Source
r/Physics•
hypertruth

If a Boeing 747 was scaled to the size of a shoe, how soft and fragile would it be?

I was thinking recently about properly scaling down real world objects into a smaller version. Take a 747: If you accurately scaled it down to the size of a shoe, how thin would the metal be? How easy would it be to squash. How much would it weigh? Put another way, if I was a giant and a 747 was the size of my shoe, would it still be resilient and heavy in my hand, or would i be able to crush it like a soda can?

Posted Feb 16, 2010, 2:57 PM UTC

2737
Differentiate•

Conversely, If a shoe was scaled to the size of a 747, how tough and resistant to scuffing would it be?

20
[deleted]•

upvoted for Conversely.

14
dtardif•

To the best of my knowledge, airplanes have a skin of 3-4 mm. Scaled down from 70 feet to 1 foot, you're looking at ~50 microns thick. That is thin.

13
hypertruthOP•

I thought it was as simple as that, but if my university wasn't a complete waste of money, material strength doesn't scale linearly. So yes, the metal would be 50 microns thick, but have way more strength than 50 micron-thick aluminium if it was correctly scaled. Such a metal doesn't necessarily exist, but the properties are what is important, which is why I considered the 'giant' scenario.

EDIT: According to this article http://en.wikipedia.org/wiki/Aluminium_foil , you do get foil in 50 microns or less. So it is possible to build a model. But the strength would still be way off.

13
AnthonyA7•

I was curious, so I took a quick gander at my formula book. There's an inverse relationship with shell thickness for the stresses in a cylindrical pressure vessel:

  • axial stress: σ = pr/(2t)
  • hoop stress: σ = pr/t

Where p = internal pressure, r = shell radius, and t = shell thickness and t << r.

3
warner62•

Those are the stresses in a perfectly cylindrical vessel under uniform pressure, not necessarily the stress from a point or distributed load. Keep in mind that the wings would need to be examined just as precisely lest they fail before the fuselage.

2
AnthonyA7•

Good point. Neglecting aerodynamic forces, an aircraft meant to fly at altitude should have relatively minute point/distributed loading on the fuselage skin, though (for example at stringer rivets). The shear+moment due to lift at the wing is handled at the wingbox within the fuselage.

1
[deleted]•

I've always wondered how heavy a car would be if you scaled a Matchbox up to full size. Matchbox cars are virtually indestructible when you simulate real world driving scenarios, i.e. crashing into other matchboxes, walls, flying off cliffs, etc.

11
paholg•

Well, as the OP mentioned in another comment, material properties don't scale linearly. It's why there's no such thing as giant ants.

16
SleepingSheeple•

I thought ants did not get big because they do not have a respiratory system that could carry the oxygen far enough

http://www.physorg.com/news79804314.html

5
paholg•

Huh, that's really interesting. I was thinking, say we go to our good friend Rick Moranis (are people here old enough to get this reference?) and have him blow up an ant to human size: The properties of the ant just wouldn't scale nicely, which that article kind of shows. I was just thinking more in terms of muscles and such.

Take a look at mice and elephants, for example. Mice are about as small as mammals get, and they have tiny little legs and have issues with heat retention, and can freeze to death very easily. Elephants have, proportionally, much thicker legs, and they're fighting the opposite heat issue: they overheat very easily.

If you double the length of an animal, then you multiple its volume by eight (2*2*2), and its mass by eight, so suddenly your legs, which are now twice as long and have four times the cross section need to support 8 times the weight... doesn't work so well.

2
Cq197•

http://fathom.lib.uchicago.edu/2/21701757/

5
lisatomic•

You might like this too.

1
clayjohnson•

Ants don't get big because it's not favorable. O2 delivery is probably a factor (they basically take in O2 from their joints if I recall correctly.) Other factors: easy for a predator to see, harder to build tunnels, little benefit for cooperative efforts.

0
[deleted]•

Also: open circulatory system, exoskeleton.

1
mordaunt0•

O'RLY? http://en.wikipedia.org/wiki/Japanese_spider_crab

0
paholg•

Man, that's crazy. But I bet it has nothing like the relative strength of an ant. Ants can carry many times their own weight.

Leaf-cutter ants have powerful jaws which vibrate a thousand times a second to slice off pieces of leaf. Size for size, their bodies are amazingly powerful, able to carry pieces of leaf that weigh at least 20 times their own body weight - that's the same as a human carrying a one ton load.... Soldier leaf-cutters have huge jaws, strong enough to cut through leather

http://www.bristolzoo.org.uk/learning/animals/invertebrates/ant

An ant that can cut through leather? Imagine that the size of a person. She could snap you in half like a twig.

1
JasonHears•

This reminds me of a conversation I had with my brother when I was a kid. He always had a way of smashing my dreams and bringing me down. One day when I was about 8, I was playing with a larger scale model Ferrari (probably like 1:25 scale). I said how cool it would be if I had a growth ray and could make it life size. He said I was stupid because just the thickness of the metal used in the body would make it impossible to even open the door.

7
RedSalesperson•

Fuck that. I had some Hot Wheels cars with opening doors. So put that in his pipe and smoke it.

That being said, I'd rather become miniature so I could ride in it on the tracks.

3
2oonhed•

Your brains would rattle out of your ear holes, right after they beat the crap out of the inside of your skull.

4
kaiise•

a touching reddit family reunion.

5
hypertruthOP•

This reminds me of another question i had. What material could we make a matchbox car out of, so that at a "scaled" 40mph speed, it would crumple realistically when hitting a wall. Even aluminum foil is probably too thick.

3
lunarbase•

Interesting this. I always thought about the fragility of these planes and big stuff. I always thought about the hardness of these matchbox cars that you can throw it on the wall with all your force and it will never squash. These planes are fragile as hell compared with miniature planes. And they put no security measures in case of fall, like giant parachutes that could at least reduce the falling speed. They fail and fall like a rock.

2
2oonhed•

They are working their way up to it : The Parachute Recovery System

3
thibit•

Cool! I was unaware that the Martin parachute research, specifically what has been done for use in flight-based probes, had been applied here on Terra yet.

1
lunarbase•

wow, nice to see this.

1
Elrox•

I dont think the hard part would be the material, it would be emulating the monocoque chassis design of a modern car in order to make it crumple the right way and having the right mass/size ratio.

1
Jasper1984•

Mass goes by volume goes by power of three, strength goes ~ by surface area goes by power two.

70.6 m -> 30 cm ~ factor of 235

Empty weight: 162,400 kg -> 12grams

Cross section of the construction is a rough indicator of strength, it can take ~60k times less weight. Lets say you can mount one of these 104,328 kg, dammit, 18 kg ? I doubt that..

4
TuxThePenguin•

Wing Break Test: http://www.youtube.com/watch?v=pe9PVaFGl3o The wings sure are strong...

3
zelo•

Blast!

This video is no longer available due to a copyright claim by The Boeing Company and its wholly-owned subsidiaries (Boeing).

3
blubloblu•

Someone on reddit works for Boeing.

5
Acidictadpole•

I thought it was a documentary! I didn't think Boeing made documentaries.

1
yel02•

Those tests are amazing and the predictions are so accurate. They have to hit 150, but too far past 150 and the plane is too heavy so they can't get the right fuel economy. I hear boeing is one of the best at getting the wing break test analysis perfect .... given that the wing isn't on a 787 that is.

2
AnthonyA7•

I find those kind of predictions so cool. I would love to see the some of the computing hardware that Boeing uses- they must have massive computer farms for a full FEM analysis of a 747 wing break. (Not to mention their god-knows-how-sophisticated CFD codes)

Does anyone know more about Boeing's computing facilities?

1
vilette•

i do that on my quad-cores

1
sealclubber•

Make 2 of them... then ponder what happens when the other one drops.

1