Forelimbs Robusticity and Bending Strength of Theropod taxaMaterials and MethodologyT.rex (Sue)'s forelimbs data from
Brochu (2003). Allosaurus ('Antredemus') from
Gilmore (1920). Acrocanthosaurus (Fran) from
Currie & Carpenter (1999)Humerus, radis, and ulna measurements will be used to calculate Robusticity and Bending Strength. Measurements are in mm
Robusticy = width (supposedly mediolateral width) at the mid shaft / bone length
The rationale for this is because the long bones are most thin at the midshaft and thus if it ever break, the midshaft will be the most probable place. Robusticity at midshaft had been used on Carnivorans as an assessment of the animal bone's resistive strength (
Doyle, 2009;
Meachen, 2009;
Meachen, 2012)
Bending Strength =
Section Modulus / Moment Arm Length
Following the principle established in
Therrien (2005);
Christiansen (2007a);
Christiansen (2007b)Section modulus is calculated at the midshaft. The assumption is that the midshaft will be a solid circle in cross section. Which is not correct as the actual midshaft would be more like hollow oval in cross section. However, i cannot find the data to follow the more accurate approach so some assumptions have to be made. Moment arm length will be half the bone length as the force applied is assumed at the distal-most section of the respective bones. Measurements in mm^2
Strength is only relevant in relative term as larger animals are indeed stronger. Strength will be adjusted based on estimated body mass.
Relative strength = Absolute Bending Strength / Body Mass^(2/3)
As Body mass increases at a faster rate then Strength, adjustments have to be made. Body mass of T.rex is 8500 kg; Allosaurus is 1500 kg; Acrocanthosaurus is 6000 kg.
The stress on the antebrachii would most likely spread between ulna and radius and not on each bone individually. Thus a sum of strength of ulna and radius, both in absolute and relative term will be calculated for interpretation of forearm (antebrachii) strength. A sum of all limb bone strength will be calculated for an overall strength assessment.
Result and DiscussionThe larger Theropods (T.rex, Acro) in this case are both more robust than the smaller one (Allo). However, Robusticity may not be good indicator for Strength especially on animals with different limb length such as this case. As Strength grows at the 2nd power, a larger bone will be stronger than a smaller one even though its robusticity is similar. Thus Bending Strength is a more meaningful measurement for interpretation purposes.
Humeus: In absolute term, obviously, the larger Theropod have much stronger humerus. T.rex and Acro score similar in this regard, thus it suggest similar resistive strength in absolute term. For example, if Acro's humerus is strong enough to withstand the force of a 6000 kg struggling prey then T.rex's humerus should be able to withstand similar force. When adjusted for weight, both Allosauroid score higher than T.rex does, suggesting stronger humerus relative strength (albeit not significantly so, about 25% stronger)
Radidus: In absolute term, Acro's strength scores the highest, then T.rex, then Allo. In relative term, Allo and T.rex are similar in strength while Acro is significantly stronger than the others.
Ulna: In absolute term, T.rex's strength scores the highest, then Acro, then Allo. In relative term, T.rex scores only slightly higher than Acro. Both larger Theropods score significantly higher than the smaller one, even in relative term.
Antebrachii (forearms): In absolute term, Acro scores highest in strength, follow closely by T.rex and then Allo.
The trend in relative term is quite interesting. In relative term, the antebrachii of T.rex is significantly stronger than that of Allo (about 40% stronger). This is due to the fact that T.rex has significantly stronger ulna than Allo even though the radius is similar in strength. As expected, Acro is stronger than both in this aspect (about 30% stronger than T.rex).
Total forelimbs: In absolute term, Acro and T.rex scores similar to each other which suggests similar forelimbs resistive strength. This means that T.rex and Acro's forelimbs should be able to resist force from struggling preys of the same size. Obviously, in absolute term, both larger animals are so much stronger than the smaller one.
In relative term, T.rex and Allo scores similar in this regard. Allo has stronger relative humerus than T.rex but T.rex has stronger antebrachii than Allosaurus so the total forelimb strength is similar. At first glance, this seems to suggest proportionally similar prey restraining capabilities of the forelimbs due to having proportionally similar forelimb strength. For instance, if a 2 tonne Allo can restrain a 1 tonne struggling prey then a 8 tonne should be able to restrain a 4 tonne prey.
However, there are issues with this interpretation. Terrestrial animals muscle force (hence Strength) probably increases at positive allometry in response to increase in size (
Arthur et al, 2015). The reason for this is because mass increase at a much faster rate than Strength does (assuming isometry). If the muscle force of terrestrial animals only increases at isometry, they will not be strong enough to move themselves at larger size. This means that the force of struggling prey animals probably also increase at positive allometry too. On the other hand, T-rex's forelimbs only increases at isometry when compared to Allosaurus. This suggests that the prey-predator mass ratio of T-rex's forelimbs will be less than that of Allosaurus despite not having weaker forelimbs proportionally. So if a 2 tonne Allo can restrain a 1 tonne prey, an 8 tonne T-rex can only restrain preys that weigh less than 4 tonnes.
Acro scores higher than both in relative term, having the strongest humerus and antebrachii. Thus, it should be adapted for restraining rather large preys. Acro increase at positive allometry to Allo. This means that Acro probably can maintain similar prey/predator mass ratio as Allo or possibly achieve even higher ratio than Allo.
Conclusion: Relative to its size, T.rex forelimbs are as strong as those of Allosaurus. However, due to its larger size, its forelimbs may be proportionally weaker compared to its preys. Thus this suggests that T.rex forelimbs would only be capable of restraining smaller prey/predator mass ratio than Allo would. Acro's forelimbs scale in positive allometry to Allo. This suggests that Acro can either maintain similar prey/predator mass ratio or possibly achieve a higher ratio than Allo (big game adaptions?)
Limitations: Assumption that the bone is solid circle in cross section may be inappropriate. One specimen per species may be too low and may not account for the varied morphology across specimens. Analysis is quite sensitive to Body mass and the body mass assigned here may be inappropriate. Need to collect more data on other Theropods such as Deinonychus and Torvosaurus for wider cross-species comparison.
Comprehensive Forelimbs Comparison and Implication: T-rex vs AllosaurusIntroductionIn my previous quantitative comparison between T-rex and 2 Allosauroid based on several principal forelimb bones, which are Humerus, Radius, and Ulna. I concluded that proportionally speaking, T-rex's forelimbs are as strong as those of Allosaurus, which is impressive considering T-rex has visually quite reduced forelimbs compared to Allo (however, it is still only able to restrain proportionally smaller preys due to scaling of prey size). In absolute terms, T-rex forelimbs are as strong as those of Acrocanthosaurus. This means that while T-rex forelimbs are not as strong as those of Allosauroid relative to its massive size (Sue the T-rex is one of the largest Theropod ever found), it should still be strong enough in absolute term to serve as a secondary tool to help T-rex increase its grip on its prey in addition to its already impressive jaw. My first post quantitatively supported the hypothesis of the usage of forelimbs for raptorial purposes.
However, other members (
theropod ) pointed out some issues. T-rex has visually tapered forelimbs. The limb starts out at really robust at the scapulacoracoid, and it gets increasing less so till it gets to the metacarpal and the phalanges where it appears quite slim and fragile. And it also does not help that T-rex only has 2 metacarpal bones to distribute stress in comparison to Allosauroid who have 3 bones for the same job. He concerns that the distal limb segments of T-rex may not be strong enough and thus it may be a bottleneck to prey-grappling hypothesis. Thus, i will quantitatively compare the Bending Strength between T-rex's metacarpal and Allosaurus's metacarpal to see if the prey-grappling theory of T-rex forelimbs still holds up.
Material and MethodologyThe materials are from the same sources and from the same specimens that i cited above, nothing really changes. The reason Acrocanthosaurus is not included in this post is because i cannot find the required materials for it to compute figures.
Methodology stays the same, Bending Strength will be assessed at the mid shaft of each metacarpal bones. The applied force is assume to be at the distal-most part of the metacarpal and thus the Moment arm length will be half of the shaft. After that, i will sum the Strength of each metacarpal bones to get the overall metacarpal Strength (the strength of the 'paw' if you will).
Result and DiscussionOnly metacarpal figures will be included here because i already discussed other forelimb bones above (the excel file will have all the figures). I included Robusticity figures here. However, i already pointed out above that comparing Robusticity in this context may not be meaningful. Thus, there will be no assessments based on the Robusticity figures.
Metacarpal 1: In absolute term, the result of M1 is surprising. The M1 of Allosaurus is actually significantly stronger in absolute term!. This is unexpected due to the large size differences between two animals. The Allo size here is uncertain but i think it's unlikely that it can weigh above 2000 kg. On the other hand, Sue the T-rex can easily be estimated to weigh over 8000 kg. At bare minimum, the T-rex here is 4x the size of Allo, yet its M1 is nowhere near as strong. Needless to say, T-rex M1 is much weaker in relative term as well.
Metacarpal 2: In absolute term, as expected, the much larger T-rex also has much stronger M2. In relative term, T-rex's M2 is still stronger, albeit insignificantly so. This suggests that T-rex M2 is as strong as that of an isometrically scaled-up Allo. As we already discussed above, this also means lesser prey-predators mass ratio due to positive allometry scaling of preys' Strength.
Metacarpal 3: Well, Allo's M3 is the weakest in both absolute and relative term when compared to M1 and M2. But i guess it's still better than nothing. T-rex M3 is not included because there is no data for it. Also, i can't see it plays any roles in stress dispersion.
Total metacarpal: The result in absolute term is unexpected. T-rex's metacarpal is only as strong as that of Allosaurus, despite being 4x more massive. In relative term, needless to say, Allo is significantly stronger. This confirms the bottleneck concern. T-rex's humerus and antebrachii are similar in strength to that of Acrocanthosaurus, however its metacarpal is not in anyway stronger than that of a much smaller Allosauroid. The weak metacarpal here will constrain the entire forelimb raptorial capacity ('a chain is only as strong as its weakest link' principle). If one assume that Allo's forelimbs are adapted to restrain preys similar to its body mass (about 1500 kg) then that should be the maximum amount T-rex can restrain too. If T-rex tries to restrain larger preys with its forelimbs, its metacarpal will just come off.
Total forelimb: The T-rex's forelimbs are still stronger in absolute term overall (due to having stronger humerus and antebrachii in absolute). However, i don't think that has any relevance here because T-rex forelimb is already constrained at its metacarpal (as its metacarpal is not in anyway stronger than that of Allosaurus).
Conclusion:With a metacarpal only as strong as an animal significantly smaller than T-rex is, i think we can safely conclude that T-rex's forelimbs are not adapted for restraining preys. This assessment is also consistent with qualitative one. T-rex's deltopectoral crest is not very well developed when compared to Allosauroid. The area at the olecranon process for muscle insertion is smaller than that of Allosauroid. The distal width of the humerus is very narrow, suggesting underdeveloped epicondyle (from what i have seen about Carnivoran anatomy, epicondyle is related to wrist stabilising muscles, but i don't know if the same principle can be applied here;
Meachen, 2009;
Meachen, 2012).
There is a 'forelimb slashing' hypothesis around but we have to wait for the published paper to come out to assess if it can hold any water. However, i think we can safely disprove the 'large game, Felids forelimb grappling' hypothesis for T-rex.
Criticism:Some may argue that Allosaurus's metacarpal is simply overbuilt compared to the rest of its forelimb bones. This is because the metacarpal Strength value is significantly higher than that of other bones as in the table i posted. However, i don't think this is the case. My assessment is based on using the Bending Strength of metacarpal at the mid shaft. However, because the metacarpal are such short bones, it's very difficult for something so short to break under Bending Stress. In reality, the metacarpal is more likely to break under shear stress if it ever to break at the mid shaft. However, there are several joints in the metacarpal section that are much more prone to stress than the bone itself. For instance, the joint between carpal and metacarpal (which i assume is probably cartilage) can be prone to tensile stress due to it being made out of less resistive materials. Heck, that cartilage joint is certainly more prone to break under Bending Stress and shear stress than the bone shaft itself. Long story short, it's very daunting and unnecessary (not to mention, such data are not available) to try accurately comparing each limb sections of an animal relative to each other in Strength. However, for cross-species comparison, it's still meaningful. If T-rex's metacarpal is comparable to that of Allo under Bending Stress at the mid shaft, then one could also reasonably expected its comparable in strength to Allo when under other more relevant metacarpal-breaking stress as well.
For the record, the metacarpal value of T-rex is also higher than those of its robust humerus and antebrachii. There is no reason to believe that the puny-looking metacarpal of T-rex is 'overbuilt' compared to its clearly more massive limb elements. Thus, the 'overbuilt' argument does not hold any water.
Final Verdict:Well, perhaps Rex should have stuck to the thing he does best
P/S: Most exhausting post i ever made on this forum
Attachments:Theropod Forelimb.xlsx (17.42 KB)