per pixel. In response, the program is extremely sensitive to irregularities in the silho


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:

svpow.com/2011/01/20/tutorial-…

Some discussing about Tyrannotitan size and overall proportions:

The skeletal used was made by me from scratch, using mainly the information (figures, measurements, and descriptions) in Novas (2005) and Canale , Novas (2014); using Sereno 1996, Coria 1995, and Currie and Carpenter 2000 to fill in the gaps, because Tyrannotitan is not complete, even if it is one of the most complete Carcharodontosaurids that we have by far and long. And it also is one to have a detailed description with a well documented supplementary materials, unlike others like Giganotosaurus which never seems to get a detailed osteological study, even 22 years after the brief and undetailed (and now vastly outdated in every possible sense) description of Mucpv Ch1.

The top view was again modified from Acrocanthosaurus. The width of the skull, and consequently that of the anterior portion of the neck, is intermediate between Carcharodontosaurus and Giganotosaurus, the two most closely related animals to Tyrannotitan, which also preserve a decent portion of their respective skulls. It wouldn't surprise me that the head was wider than what I gave it credit for, since after all, Tyrannotitan is strongly bounded to the tribe Giganotosaurini, even more so than to the subfamily Carcharodontosaurinae, which includes Carcharodontosaurus.

I gave Tyrannotitan an equivalent ribcage width as to Acrocanthosaurus based on comparisons of the vertebrae of the former with that of later. The hips however are wider, following the suggestion of a 40 cm wide hip for Tyrannotitan holotype, as per suggested by Canale 2014. If the paratype was about 7% bigger in average as Novas 2005 suggests, the hip of the paratype would be 42.8 cm wide, which was wider than the Acrocanthosaurus hip scaled to match the length of that of Tyrannotitan.

There are more indications of Tyrannotitan being bulky for it's length compared to other Carcharodontosaurids and Allosauroids, like it's femur circumference; which at 541 mm (Canale 2014 supp materials) would be greater than that of Giganotosaurus holotype ( 520 mm, Campione et al 2014). 

Tyrannotitan of course also has other peculiarities that are woth discussing and that had an impact on it's body mass; for example it's dorsal vertebrae being anteroposteriorly short. None of the vertebrae of the paratype has a centrum over 14 cm long (Canale 2014, supp materials) except one, which barely pushes 15.5 m, furtheremore the 1st and the 14th dorsal are very reduced compared to the other vertebrae wich yields a torso length of about 85% that of Giganotosaurus, which explains the (perhaps) lower than expected body length estimation.

The most cited length of 12.2 m is cited from the theropod database, and the estimation was made way before the detailed osteological study came out, and was probably based on femur scaling using Giganotosaurus as a base. However after the publication of Canale 2014 Tyrannotitan having an equivalent body length to Giganotosaurus doesn't hold up.

Tyrannotitan also shows very tall neural spines, much taller than those of Giganotosaurus. Such feature helps expanding the torso depth and incrementing it's mass, furtheremore the pubis is 11 cm longer than the measurement for Giganotosaurus in the theropod database and 10 cm longer than the extrapolated pubis length of the biggest Carcharodontosaurus specimen (SGM din 1). Even if we were to be skeptical about the extrapolation, Carcharodontosaurus (IPHG 1922) reconstructed pubis was only 1 meter long compared to a 1.26 m long femur, or 79% the length of the femur, while in Tyrannotitan the reconstructed pubis is 86% the femur length, suggesting again that Tyrannotitan had a deep torso, despite it being relatively shorter than in Giganotosaurus.

The skull elements suggest a skull of very large size, specially length; the jugal matches almost exactly in size and shape to the same element in Carcharodontosaurus (SGM din 1) and the dentary of the Tyrannotitan paratype is comparable in size to that of both Giganotosaurus specimens, so Tyrannotitan is certainly a big headed animal, as are all of the members of Carcharodontosaurinae. The preserved quadratojugal in Tyrannotitan and how it articulates and compares in size with the jugal offers valuable information on to how to restore the rear portions of Carcharodontosaurines' skulls.

Link to the Tyrannotitan restorations:

Tyrannotitan chubutensis Skeletal Diagrams. by Franoys

Carcharodontosaurus will be the next, and will come with a couple surprises. Stay tuned!

References:

Juan Ignacio Canale, Fernando Emilio Novas & Diego Pol , Historical Biology (2014): Osteology and phylogenetic relationships of Tyrannotitan chubutensis Novas, de Valais, Vickers-Rich and Rich, 2005 (Theropoda: Carcharodontosauridae) from the Lower Cretaceous of Patagonia, Argentina, Historical Biology: An International Journal of Paleobiology.

Fernando E Novas, Silvina de Valais, Pat Vickers-Rich, Tom Rich (2005): A large Cretaceous theropod from Patagonia, Argentina, and the evolution of carcharodontosaurids

Paul C. Sereno, Didier B. Dutheil, M. Larochene, Hans C. E. Larsson, Gabrielle H. Lyon, Paul M. Magwene, Christian A. Sidor, David J. Varricchio, Jeffrey A. Wilson (1996): Predatory Dinosaurs from the Sahara and Late Cretaceous Faunal Differentiation. Science, New Series, Vol. 272, No. 5264 (May 17, 1996), pp. 986-991

Rodolfo A.Coria, Leonardo Salgado (1995) A new giant carnivorous dinosaur from the Cretaceous of Patagonia. Nature, Vol 377 (September 21 1995)

Currie P. J. & Carpenter K. 2000. — A new specimen of Acrocanthosaurus atokensis (Theropoda, Dinosauria) from the Lower Cretaceous Antlers Formation (Lower Cretaceous, Aptian) of Oklahoma, USA. Geodiversitas 22 (2) : 207-246.

Stromer 1931 II. Vertebrate remains from the Baharîje Beds (lowermost Cenomanian). 10. A skeletal remain of Carcharodontosaurus nov. gen. 
First of all, the results:

GigaGDI2 by Franoys


GigaGDIresults by Franoys

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 A mathematical analysis on Spinosaurus mass.Description of the method:
Graphical double integration performed by Matblab program.
We calculated the mass of the North african theropod dinosaur Spinosaurus aegyptiacus, using a graphical double integration method. We believe GDI is in itself, and without a doubt, one of the best methods to calculatte the mass of extint organisms, and the best that can be used using a multi views silhouette from the animal. The method averages a big amount of eliptical sections to aproximate the volume of a complex 3D object. The more eliptical sections, the more accurate the result will be, when a number of slices made is surpassed the result will be almost real life-like.
This matlab program utilizes digital image processing technology to analize two silhouettes from different views. It counts the number of non white pixels in every pixel-wide column from the image, and produces one slice per pixel. In response, the program is extremely sensitive to irregularities in the silho
, another legendary carnivorous dinosaur; and this excelent post by SVPOW. svpow.com/2011/01/20/tutorial-…

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 with pixel accuracy.

The skeletal used is my own bet on the animal. Sadly, and despite more than 22 years having passed since the animal was first (and very briefly) described, most of it's material is not described in detail, specially the axial skeleton. No photographs, ilustrations, measurement tables, nothing. So even if I used my skeletal for the GDI, the axial skeleton ( the vertebral column) had to be scaled after :iconscotthartman: work. I didn't have much of a choice in that regard.

Most of the skull and the apendicular material has however been mentioned, briefly described, and has several measurements published in the literature (Coria 2003, Coria and Currie 2006, Carrano 2012, Canale 2014, Canale& Carbajal 2015, and other studies, a good deal of them are compiled in the theropod database) I tried for the skeletal to be as up to date and to match as many of the measurements and the descriptions in Coria and Currie 2006 and the other studies as much as possible. The missing elements of the skeleton, like the forelimbs or the feet, were restored after my Tyrannotitan skeletal.

The top view is scaled and drawn after Acrocanthosaurus (Bates 2008) , a similarly sized Carcharodontosaurid, edited to have similar proportions to those of Giganotosaurus. By superimposing Hartman's Giganotosaurus top view with the dorsal view of Bates et al Acrocanthosaurus, it seems to be what he did, or at the very least the results are pretty much identical. I used Hartman's dorsal view to have an idea of how much soft tissue should I add for it to be a fair comparison with other theropod GDIs.

The results pretty much replicate his estimation (6800 kgs), despite several bones differing a substantial deal from his version. They are also coherent with other mass estimations published for Mucpv Ch1 (Mazzeta et al 2004; 6510 kg , Campione et al. 2014;  6349 kg,   Seebacher 2001 ; 6,594.8 kg)

Link to Giganotosaurus restoration:

Giganotosaurus carolinii skeletal diagram. by Franoys

Description of the method:

Graphical double integration performed by Matblab program.

We calculated the mass of the North african theropod dinosaur Spinosaurus aegyptiacus, using a graphical double integration method. We believe GDI is in itself, and without a doubt, one of the best methods to calculatte the mass of extint organisms, and the best that can be used using a multi views silhouette from the animal. The method averages a big amount of eliptical sections to aproximate the volume of a complex 3D object. The more eliptical sections, the more accurate the result will be, when a number of slices made is surpassed the result will be almost real life-like.

This matlab program utilizes digital image processing technology to analize two silhouettes from different views. It counts the number of non white pixels in every pixel-wide column from the image, and produces one slice per pixel. In response, the program is extremely sensitive to irregularities in the silhouette's perimeter.

This all means that being the torso 910 pixels long in axial length, the program produced 910 slices, and thus 910 eliptical sections for the torso, preserving the shape of the silhoettes intact in the process, and being as accurate as it can be from a mathematical point of view (when using this GDI method).

We associate the error bars to the human factor when drawing the silhouettes, and the non exact numbers for the density figures.

Figures used:

The densities aim to replicate those used by the renowned paleontologist and paleoartist known as Scott Hartman, owner of www.skeletaldrawing.com. Theese average density figures were the ones he used for calculating the mass of other two big Cretaceous theropods; Tyrannosaurus and Giganotosaurus. We did this because we intended our spinosaurus stimate to be fairly comparable to theese other stimates.

The silhouette for the Spinosaurus was made using the proportions suggested by Ibrahim et al (2014). The silhouette itself was made by RandomDinos, giving the Spinosaurus a similar amount of added soft tissue to that of Hartman's reconstructions of Giganotosaurus and Tyrannosaurus.

The dorsal view was infered from the 3D models from Ibrahim et al and anterior views from the composite Spinosaurus mount, which is now housed at Berlin's Museum für Naturkunde. The result is a barrel- like chested Spinosaurus. The gastrila was repositioned and as a result the torso got a more rounded shape compared to Ibrahim's totally speculative figure.

What we don't intend to do:

We don't inted to do an study of Spinosaurus lifestyle, locomotion, stance, biomechanis, or swimming or fighting capabilites. This is purely an study on the dimensions of the animal, linear measurements and specially and more importantly, mass.

Although the results of this study can be used by anyone as he pleases and for any kind of study/ investigation that person wants to make.

Example of the matlab script working: (The results at the end are for the torso of Giraffatitan Brancai)

Captura de pantalla 2016-09-20 02.30.19 by Franoys



Silhouettes used:

Forearms: (Anterior/Lateral views)

Dorsalview by Franoys

Lateralview by Franoys


Torso: (Dorsal/Lateral views)

Torsoviews by Franoys



Tail: (Dorsal/ Lateral views)

Dorsalview by Franoys

Lateralview by Franoys



Sail: (Dorsal/Lateral views)

Dorsalview by Franoys


Lateralview by Franoys

Hindlimbs (distal): (Anterior/Lateral views)

Spinohindlfrontal by Franoys

Lateralview by Franoys

Head: (Lateral/dorsal views)
Lateralview by Franoys

Dorsalview by Franoys

We used a 15,16 meters long spinosaurus for the study. For it, the results went as follows.

FOR THE HYPOTHETICAL 15,16 METERS LONG SPINOSAURUS:

Total length (axial)= 14,80 meters

Total length (Over the curves)= 15,16

Total mass: 7708, 54 kgs (~7.7 tonnes)

However, then we scaled Ibrahim's model using MSNM v 4047 rostrum, which includes premaxila, maxilla, and rostral part of the nassals (988 mm) ( Dal sasso; 2005). And we got a result of 15,063 meters total length for the Spinosaurus Aegyptiacus biggest referable specimen. So we isometrically scaled the 15,16 meters results for a 15,063 spinosaurus. The accuracy of the results remains unchanged, since isometrical scale equations for the same model don't have error bars associated to them.

Spinosaurus total length calculation:
Spinosauruslength by Franoys

FOR THE LARGEST REFERABLE SPECIMEN TO SPINOSAURUS AEGYPTIACUS; MSNM v 4047. (Definitive results)

Total length measurement for MSNM v 4047: 15,06 meters. ~15,1 m

Mass for 15,06 meters: 7557 kgs. (~ 7.6 tonnes)

Compiled values for each body part:

Spinotable by Franoys

A link for Randomdinos version of this:

Weighing the Fisher King - biggest... or is it?Spinosaurus aegyptiacus has, for quite a long time (the furthest I can trace it in scientific papers is 2005, but we all know what Jurassic Park /// was like), been described as the biggest theropod that ever existed. Even the, rather, well, dramatically updated version given by Ibrahim et al. (2014) didn't seem to spark the paleocommunity into doubting this perpetual title.
But should we really be repeating that claim?
Most methods to estimate dinosaur weights are, of course, rather imprecise, and references are often difficult to find. Double Graphic Integration (GDI) is currently the, well, least inaccurate of possible methods, but I've never had the capability to do it on my own.
However, Franoys recently proposed that we should work on one of those together, and (much to my surprise) he had the mathematical skills necessary to create a program that could do it for us. I don't want to expand too much on this, as maths aren't a field I enjoy working with, but for such things you can


Special thanks to my girlfriend, who helped me inmensely with all of this and she worked as much as Randomdinos and I, but she doesn't own a Deviantart account. So a big shoutout to her! Her programming and image-analizing skills have been proven as very good and useful. I love and admire her so much.