A bunch of fossilized dinosaur footprints in the Mideast were recently discovered by Mohammed Al-Daheri who, incidentally, is a journalist (so all you folk who wanted to be paleontologists but didn’t get around to it, it’s not too late to make great discoveries!). The footprints looked like these ones:
but were in Yemen, and not in the Science Museum in Logroño, Spain (where jynus took this picture). National Geographic has a neat article about the footprints with even neater pictures here. Part of the article states, “The paleontologists were also able to infer the size, age, and speed of the sauropods based on their prints.”
Size of the sauropod is presumably related to the size of the footprints, and age might be related to size, but how did paleontologists determine the speed? To demonstrate, we’ll use footprints to determine how fast Godzilla was moving in the picture below:
The first thing we can do from the footprint is to determine the Godzilla’s leg length. From fossils and stuff “we” know that most dinosaur hind feet were ¼ of the size of their leg length, so in theory we should be able to measure the footprint and multiply by 4. It turns out, though, that Godzilla has disproportionally large feet, so we’ll cheat and measure his leg length exactly. Our Godzilla’s leg length is 6.5″, which we’ll translate to 0.1651 meters so we can be all metricy like the scientists.
Next we have to measure the stride length.
Exactly 8 inches, which is 0.2032 meters.
Now we find the relative stride length with the following formula:
Relative Stride Length (RSL) = (Stride Length)/(Leg Length).
Godzilla’s Relative Stride Length is about 1.23.
Now it gets complicated. A famous scientist guy in the Biology department at Leeds University, R.M. Alexander, published something about something called Dimensionless Speed. (See how well I understand it? I think it takes into account that similar animals move in a similar way, regardless of size. ) He came up with the following equation:
Speed = (Dimensionless Speed)√(leg length ·g)
The constant “g” is that familiar gravitational constant 9.80665 meters per second per second. Bet you never expected to see that here, right?
So now we just need to figure out the Dimensionless Speed, and we do that using the Relative Stride Length. There’s a graph in Figure 2 of this article, but it didn’t have a category for “Giant Monsters”. If Godzilla were like a human, then a Relative Stride Length of 1.23 would correspond to a Dimensionless Speed of about 0.3. On the other hand, in this activity (an outline of doing a lesson like this in High School Classes) there is a chart of four dinosaurs’ RSL and DS, and plugging those numbers into my calculator gives:
(Dimensionless Speed) = 0.6425(Relative Stride Length)-0.4679
(with a correlation r=.9997, so it’s pretty good).
If we treat Godzilla like a dinosaur, then plugging in his RSL of 1.2308, we get a Dimensionless Speed of 0.3228, which is close to the 0.3 we estimated above. So let’s use that.
Now we plug in DS=0.3228, leg length = 0.1651 meters, and g=9.80665 into
Speed = (Dimensionless Speed)√(leg length·g)
and we find that Godzilla’s speed is a whopping 0.41 meters per second! That’s 41 centimeters per second, which is pretty fast for a guy whose barely a foot tall. To put it into perspective, if you multiply by the scaling factor of 133.3 (from when we calculated Godzilla’s weight), it’s equivalent to the original 50 meter Godzilla running at just over 54 meters per second, or just over 122 miles per hour! Boy, you’d never know that he could run that fast, could you?
Makes you wonder just how fast those Yemeni sauropods were booking, doesn’t it?
I’m thinking that if I’d done the calculations before writing all this up, Godzilla’s footprints would have been placed a little closer together. Thanks to Bill Korth, who demonstrated this method of figuring out dinosaur speeds at a teacher workshop. He found it in Dinosaurs: The Textbook (3rd ed.) by Spencer G. Lucas.