Yutyrannus huali

[DinoFan83]

Old post deleted and redone. I made a couple of errors on the old one and have expanded my information, so this should be more accurate.

Although often overlooked in terms of proportional bite force, I have reason to believe Yutyrannus would have been among the harder-biting theropods for its size because its skull is so proportionally large and robust. However, there have been no bite force studies published, and so my estimates here will be based on comparison to other animals. Exact bite force ballpark is therefore unknown but this is very likely close.  

Specimens used (both estimated species and species being used as a base for the bite force), their estimated sizes, their estimated skull lengths, and (for the base species) their estimated bite forces:  

Allosaurus jimmadseni (SMA 0005): 1600 kg based on Randomdinos' chart, 79 cm skull as per discussion in comments of said chart, 8724 newton bite force based on Bates & Falkingham (2012).  

Sinotyrannus kazuoensis (KZV-001): Can be estimated at a mean of about 1000 kg based on the average estimate of ilium length comparison with the estimates for the Yutyrannus specimens below, 93.1 cm skull based on Daniel Barrera's skeletal.  
(This is a 'bonus' specimen of which the bite force can tentatively be estimated).

Tyrannosaurus spp. (BHI 3033): 6500 kg following Asier Larramendi, 140 cm skull as per the Theropod Database, 35000-57000 newton bite force following Bates & Falkingham.  

Yutyrannus huali (ZCDM V5000 and ZCDM V5001): The holotype specimen can be estimated at 935 kg as per the above weight estimates, and its skull is estimated at 90.5 cm long by Xu et al. (2012) supplementary information. Also as per the estimates in the above posts, the paratype can be estimated at 419 kg based on femoral length comparisons with the holotype (85 vs 65 cm), and Xu et al. estimates its skull at 80 cm long.  

Skull comparison and (tentative) bite force estimates:

Here is a skull comparison I put together of ZCDM V5001 and SMA 0005, based on the above measurements. Note that MOR 693 was used in place as it had both a good quality lateral and dorsal view available while SMA 0005 did not.  
As we can see, ZCDM V5001's skull compares very favorably. In regards to bite force, it has all the following going for it:

-Larger overall (79 vs 80 cm) despite the animal's size disadvantage of over 3.8-fold.
-Much deeper for its length.
-Notably wider for its length.
-Fused nasal bones (these aren't exactly visible, but tyrannosauroids have them), increasing rigidity and thus bite force.

And while I'm not aware of how to factor in the fused nasals, the length, depth, and width can be used for a tentative extrapolation of ZCDM V5001's bite force - based on my combined measurements of length, jugal-postorbital depth, eye socket width, and anterior anteorbital fenestra width, ZCDM V5001's skull is some 14.9% larger overall. That suggests a bite force estimate for the specimen of 11517 newtons (8724x1.149^2).

This tentative estimate for ZCDM V5001's bite force also allows for estimations via skull length for the bite forces of ZCDM V5000 (90.5/80 (11517)^2=14739 newtons) and KZV-001 (93.1/80 (11517)^2=15598 newtons), as their skulls seem to be similarly solidly built.  

Now, you may be wondering at this point how Yutyrannus (and 'bonus' Sinotyrannus as well) compare to the provided bite force estimates for Allosaurus and Tyrannosaurus on a 'pound for pound' basis. Assuming the above is relatively accurate, they stack up better than one might expect.  

Proportional bite force compared to Allosaurus:
 
1600/419 (11517)^0.667=28151 newtons can be estimated as the bite force for a hypothetical SMA 0005-sized ZCDM V5001.
1600/935 (14739)^0.667=21091 newtons can be estimated as the bite force for a hypothetical SMA 0005-sized ZCDM V5000.
1600/1000 (15598)^0.667=21342 newtons can be estimated as the bite force for a hypothetical SMA 0005-sized KZV-001.

If this is roughly on point, the estimates suggest ZCDM V5001 could bite about 3.23 times as hard as an equally sized Allosaurus, and ZCDM V5000 would be able to bite 2.42 times as hard (which gives us a mean 'pound-for-pound' Yutyrannus bite force 2.83 times as great as that of Allosaurus). Similarly, the 'bonus' KZV-001 would bite some 2.45 times as hard. 
I don't find this surprising in the least, given how all 3 tyrannosauroids have larger and more solidly built skulls than the allosauroid despite substantial disadvantages in size.

Proportional bite force compared to Tyrannosaurus:

6500/419 (11517)^0.667=71705 newtons can be estimated as the bite force for a hypothetical BHI 3033-sized ZCDM V5001.
6500/935 (14739)^0.667=53723 newtons can be estimated as the bite force for a hypothetical BHI 3033-sized ZCDM V5000.
6500/1000 (15598)^0.667=54362 newtons can be estimated as the bite force for a hypothetical BHI 3033-sized KZV-001.

Both Yutyrannus specimens and 'bonus' Sinotyrannus compare to BHI 3033 very well in terms of 'pound-for-pound' bite force. ZCDM V5000 is very close to the proportional upper end of 35000-57000 newtons Bates & Falkingham gave to BHI 3033, while ZCDM V5001 significantly exceeds even the upper end of it(!), and with the mean proportional bite force of both Yutyrannus specimens being greater than the range (62714 newtons), this suggests that Yutyrannus just might have been able to match up to or exceed similarly sized bone crushing tyrannosaurids for bite force.
Our 'bonus' Sinotyrannus also fits well into the given range, close to the upper end.

Such high proportional bite forces for Yutyrannus (and Sinotyrannus) may come as a surprise to many, but given the quite large skulls the used specimens have for their size compared to BHI 3033, it is perhaps less such. In the order written above, if they were hypothetically the same size, the estimated specimens would possess skulls 42.5% larger, 23.4% larger, and 24.2% larger respectively (and as the link shows, these skulls are no less robust for their length than that of BHI 3033), so I personally do not find it to be a stretch to say that while Yutyrannus-grade tyrannosauroids were not bone crushers like giant tyrannosaurids were, they could be able to match or exceed the high bite force proportionally (if only by their proportionally larger heads).

In summary, I can say that without testing this, I never would have known the bite forces of Yutyrannus and its kin could have been so proportionally high. And it also does show well that you don't need to be a bone crusher at all for a high proportional bite force on par with or greater than a bone crusher. Reply