Saturday, April 21, 2007

Maximum bite force in Tyrannosaurus rex

I'm on a roll today. Might as well post another.

So obviously, this is a Tyrannosaurus rex. It's so famous I'm afraid I don't really know what else to write about. Oh well, I'll just ramble on about bite forces then.

T. rex has been the focus of many biomechanical studies. Bite force is no exception. However, as much of a celebrity T. rex is, as far as I'm aware, there have only been two studies so far that have attempted to estimate the bite force of T. rex: Erickson et al. (1996) and Meers (2002).

Erickson et al. (1996) had an interesting approach of reproducing bite marks using cast replicas of a T. rex tooth and ramming it into a cow bone. They recorded the forces needed in order to penetrate the bone to different depths. The depths of T. rex bite marks found on a Triceratops ilium was compared to this relationship of puncture depth and forces needed. As a result they found out that a bite force of 6.4 kN were needed in order to to make that bite mark. From the shape and size of the tooth, Erickson et al. (1996) suggested that the bite may have been made from a mid maxillary tooth. So they extrapolated a possible bite force for the posterior-most tooth position. Further, they suggest that up to 30% of the original bite force may have been lost due to several layers of soft tissues that the tooth would have had to penetrate before it reached the bone. In conclusion, they proposed a maximum bite force of 13.4 kN.

Mason Meers (2002) on the other hand employed a much simpler approach. He regressed bite force against body mass and extrapolated the relationship to a 5 tonne T. rex. As a result, his maximum bite force was 183 to 235 kN, an order of magnitude higher than Erickson et al.'s (1996).

So which is closer to the truth?

I would say somewhere in between the two.

Through my own studies, I'm confident to say that Erickson et al.'s (1996) bite force estimate is not really a maximal value. This isn't restricted to just Erickson et al.'s (1996) estimates but for other theropods as well (Rayfield et al. 2001; Mazzetta et al. 2004a, b). With Rayfield et al. (2001) and Mazzetta et al. (2004a, b), their methods in bite force estimation may have the tendency to underestimate. Erickson et al. (1996) on the other hand probably estimated their bite force fairly accurately. The only problem is that the T. rex that produced the bite mark may not have exerted its maximum bite force. The position of the bite on the Triceratops (in the pelvic region) strongly suggests that these bite marks were produced post-mortem and were probably not killing bites but feeding bites. It is unclear just how hard it was biting, but the safe bet is, it was probably just happily munching away at a leisurely (or necessary) bite. I had a chat with Greg Erickson at a conference and he seems to have an opinion along this line as well.

Meers (2002) on the other hand may have overestimated maximum bite force. This is mostly because his slope on the regression equation is closer to 1, or proportional increase of bite force with increasing body mass. So the bigger the animal the stronger the bite. However, my own studies suggest that this slope may actually be significantly lower than 1, so in other words, the bigger the animal, the progressively weaker the bite gets relative to its increase in body mass.

So this puts maximum bite force for T. rex with various body mass estimates at somewhere between 50 to 80 kN.

References:
  • Erickson, G. M. , Van Kirk, S. D., Su, J., Levenston, M. E., Caler, W. E. and Carter, D. R. 1996. Bite- force estimation for Tyrannosaurus rex from tooth-marked bones. Nature, 382:706-708.
  • Gerardo V. MAZZETTA, Adrián P. CISILINO y R. Ernesto BLANCO. 2004a. Distribución de tensiones durante la mordida en la mandíbula de Carnotaurus sastrei Bonaparte, 1985 (Theropoda: Abelisauridae). Ameghiniana 41: 605-617.

  • Gerardo V. MAZZETTA, R. Ernesto BLANCO y Adrián P. CISILINO. 2004b. Modelización con elementos finitos de un diente referido al género Giganotosaurus Coria y Salgado, 1995 (Theropoda: Carcharodontosauridae). Ameghiniana 41: 619-626.

  • Rayfield EJ et al, 2001, Cranial design and function in a large theropod dinosaur, Nature 409: 1033-7
Images from National Geographic and BBC.

7 comments:

Zach Miller said...

I don't pay too much attention to biomechanical papers, because in truth, it's not something that's ever actually knowable. Bone strength is great, but muscle strength and behavior are also important, but sadly unknown, variables.

Mambo-Bob said...

Very much true...I'm working on how we can constrain some of these unknowns - only to a possible range, that is.

Kevin said...

Sorry Manabu but you are wrong in interpreting the figures from the 2 authors. The disparity between the results of Meers and Erickson is not as great as it looks. Erickson et al calculated the bite force at a single tooth, whilst Meers calculated it for the entire tooth row (i.e. both sides). Given its dental morphology, T. rex was unlikely to ever bite down at just one tooth. As Rayfield (2004) shows, if you take Erickson's measurement and extend it across the entire tooth row, allowing for geometry, then you get an estimate of 156KN, which is close to the range calculated by Meers.
Sorry Manabu but you are wrong in interpreting the figures from the 2 authors. The disparity between the results of Meers and Erickson is not as great as it looks. Erickson et al calculated the bite force at a single tooth, whilst Meers calculated it for the entire tooth row (both sides). Given its dental morphology, T. rex was unlikely to ever bite down at just one tooth. As Rayfield (2004) shows, if you take Erickson's measurement and extend it across the entire tooth row, allowing for geometry, then you get an estimate of 156KN, which is close to the range calculated by Meers.

Manabu said...

Well, that's quite straightforward of you....

Ok, first of all, Meers (2002) extrapolated a bite force from a regression equation of bite force against body mass in modern predators. This is just a maximum bite force value, independent of how many teeth are involved in the bite.
Secondly, and more importantly, you can't extend a single-tooth bite force and multiply that along the entire tooth row. No matter how many teeth the force is distributed over, it will never be higher than the maximum bite force at the posterior-most tooth position. That would be the maximum bite force and if you were to distribute that across multiple teeth, then bite force at those individual teeth would be considerably lower - i.e. accordinly distributed depending on how long the moment arm is.

Imagine that you are standing on a scale balanced on one leg. The scale will read 60 kg or however you may weigh. Now, if you stand on the scale on both legs, you will still weigh 60 kg. On the other hand, if you stand on two scales, one leg on each scale, then, your weight would be equally distributed between the two scales and the scales should each read 30 kg, which you can add up to 60 kg in total.

So in summary, a maximum bite force is in fact the maximum bite force. It does not matter if it is centralised on one tooth or distributed over multiple tooth, the net total should be the same.

Kevin said...

From what you just said we both have the same interpretation on the study by Meers but NOT on Erickson's.

Erickson et al stimulated the force required to produce a SINGLE bite mark left by T. rex with a SINGLE T. rex tooth. As you mentioned, if I stand on two scales, one leg on each scale, then, my weight would be distributed between the two scales and the scales should each read 30 kg, which I can add up to 60 kg in total. This is exactly the case of Erickson's study. Applying his study to your example, he was measuring the force exerted by my left leg on a scale (while my right leg is on another scale, of which he was unable to determine the reading). If it reads 30kg, my weight must be more than 30kg since I have two legs on 2 scales. As I said, given the dental morphology of T. rex, it was unlikely to ever bite down at just one tooth. If that single tooth mark was produced at a force of 6.4KN by a single tooth, the bite force must be much higher than this value since other teeth (legs) were probably biting to other parts (scales) of the bone, distributing the bite force of the jaws to produce varying degrees of deep bite marks on other areas of the prey.

Since the study measures the force exerted by a single tooth from a single tooth mark, you cannot distribute the force across multiple teeth as the bite mark was made by a single tooth. Similarly you cannot conclude that I only weight 30kg if the scale on my left leg reads 30kg if my right leg is on another scale reading 30kg. You must add the two values together for my actual weight, which is 60kg in this example.

As Rayfield (2004) shows, if you take Erickson's measurement and extend it across the entire tooth row, ALLOWING FOR GEOMETRY, then you get an estimate of 156KN for the maximum bite force, which is close to the range calculated by Meers. An estimate of 156KN by Rayfield (2004) is NOT a simple multiply along the entire tooth row and it has already taken the moment arm into account.

In conclusion, Erickson measures the maximum force exerted by a single posterior tooth, while Meers measures the maximum bite force of the jaws.

Mambo-Bob said...

Kevin,

I have no problem with what you're saying regarding Erickson et al.'s (1996) bite force.

I completely agree that it is measured from a single tooth, in which we do not know exactly how many teeth were in contact with the bone during biting, thus making it likely that the "true" bite force is higher.

I don't think I cite Erickson et al.'s (1996) value explicitly as the absolute maximum bite force in my original post. But whatever...

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