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![Page 1: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage Michael P. Taylor School of Earth and Environmental.](https://reader035.fdocuments.net/reader035/viewer/2022070306/5515e71b55034638038b4ec2/html5/thumbnails/1.jpg)
Upper limits on the mass of land animalsestimated through the articular area of limb-bone cartilage
Michael P. Taylor
School of Earth and Environmental SciencesUniversity of Portsmouth
Portsmouth PO1 3QL
![Page 2: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage Michael P. Taylor School of Earth and Environmental.](https://reader035.fdocuments.net/reader035/viewer/2022070306/5515e71b55034638038b4ec2/html5/thumbnails/2.jpg)
Upper limits on the mass of land animalsestimated through the articular area of limb-bone cartilage
Michael P. Taylor
School of Earth and Environmental SciencesUniversity of Portsmouth
Portsmouth PO1 3QL
(featuring BIG SAUROPODS)
![Page 3: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage Michael P. Taylor School of Earth and Environmental.](https://reader035.fdocuments.net/reader035/viewer/2022070306/5515e71b55034638038b4ec2/html5/thumbnails/3.jpg)
Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
How big can land animals get?
![Page 4: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage Michael P. Taylor School of Earth and Environmental.](https://reader035.fdocuments.net/reader035/viewer/2022070306/5515e71b55034638038b4ec2/html5/thumbnails/4.jpg)
Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
How big can land animals get?
Palaeontologist: 80 kg
![Page 5: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage Michael P. Taylor School of Earth and Environmental.](https://reader035.fdocuments.net/reader035/viewer/2022070306/5515e71b55034638038b4ec2/html5/thumbnails/5.jpg)
Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
How big can land animals get?
Palaeontologist: 80 kg100
![Page 6: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage Michael P. Taylor School of Earth and Environmental.](https://reader035.fdocuments.net/reader035/viewer/2022070306/5515e71b55034638038b4ec2/html5/thumbnails/6.jpg)
Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
How big can land animals get?
Palaeontologist: 100 kgRhino: 1000 kg
![Page 7: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage Michael P. Taylor School of Earth and Environmental.](https://reader035.fdocuments.net/reader035/viewer/2022070306/5515e71b55034638038b4ec2/html5/thumbnails/7.jpg)
Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
How big can land animals get?
Palaeontologist: 100 kgRhino: 1000 kg
Elephant: 10000 kg
![Page 8: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage Michael P. Taylor School of Earth and Environmental.](https://reader035.fdocuments.net/reader035/viewer/2022070306/5515e71b55034638038b4ec2/html5/thumbnails/8.jpg)
Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
How big can land animals get?
Palaeontologist: 100 kgRhino: 1000 kg
Elephant: 10000 kgSauropod: 100000 kg
![Page 9: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage Michael P. Taylor School of Earth and Environmental.](https://reader035.fdocuments.net/reader035/viewer/2022070306/5515e71b55034638038b4ec2/html5/thumbnails/9.jpg)
Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
How big can land animals get?
Palaeontologist: 100 kgRhino: 1000 kg
Elephant: 10000 kgSauropod: 100000 kg
????: 1000000 kg
![Page 10: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage Michael P. Taylor School of Earth and Environmental.](https://reader035.fdocuments.net/reader035/viewer/2022070306/5515e71b55034638038b4ec2/html5/thumbnails/10.jpg)
Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
How big can land animals get?
Palaeontologist: 100 kgRhino: 1000 kg
Elephant: 10000 kgSauropod: 100000 kg
???: 1000000 kgGodzilla: 10000000 kg
![Page 11: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage Michael P. Taylor School of Earth and Environmental.](https://reader035.fdocuments.net/reader035/viewer/2022070306/5515e71b55034638038b4ec2/html5/thumbnails/11.jpg)
Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
What limits the size of land animals?
![Page 12: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage Michael P. Taylor School of Earth and Environmental.](https://reader035.fdocuments.net/reader035/viewer/2022070306/5515e71b55034638038b4ec2/html5/thumbnails/12.jpg)
Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
What limits the size of land animals?
* Bone strength (Hokkanen 1985)
![Page 13: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage Michael P. Taylor School of Earth and Environmental.](https://reader035.fdocuments.net/reader035/viewer/2022070306/5515e71b55034638038b4ec2/html5/thumbnails/13.jpg)
Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
What limits the size of land animals?
* Bone strength (Hokkanen 1985)
* Muscle mass (Hokkanen 1985)
![Page 14: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage Michael P. Taylor School of Earth and Environmental.](https://reader035.fdocuments.net/reader035/viewer/2022070306/5515e71b55034638038b4ec2/html5/thumbnails/14.jpg)
Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
What limits the size of land animals?
* Bone strength (Hokkanen 1985)
* Muscle mass (Hokkanen 1985)
* Metabolic scaling (Seymour and Lillywhite 2000)
![Page 15: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage Michael P. Taylor School of Earth and Environmental.](https://reader035.fdocuments.net/reader035/viewer/2022070306/5515e71b55034638038b4ec2/html5/thumbnails/15.jpg)
Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
What limits the size of land animals?
* Bone strength (Hokkanen 1985)
* Muscle mass (Hokkanen 1985)
* Metabolic scaling (Seymour and Lillywhite 2000)
* Metabolic overheating (Alexander 1998)
![Page 16: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage Michael P. Taylor School of Earth and Environmental.](https://reader035.fdocuments.net/reader035/viewer/2022070306/5515e71b55034638038b4ec2/html5/thumbnails/16.jpg)
Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
What limits the size of land animals?
* Bone strength (Hokkanen 1985)
* Muscle mass (Hokkanen 1985)
* Metabolic scaling (Seymour and Lillywhite 2000)
* Metabolic overheating (Alexander 1998)
* Limits on limb-bone allometry (Christiansen 2002)
![Page 17: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage Michael P. Taylor School of Earth and Environmental.](https://reader035.fdocuments.net/reader035/viewer/2022070306/5515e71b55034638038b4ec2/html5/thumbnails/17.jpg)
Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
What limits the size of land animals?
* Bone strength (Hokkanen 1985)
* Muscle mass (Hokkanen 1985)
* Metabolic scaling (Seymour and Lillywhite 2000)
* Metabolic overheating (Alexander 1998)
* Limits on limb-bone allometry (Christiansen 2002)
* Strength of articular cartilage (THIS STUDY!)
![Page 18: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage Michael P. Taylor School of Earth and Environmental.](https://reader035.fdocuments.net/reader035/viewer/2022070306/5515e71b55034638038b4ec2/html5/thumbnails/18.jpg)
Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
Were sauropods terrestrial?
... Orthodoxy has changed over time ...
Zallinger's mural(1947)
BBC's WalkingWith Dinosaurs(1999)
![Page 19: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage Michael P. Taylor School of Earth and Environmental.](https://reader035.fdocuments.net/reader035/viewer/2022070306/5515e71b55034638038b4ec2/html5/thumbnails/19.jpg)
Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
Aquatic/amphibious sauropods
Most early workers considered sauropods to be aquatic,or at least “amphibious”.
![Page 20: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage Michael P. Taylor School of Earth and Environmental.](https://reader035.fdocuments.net/reader035/viewer/2022070306/5515e71b55034638038b4ec2/html5/thumbnails/20.jpg)
Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
Aquatic/amphibious sauropods
Most early workers considered sauropods to be aquatic,or at least “amphibious”.
* Owen (1859) thought that Cetiosaurus was a marine crocodile.
![Page 21: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage Michael P. Taylor School of Earth and Environmental.](https://reader035.fdocuments.net/reader035/viewer/2022070306/5515e71b55034638038b4ec2/html5/thumbnails/21.jpg)
Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
Aquatic/amphibious sauropods
Most early workers considered sauropods to be aquatic,or at least “amphibious”.
* Owen (1859) thought that Cetiosaurus was a marine crocodile.
* Colbert (1961) argued that the dorsally positioned nares of Diplodocus indicated an aquatic lifestyle.
![Page 22: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage Michael P. Taylor School of Earth and Environmental.](https://reader035.fdocuments.net/reader035/viewer/2022070306/5515e71b55034638038b4ec2/html5/thumbnails/22.jpg)
Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
Aquatic/amphibious sauropods
Most early workers considered sauropods to be aquatic,or at least “amphibious”.
* Owen (1859) thought that Cetiosaurus was a marine crocodile.
* Colbert (1961) argued that the dorsally positioned nares of Diplodocus indicated an aquatic lifestyle.
* Hatcher (1901), Hay (1910) and others felt that the cartilaginous joints of sauropod limbs would not support their weight on land.
![Page 23: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage Michael P. Taylor School of Earth and Environmental.](https://reader035.fdocuments.net/reader035/viewer/2022070306/5515e71b55034638038b4ec2/html5/thumbnails/23.jpg)
Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
Aquatic/amphibious sauropods
Most early workers considered sauropods to be aquatic,or at least “amphibious”.
* Owen (1859) thought that Cetiosaurus was a marine crocodile.
* Colbert (1961) argued that the dorsally positioned nares of Diplodocus indicated an aquatic lifestyle.
* Hatcher (1901), Hay (1910) and others felt that the cartilaginous joints of sauropod limbs would not support their weight on land.
* Burian (1957) restored Brachiosaurus walking on the bottom of a lake, “snorkelling” with its long neck and high nostrils.
![Page 24: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage Michael P. Taylor School of Earth and Environmental.](https://reader035.fdocuments.net/reader035/viewer/2022070306/5515e71b55034638038b4ec2/html5/thumbnails/24.jpg)
Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
Terrestrial sauropods
Many lines of evidence show that sauropods were primarilyterrestrial.
![Page 25: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage Michael P. Taylor School of Earth and Environmental.](https://reader035.fdocuments.net/reader035/viewer/2022070306/5515e71b55034638038b4ec2/html5/thumbnails/25.jpg)
Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
Terrestrial sauropods
Many lines of evidence show that sauropods were primarilyterrestrial.
* Extreme lightening of vertebrae (skeletal pneumaticity) is an adaptation for terrestrial life (Wedel 2003)
![Page 26: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage Michael P. Taylor School of Earth and Environmental.](https://reader035.fdocuments.net/reader035/viewer/2022070306/5515e71b55034638038b4ec2/html5/thumbnails/26.jpg)
Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
Terrestrial sauropods
Many lines of evidence show that sauropods were primarilyterrestrial.
* Extreme lightening of vertebrae (skeletal pneumaticity) is an adaptation for terrestrial life (Wedel 2003)
* Sauropod feet were too compact for walking in swamps: individuals have been found mired (Russell et al. 1980)
![Page 27: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage Michael P. Taylor School of Earth and Environmental.](https://reader035.fdocuments.net/reader035/viewer/2022070306/5515e71b55034638038b4ec2/html5/thumbnails/27.jpg)
Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
Terrestrial sauropods
Many lines of evidence show that sauropods were primarilyterrestrial.
* Extreme lightening of vertebrae (skeletal pneumaticity) is an adaptation for terrestrial life (Wedel 2003)
* Sauropod feet were too compact for walking in swamps: individuals have been found mired (Russell et al. 1980)
* Tall, relatively narrow torsos characterise terrestrial animals and are biomechanically adapted for heavy loads (Coombs 1975)
![Page 28: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage Michael P. Taylor School of Earth and Environmental.](https://reader035.fdocuments.net/reader035/viewer/2022070306/5515e71b55034638038b4ec2/html5/thumbnails/28.jpg)
Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
Terrestrial sauropods
Many lines of evidence show that sauropods were primarilyterrestrial.
* Extreme lightening of vertebrae (skeletal pneumaticity) is an adaptation for terrestrial life (Wedel 2003)
* Sauropod feet were too compact for walking in swamps: individuals have been found mired (Russell et al. 1980)
* Tall, relatively narrow torsos characterise terrestrial animals and are biomechanically adapted for heavy loads (Coombs 1975)
* Many sauropods found in seasonally dry environments, e.g. Morrison Formation (Dodson et al. 1980)
![Page 29: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage Michael P. Taylor School of Earth and Environmental.](https://reader035.fdocuments.net/reader035/viewer/2022070306/5515e71b55034638038b4ec2/html5/thumbnails/29.jpg)
Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
Limbs of dinosaurs and mammals compared
Jensen 1988 compared dinosaur limb-bones unfavourably with thoseof mammals.
“The limb and foot joints in the most agile dinosaur,large or small, are structurally and functionally inferiorto those of proboscidians and, in large measure, to allmammals [because mammals have] compact, bone-to-bone join geometry that includes ball-and-socket jointsand curvilinear flanged joints mating perfectly withmatching incurvate forms”
![Page 30: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage Michael P. Taylor School of Earth and Environmental.](https://reader035.fdocuments.net/reader035/viewer/2022070306/5515e71b55034638038b4ec2/html5/thumbnails/30.jpg)
Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
Limbs of dinosaurs and mammals compared
Jensen 1988 compared dinosaur limb-bones unfavourably with thoseof mammals.
“The limb and foot joints in the most agile dinosaur,large or small, are structurally and functionally inferiorto those of proboscidians and, in large measure, to allmammals [because mammals have] compact, bone-to-bone join geometry that includes ball-and-socket jointsand curvilinear flanged joints mating perfectly withmatching incurvate forms”
... which is a bit rude in a paper that named a new sauropod(Cathetosaurus, currently considered a species of Camarasaurus).
![Page 31: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage Michael P. Taylor School of Earth and Environmental.](https://reader035.fdocuments.net/reader035/viewer/2022070306/5515e71b55034638038b4ec2/html5/thumbnails/31.jpg)
Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
Limbs of dinosaurs and mammals compared
Humeri of Camarsaurus and Brontops
![Page 32: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage Michael P. Taylor School of Earth and Environmental.](https://reader035.fdocuments.net/reader035/viewer/2022070306/5515e71b55034638038b4ec2/html5/thumbnails/32.jpg)
Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
Limbs of dinosaurs and mammals compared
But sauropods, like extant dinosaurs (birds), would have had large caps of hyaline cartilage on each articular surface.
These would achieve the close fitting that is otherwise not possible.
![Page 33: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage Michael P. Taylor School of Earth and Environmental.](https://reader035.fdocuments.net/reader035/viewer/2022070306/5515e71b55034638038b4ec2/html5/thumbnails/33.jpg)
Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
Digression: how thick were cartilage caps?
Brachiosaurus brancai (HMN S II) mount in the Humbold Musuem, Berlin.
Cartilage must have filled the large part of the acetabulum not filled by the head of the femur.
So pretty darned thick!
![Page 34: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage Michael P. Taylor School of Earth and Environmental.](https://reader035.fdocuments.net/reader035/viewer/2022070306/5515e71b55034638038b4ec2/html5/thumbnails/34.jpg)
Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
Were the cartilage caps strong enough?
The method is simple:
1. Choose a big dinosaur.
![Page 35: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage Michael P. Taylor School of Earth and Environmental.](https://reader035.fdocuments.net/reader035/viewer/2022070306/5515e71b55034638038b4ec2/html5/thumbnails/35.jpg)
Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
Were the cartilage caps strong enough?
The method is simple:
1. Choose a big dinosaur.
2. Find the mass of the dinosaur.
![Page 36: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage Michael P. Taylor School of Earth and Environmental.](https://reader035.fdocuments.net/reader035/viewer/2022070306/5515e71b55034638038b4ec2/html5/thumbnails/36.jpg)
Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
Were the cartilage caps strong enough?
The method is simple:
1. Choose a big dinosaur.
2. Find the mass of the dinosaur.
3. Calculate the articular area of its limb-bone cartilage.
![Page 37: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage Michael P. Taylor School of Earth and Environmental.](https://reader035.fdocuments.net/reader035/viewer/2022070306/5515e71b55034638038b4ec2/html5/thumbnails/37.jpg)
Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
Were the cartilage caps strong enough?
The method is simple:
1. Choose a big dinosaur.
2. Find the mass of the dinosaur.
3. Calculate the articular area of its limb-bone cartilage.
4. Divide mass by area to find the stress acting of the cartilage.
![Page 38: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage Michael P. Taylor School of Earth and Environmental.](https://reader035.fdocuments.net/reader035/viewer/2022070306/5515e71b55034638038b4ec2/html5/thumbnails/38.jpg)
Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
Were the cartilage caps strong enough?
The method is simple:
1. Choose a big dinosaur.
2. Find the mass of the dinosaur.
3. Calculate the articular area of its limb-bone cartilage.
4. Divide mass by area to find the stress acting of the cartilage.
5. Compare this with the known compressive strength of cartilage.
![Page 39: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage Michael P. Taylor School of Earth and Environmental.](https://reader035.fdocuments.net/reader035/viewer/2022070306/5515e71b55034638038b4ec2/html5/thumbnails/39.jpg)
Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
Were the cartilage caps strong enough?
The method is simple IN PRINCIPLE:
1. Choose a big dinosaur.
2. Find the mass of the dinosaur.
3. Calculate the articular area of its limb-bone cartilage.
4. Divide mass by area to find the stress acting of the cartilage.
5. Compare this with the known compressive strength of cartilage.
BUT EVERY STEP EXCEPT #4 IS A MINEFIELD.
![Page 40: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage Michael P. Taylor School of Earth and Environmental.](https://reader035.fdocuments.net/reader035/viewer/2022070306/5515e71b55034638038b4ec2/html5/thumbnails/40.jpg)
Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
1. Choose a big dinosaur
We need a dinosaur that:* is huge* is well enough represented to estimate its mass* is known from material including femur and humerus
![Page 41: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage Michael P. Taylor School of Earth and Environmental.](https://reader035.fdocuments.net/reader035/viewer/2022070306/5515e71b55034638038b4ec2/html5/thumbnails/41.jpg)
Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
1. Choose a big dinosaur
We need a dinosaur that:* is huge* is well enough represented to estimate its mass* is known from material including femur and humerus
Amphicoelias fragillimus and Bruhathkayosaurus are truly huge, butare known only from scraps.
![Page 42: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage Michael P. Taylor School of Earth and Environmental.](https://reader035.fdocuments.net/reader035/viewer/2022070306/5515e71b55034638038b4ec2/html5/thumbnails/42.jpg)
Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
1. Choose a big dinosaur
We need a dinosaur that:* is huge* is well enough represented to estimate its mass* is known from material including femur and humerus
Amphicoelias fragillimus and Bruhathkayosaurus are truly huge, butare known only from scraps.
Argentinosaurus and Paralititan are huge and their masses can bemeaningfully estimated, but the humerus of the former and the femurof the latter are unknown.
![Page 43: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage Michael P. Taylor School of Earth and Environmental.](https://reader035.fdocuments.net/reader035/viewer/2022070306/5515e71b55034638038b4ec2/html5/thumbnails/43.jpg)
Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
1. Choose a big dinosaur
We need a dinosaur that:* is huge* is well enough represented to estimate its mass* is known from material including femur and humerus
Amphicoelias fragillimus and Bruhathkayosaurus are truly huge, butare known only from scraps.
Argentinosaurus and Paralititan are huge and their masses can bemeaningfully estimated, but the humerus of the former and the femurof the latter are unknown.
Brachiosaurus is well-known; its mass can be estimated from the typespecimen of B. brancai and both humerus and femur are well preservedin the type specimen of B. altithorax ... which is close enough.
![Page 44: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage Michael P. Taylor School of Earth and Environmental.](https://reader035.fdocuments.net/reader035/viewer/2022070306/5515e71b55034638038b4ec2/html5/thumbnails/44.jpg)
Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
2. Find the mass of the dinosaur
Mass estimates for Brachiosaurus have varied wildly:
![Page 45: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage Michael P. Taylor School of Earth and Environmental.](https://reader035.fdocuments.net/reader035/viewer/2022070306/5515e71b55034638038b4ec2/html5/thumbnails/45.jpg)
Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
2. Find the mass of the dinosaur
Mass estimates for Brachiosaurus have varied wildly:Colbert 1962: 78 tonnes (volume of model)Russell et al. 1980: 15 tonnes (limb-bone allometry)Alexander 1989: 47 tonnes (model)Anderson et al. 1985: 29 tonnes (allometry)Paul 1988: 32 for B. brancai, 35 for B. altithorax (model)Gunga et al. 1995: 74 tonnes (model)Christiansen 1997: 37 tonnes (model)Henderson 2003: 26 tonnes (model)
![Page 46: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage Michael P. Taylor School of Earth and Environmental.](https://reader035.fdocuments.net/reader035/viewer/2022070306/5515e71b55034638038b4ec2/html5/thumbnails/46.jpg)
Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
2. Find the mass of the dinosaur
Mass estimates for Brachiosaurus have varied wildly:Colbert 1962: 78 tonnes (volume of model)Russell et al. 1980: 15 tonnes (limb-bone allometry)Alexander 1989: 47 tonnes (model)Anderson et al. 1985: 29 tonnes (allometry)Paul 1988: 32 for B. brancai, 35 for B. altithorax (model)Gunga et al. 1995: 74 tonnes (model)Christiansen 1997: 37 tonnes (model)Henderson 2003: 26 tonnes (model)
Estimates based on limb-bone allometry are not measurements: ignore.
![Page 47: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage Michael P. Taylor School of Earth and Environmental.](https://reader035.fdocuments.net/reader035/viewer/2022070306/5515e71b55034638038b4ec2/html5/thumbnails/47.jpg)
Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
2. Find the mass of the dinosaur
Mass estimates for Brachiosaurus have varied wildly:Colbert 1962: 78 tonnes (volume of model)Russell et al. 1980: 15 tonnes (limb-bone allometry)Alexander 1989: 47 tonnes (model)Anderson et al. 1985: 29 tonnes (allometry)Paul 1988: 32 for B. brancai, 35 for B. altithorax (model)Gunga et al. 1995: 74 tonnes (model)Christiansen 1997: 37 tonnes (model)Henderson 2003: 26 tonnes (model)
Estimates based on limb-bone allometry are not measurements: ignore.Colbert's model was grotesquely fat – probably on steroids.
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Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
2. Find the mass of the dinosaur
Mass estimates for Brachiosaurus have varied wildly:Colbert 1962: 78 tonnes (volume of model)Russell et al. 1980: 15 tonnes (limb-bone allometry)Alexander 1989: 47 tonnes (model)Anderson et al. 1985: 29 tonnes (allometry)Paul 1988: 32 for B. brancai, 35 for B. altithorax (model)Gunga et al. 1995: 74 tonnes (model)Christiansen 1997: 37 tonnes (model)Henderson 2003: 26 tonnes (model)
Estimates based on limb-bone allometry are not measurements: ignore.Colbert's model was grotesquely fat – probably on steroids.Gunga et al.'s model is made from round (not elliptical) sections.
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Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
2. Find the mass of the dinosaur
Mass estimates for Brachiosaurus have varied wildly:Colbert 1962: 78 tonnes (volume of model)Russell et al. 1980: 15 tonnes (limb-bone allometry)Alexander 1989: 47 tonnes (model)Anderson et al. 1985: 29 tonnes (allometry)Paul 1988: 32 for B. brancai, 35 for B. altithorax (model)Gunga et al. 1995: 74 tonnes (model)Christiansen 1997: 37 tonnes (model)Henderson 2003: 26 tonnes (model)
Estimates based on limb-bone allometry are not measurements: ignore.Colbert's model was grotesquely fat – probably on steroids.Gunga et al.'s model is made from round (not elliptical) sections.
Average of Alexander, Paul, Christiansen and Henderson is 36 tonnes.
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Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
3. Calculate the articular area of limb-bone cartilage
Proximal surfaces of humerus and femur(Reconstruction from Janensch 1950)
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Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
3. Calculate the articular area of limb-bone cartilage
I scanned plate LXXIV (limb bones) of Riggs 1904 on Brachiosaurus.
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Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
3. Calculate the articular area of limb-bone cartilage
I scanned plate LXXIV (limb bones) of Riggs 1904 on Brachiosaurus.I threw away the anterior views and just kept the proximal views.
Femur Humerus
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Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
3. Calculate the articular area of limb-bone cartilage
I scanned plate LXXIV (limb bones) of Riggs 1904 on Brachiosaurus.I threw away the anterior views and just kept the proximal views.I mapped all the bone to black and background to white.
Femur Humerus
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Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
3. Calculate the articular area of limb-bone cartilage
I scanned plate LXXIV (limb bones) of Riggs 1904 on Brachiosaurus.I threw away the anterior views and just kept the proximal views.I mapped all the bone to black and background to white.I counted the black pixels.
Femur96447 pixels
Humerus96023 pixels
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Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
3. Calculate the articular area of limb-bone cartilage
I scanned plate LXXIV (limb bones) of Riggs 1904 on Brachiosaurus.I threw away the anterior views and just kept the proximal views.I mapped all the bone to black and background to white.I counted the black pixels.From the 204cm length of humerus, I measured 97 pixels per 10cm
Femur96447 pixels= 0.1025 m2
Humerus96023 pixels= 0.1021 m2
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Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
4. Stress on cartilage
Proximal articular areas of Brachiosaurus are:0.1025 m2 (femur) and 0.1021 m2 (humerus)
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Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
4. Stress on cartilage
Proximal articular areas of Brachiosaurus are:0.1025 m2 (femur) and 0.1021 m2 (humerus)
=> Total area for two femora and two humeri:2 x 0.1025 + 2 x 0.1021 = 0.4092 m2
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Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
4. Stress on cartilage
Proximal articular areas of Brachiosaurus are:0.1025 m2 (femur) and 0.1021 m2 (humerus)
=> Total area for two femora and two humeri:2 x 0.1025 + 2 x 0.1021 = 0.4092 m2
For Brachiosaurus we assume even distribution of mass (Alexander 1989)
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Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
4. Stress on cartilage
Proximal articular areas of Brachiosaurus are:0.1025 m2 (femur) and 0.1021 m2 (humerus)
=> Total area for two femora and two humeri:2 x 0.1025 + 2 x 0.1021 = 0.4092 m2
For Brachiosaurus we assume even distribution of mass (Alexander 1989)(Not true for all sauropods: Diplodocus carried 80% mass on hindlimbs.)
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Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
4. Stress on cartilage
Proximal articular areas of Brachiosaurus are:0.1025 m2 (femur) and 0.1021 m2 (humerus)
=> Total area for two femora and two humeri:2 x 0.1025 + 2 x 0.1021 = 0.4092 m2
For Brachiosaurus we assume even distribution of mass (Alexander 1989)(Not true for all sauropods: Diplodocus carried 80% mass on hindlimbs.)
Mass estimated at 36 metric tonnes = 36000 kg
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Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
4. Stress on cartilage
Proximal articular areas of Brachiosaurus are:0.1025 m2 (femur) and 0.1021 m2 (humerus)
=> Total area for two femora and two humeri:2 x 0.1025 + 2 x 0.1021 = 0.4092 m2
For Brachiosaurus we assume even distribution of mass (Alexander 1989)(Not true for all sauropods: Diplodocus carried 80% mass on hindlimbs.)
Mass estimated at 36 metric tonnes = 36000 kgAcceleration due to gravity is 9.8 m2
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Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
4. Stress on cartilage
Proximal articular areas of Brachiosaurus are:0.1025 m2 (femur) and 0.1021 m2 (humerus)
=> Total area for two femora and two humeri:2 x 0.1025 + 2 x 0.1021 = 0.4092 m2
For Brachiosaurus we assume even distribution of mass (Alexander 1989)(Not true for all sauropods: Diplodocus carried 80% mass on hindlimbs.)
Mass estimated at 36 metric tonnes = 36000 kgAcceleration due to gravity is 9.8 m2
=> weight = 9.8 x 36000 = 352800 Newtons
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Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
4. Stress on cartilage
Proximal articular areas of Brachiosaurus are:0.1025 m2 (femur) and 0.1021 m2 (humerus)
=> Total area for two femora and two humeri:2 x 0.1025 + 2 x 0.1021 = 0.4092 m2
For Brachiosaurus we assume even distribution of mass (Alexander 1989)(Not true for all sauropods: Diplodocus carried 80% mass on hindlimbs.)
Mass estimated at 36 metric tonnes = 36000 kgAcceleration due to gravity is 9.8 m2
=> weight = 9.8 x 36000 = 352800 Newtons=> compressive stress = 352800 / 0.4092 = 862 KPascals
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Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
4. Stress on cartilage
Proximal articular areas of Brachiosaurus are:0.1025 m2 (femur) and 0.1021 m2 (humerus)
=> Total area for two femora and two humeri:2 x 0.1025 + 2 x 0.1021 = 0.4092 m2
For Brachiosaurus we assume even distribution of mass (Alexander 1989)(Not true for all sauropods: Diplodocus carried 80% mass on hindlimbs.)
Mass estimated at 36 metric tonnes = 36000 kgAcceleration due to gravity is 9.8 m2
=> weight = 9.8 x 36000 = 352800 Newtons=> compressive stress = 352800 / 0.4092 = 862 KPascals
Is that a lot?
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Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
5. Strength of cartilage
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Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
5. Strength of cartilage
The compressive strength of cartilageis a most holy and sacred secret
that cannot and must not be divulged!
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Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
5. Strength of cartilage
“Fresh compact bone loaded parallel to its grain has a compressive strengthof 1330 to 2100 kg/cm^2 (19,000 to 30,000 lb/in^2) ... Values for cartilagevary, but are lower than those for bone.”
– Hildebrand 1988.
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Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
5. Strength of cartilage
“Fresh compact bone loaded parallel to its grain has a compressive strengthof 1330 to 2100 kg/cm^2 (19,000 to 30,000 lb/in^2) ... Values for cartilagevary, but are lower than those for bone.”
– Hildebrand 1988.
“The strength of cartilage is considerably less than that of bone.” – McGowan 1999.
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Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
5. Strength of cartilage
“Fresh compact bone loaded parallel to its grain has a compressive strengthof 1330 to 2100 kg/cm^2 (19,000 to 30,000 lb/in^2) ... Values for cartilagevary, but are lower than those for bone.”
– Hildebrand 1988.
“The strength of cartilage is considerably less than that of bone.” – McGowan 1999.
“ ”– Alexander 1989.
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Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
5. Strength of cartilage
“Fresh compact bone loaded parallel to its grain has a compressive strengthof 1330 to 2100 kg/cm^2 (19,000 to 30,000 lb/in^2) ... Values for cartilagevary, but are lower than those for bone.”
– Hildebrand 1988.
“The strength of cartilage is considerably less than that of bone.” – McGowan 1999.
“ ”– Alexander 1989.
“Compression strength is a mechanical property that has meaning withrespect to the hardness of rigid materials. Applying this concept toresilient materials is not something I'm comfortable with.”
– pers. comm., permission to cite not sought.
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Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
5. Strength of cartilage
In the end I only found one paper containing hard numbers:
“Axial load up to 5 MPa produces an almost elasticdeformation, an increasing axial load results in aplastic deformation [...] An axial load of 25.8 +/-5.2 MPa (sigma max) causes a break of cartilage.
– Spahn and Wittig 2003.
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Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
5. Strength of cartilage
In the end I only found one paper containing hard numbers:
“Axial load up to 5 MPa produces an almost elasticdeformation, an increasing axial load results in aplastic deformation [...] An axial load of 25.8 +/-5.2 MPa (sigma max) causes a break of cartilage.
– Spahn and Wittig 2003.
THANK YOU, SPAHN! THANK YOU, WITTIG!
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Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
Conclusions
* Assume a mass of 36 tonnes for Brachiosaurus* Assume even distribution of bodyweight on fore and hind limbs
The total area of proximal articular facets is 0.409 m2
When standing still, compressive stress on cartilage is 862 KPa
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Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
Conclusions
* Assume a mass of 36 tonnes for Brachiosaurus* Assume even distribution of bodyweight on fore and hind limbs
The total area of proximal articular facets is 0.409 m2
When standing still, compressive stress on cartilage is 862 KPa
This is about 1/6 of Spahn and Wittig's figure of 5 MPa before plastic deformation of cartilage occurs.
So a stationary Brachiosaurus would be comfortable on land.
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Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
Conclusions
Locomotory stress is about twice that of standing (Jayes and Alexander1978). For Brachiosaurus, this is about 1.7 MPa, which is still safe.
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Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
Conclusions
Godzilla's mass is approximately10000000 kg.
Assuming his leg bones scale isometricallyfrom those of Brachiosaurus, and that hemaintains bipedal posture, he will suffer11 times the stress on his cartilage.
18.7 MPa should suffice to crush hisarticular cartilage caps like over-ripewater-melons.
So the world is safe ... for now.
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Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
Conclusions
Crap.Godzilla's mass is approximately10000000 kg.
Assuming his leg bones scale isometricallyfrom those of Brachiosaurus, and that hemaintains bipedal posture, he will suffer11 times the stress on his cartilage.
18.7 MPa should suffice to crush hisarticular cartilage caps like over-ripewater-melons.
So the world is safe ... for now.
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Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
Afterword: why you shouldn't trust these figures
The findings of this study should be regarded as a first step, withcorrections and refinements hopefully to follow.
Some areas where refinement is needed:
* How much of the articular cartilage is in contact at once?
* What is the strength of articular cartilage?
* How is mass distributed between fore and hind limbs?
* How does joint reaction force compare with weight?
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Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
How much of the articular surface is in contact at once?
Nocartilage
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Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
Nocartilage Thin
cartilage
How much of the articular surface is in contact at once?
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Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
Nocartilage Thin
cartilage
Bird-likecartilage
How much of the articular surface is in contact at once?
The whole articulararea is in contact.
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Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
What is the strength of articular cartilage?
Although I am using Spahn and Wittig's figure of 5MPa, the issueis not resolved.
“It can be estimated from Lucas and Bresler's (1961)analysis of weightlifting that stresses of up to 6 MPaare liable to occur in human intervertebral discs.”
– Alexander 1985
30 MPa of force can be experienced in the human knee (Grodzinskyet al. 2000) – six times Spahn and Wittig's elastic limit!
Cartilage is a complex material, so its compressive strength dependson how quickly the force is applied, how much shear acts, the watercontent of the cartilage, etc.
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Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
How is mass distributed between fore and hind limbs?
For Brachiosaurus, mass appears to be evenly distributed betweenfore and hind limbs (Alexander 1989), and the articular areas of thehumerus and femur are similar. This does not apply to all sauropods.
For example, diplodocids carry about 84% of their mass on their hindlegs (Alexander 1985's figure for Diplodocus) – but the articular areasof their humerus and femur are similar (measurement of Apatosaurus).
Calculations for diplodocids must take uneven distribution into account.
Why does Apatosaurus have such disproportionately large articular areasin its forelimbs?
(Guess: to absorb shock when descending abruptly from bipedal rearing.)
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Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
How does joint reaction force compare with weight?
It is “obvious” that the force acting at a joint is equal to weight.
Obvious – yes. True – no.
Hip joint reaction forces in stationary humans is 4.2 times weight!
Why? I don't know but I intend to find out.
If this were also true in Brachiosaurus, locomotion would seem to beimpossible.
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Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
Help! Too much uncertainty!
We don't confidently know:
* The masses of dinosaurs (factor of perhaps 5)* The relationship between mass and joint reaction force (4.2)* The extent of articulation between limb bones (?2)* How locomotory forces exceeds static forces (?3)* The strength of articular cartilage (6!)
So my figures are correct within a factor of 756.
So are these results worth anything?
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Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
Help! Too much uncertainty!
We don't confidently know:
* The masses of dinosaurs (factor of perhaps 5)* The relationship between mass and joint reaction force (4.2)* The extent of articulation between limb bones (?2)* How locomotory forces exceeds static forces (?3)* The strength of articular cartilage (6!)
So my figures are correct within a factor of 756.
So are these results worth anything?
“The best way to get information [on the Internet]isn't to ask a question, but to post the wrong information.”
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Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage
Acknowledgements
Thanks to my supervisor David M. Martill.
Thanks to John R. Hutchinson, Adam P. Summers and H. ToddWheeler for email discussions concerning the properties ofcartilage.
Thanks to Mathew J. Wedel for supplying literature andenthusiasm.
Thanks to Spahn and Wittig for actually writing down a numberfor the compressive strength of hyaline cartilage!