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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.

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Presentation on theme: "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."— Presentation transcript:

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 Sciences University of Portsmouth Portsmouth PO1 3QL

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 Sciences University of Portsmouth Portsmouth PO1 3QL (featuring BIG SAUROPODS)

3 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?

4 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

5 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 100

6 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 kg Rhino: 1000 kg

7 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 kg Rhino: 1000 kg Elephant: kg

8 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 kg Rhino: 1000 kg Elephant: kg Sauropod: kg

9 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 kg Rhino: 1000 kg Elephant: kg Sauropod: kg ? ???: kg

10 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 kg Rhino: 1000 kg Elephant: kg Sauropod: kg ???: kg Godzilla: kg

11 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?

12 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)

13 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)

14 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)

15 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)

16 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)

17 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!)

18 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 Walking With Dinosaurs (1999)

19 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.

20 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.

21 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.

22 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.

23 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.

24 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 primarily terrestrial.

25 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 primarily terrestrial. * Extreme lightening of vertebrae (skeletal pneumaticity) is an adaptation for terrestrial life (Wedel 2003)

26 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 primarily terrestrial. * 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)

27 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 primarily terrestrial. * 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)

28 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 primarily terrestrial. * 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)

29 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 those of mammals. The limb and foot joints in the most agile dinosaur, large or small, are structurally and functionally inferior to those of proboscidians and, in large measure, to all mammals [because mammals have] compact, bone-to- bone join geometry that includes ball-and-socket joints and curvilinear flanged joints mating perfectly with matching incurvate forms

30 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 those of mammals. The limb and foot joints in the most agile dinosaur, large or small, are structurally and functionally inferior to those of proboscidians and, in large measure, to all mammals [because mammals have] compact, bone-to- bone join geometry that includes ball-and-socket joints and curvilinear flanged joints mating perfectly with matching incurvate forms... which is a bit rude in a paper that named a new sauropod (Cathetosaurus, currently considered a species of Camarasaurus).

31 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

32 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.

33 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!

34 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.

35 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.

36 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.

37 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.

38 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.

39 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.

40 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

41 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, but are known only from scraps.

42 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, but are known only from scraps. Argentinosaurus and Paralititan are huge and their masses can be meaningfully estimated, but the humerus of the former and the femur of the latter are unknown.

43 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, but are known only from scraps. Argentinosaurus and Paralititan are huge and their masses can be meaningfully estimated, but the humerus of the former and the femur of the latter are unknown. Brachiosaurus is well-known; its mass can be estimated from the type specimen of B. brancai and both humerus and femur are well preserved in the type specimen of B. altithorax... which is close enough.

44 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:

45 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)

46 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.

47 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.

48 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.

49 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.

50 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)

51 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.

52 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. FemurHumerus

53 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. FemurHumerus

54 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. Femur pixels Humerus pixels

55 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 Femur pixels = m 2 Humerus pixels = m 2

56 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: m 2 (femur) and m 2 (humerus)

57 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: m 2 (femur) and m 2 (humerus) => Total area for two femora and two humeri: 2 x x = m 2

58 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: m 2 (femur) and m 2 (humerus) => Total area for two femora and two humeri: 2 x x = m 2 For Brachiosaurus we assume even distribution of mass (Alexander 1989)

59 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: m 2 (femur) and m 2 (humerus) => Total area for two femora and two humeri: 2 x x = m 2 For Brachiosaurus we assume even distribution of mass (Alexander 1989) (Not true for all sauropods: Diplodocus carried 80% mass on hindlimbs.)

60 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: m 2 (femur) and m 2 (humerus) => Total area for two femora and two humeri: 2 x x = m 2 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 = kg

61 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: m 2 (femur) and m 2 (humerus) => Total area for two femora and two humeri: 2 x x = m 2 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 = kg Acceleration due to gravity is 9.8 m 2

62 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: m 2 (femur) and m 2 (humerus) => Total area for two femora and two humeri: 2 x x = m 2 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 = kg Acceleration due to gravity is 9.8 m 2 => weight = 9.8 x = Newtons

63 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: m 2 (femur) and m 2 (humerus) => Total area for two femora and two humeri: 2 x x = m 2 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 = kg Acceleration due to gravity is 9.8 m 2 => weight = 9.8 x = Newtons => compressive stress = / = 862 KPascals

64 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: m 2 (femur) and m 2 (humerus) => Total area for two femora and two humeri: 2 x x = m 2 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 = kg Acceleration due to gravity is 9.8 m 2 => weight = 9.8 x = Newtons => compressive stress = / = 862 KPascals Is that a lot?

65 Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage 5. Strength of cartilage

66 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 cartilage is a most holy and sacred secret that cannot and must not be divulged!

67 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 strength of 1330 to 2100 kg/cm^2 (19,000 to 30,000 lb/in^2)... Values for cartilage vary, but are lower than those for bone. – Hildebrand 1988.

68 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 strength of 1330 to 2100 kg/cm^2 (19,000 to 30,000 lb/in^2)... Values for cartilage vary, but are lower than those for bone. – Hildebrand The strength of cartilage is considerably less than that of bone. – McGowan 1999.

69 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 strength of 1330 to 2100 kg/cm^2 (19,000 to 30,000 lb/in^2)... Values for cartilage vary, but are lower than those for bone. – Hildebrand The strength of cartilage is considerably less than that of bone. – McGowan – Alexander 1989.

70 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 strength of 1330 to 2100 kg/cm^2 (19,000 to 30,000 lb/in^2)... Values for cartilage vary, but are lower than those for bone. – Hildebrand The strength of cartilage is considerably less than that of bone. – McGowan – Alexander Compression strength is a mechanical property that has meaning with respect to the hardness of rigid materials. Applying this concept to resilient materials is not something I'm comfortable with. – pers. comm., permission to cite not sought.

71 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 elastic deformation, an increasing axial load results in a plastic deformation [...] An axial load of /- 5.2 MPa (sigma max) causes a break of cartilage. – Spahn and Wittig 2003.

72 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 elastic deformation, an increasing axial load results in a plastic deformation [...] An axial load of /- 5.2 MPa (sigma max) causes a break of cartilage. – Spahn and Wittig THANK YOU, SPAHN! THANK YOU, WITTIG!

73 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 m 2 When standing still, compressive stress on cartilage is 862 KPa

74 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 m 2 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.

75 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 Alexander 1978). For Brachiosaurus, this is about 1.7 MPa, which is still safe.

76 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 approximately kg. Assuming his leg bones scale isometrically from those of Brachiosaurus, and that he maintains bipedal posture, he will suffer 11 times the stress on his cartilage MPa should suffice to crush his articular cartilage caps like over-ripe water-melons. So the world is safe... for now.

77 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 approximately kg. Assuming his leg bones scale isometrically from those of Brachiosaurus, and that he maintains bipedal posture, he will suffer 11 times the stress on his cartilage MPa should suffice to crush his articular cartilage caps like over-ripe water-melons. So the world is safe... for now.

78 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, with corrections 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?

79 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? No cartilage

80 Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage No cartilage Thin cartilage How much of the articular surface is in contact at once?

81 Michael P. Taylor: Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage No cartilage Thin cartilage Bird-like cartilage How much of the articular surface is in contact at once? The whole articular area is in contact.

82 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 issue is not resolved. It can be estimated from Lucas and Bresler's (1961) analysis of weightlifting that stresses of up to 6 MPa are liable to occur in human intervertebral discs. – Alexander MPa of force can be experienced in the human knee (Grodzinsky et al. 2000) – six times Spahn and Wittig's elastic limit! Cartilage is a complex material, so its compressive strength depends on how quickly the force is applied, how much shear acts, the water content of the cartilage, etc.

83 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 between fore and hind limbs (Alexander 1989), and the articular areas of the humerus and femur are similar. This does not apply to all sauropods. For example, diplodocids carry about 84% of their mass on their hind legs (Alexander 1985's figure for Diplodocus) – but the articular areas of 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 areas in its forelimbs? (Guess: to absorb shock when descending abruptly from bipedal rearing.)

84 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 be impossible.

85 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?

86 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. –

87 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. Todd Wheeler for discussions concerning the properties of cartilage. Thanks to Mathew J. Wedel for supplying literature and enthusiasm. Thanks to Spahn and Wittig for actually writing down a number for the compressive strength of hyaline cartilage!


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