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klotza submitted a new PF Insights post
Scaling Laws and the Speed of Animals
Continue reading the Original PF Insights Post.
Scaling Laws and the Speed of Animals
Continue reading the Original PF Insights Post.
The additional constraint they apply on large animals, which oscillate their length L with some frequency f, is that there is a maximum angular acceleration that can be applied. The maximum torque depends on the muscle fibre force, the cross sectional area, and the length of the "lever arm," while the moment of inertia depends on the density, volume, and distribution of the shape. Comparing torque to moment of inertia they get a second-order ODE for the angle of the oscillating part (tail, leg, whatever) over time, which they integrate to find the time required to oscillate to a certain angle. This gives them an *absolute* maximum speed. So they compare their "maximum speed per body length" to the "absolute maximum speed" and solve for the body length at which the two are equal.jerromyjon said:This 1.4m "dominance zone" I guess I would call it keeps nagging at me. I'd be grateful for any elaborations you could offer there... as I'm not able to access the paper.
The second is that all motility is caused by the contraction of muscle proteins that have a similar structure across all life-forms.
Bandersnatch said:I couldn't help but be reminded of another similar study - the one finding (statistically) constant time of emptying the bladder across five orders of magnitude of animal mass (what the authors dubbed 'the law of urination'):
http://arxiv.org/abs/1310.3737
I'm wondering, is the same true for animals like spiders that don't use the same mechanisms to move as most animals do?klotza said:Hi everybody, this is the author. I hope enjoy what I have written, and let me know if anything needs clarification.
My source is mainly experience from when I used to be into powerlifting. However this paper also asserts the claim, with better data.PiTHON said:You said, "Above that it breaks down because the lifters generally get fatter without getting much more muscular."; do you have a source on that?
All I know is that ants and beetles appear to be on the image.Tom Rayder said:I'm wondering, is the same true for animals like spiders that don't use the same mechanisms to move as most animals do?klotza said:Hi everybody, this is the author. I hope enjoy what I have written, and let me know if anything needs clarification.
klotza said:The additional constraint they apply on large animals, which oscillate their length L with some frequency f, is that there is a maximum angular acceleration that can be applied. The maximum torque depends on the muscle fibre force, the cross sectional area, and the length of the "lever arm," while the moment of inertia depends on the density, volume, and distribution of the shape. Comparing torque to moment of inertia they get a second-order ODE for the angle of the oscillating part (tail, leg, whatever) over time, which they integrate to find the time required to oscillate to a certain angle. This gives them an *absolute* maximum speed. So they compare their "maximum speed per body length" to the "absolute maximum speed" and solve for the body length at which the two are equal.
Hope that made sense. Picturing a cheetah, they are about 1.4 meters long, and plugging in their values for the "maximum speed" you actually get a fast jog, about 4 m/s. If you apply 10 bodies/second to 1.4 meters, you get 14 m/s=50 km/h which is about half a cheetah's top speed.
Scaling laws are mathematical relationships that describe how a particular physical or biological attribute changes as a function of body size. In the case of the speed of animals, scaling laws can help us understand how the size of an animal affects its maximum speed.
There are several methods that scientists use to measure the speed of animals, including high-speed cameras, radar guns, GPS tracking, and even simple stopwatch measurements. Each method has its own advantages and limitations, so scientists often use a combination of techniques to get the most accurate results.
The speed of an animal is influenced by a variety of factors, including body size, muscle strength, stride length, leg length, and overall body shape. Additionally, environmental factors such as terrain, temperature, and altitude can also impact an animal's speed.
Scaling laws can apply to all types of animals, from insects to mammals. However, the specific relationships between body size and speed may vary depending on the animal's anatomy and evolutionary history. For example, larger animals tend to have longer legs, which allows them to take longer strides and potentially run faster.
Yes, scaling laws can be used to estimate the speed of extinct animals based on their fossilized remains. By comparing the body size and proportions of extinct animals to living animals with similar characteristics, scientists can make educated guesses about their potential speed. However, these predictions may not always be accurate due to other factors such as diet and behavior that also play a role in an animal's speed.