Using Scientifically Accurate Figures to Calculate Body Mass

[Ajax88]

In the annals of paleontological history, some of the earlier mass estimates for dinosaurs were obtained from rather simple methods. Some notable researchers would simply acquire a model of the dinosaur of interest and simple find its displacement in water, and using the square-cube law, estimate the mass of the living creature. This method assumed that dinosaurs had a density of 1g/cubic cm (the same as water). Now, these early models were often extremely inaccurate and in some instances, downright obese in proportion. This of course led to inflated results when scaled up to life-size. Including the 50-80 ton Giraffatitan estimations of the middle 20th century.

Now, it occurred to me that with the new wave of very scientifically accurate Dino toys available to us commoners, I could do a little math and see what weight my figures would equate to in a real-life scaled up animal!

The math:

-Find the scale of the model, e.g. 1/35th

-Weigh the model, and adjust to the proper density. Most of our modern models are rigid plasticized PVC, which typically has a density of around 1.45g/cm^3.  Most dinosaurs on the other hand probably had whole body densities between .85g/cm^3 in large sauropods with very large, light necks, and 1.1g/cm^3 in the heavily armored ankylosaurids.

-Scale the mass of the model back up to life size using the cube root law, and viola! You now have an estimate of how much your model would mass at life size and real-world flesh density.

Here are a few I have already tried:

Eofauna Ankylosaurus

Scale: 1/35. 24cmx35=8.4m pretty spot on for the largest Ankylosaurus specimens.
Mass of the figure: 210g
Density factor: Ankylosaurus density ~1.1g/cm^3 divided by PVC density.  1.1/1.45=.758
Final mass: 210 x .758 x 35^3 = 6.8 tons

Haolonggood Triceratops

Scale: 1/33, an 8.8cm head at 1/33 scale is about 2.9m long, roughly the size of the largest partial Triceratops skulls out there.
Mass of the figure: 434g
Density factor: Triceratops density ~1g/cm^3.   1/1.45=.69
Final mass: 434 x .69 x 33^3 = 10.76 tons.

Halolonggood Argentinosaurus

Scale: 1/32 105cmx32=33.6m  1/35 would probably be a couple meters longer than the specimen we have, but likely well within the spectrum of variation in the species.
Mass of the figure: 4,925g :0
Density factor: Sauropod density ~.85g/cm^3  .85/1.45=.58
Final Mass: 4925 x .58 x 32^3= 93.6 tons!
That mass for Argentinosaurus is a little high, perhaps HLGs model is a bit too wide? Or perhaps the estimates in the literature are a bit too conservative? Or perhaps its just too dang hard to estimate the weight of a critter known from like 9 bones total? 

Anyway, enjoy weighing your own models and seeing how the numbers turn out. Feel free to post them here if this kind of thing interests you at all, haha.

[Ajax88]

Also for what it's worth Eofauna's Sue and PNSO's Mapusaurus, which at it's length is a better stand in for Giganotosaurus, are very precisely in 1/35 scale and weigh 351g and 328g respectively. This equates to live weights of around 9.33 tons for ol' Sue and 8.7 tons for Giganotosaurus. Pretty close to each other, and pretty close to the current consensus on these animals weights, if not a smidge heavy!

[Protopatch]

In the annals of paleontological history, some of the earlier mass estimates for dinosaurs were obtained from rather simple methods. Some notable researchers would simply acquire a model of the dinosaur of interest and simple find its displacement in water, and using the square-cube law, estimate the mass of the living creature. This method assumed that dinosaurs had a density of 1g/cubic cm (the same as water). Now, these early models were often extremely inaccurate and in some instances, downright obese in proportion. This of course led to inflated results when scaled up to life-size. Including the 50-80 ton Giraffatitan estimations of the middle 20th century.

Now, it occurred to me that with the new wave of very scientifically accurate Dino toys available to us commoners, I could do a little math and see what weight my figures would equate to in a real-life scaled up animal!

The math:

-Find the scale of the model, e.g. 1/35th

-Weigh the model, and adjust to the proper density. Most of our modern models are rigid plasticized PVC, which typically has a density of around 1.45g/cm^3.  Most dinosaurs on the other hand probably had whole body densities between .85g/cm^3 in large sauropods with very large, light necks, and 1.1g/cm^3 in the heavily armored ankylosaurids.

-Scale the mass of the model back up to life size using the cube root law, and viola! You now have an estimate of how much your model would mass at life size and real-world flesh density.

Here are a few I have already tried:

Eofauna Ankylosaurus

Scale: 1/35. 24cmx35=8.4m pretty spot on for the largest Ankylosaurus specimens.
Mass of the figure: 210g
Density factor: Ankylosaurus density ~1.1g/cm^3 divided by PVC density.  1.1/1.45=.758
Final mass: 210 x .758 x 35^3 = 6.8 tons

Haolonggood Triceratops

Scale: 1/33, an 8.8cm head at 1/33 scale is about 2.9m long, roughly the size of the largest partial Triceratops skulls out there.
Mass of the figure: 434g
Density factor: Triceratops density ~1g/cm^3.   1/1.45=.69
Final mass: 434 x .69 x 33^3 = 10.76 tons.

Halolonggood Argentinosaurus

Scale: 1/32 105cmx32=33.6m  1/35 would probably be a couple meters longer than the specimen we have, but likely well within the spectrum of variation in the species.
Mass of the figure: 4,925g :0
Density factor: Sauropod density ~.85g/cm^3  .85/1.45=.58
Final Mass: 4925 x .58 x 32^3= 93.6 tons!
That mass for Argentinosaurus is a little high, perhaps HLGs model is a bit too wide? Or perhaps the estimates in the literature are a bit too conservative? Or perhaps its just too dang hard to estimate the weight of a critter known from like 9 bones total? 

Anyway, enjoy weighing your own models and seeing how the numbers turn out. Feel free to post them here if this kind of thing interests you at all, haha.

Interesting approach as well as a fun math training. I'm wondering if the toy makers made the reverse operation to design their figures ie started from the estimated body weight of the dinosaurs ?

[danmalcolm]

If I had the time to perform this tremendously interesting experiment, I think I'd be inclined to use water displacement instead of PVC density. I think the margin for error would be smaller.  But it's honestly a great idea.  Keep us posted if you do more!

[Ajax88]

If I had the time to perform this tremendously interesting experiment, I think I'd be inclined to use water displacement instead of PVC density. I think the margin for error would be smaller.  But it's honestly a great idea.  Keep us posted if you do more!

I actually did double check by dunking one of my smaller models in water and came up with a PVC density of 1.48g/cm^3 close enough to the density listed online that I felt ok using 1.45 for all the calculations.

[Dino_W]

I've been working on display plaques for all my figures which has led me to do the same thing. I've been calculating assuming every figure is 1/35 scale. It has actually been quite helpful for identifying proportion errors on models. The method only seems to work on animals larger than 1 ton in body mass at 1/35 scale, as smaller animals are harder to mold perfectly.

1/35 Scale figure calcs

[thomasw100]

I've been working on display plaques for all my figures which has led me to do the same thing. I've been calculating assuming every figure is 1/35 scale. It has actually been quite helpful for identifying proportion errors on models. The method only seems to work on animals larger than 1 ton in body mass at 1/35 scale, as smaller animals are harder to mold perfectly.

1/35 Scale figure calcs

Very interesting data. Did you also compile the range of weight estimates in the paleotological literature for these species?

[Dino_W]

Very interesting data. Did you also compile the range of weight estimates in the paleotological literature for these species?

I have not yet, though the figures listed as 1/35 scale generally trend towards the higher end of mass estimates for the species. So far in terms of mass accuracy, Eofauna ranks the highest (flawless for advertised scales), closely followed by PNSO (Edmontosaurus weight does not match length due to the tail being too short), and then Haolonggood with two small errors (Carcharodontosaurus and Triceratops are slightly too large though still within the realm of plausibility) and one large error (Pachyrhinosaurus is disproportionally bulky and is far too heavy).

[thomasw100]

I have not yet, though the figures listed as 1/35 scale generally trend towards the higher end of mass estimates for the species. So far in terms of mass accuracy, Eofauna ranks the highest (flawless for advertised scales), closely followed by PNSO (Edmontosaurus weight does not match length due to the tail being too short), and then Haolonggood with two small errors (Carcharodontosaurus and Triceratops are slightly too large though still within the realm of plausibility) and one large error (Pachyrhinosaurus is disproportionally bulky and is far too heavy).

How about the Haolonggood Argentinosaurus? I read somewhere that this would come out at something like 90 to even more than 100 tons using your method. This seems too high mass and this could potentially indicate that the figure would have too much girth.

[Turkeysaurus]

Wouldn't how much plastic used depends on model to model, not just depends size of the model but to how balance or mold it?

I think using volume ( with water displacement method) instead of mass would be better to calculate but it's too much work lol.

[Dino_W]

How about the Haolonggood Argentinosaurus? I read somewhere that this would come out at something like 90 to even more than 100 tons using your method. This seems too high mass and this could potentially indicate that the figure would have too much girth.

Oh yeah, the Haolonggood Argentinosaurus is definitely too bulky (at least for current reconstructions). Even if we use a very low specific gravity of 0.85g/cc, at 1/35 scale: 4925*35^3/1.45*0.85/1000000 = 123.8 tonnes.

Wouldn't how much plastic used depends on model to model, not just depends size of the model but to how balance or mold it?

I think using volume ( with water displacement method) instead of mass would be better to calculate but it's too much work lol.

I was actually considering just straight-up scanning in models using photogrammetry apps to check the volume. I did that for the PNSO Edmontosaurus, and that confirmed the density value that I was using.

[Ajax88]

How about the Haolonggood Argentinosaurus? I read somewhere that this would come out at something like 90 to even more than 100 tons using your method. This seems too high mass and this could potentially indicate that the figure would have too much girth.

Oh yeah, the Haolonggood Argentinosaurus is definitely too bulky (at least for current reconstructions). Even if we use a very low specific gravity of 0.85g/cc, at 1/35 scale: 4925*35^3/1.45*0.85/1000000 = 123.8 tonnes.

Wouldn't how much plastic used depends on model to model, not just depends size of the model but to how balance or mold it?

I think using volume ( with water displacement method) instead of mass would be better to calculate but it's too much work lol.

I was actually considering just straight-up scanning in models using photogrammetry apps to check the volume. I did that for the PNSO Edmontosaurus, and that confirmed the density value that I was using.

I suppose since we have zero ribcage material from Argentinosaurus we can be a bit lenient on bulk for HLG. In any case, I'm sure there was some Argentinosaurus out there out of millions of individuals that massed around 100 tons. Since we have a whopping sample size of 2!