How Do Size and Scale Affect Animal Movement Speeds?

[billy_boy_999]

not the best example, but why does an elephant lumber around at such a ponderous pace and little ants seem to zip around at 3 or 4 times human speed? is it air resistance? gravity to muscle mass ratio? if we enlarged a 6 foot human being to 50 feet, would he walk around in slow motion? if we tapped his knee with a large mallet, would his reflex time differ from previously? what is going on here?

 

[Nenad]

the reason an eliphans lumbers around so slowly is because of many reasons. Gravity's weight is pulling down on him with a harder force (mg). Also, eliphants are not composed of lots of muscle, they have mostly fat, while an ant has very quick joints, and the weight of gravity on him is small. If we made a human 50 feet tall, he would walk and run a lot faster than anybody else, since his muscle structure would be the same as ours.

 

[pmb_phy]

not the best example, but why does an elephant lumber around at such a ponderous pace and little ants seem to zip around at 3 or 4 times human speed? is it air resistance? gravity to muscle mass ratio? if we enlarged a 6 foot human being to 50 feet, would he walk around in slow motion? if we tapped his knee with a large mallet, would his reflex time differ from previously? what is going on here?

How do you think you're legs would swing if they were 8 feet long?

Pete

 

[billy_boy_999]

yeah, a fifty foot guy would be a lot faster than anyone else, i'll grant you that, i just don't think he'd be that much faster, probably slower than a tyrannosaur, for example...

and yes, gravity pulls on him harder and he also has more inertia which would make him especially unwieldy...

how would the legs swing - exactly! except, its more like 20 feet of leg...so picture a 20 feet long 5 feet thick beam of wood swinging back and forth...the image is not good but we generally walk at the pace with which our legs swing naturally, or a little faster...but i think the added gravity and inertia would overcome the extra muscle mass by a long ways, meaning we'd be much slower relative to our size...

here's a question - can there possibly be enough muscle mass in a giant creature to be able to move at human speed in a larger frame? if giant hundred foot crabs from outer space pay us a visit, will we be able to zip under awnings in time? intuitively, i'd think so, there is a kind of speed compensation with size no matter the muscle mass...why though? i don't understand this...

 

[Janus]

the reason an eliphans lumbers around so slowly is because of many reasons. Gravity's weight is pulling down on him with a harder force (mg). Also, eliphants are not composed of lots of muscle, they have mostly fat, while an ant has very quick joints, and the weight of gravity on him is small. If we made a human 50 feet tall, he would walk and run a lot faster than anybody else, since his muscle structure would be the same as ours.

If we made a human 50 ft tall, he wouldn't walk at all!. He would fall victim to the square-cube law.

Let's assume we started with a man 6 ft tall of average build (185 lbs or so). To make him 50 ft tall we would have to increase his dimensions by a factor of 8.33. This means his volume and mass would increase by 8.33³= 578.7 Now the cross section of his muscles, which determines muscle stength, would only increase by 8.33² = 96.4 times. This is the equivalent of our original 185lb man finding himself weighing 1541.66 lbs, or over a quarter ton, without any addition to his strength!

Thus the old wive's tale that if an ant were enlarged to the size of a man it could lift a truck is just not true. If such were to happen, the ant would quickly suffocate because it wouldn't even be able to lift its body mass enough to even breath.

 

[pervect]

not the best example, but why does an elephant lumber around at such a ponderous pace and little ants seem to zip around at 3 or 4 times human speed? is it air resistance? gravity to muscle mass ratio? if we enlarged a 6 foot human being to 50 feet, would he walk around in slow motion? if we tapped his knee with a large mallet, would his reflex time differ from previously? what is going on here?

It's basically the result of scaling laws. If King Kong throws cars around, they should look like they are falling "realistically", rather than like they are falling on a planet with a lower or higher gravity than our own.

In order to make gravity "look like" it has the right value, one must slow down films taken of minatures. See for example

http://farside.ph.utexas.edu/teaching/301/lectures/node8.html

or just note that s= .5 a * t^2, so that if we increase all distances by a factor of 16, we should multiply all times by a factor of 4, to make the acceleration of gravity appear correct.

There's lots of things that can't be made to come out quite right - King Kong would have to be made of amazingly strong stuff to stand so tall - but we can at least make the acceleration of gravity look "right". People don't consciously analyze the motions of King Kong, but since we've had a lot of experience with how things fall, we know when things look "wrong", even without pulling out the calculators.

Picking the right set of scaling laws is a bit of an art-form, as it's the psychological impression that is ultimately important. Agreement with physical laws is secondary, it comes about mainly because the audience has an intuitive grasp of how things act based on experience.

For instance, I don't know exactly what formula "The Matrix" used in their slow-motion scenes, but they managed to make it "look good".

 

[billy_boy_999]

yes! scaling! thank you guys, that is exactly the answer i needed there, of course...if there is an earthly standard of muscle mass to volume ratio, as in a standard beyond which body control becomes more and more difficult due to gravity considerations et al. then this kind of scaling of the cross section of muscle mass provides the curve we see with ants and godzilla...beautful, OK...

it would maybe be interesting to try and analyze this muscle-mass scaling curve and try it with different amounts of gravity...

 

[Nenad]

If we made a human 50 ft tall, he wouldn't walk at all!. He would fall victim to the square-cube law.

Let's assume we started with a man 6 ft tall of average build (185 lbs or so). To make him 50 ft tall we would have to increase his dimensions by a factor of 8.33. This means his volume and mass would increase by 8.33³= 578.7 Now the cross section of his muscles, which determines muscle stength, would only increase by 8.33² = 96.4 times. This is the equivalent of our original 185lb man finding himself weighing 1541.66 lbs, or over a quarter ton, without any addition to his strength!

Thus the old wive's tale that if an ant were enlarged to the size of a man it could lift a truck is just not true. If such were to happen, the ant would quickly suffocate because it wouldn't even be able to lift its body mass enough to even breath.

I don't understand your argument. If volume increases, so does muscle size. The volume of a human is muscle too. I don't get what youre talking about cross section of muscle.

 

[billy_boy_999]

forgive me for not understanding how muscles work exactly but i think janus was suggesting that your muscle strength depends on the 2-dimensional area or the cross-section of your muscles, probably with muscles it has to do with tension more than volume, per se, but i myself do not know exactly how that works...but the fact that with size increase your muscle mass increases in 3-dimensions doesn't help you enough with the square/cube rule thing as when you increase the size of a two dimensional cross section you're not getting as much as the 3 dimensional volume increase...i thought that's what she was saying...

 

[Gza]

I don't understand your argument. If volume increases, so does muscle size. The volume of a human is muscle too. I don't get what youre talking about cross section of muscle.

I guess it seems to make sense if you think about it from a more fundamental perspective. The laws of physics maintain a symmetry under translation as well as rotation. Symmetry is broken under the transformation of scaling. Rotate or translate a 6 foot human in any manner, and the physical behavior of the human system is the same. Now scale it, and you've broken the symmetry. You don't know how it'll respond.

 

[cuffnstuff]

But if a 6 foot man is increased proportionaly to a 50 foot man, the muscle size would also be proportional to the increase. A 6ft frame carrying 190 lbs, proportionaly the same frame at 50 feet would be 1583.33 pounds of mass. And maintaining that gravity would remain a constant factor, there should be no reason why the 50foot man can overcome and run the same speeds as a normal man. If he could run at 6ft, then if exact preportions are used he should have no problem running at 50 feet.It would be difficult to compare a dinosaur or godzilla in the same context, since the muscle mass, bone density and all around design in different. These animals moved slow because their evolution instilled that in them. A 5 ton elephant would move the same as a 500 ton elephant as long as everything was propartioned exatly as the original.

 

[Galileo]

You guys might want to have a look at this MIT lecture video.
http://mfile.akamai.com/7870/rm/mit...870/8/8.01/f99/videolectures/wl99lec1-300k.rm

The topic of the sizes of animals (mammals) are brought up.
It starts at 11:15 minutes, so you can skip the rest.

 

[Fredrik]

But if a 6 foot man is increased proportionaly to a 50 foot man, the muscle size would also be proportional to the increase. A 6ft frame carrying 190 lbs, proportionaly the same frame at 50 feet would be 1583.33 pounds of mass.

If you resize a man who is 6 feet tall and weighs 190 pounds, so that he becomes 60 feet tall, he will not weigh (50/6)*190 pounds. He will weigh (50/6)^3*190 pounds. This is about 110000 pounds. Now suppose that his legs were able to lift 400 pounds before he was resized. He will now only be able to lift (50/6)^2*400 pounds. This is less than 28000 pounds. So he will not be able to move. He probably wouldn't even be able to breathe.

 

[Artman]

Part of the reason for the slow movement is that the longer the legs are, the more rotational inertia there is to be overcome to start and stop them moving.

 

[Nenad]

If you resize a man who is 6 feet tall and weighs 190 pounds, so that he becomes 60 feet tall, he will not weigh (50/6)*190 pounds. He will weigh (50/6)^3*190 pounds. This is about 110000 pounds. Now suppose that his legs were able to lift 400 pounds before he was resized. He will now only be able to lift (50/6)^2*400 pounds. This is less than 28000 pounds. So he will not be able to move. He probably wouldn't even be able to breathe.

I see what youre sying, but why? Why is it that with the volume change, the muscle strength only changes by a factor of ^2.

 

[Gokul43201]

Part of the reason for the slow movement is that the longer the legs are, the more rotational inertia there is to be overcome to start and stop them moving.

The counter to this would be that you now have more muscle, so you can handle the extra inertia.

The counter to this counter would be that while the muscle mass increases as the cube of the linear scaling factor, the moment of inertia increases as the fifth power (I=Mk^2).

 

[Janus]

I see what youre sying, but why? Why is it that with the volume change, the muscle strength only changes by a factor of ^2.

Which is stronger and will hold more weight?

A cord 1 mm in diameter 4cm long or a cord of the same material 2mm in diameter and 1cm long? The masses will be the same. The mass doesn't matter, only the thickness of the cord.

Four 1mm cords in parallel will be four times stronger than one 1mm cord, correct?

Now let's take 1 1mm cord of 4cm in length, increase its length by 2 and add three more indentical cords in parallel. The entire mass of this combination will be 8 times that of the cord we started with (1 mm and 4cm), but it will still be only 4 time stronger. The extra mass does nothing towards increasing the strength of the cord. All that counts is the thickness of the cord.

The same is true for muscles, what counts is the "thickness", or more properly, the surface area of the cross section of the muscle, not the mass. If I double the size of the muscle, I only increase the cross section by a factor of 4, but I increase the mass by a factor of 8. The extra mass does not contribute to the strength of the muscle, but does add to the weight the muscle must support.

 

[Nenad]

Which is stronger and will hold more weight?

A cord 1 mm in diameter 4cm long or a cord of the same material 2mm in diameter and 1cm long? The masses will be the same. The mass doesn't matter, only the thickness of the cord.

Four 1mm cords in parallel will be four times stronger than one 1mm cord, correct?

Now let's take 1 1mm cord of 4cm in length, increase its length by 2 and add three more indentical cords in parallel. The entire mass of this combination will be 8 times that of the cord we started with (1 mm and 4cm), but it will still be only 4 time stronger. The extra mass does nothing towards increasing the strength of the cord. All that counts is the thickness of the cord.

The same is true for muscles, what counts is the "thickness", or more properly, the surface area of the cross section of the muscle, not the mass. If I double the size of the muscle, I only increase the cross section by a factor of 4, but I increase the mass by a factor of 8. The extra mass does not contribute to the strength of the muscle, but does add to the weight the muscle must support.

Ohh, I get it. Thanks for the good explanation.

 

[Mk]

Wow! For somereason I have to say the Pauli Uncertinty Principal

 

[Nenad]

Wow! For somereason I have to say the Pauli Uncertinty Principal

? There is no such thing.