Another interesting aspect of the paradox of giants feels like it cuts the other direction. Wind resistance is proportional to cross section, so grows as a square. But the energy available is proportional to the number of mitochondria, which is the same as the number of cells, which grows as a cube. All other things being equal, larger beings can fly faster. This is why birds can catch insects, and why falcons can catch pigeons, and eagles are kings of the sky. Hand-held drones are slower than the big ones, and the big ones are slower than the very big Shaheds, which still rain down on Ukraine at a rate of hundreds per day. But even the newest jet Shaheds can be hunted by the larger fighter jets. And a swarm of flying nano-bots will chase you with the speed of a glacier.
Of course, all other things are not equal, and it becomes challenging to bring all the energy produced by a body into one purpose (flight) as the body gets large. We don't have jumbo-jet-size fighters, and we don't have pteradactyl-sized eagles.
The paradox of giants is also why large people sweat more with the same workout: generated heat is a cubic, but the surface area to release that heat is only quadratic.
Another point for you, Kevin: I recall once discussing with you in my CUNY office various methods for estimating the weight of large objects, such as the Empire State Building. You proposed to imagine a smaller copy of it on your desk and thinking about how much it would weigh, and then multiplying by the appropriate scale, but cubed. I wonder, however, how much of a distortion in that method would be caused by the strength-scaling observation of Galileo? After all, the smaller copy could be proportionally thinner, just as insects are in comparison to elephants.
I recall that conversation. We also guesstimated the mass of a stone basketball as a way to estimate the mass of the Earth.
As for the other point, I sometimes read that engineers build scale models to measure how their designs will stand up to earthquakes and windshear and tsunamis, et cetera. I imagine there’s a vast literature about how to handle all the different scaling factors in those models.
Another interesting aspect of the paradox of giants feels like it cuts the other direction. Wind resistance is proportional to cross section, so grows as a square. But the energy available is proportional to the number of mitochondria, which is the same as the number of cells, which grows as a cube. All other things being equal, larger beings can fly faster. This is why birds can catch insects, and why falcons can catch pigeons, and eagles are kings of the sky. Hand-held drones are slower than the big ones, and the big ones are slower than the very big Shaheds, which still rain down on Ukraine at a rate of hundreds per day. But even the newest jet Shaheds can be hunted by the larger fighter jets. And a swarm of flying nano-bots will chase you with the speed of a glacier.
Of course, all other things are not equal, and it becomes challenging to bring all the energy produced by a body into one purpose (flight) as the body gets large. We don't have jumbo-jet-size fighters, and we don't have pteradactyl-sized eagles.
The paradox of giants is also why large people sweat more with the same workout: generated heat is a cubic, but the surface area to release that heat is only quadratic.
Fascinating points, thanks very much! I like this energy consideration quite a lot.
Another point for you, Kevin: I recall once discussing with you in my CUNY office various methods for estimating the weight of large objects, such as the Empire State Building. You proposed to imagine a smaller copy of it on your desk and thinking about how much it would weigh, and then multiplying by the appropriate scale, but cubed. I wonder, however, how much of a distortion in that method would be caused by the strength-scaling observation of Galileo? After all, the smaller copy could be proportionally thinner, just as insects are in comparison to elephants.
I recall that conversation. We also guesstimated the mass of a stone basketball as a way to estimate the mass of the Earth.
As for the other point, I sometimes read that engineers build scale models to measure how their designs will stand up to earthquakes and windshear and tsunamis, et cetera. I imagine there’s a vast literature about how to handle all the different scaling factors in those models.