Which Dinosaur is the Fastest? The Maths of Dinosaurs
University of Oxford Mathematician Dr Tom Crawford explains how to mathematically calculate the fastest dinosaur. Its the Maths of Dinosaurs!
Using a mathematical formula which gives the top speed of a land-based animal, we use the tools of calculus to determine the ideal mass to maximise velocity. Too small and the animal does not have enough capacity to go quickly, but too big and it cannot accelerate quickly enough to reach its theoretical maximum speed. The location of the 'sweet spot' in the middle is found by calculating the turning point of the velocity function. The solution is then applied to dinosaurs to determine which is the fastest.
Check out the table of all calculated top speeds here: tomrocksmaths.files.wordpress...
The formula for the top speed is taken from the work of Myriam Hirt - link to publication below.
Hirt, M.R., Jetz, W., Rall, B.C. et al. A general scaling law reveals why the largest animals are not the fastest. Nat Ecol Evol 1, 1116-1122 (2017). doi.org/10.1038/s41559-017-02...
Filmed on location at Lourinha Dino Park in Portugal.
Produced by Dr Tom Crawford at the University of Oxford. Tom is Public Engagement Lead at the Oxford University Department of Continuing Education: www.conted.ox.ac.uk/
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Thanks to
Lourinha Dino Park
Steve Sheridan • Cheetah Run
Wildest Nature • Top 10 Fastest Animal ...
Hoedspruit Endangered Species Centre • Shelly the cheetah in ...
Using the same "sweet point" for pokemon, the fastest are: Mega Blastoise 101.1kg, type: water Kleavor 89kg type: rock Natu 2kg type: flying
I LOVE dinosaurs and physics and I have mixed feelings about maths; really cool video! I have a t-Shirt with a velociraptor on it and the equation Velociraptor = Distanceraptor/Timeraptor Not with mass, but it’s funny
Tom rocks Dinosaur 🦖 Maths 🧮 (Australian High School Teacher) 🧑🏫
Good that you went back to past in that time machine. Lucky you did tie that stop watch in your neck while being chased by every type of Dinosaur. Otherwise this research would have been impossible. We are also glad that you were able to reach to that time machine on time to return back to the future. A split second difference would have meant the machine stamped out by the Dinosaur. Keep it up. Next time you go back, remember to take some video.Regards.
I don't challenge the paper, but conceivably energy reserves could scale with volume just like mass does, so naively it would seem to be possible that is cancels out?
Let's all stay 10 years old forever; dinos! Yeah3🎉😊 (nice video )
There wasn't any flying or swimming dinosores (an exception is a family of Spinosores).
According to this I should be the fastest animal.........
I'm curious about whether the flying figures are for horizontal flight or for (survivable) dives? Guinness tracks the two separately, with the record for horizontal flight speed going to the (~0.12kg) White-throated Needletail at 170kph, while fastest stoop goes to the (0.7-1.5kg) female Peregrine Falcon at 389kph. I'm guessing the figures are for the latter, which means they're looking at the faster increase of mass than surface area with scale increasing terminal velocity, and that running into the ability of the birds to stop falling and pull out of the dive without damaging themselves, which depends on their mass, and ability to keep their wings from being torn off...
Waiting 🎉
What people will find interesting is that my cyber stalker used my being banned from the naked scientists website as an example of why I need him to moderate me. He's never been banned from a forum. Why is it a stalker is well liked online while discussing math and science will get me banned from forums? I could tell you your first mistake when considering how fast dinosaurs moved. It's something that math and science suggests. By any chance, do you know anyone who likes math? The problem today is that as an example a teacher speaks and a student repeats.
While reading through the paper, I got confused quickly. Kind of missed that `i` was defined and NOT the imaginary number... 😅
But if the sweet spot is 89kg, how come cheetahs have a maximum adult weight (according to Wikipedia) of only 72kg ? Surely cheetahs would have evolved to be heavier therefore faster therefore more successful ?
From what I can tell (if I inputted the formula correctly into WolframAlpha), the estimated ideal top speed of an animal on land weighing 72kg is 63.23kph vs. 63.43kph for an animal weighing 89kg. You get ideal top speeds above 60kph for animals between 39kg and 220kg (about the size of a Bengal Tiger) It could just be that, around about that weigh/speed range, as they're approaching the ideal maximum, there might be little evolutionary pressure causing them to gain the extra mass and increased speed (increase mass by 26%, gain a 0.3% boost in speed) Like, from a brief search, the Thomson's gazelle weighs around 35kg, and has a sustained top speed of around 55-60kph (although apparently quick bursts of 80-90kph), so as long as the cheetah is faster than that, and can still maintain a successful hunting strategy, and get enough food (again, quick search, seems they have a success rate around 60%) it might be that they're more or less getting as fast as there's any pressure for them to be, so no pressure to be bigger. Plus they'd have to hunt more to maintain the additional mass, maybe? Which means spending more energy, so there might be a sort of resource boundary. Not to mention the number of successful hunts that end up getting stolen by lions and hyenas that they have to run from. Cheetah's, unlike leopards, for example, can't drag a gazelle up into a tree
Cool analysis Tom 👍. But I’d like to look at the derivation of the model. It seems a bit over simplified. There maybe are factors that has a minimal effect, and therefore was dropped, but still I’d like to know them.
I've linked the paper in the description which includes the full derivation :)
@@TomRocksMaths Cool thanks. I didn’t look in the description.
How come this being out for over half an hour an still only
Hello ❤
hey!
but, how fast would an elephant run if placed on a terraformed mars ?
I think it would be another humped-curve when plotted against gravity: Super gravity - harder to move, minimal gravity - no traction! Mars' gravity is about twice the Moon's I think, that might potentially be close to ideal? Elephants on lower gravity worlds may eventually develop different gaits, unlocking higher speeds. Horses on heavier planets would have to abandon galloping. In very low gravity (lower than Mars'), some kind of jumping would be good, I guess.
A 6 ton T-Rex? Where did you get your data from? Current estimates average at about 10!
Cool. But your calculation is scientifically inaccurate. Because the parameters are dependent on environmental conditions e.g. O2 percentage in the atmosphere. 65mio years ago O2 in atmosphere and temperature were higher than today, therefore supersized animals were common as today. Conclusion: the model in paper will only describe animals live in today' environmental conditions - we do not have time machine to travel back to collect the data. We are making assumptions, but from maths aspect does not make difference. Cool video.
I love math, but I could understand it even better if you wore less clothes. In my opinion, you are welcome to take off your clothes again.🫣😉😇