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For all machines (cars, elevators, computers, etc), when size, power requirements, dimensions are scaled by a constant N, will it work just as is?

Will a car with all its parts 10x larger still work like a normal car, just larger?

DanielSank
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Zaenille
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    For a very simple case, consider a body that generates heat relative to its volume, but can only transfer heat relative to its surface area. As you scale it up, it will get hotter and hotter until it breaks down. – raptortech97 Oct 07 '14 at 01:15
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    Same question but for animals: http://physics.stackexchange.com/questions/72641/why-is-there-a-size-limitation-on-animals –  Oct 07 '14 at 06:01
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    A car that is 10 times bigger doesn't 'work' because you can't reach the pedals. An elevator that is 10 times bigger wouldn't 'work' because it would occupy all stories of the building at once. A computer with a transistor that is 10 times bigger is probably comletely useless because the electricity has to travel through a very long path. – Dennis Jaheruddin Oct 07 '14 at 10:16
  • even worse, a car that's 10 times as large in size has a volume of material that's 1000 times as large while not having 1000 times as much engine power... And the same with most things when scaled up. – jwenting Oct 07 '14 at 14:29
  • Perhaps a better question would be "are there any machines which are linearly scalable which remain useful"? Consider the lever - a ten-foot-long lever might be very useful for moving something. A 100-foot-long lever? Maybe not so much... – Bob Jarvis - Слава Україні Oct 07 '14 at 22:48
  • Lazy answer is that any machine eventually collapses under it's own gravity provided it's huge enough. – Tomáš Zato Nov 09 '15 at 10:16

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This is a great question. An influential early discussion of it was given in a 1959 talk by Richard Feynman, There's Plenty of Room at the Bottom. Basically the answer is no, machines are not linearly scalable. For example, lubrication doesn't work for very small machines. A general way of looking at this is that we have various physical quantities, and they scale in different ways. For example, area is proportional to length squared, while volume goes like length cubed. Because different things scale differently, what works on one scale doesn't work on another. A good example is the animal world -- after all, animals are a type of machine. A spider the size of an elephant would collapse under its own weight. This is because the strength of the animal's limbs go like the cross-sectional area, while the weight the limbs have to support is proportional to volume.

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    tl,dr: Weight scales like $\text{length}^3$ but strength of an e.g. bone scales like cross sectional area $=\text{length}^2$. Therefore, as you make an animal or machine bigger, the strength to weight ratio goes down. – DanielSank Oct 07 '14 at 01:12
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    An even earlier influential discussion was Discourses and Mathematical Demonstrations Relating to Two New Sciences (Galileo, 1638). As I understand it from second-hand accounts, one of the two sciences was the relation between material strength and scaling, and the other was kinematics. – N. Virgo Oct 07 '14 at 02:52
  • Nathaniel is correct. Galileo had this figured out, already. I would strongly suggest to read his book, it's enormously enlightening about the state of knowledge of his time and about the genius of the man. – CuriousOne Oct 07 '14 at 07:00
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    The flip side of scaling a spider to the size of an elephant is scaling a shark to the size of a rotifer (< 1 millimeter). The shark would be easy prey for the rotifer because the miniaturized shark can't move. The thunniform locomotion used by sharks doesn't work at exceedingly low Reynolds numbers. – David Hammen Oct 07 '14 at 12:55
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    Things get even more (or less, depending on your perspective) interesting when you scale down near Planck scale or up to a scale where relativity kicks in and propagation of pure mechanical motion from one part of the machine to another would take place spread out over years. – R.. GitHub STOP HELPING ICE Oct 07 '14 at 15:23
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    Nice answer. I'll just add that for further reading the principle is often termed "allometry", "allometric scaling", or the "square-cube law". The canonical examples are often the bone structures and metabolic rates of a mouse and an elephant. – DeveloperInDevelopment Oct 07 '14 at 19:58
  • +1, furthermore, taking into account non-linear dynamics and self-similarity under scale transformations. The answer is that there are many concepts of scaling involved and invariance under scale change doe not apply to all these concepts of scaling. – Nikos M. Oct 09 '14 at 21:33
  • So it is not true when they say bugs (e.g. ants) are very strong: "That’s the same as a human lifting a truck with its teeth." (from http://www.onekind.org/be_inspired/top_10_lists/strongest/ but I've read similar statements somewhere else) – algiogia Oct 29 '14 at 14:26
  • I'm glad you gave a spider-based example in your answer... the movie Big Ass Spider! should have hired some physicists before the CGI team started working. – Chris Cirefice Oct 30 '14 at 19:22