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Looking at all the movies that involve robots made from materials available from planet earth (think Pacific Rim, Iron Man etc. but not Transformers), what is the theoretical limit of the capabilities of robots in terms of impact damage absorbed (e.g. falling off or crashing into a building).

I would like to work out what the maximum height that a robot of an 'average' human size and form can fall from and not sustain any damage (i.e. within its normal operational condition), and then theorize about new technologies that can be used to improve upon the design so that it doesn't sound too far fetched. This would be based on everything that we know and perhaps forecasting around 20 years into the future.

If that's too broad, then I would like to know how it is that Iron Man can survive the impact damage from falling at various heights (most times with added speed) and not suffer impact or shock damage to put it out of operation. Is the material and engineering of the suit plausible at all?

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  • $\begingroup$ This is really broad. Impact damage absorbed can be reduced by a lot of different methods. For example, having layered metal with springy material inbetween to absorb force. Without an actual robot design to evaluate, this is way too broad. $\endgroup$ – Aify Jun 16 '15 at 23:06
  • $\begingroup$ @Aify thanks for the comment. I have updated the question to only consider human sized robots with similar form. $\endgroup$ – Michael Lai Jun 16 '15 at 23:09
  • $\begingroup$ It doesn't help to reduce the broadness of the question. It's the fact that there are a million different ways to build a robot, regardless of size. Ex: the method proposed in my first comment can be applied to smaller robots as well as larger robots. Not to mention, "force that it can sustain" is very broad in itself, since there are lots of different kinds of forces in every fall and impact. Also, "destroyed" isn't very descriptive. When is it considered "destroyed"? When it can't stand? When it blows up? When there is a dent? $\endgroup$ – Aify Jun 16 '15 at 23:12
  • $\begingroup$ @Aify thanks for the feedback. Hopefully this is better now? $\endgroup$ – Michael Lai Jun 16 '15 at 23:40
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    $\begingroup$ I would say that the only limit is the Human body, at some point even if armor survive or stops penetration you will still die inside the armor...we are the weakest link and not the armor $\endgroup$ – Freedo Jun 17 '15 at 15:02
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If you forget the "robot" part and just look at the material properties governing armor's ability to stop penetration, you can get a rough answer to your question.

Armor
From that answer, you learn that the most relevant material property to armor strength is "toughness". Here's a chart with some common materials and their toughness (note Nickel & Nickel Steels top the chart on "toughness"):

Material Strength / Toughness Chart:
Material Strength / Toughness Chart

Molecular bond strength very strongly influences material toughness but it isn't the only factor!

Use Tensile Strength as a proxy for molecular bond strength
Using tensile strength as a proxy for molecular bond strength

enter image description here

I get tensile strengths coming out around:

  • High Nickel steel ~ $1.5 GPa$
  • Nanotube ~ $200 GPa$

So we can estimate that the theoretical maximum toughness of carbon nanotubes might be around 150x the toughness of high nickel steel.

Calculating material toughness
But we can assume that using the simple formula expressed in the first link and then comparing the tensile strength between steels and carbon nanotubes (I chose carbon nanotubes because they have close to the strongest molecular bonds that we know of - there are just a one or a few real world examples that are stronger). So it provides us with a maximum stopping power of armor based upon our current knowledge of materials.

  • $1 MPa = 1 \frac {J}{cm^2}$
  • $1 GPa = 1 \frac {kJ}{cm^2}$
  • Nickel steel toughness ~ $2000 MPa = 2000 \frac {J}{cm^2}$
  • Carbon nanotube might approach toughness ~ $30,000 GPa = 30,000 \frac {J}{cm^2}$

Calculating Stopping Power
Knowing the "toughness" of a material, doesn't really tell us much. So let's plug these numbers into the kinetic energy equation.

Steel
$$E_k = 2000 \frac{J}{cm^2} = \frac{1}{2}m \cdot v^2 $$

Density of lead shot $m_{lead} = 11.3 \frac {g}{cm^3} $
Use 1 $cm^3$ of lead

For steel armor plate $$v = \sqrt{\frac{2000 \frac{J}{cm^2} \cdot 2}{ 11.3 \frac {g}{cm^3}}} = 19 \frac{m}{s} $$

For "carbon nanotube" plate $$v = \sqrt{\frac{30000 \frac{J}{cm^2} \cdot 2}{ 11.3 \frac {g}{cm^3}}} = 230 \frac{m}{s} $$

Basically the armor's stopping power scales as the square root of its toughness.

Reality
The reality is this is an extremely complicated subject that keeps scientists and engineers employed for their entire careers theorizing and experimenting to improve armor systems.

Furthermore, modern armor systems no longer rely upon a single material type, alloy, etc. but rather are layers of different materials each layer contributing it's best features to the overall armor system. So no simple SE answer can possibly give an accurate answer, we can only give you an idea of what could be done.

Answering the Question
The answer is, no armor system could stop any threat. The weapons and knowledge we have now would enable us to either use an existing weapon or design a new one that could defeat any armor system made out of non-degenerate state matter (meaning we aren't likely to succeed in destroying neutron star materials).

When I watch movies like those you cited, I as an engineer look at the damage inflicted by weapons on those robots and know that they could NOT have withstood the shown damage. This goes as much for Iron Man's suit as it does for the Pacific Rim's Jaggers or even Transformers.

Basically, if you can only use chemical bonds you just can't make armor much stronger than the laboratory materials we're already working with.

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  • $\begingroup$ It's hard to just forget about robots, since they are just armour and guns that can walk :D So what can the current laboratory materials withstand at the moment? I assume that they wouldn't be able to save you if you jumped off a building? I can imagine just how the Myth Busters would test this... $\endgroup$ – Michael Lai Jun 17 '15 at 4:22
  • $\begingroup$ For jumping off a building, I'd use the suit legs as massive shock absorbers. The key measure for full-body deceleration (as opposed to concentrated loads such as gunshots or axe blows) is impulse: you can handle a much higher deceleration if it occurs over a meter of knee-flexing than if it occurs over a centimeter of skeletal compression. $\endgroup$ – Mark Jun 17 '15 at 8:56
  • $\begingroup$ Right, but that "meter of knee-flexing" only gives you so much ability to absorb impact (deceleration). When your velocity exceeds that deceleration you get squished regardless of what happens to the suit. The same is true for any hit to your chest. Even if the armor stops penetration, you're going to take a massive impact (acceleration). There are limits to what the human body can endure. $\endgroup$ – Jim2B Jun 17 '15 at 13:26
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    $\begingroup$ Yes, every time Iron Man is smashed to the ground or another hard surface I can't help but think about the impossibility to survive that inside the armor. You can handwave the armor being almost intact, but not Tony inside. He's still a squishy fluid bag, without meters of impact absorbing materials the toughness of the armor matters little. $\endgroup$ – zovits supports GoFundMonica Jun 24 '15 at 9:04
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You asked about falling damage. I can't give you a detailed materials science answer like the above, but think about the physics of falling. The damage depends on acceleration: how quickly do you go from falling to not-falling? F=ma, so a near-instant stop (like hitting concrete) imposes a much higher force on a falling object than a more gradual stop (like hitting water). So, look at how we deal with falling damage now: parachutes to slow the impact speed (NASA just tested a new design), balloons to slow the impact itself (airbags, used in cars and in NASA probes), and heat-resistant materials to handle re-entry when talking about space. Another option is ablative materials, those designed to break to absorb impacts. Finally, there's the idea of springs. Look at how "parkour" experts fall: bending as much has possible, landing in a crouch to make their impact gradual. Cars today are designed with "crumple zones" for the same reason, made to break while keeping the passenger cabin mostly intact.

So, for a humanoid robot or power armor, I'd expect a mix of systems. Parachute, springy limbs, software to bend the limbs on impact, materials that shatter (or even rocket-punch themselves downward!). Ultimately though, for a human your limit is probably going to be based on human physiology. High acceleration kills people. Check out how fighter pilots operate today in high-G equipment and training, and note that future fighter jets are likely to be AI-driven because of this limit.

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