In length, the Sperm Whale’s skeleton at Tranque measured seventy-two Feet; so that when fully invested and extended in life, he must have been ninety feet long; for in the whale, the skeleton loses about one fifth in length compared with the living body. Of this seventy two feet, his skull and jaw comprised some twenty feet, leaving some fifty feet of plain back-bone. Attached to this back-bone, for something less than a third of its length, was the mighty circular basket of ribs which once enclosed his vitals.

- Excerpt from "Measurement of The Whale's Skeleton" - Chapter 103 of Moby-Dick; or The Whale by Herman Melville

Earlier in the chapter, Melville/Ishmael tells us that a Sperm Whale of the largest magnitude measures between eighty-five and ninety feet long and by his reckoning weighs at least 90 tons, or as much as a village of 1,100. By my own reckoning in this previous post, I pegged a 19.5 meter (67'11") bull at around 90 tonnes (~100 tons) and I estimated a 27.5 m (90 foot) bull to weigh a stupefying 210 tonnes/230 tons. If the whale of Tranque was as big as Melville/Ishmael claimed*, it would have rivaled the largest blue whales (Balaenoptera musculus) for size.

* How can a 72 foot skeleton possibly correspond to a 90 foot whale? A ~20 foot mandible would be at a 1:3.6 ratio to the skeleton length, which agrees well with the 1:3.8 m estimate below. The modified Gore et al. (2007) formula (see further below) estimates the whale's length at 21.4 meters (70 feet) using a skull length of 6 meters - could this have been based off a real specimen?

* How can a 72 foot skeleton possibly correspond to a 90 foot whale? A ~20 foot mandible would be at a 1:3.6 ratio to the skeleton length, which agrees well with the 1:3.8 m estimate below. The modified Gore et al. (2007) formula (see further below) estimates the whale's length at 21.4 meters (70 feet) using a skull length of 6 meters - could this have been based off a real specimen?

Skeletons of gigantic sperm whales (Physeter macrocephalus sometimes P. catodon) do not currently exist in museums as far as I know (if they ever did) and the only possible evidence of colossal bulls rests in preserved mandibles. In my previous post I discussed a 5 meter (16'4.75") mandible in the British Museum which Wood (1982) estimated to have come from a 25.5 meter bull; I extended Wood's reasoning to estimate a 5.5 meter mandible from the Nantucket Whaling Museum to correspond with a 27.5 meter bull. Wood (1982) noted that a 14.7 m whale had a mandible:body length ratio of 1:6.2 and a 16.28 m whale had a ratio of 1:5.4; he extended the graph to estimate a 1:5.1 ratio for his monstrous mandible and I extended it further to 1:5 for the even bigger mandible. I'm now quite certain that all of these estimated lengths and ratios are, in fact, hogwash.

The book, The Marine Mammals in the Anatomical Museum of the University of Edinburgh (courteously digitized by Google) notes that a 15'10" (4.83 m) mandible probably corresponded with a sperm whale 60 feet (18.3 m) in length - let's assume that this estimate is accurate. This whale would have had a mandible:body length ratio of around 1:3.8; if we assume there is little allometric change, the 5 m mandible would thus correspond to a 19 meter bull and the 5.5 meter mandible would correspond to a 21 meter bull. Given that the record length sperm whale was 20.7 meters in length, I'd say that these seem like plausible figures. But is this accurate?

Unfortunately, there is a lack of data on sperm whale mandible length:body length. However, if we assume that the length of the mandible is nearly the same as that of the skull, this gives us more data to work with. I'll give a range of estimates just to be safe, the first will assume a 1:1 mandible:skull ratio and the second will assume that the mandible is roughly 90% of the skull's length. Data on head length should be avoided since soft tissue can make it considerably longer. Gordon (1991) used data on sperm whale spermaceti length in comparison to body length to come up with a formula which Gore et al. (2007) in turn used to estimate body length from skull length. It is as follows:

Total body length = 9.75 − 0.521 (SL) + 0.068 (SL^2) + 0.057 (SL^3)

Where SL = skull length

This is quite a bit more complicated than what I was using as it appears to take allometry into account (where I previously sorta ignored it). Here is what happens when we plug in numbers:The book, The Marine Mammals in the Anatomical Museum of the University of Edinburgh (courteously digitized by Google) notes that a 15'10" (4.83 m) mandible probably corresponded with a sperm whale 60 feet (18.3 m) in length - let's assume that this estimate is accurate. This whale would have had a mandible:body length ratio of around 1:3.8; if we assume there is little allometric change, the 5 m mandible would thus correspond to a 19 meter bull and the 5.5 meter mandible would correspond to a 21 meter bull. Given that the record length sperm whale was 20.7 meters in length, I'd say that these seem like plausible figures. But is this accurate?

Unfortunately, there is a lack of data on sperm whale mandible length:body length. However, if we assume that the length of the mandible is nearly the same as that of the skull, this gives us more data to work with. I'll give a range of estimates just to be safe, the first will assume a 1:1 mandible:skull ratio and the second will assume that the mandible is roughly 90% of the skull's length. Data on head length should be avoided since soft tissue can make it considerably longer. Gordon (1991) used data on sperm whale spermaceti length in comparison to body length to come up with a formula which Gore et al. (2007) in turn used to estimate body length from skull length. It is as follows:

Total body length = 9.75 − 0.521 (SL) + 0.068 (SL^2) + 0.057 (SL^3)

Where SL = skull length

5 meter mandible:

5 meter skull = 15.97 meters (52 feet)

5.5 meter skull = 18.42 meters (60 feet)

Wood's 25.5 meter estimate was probably off by 138% to 160%.

Using a 1:3.8 ratio gives estimates that are off by 114% to 119%

5.5 meter mandible:

5.5 meter skull = 18.42 meters (60 feet)

6.0 meter skull = 21.384 meters (70 feet)

My 27.5 meter estimate (based off of Wood's allometry) is probably off by 128% to 149%

Using a 1:3.8 ratio gives estimates that are off by 113% and 106%

A 6 meter skull was also present in the (fictional?) Tranque whale, and Melville/Ishmael's estimate for skeletal length (72 feet) is off by 103%. The estimation for body length in the flesh is off by 129%.

Hard data is needed on the mandible:body length ratio in sperm whales so these equations can be refined. I'd say that as is, the data suggests that the 5 and 5.5 meter mandibles do not correspond with bulls greatly exceeding the known 20.7 meter record. It could be possible that these mandibles are the product of abnormal growth analagous to acromegaly in humans (as suggest by Alan Hazen). There is currently no non-anecdotal evidence of bulls greatly exceeding 20.7 meters and while specimens somewhat larger than this probably existed in the past due to a larger average length, sperm whales do not appear to rival blue whales for the title of the largest animal ever to have lived.

I was planning to make this an addendum, but it quickly got out of hand...

For information on sperm whale jaw oddities, see the post at Tetrapod Zoology

References:

Gordon, Jonathan C. D. 1991. Evaluation of a method for determining the length of sperm whale (Physeter catodon) from their vocalizations. Journal of Zoology 224, 301-314

Gore, M. A. et al. 2007. Sperm whale, Physeter macrocephalus, stranding on the Pakistani coast. J. Mar. Biol. Ass. 87, 363–364

Wood, Gerald. 1982. Guinness book of Animal Facts and Feats. Guinness Superlatives, Middlesex.