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Let's say I have a device that can produce an area of artificial gravity. Never mind how, or what universe-rending effects this has; I flip a switch, and the gravitational gradient in the drive's area of effect changes.

What limits, if any, would exist on the maximum acceleration of a spaceship using this device as a propulsion system?

Ignore the energy cost of using the drive, and assume it can produce any amount of artificial gravity. Also ignore issues due to relative velocity (e.g. running into micrometeorites). I'm not interested in limits due to operation costs or navigation factors, but due to mechanical limitations of the ship and its crew. (This also implies that the answer may differ for crewed vs. unmanned ships...)

Please note, this is a "share my knowledge" post (inspired by How fast would this gravity engine let planes fly?). I'm posting this partly as a long rant, but also to solicit other thoughts and/or to get other input on my conclusions. Please read my answer before replying. (If someone wants to offer a more concrete answer on calculating shear forces for a given drive configuration, that would be most welcome!)


Edit: No, this is not a duplicate. The OP of the linked question appears to share my belief that acceleration of such a drive is potentially unlimited. I am attempting to explain why that is the case and/or solicit other views whether or not this understanding is correct. The linked question is asking about factors limiting velocity, which I am explicitly disregarding here.

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  • $\begingroup$ Can you explain again why you posted a duplicate question and self answered it instead of answering the original one? $\endgroup$
    – L.Dutch
    Sep 15, 2020 at 16:31
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    $\begingroup$ @L.Dutch-ReinstateMonica, that's asking about velocity and appears to make an assumption about acceleration. I'm asking about acceleration; in particular, I'm investigating/explaining said assumption made in the other question. Also, the other question is asking about atmospheric vehicles, whereas I'm ignoring running into things. The answer here is not an answer to the other question, but an explanation of one of the other question's implied assumptions. $\endgroup$
    – Matthew
    Sep 15, 2020 at 17:47
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    $\begingroup$ @JBH, alas, I cannot apply "reality check" to an answer, but perhaps this would have been better as a reality-check. Alas, too late now. While I'll admit this is something of a pet peeve of mine, the intent was to provide useful information, which, given the ability to "share your knowledge by answering your own question" would seem to be acceptable. If you'd prefer, feel free to propose edits to make it less rant-like. $\endgroup$
    – Matthew
    Sep 16, 2020 at 1:10
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    $\begingroup$ @JBH , I don't see how this violates any help center limitation. Answering your own question is encouraged on SE, and the question is specific and detailed enough that it doesn't rely on any details in the answer; anyone can answer this question. The fact that it is self-described as a rant is trivial. $\endgroup$
    – cowlinator
    Sep 16, 2020 at 3:13
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    $\begingroup$ @JBH, my goals were a) indeed, to share information, and b) as you noted, to get a reality-check if I'm talking out the wrong end. Not to start a general discussion, but to invite people to either expand on what I provided or to tell me if I'm totally off-base. $\endgroup$
    – Matthew
    Sep 16, 2020 at 13:54

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So... this is one of those fun areas that seems to get overlooked a lot.

The ISS is experiencing a constant gravitic acceleration of a little less than 1G (relative to Earth), but the mechanical stresses are negligible because its sitting in a near-uniform gravitic field. If we were to move it to, say, Jupiter, that number would likely increase (depending on the oribtal distance), but the effect on the station (and its occupants) — at least due to the increased acceleration — would be negligible.

This is because of the different way that gravity and conventional propulsion systems work. A rocket (or ion thruster, Orion drive, ...) works by transmitting a force to some object (pusher plate, back wall of the rocket nozzle, etc.). That force must then be translated mechanically through the structure of the space ship and, if it's manned, the bodies of its crew. This is also why you "feel" acceleration. Take standing on a planet; gravity is pulling on you uniformly, but the ground/floor/whatever is opposing that force. However, that opposing force is only being applied to a small part of you (e.g. the bottoms of your feet). That force then gets transmitted through your bones and tissues. In water, you feel lighter because this force is much more spread out, while in free fall the opposing force (nearly) goes away, even though you are still accelerating.

What does this mean for our hypothetical drive?

If the drive produces a uniform gravitic field, I can't think of any reason why there should be a mechanical limit; the limits will be "whatever the drive can do given how much power you can feed it" (which we're ignoring).

That said, a uniform gravitic field is probably not plausible, since AFAIK such a thing does not exist in nature. Rather, gravity (at any point) is:

$a_g = \sum \frac {GM_pV_p}{|V_p|^3}$ for all points of matter, where:

  • $G$ is the gravitational constant
  • $M_p$ is the mass of each such point
  • $V_p$ is the direction vector from wherever we are measuring gravity to such point

Since far-away masses have near-zero influence and close-together masses act almost like a single mass, we can usually simplify this (also ignoring direction) to:

$a_g = \frac {GM}{d^2}$

Let's say that, rather than producing a uniform field, our hypothetical drive produces a point of immense "virtual mass". Now our drive looks like falling into a gravity well, except that the center of gravity conveniently keeps receding such that we never reach it. (Again, we're ignoring the pretzel this makes out of physics as part and parcel of the whole idea of "artificial gravity".) Now we do have a practical limit, because different parts of the ship are subject to different gravitic fields. This difference is "shear" or "tidal force", and too much of it isn't good for ships (or people). At sufficient levels, this leads to the delightfully-named effect of spaghettification.

This is why you hope your drive really can create a uniform field, or at least, can create multiple and/or spread out "virtual masses" in a way that is carefully tuned to minimize shear within the ship's volume. (Shear outside the ship can be tremendously useful as a defense, since it may be nigh-impenetrable, potentially even to photons.)

Suffice to say, the mathematics for computing maximum gravitic shear can get complicated. I'm also unsure how much shear the average human can take, though I wouldn't be surprised if 1G is structurally acceptable. (The effects it would have on equilibrium may be another matter! On the other hand, How much variation in gravity between feet and head is noticable? suggests I might be wildly optimistic with that number.) Ironically, a large spaceship might actually be more susceptible to shear than its crew.

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  • $\begingroup$ "So... this is one of those fun areas where a lot of creators don't seem to understand physics." Full stop there. There is a massive, huge, humongous difference between "not understanding physics" and "trying to write down entertaining stuff". I know full well that it is impossible to make my flying city stay afloat by using a a ton of mini-propellers, but I'm doing a deliberate choice of writing it that way because it is evocative and fun. Not all science fiction must be hard science fiction. A lot of us authors know full well that we're writing things that won't work for real. $\endgroup$
    – Mermaker
    Sep 16, 2020 at 12:00
  • $\begingroup$ So don't go out there judging what people understand or not for the work they choose to write. It might not be your thing and you are fully entitled to not like pseudo or blatantly incorrect physics, but you are in no position to judge what authors know or not by their works on fiction. If I can create hypothetical physics to make my Gravity Drive work, I can also make any other sort of hypothetical physics to make it work just the way I want. If you can handwave things like energy source and building materials, you can handwave anything else. $\endgroup$
    – Mermaker
    Sep 16, 2020 at 12:07
  • $\begingroup$ And yes, this is a personal matter for me, as someone that writes several "quasi-magical" propulsion methods on their sci-fi works. I know full well that the Gravity Warp Drive, the Alcubierre Drive, the Ion thruster and so many other engines don't work exactly like the way I described on my works. Doesn't matter. It is science fiction. It is supposed to be a "what if things worked this way?" work. it is supposed to be entertaining, not physically correct down to the smallest detail. $\endgroup$
    – Mermaker
    Sep 16, 2020 at 12:13
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    $\begingroup$ '...while in free fall the opposing force (nearly) goes away, even though you are still accelerating.' The fall doesn't kill you, it is the sudden stop at the end. $\endgroup$ Sep 16, 2020 at 12:31
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    $\begingroup$ @Matthew you still added unnecessary judgement for no reason to your answer. If you want to talk to the gravity drive, go ahead and do it to your heart's content. Do not use this as an excuse to judge others. $\endgroup$
    – Mermaker
    Sep 16, 2020 at 14:03
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Here's what I think. I'd add this to the wiki, but I'm not sure if it's actually correct and is just me theorizing stuff that may or may not have already been said or actually be possible.

If we ignore the human squishieness factor and assume the craft is strong enough to withstand your forces, then we go down to a max speed you can change to your liking. According to this sketchy looking quora post the max speed of an aircraft in a dive(which would basically be what your craft is doing) is about mach 1. I think they're a bit off, so I checked this SE aviation question, and the first answer puts your dive speed at about 120 MPH, which seems a bit slow. I'm not sure what I should use, so I'm gonna assume 9.8 m/s(terminal velocity of a human). If you can find a better number, use that.

This is the part where I'm start theorizing and am probably wrong.

Your gravity generator has no posted upper limit, but I'll assume ten times earth's gravity. The 9.8 m/s is terminal velocity under earth's gravity, so ten times earth gravity you multiply by ten to get 98 m/s, or about 220 mph, which is about 1/4 of the speed of sound(I feel like that's a bit slow, so somebody check that). So to get very fast if this is right(which it probably isn't) you'd need a strong ship and a way to protect your passengers.

Doubt any of this is right, but maybe the references will help.

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The crew is the most delicate part of a spaceship and acceleration is equivalent to gravity (both are measured in meters per second per second). So, this question has already really been answered by questions like: Would the human body support living on planets with a greater gravity than Earth? ; most likely less than 2G for extended periods. People can survive higher accelerations briefly: rocket launches peak at 4G and fighter pilots with specialized equipment and training can withstand very brief periods of over 9G (see https://en.wikipedia.org/wiki/G-LOC).

For peak acceleration of the vessel itself, depends on the design. You can see the typical accelerations for various human constructs at https://en.wikipedia.org/wiki/Orders_of_magnitude_(acceleration). For a manned vessel, there's no reason to overbuild to withstand acceleration the crew itself wouldn't survive so something in the range of the 21.3 Gs in the entry for "Peak acceleration experienced by cosmonauts during the Soyuz 18a abort" would not be unreasonable as a ballpark design maximum. For unmanned ships, it wouldn't be implausible to go higher; maybe up to 100G. At a certain point, it becomes less believable for the many moving parts even in an unmanned ship to function reliably (motors to aim sensors / communication, pumping of coolant, etc.), so I would be cautious going beyond 100G.

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    $\begingroup$ ...but astronauts on the ISS don't "feel" 1G even though they are experiencing (nearly) 1G. There is a significant difference between direct-force drives and gravity drives; in particular, the only "problematic" forces with a gravity drive are shear (a.k.a. tidal). $\endgroup$
    – Matthew
    Sep 16, 2020 at 1:16
  • $\begingroup$ Astronauts on the ISS don't feel 1G because they're not experiencing 1G. They're in a free fall trajectory; i.e. orbit. Your ship is not in orbit around your drive field. And your crew would be long dead at gravity levels where tidal shear would be noticeable for a human sized object. $\endgroup$ Sep 16, 2020 at 14:05
  • $\begingroup$ You're mixing up perceived acceleration and actual acceleration (okay, maybe my use of "experiencing" is not helping). The ISS is most certainly being accelerated at ~1G. The hypothetical ship in this question may not be orbiting the drive's field, but it is in free fall in the drive's field, which is the point. (I suppose I should try to run some numbers on what sorts of field configurations would result in a "noticeable" shear... at least for a single point source. As noted, the math gets pretty involved beyond that.) $\endgroup$
    – Matthew
    Sep 16, 2020 at 14:15
  • $\begingroup$ The Earth's 1G is being translated to angular acceleration (i.e. orbiting), which is why the ISS is not flying away into space. The ISS is experiencing no linear acceleration. You have no analogue in your hypothetical space drive. You try to draw a distinction between gravitational acceleration and "mechanical acceleration" but there is none according to the equivalence principle (en.wikipedia.org/wiki/Equivalence_principle). No perceived linear acceleration = no change in velocity. $\endgroup$ Sep 16, 2020 at 15:33
  • $\begingroup$ Seriously? Isaac Newton begs to differ. And the ISS is most certainly experiencing acceleration and a change in velocity. And the difference is explained in my answer. $\endgroup$
    – Matthew
    Sep 16, 2020 at 15:46

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