For purposes of this question, assume whichever body position and/or axis of acceleration is most likely to provide a successful outcome. And if it is not possible at all, what is the maximum length of time that a human could withstand 5Gs?
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3$\begingroup$ Are your humans able to train themselves for these conditions? Or even set up habitats at the 5G environment? Perhaps they can use a graduated training procedure? All this is on the preposition that they are born and accustomed to 1G, of course. $\endgroup$– can-ned_foodCommented Mar 15, 2017 at 4:01
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13$\begingroup$ relevant: what-if.xkcd.com/116 $\endgroup$– John DvorakCommented Mar 15, 2017 at 8:53
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1$\begingroup$ There is an interesting discussion here: space.stackexchange.com/questions/6154/… $\endgroup$– SeedsCommented Mar 15, 2017 at 17:45
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$\begingroup$ I didn't realise this is an interesting question until I read the accepted answer $\endgroup$– slebetmanCommented Mar 16, 2017 at 2:32
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2$\begingroup$ Nitpick: $G$ is usually the gravitational constant (en.wikipedia.org/wiki/Gravitational_constant). Better use $g$. $\endgroup$– Martín-Blas Pérez PinillaCommented Mar 16, 2017 at 8:51
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5 Answers
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Yes*, with current technology, up to 15$g$; with liquid breathing probably up to 75$g$
Most approaches to this problem assume all forces are encountered by the test-subject with some kind of couch or padded reclined seat. This would place internal forces on the subject's internals and cause difficulties in breathing, etc, as other answers have noted.
The solution is to immerse the subject in a fluid that is roughly the same density as their own. By doing this, all forces are equalized, with this key requirement: The subject must have all pressures equalized, and for air-breathing creatures, this means either
- Breathe a breathable liquid, or
- Increase the pressure of the breathing gas (Likely Nitrox or some Trimix/Helium mixture) to counteract the external pressures.
Effectively, your pilot is going to go on a 48-hour dive trip.
Notice how I answered Yes*, with the asterisk? That is because I need to do a quick back-of-the-envelope calculation for the pressure encountered by your subject/pilot for the continuous 5$g$ burn. Note that although fighter pilots could find an immersion G-Tank really handy, the accelerations they are exposed to are very dynamic, and thus they would have to have their lungs and tissues very quickly soak and release the absorbed gasses from their breathing mixture, and would be wildly bobbing in their G-Tank Cockpit as compress-ability for their lungs and tissues would cause their buoyancy to vary. With a constant 5$g$ burn, your pilot will be at equilibrium for most of the trip.
Calculations
What is the equivalent pressure felt by your pilot in a G-Tank at 5$g$? Let's assume that the suspension fluid is water, which weights 1000 kg per cubic meter, and that our hero also is about that same density. We need to calculate pressure for when this system is exposed to 5$g$, which is about 50 m/s$^2$. Also note that at 1$g$, there should be 1 atm (about 100 kPa) ambient pressure for a given air pocket.
Water pressure is the product of the height of the column, density, and gravity. For our guy laying in a shallow tank, the column height can vary from zero to about 40 cm. At 1$g$, the pressure on the bottom of the tank is about 4 kPa higher than the top. At 5$g$, this becomes about 20 kPa greater.
Water is effectively in-compressible, but our hero is compressible, having tissues and lungs which will need to maintain constant volume. Where this gets a bit weird is that your pilot is exposed to a pressure-gradient, with the part of his body nearer the surface of the tank being under less pressure than the other. Thus far, at 5$g$, that difference is about 20 kPa, or 0.2 atm (Condition: Laying flat in the tank). If the pressure at the surface of the tank is 1 atm, the bottom of the tank is 1.2 atm. If he were a diver on Earth, this is equivalent to having his face at the surface and his back-side at 2 meters depth.
So, what is the limit? I'm currently unqualified to talk about more detailed human physiological factors for pressurized environments with gradients, perhaps a comment to this question can fill that in. My best guess: nitrogen narcosis (and oxygen toxicity) starts at around 30 meters depth (at 1$g$), so we never want any part of our pilot to be "deeper" than this. This translates to 75$g$: $$100 \text{ kPa} + (750 \text{ m/s}^2)\cdot(1000 \text{ kg/m}^3)\cdot(0.40\text{ m}) = 400 \text{ kPa},$$ or 30 meters equivalent depth plus 1 atm. At 75$g$, I'm sure there are other issues to factor in, such as how blood and other fluids can handle being circulated in the extreme pressure gradient, but for 5$g$, I'm guessing these are negligible.
Edit: As anticipated, a commentor (@VincentMalgrat) gave some insight with a link to the Wikipedia article on liquid breathing. The article states an upper limit of 15 to 20 Gs for immersion without filling all body cavities.
Conclusion
It is possible to build a "G-Tank", with current technology, which the pilot can lay in. The tank is filled with water, or another appropriate fluid with body-matched density, and the pilot is suspended near the surface. The craft is brought up to 5$g$, with the pilot being able to breath normally and be somewhat comfortable for the next 48 hours. The limitations are oxygen toxicity and nitrogen narcosis (each can be mitigated with proper gas mixture and avoiding Over-G), and potential for localized pressure "bruising" due to the pressure gradient experienced between different sides of his body, although it is likely this will be minimal.
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2$\begingroup$ The Wikipedia article on Liquid breathing suggests that an upper limit on acceleration resistance exists, not because of the pressure differential, but because of the difference in organ density. Some organs would float while others would dive, leading to physical stress. It also mentions that we would need a liquid with similar density as the body to resist the G-forces, and unfortunately no such liquid exists that is also breathable (yet). $\endgroup$ Commented Mar 15, 2017 at 16:40
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1$\begingroup$ @VincentMalgrat, Nice find! That makes sense that differences in organ density would present themselves as the acceleration increases. Sort of reminds me of a laboratory centrifuge, put your guy under too many Gs and he separates into lower- and higher-density goo. That article section mentions an upper limit of 15 to 20 Gs for immersion protection without liquid breathing, I'll update my answer accordingly. $\endgroup$– SteveCommented Mar 15, 2017 at 17:38
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1$\begingroup$ Thanks for the edits, it looks much better. I need to get more used to the Markdown/LaTeX syntax used here. (I've used Markdown syntax before, seems you used LaTeX here?) (Oh, looks like MathJax). $\endgroup$– SteveCommented Mar 15, 2017 at 17:57
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1$\begingroup$ Ben Bova's book Leviathans of Jupiter uses a breathable liquid in his "deep dive" ship. Though it isn't for G forces (it's to minimize the pressure differential) it might give some insights about operating in that environment. $\endgroup$– ShadoCatCommented Mar 15, 2017 at 18:19
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3$\begingroup$ If you put the victim in a liquid tank, you're going to have to supply him with breathing gas. Since you're going to put him on a 48-hour dive, you're going to use a rebreather. The easiest way to keep the rebreather loop pressure equal to the ambient pressure in the tank is to put the rebreather counterlung in the tank with the victim, and then the counterlung will counteract the buoyancy variations. (This is NOT hypothetical. In 1996, I dove a prototype closed-circuit rebreather in a pool. The second thing I noticed was the lack of buoyancy changes as I breathed.) $\endgroup$ Commented Mar 15, 2017 at 20:21
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Lying on their back, on a bed made of some form of comfortable and supportive material, I'd say it's likely that they could survive.
The bigger problems come from laying on your back for two days:
Hydration and Eating At 5Gs, eating anything will be difficult. Not to mention, have you tried eating anything while on your back? Not the best. Anything would have to be fed via some form of liquid. Hope you like smoothies. Realistically speaking, you CAN go two days without food/water, but that's not something I would recommend.
Urination and defecation You can't exactly get up to go to the bathroom, so an all-liquid diet would definitely help here. There's a few methods for automatically collecting urine, from diapers to catheters to simple funnels.
Getting up at the end Have you ever stayed in bed for ages? Having some help at the end might not be a bad idea. Going at 5Gs for an extended duration will probably throw off your sense of self, and moving an arm that you're used to weighing 5x as much could be bad.
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The bigger problems come from laying on your back for five days:I think you misread. The OP stated "two days", not "five". $\endgroup$– xDaizuCommented Mar 15, 2017 at 9:02 -
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According to this book (tolerance to +Gx acceleration, pg 148), accelerations of 8G can be sustained without difficulty for 'at least six minutes' (which I take as meaning they didn't bother testing for longer), without positive pressure to help with breathing. At 5G, sustaining breathing for two days is likely to become difficult, but a slight positive pressure will help. I probably wouldn't recommend an unfit person trying it.
I don't think a human would have difficulty surviving per se, but they would likely be extremely uncomfortable for that time. Urinating could pose a problem with pressure on the bladder for an extended period.
Best body position is lying on the back, by the way.
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3$\begingroup$ "they didn't bother testing for longer" - probably they did and it's just that above 6 minutes it vary from person to person. But that's just my guess based on how these things are usually written. $\endgroup$– MołotCommented Mar 15, 2017 at 6:35
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2$\begingroup$ They probably didn't want to kill any experimental subjects! $\endgroup$– nigel222Commented Mar 15, 2017 at 10:23
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I think a human would have difficulty surviving 5G for 2 days. That's 2 days without being able to relax. If you fall asleep in 5g, you may never wake up. It would put a lot of strain on your circulation and nervous system also. It may not be terribly extreme, like to the point you have to start doing the valsalva maneuver, but the same forces would be at work, slowly and constantly rather than intensely and briefly. Change in consciousness might even be so gradual, you don't even notice you're dying or starting to shut down. Like the (debunked - see comment below) frog in a cooking pot scenario.
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$\begingroup$ skeptics.stackexchange.com/questions/5402/… $\endgroup$ Commented Mar 15, 2017 at 14:56
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$\begingroup$ Good find. Answer edited accordingly. $\endgroup$– BangoCommented Mar 15, 2017 at 17:25
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We don't have the data to answer this question. I personally think it would be fatal, but that is just an opinion.
My reasoning, such as it is, is that our fluid circulation systems are definitely not built to tolerate the amount of force 5 gees would create. All of the organs of your body would need to function and I don't think that is likely.
To continue my speculation, I think that if we were able to tolerate it, it would most likely be by putting ourselves onto a couch that rotates 360° in each of the 3 dimensions (x, y, & z) so that each part of our body has the force in all directions (over a given time period (hours? minutes? seconds?)).
Of course, such spinning might just add to the fluid dynamics problems, but its my best guess. I'd speculate further that 2 Gs is likely to be sustainable for at least that long. 5 Gs just seems too much when you consider what the cells and microstructures in our bodies have to do.
