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This question hopes to make a space tug crew's life tolerable.

A supply pipeline links two civilizations. Due to the long travel time between the ends, cargo is "thrown" at the other side in unmanned and unpowered cargo barges, save for minor attitude, yaw and pitch thrusters. Tugs using antimatter drives developed with alien engineering plans push a barge up to 0.1c and release it, then reverse to catch an inbound barge coming at them at 0.1c. Barges are timed like this to prevent a tug going out or coming back with no payload.

Space Tug

(Space tug)

The human crew is going to be subjected to an environment for a long time, and will be doing this repeatedly. My goal is to:

  • Minimize the duration of each operation

  • Minimize exposure to either low or high g-force acceleration.

Below is the velocity curve for one operation: $$\text{Accelerate outbound payload:} f(a) = t_0 \rightarrow t_1 \\ \text{Release and reverse direction: } f(b) = t_1 \rightarrow t_2 \\\text{Catch and decelerate incoming payload: }f(c) = t_2 \rightarrow t_f$$ Velocity curve

(Velocity curves are not drawn to scale and are not required to be linear)

I need to make the sum of these acceleration curves $f(a)+f(b)+f(c)$ as short as possible, while preventing unreasonable forces on the crew. So the acceleration constraints are:

  • Acceleration through $f(a), f(c)$ can be no more than 1.2g

  • Acceleration through $f(b)$ should remain at 1.2g for most of the time, with no more than 1-hour bursts at 2g (possibly at night time when everyone is lying down, with forced oxygen masks)

  • Grant 2 weeks exposure to microgravity at each crew swap (expecting this twice per tour of two hauls).

What is the shortest duration for this trip $t_0 \rightarrow t_f$, and could a physically fit crew do this job twice per year without known physiological injury?

I am also curious what time dilation differences this crew would experience each flight

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    $\begingroup$ You have a supply pipeline in space which is apparently long enough that objects are able to be accelerated through it at .1c and it makes sense? How? And why can't you make the tugs unmmaned too, if all they have to do is push something forward and then decelerate? An AI can handle that. $\endgroup$
    – Halfthawed
    Nov 6, 2019 at 4:30
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    $\begingroup$ @Halfthawed, pipline here is a metaphor. It's tugs, who manage acceleration, if I got it right. $\endgroup$
    – ksbes
    Nov 6, 2019 at 7:34
  • $\begingroup$ 0.1c is very far from "high relativistic". There's less than 0.5% change to clock rates and mass and so on. And your tugs are an extremely inefficient way to do this job... they need a delta-V of ~.4c, implying the need for effective antimatter beam core engines and bulk antimatter synthesis. Laser and magnetic sails, or sailbeam mechanisms are so vastly more efficienct and appropriate I don't know why anyone would make humans do this job $\endgroup$ Nov 6, 2019 at 9:11
  • $\begingroup$ (Oh yeah, and those beam core rockets producing 1g thrust? So much gamma radiation. Your tugs ain't gonna look like that picture; they're gonna be all shields and heatsinks) $\endgroup$ Nov 6, 2019 at 9:18
  • $\begingroup$ @StarfishPrime - OK, busted. It’s good to know my model accurately depicts a pion rocket. As to the gamma radiation, fortunately the annihilation event emits gamma particles in a direction exactly perpendicular to the incident collision angle. Since the fuel is charged particles, synthesized magnetic field technology can precisely control the collision angle, and therefore the gamma particle vector. >90% gamma radiation emits near-perpendicular to the parabolic thrust shield. $\endgroup$
    – Vogon Poet
    Nov 6, 2019 at 15:03

3 Answers 3

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In the book The Three Body Problem 2: The Dark Forest, writer Liu Qixin details a kind of oxygen rich liquid that would enter a person's lungs and thus minimize the effects of acceleration. If we assume that this liquid has flooded the ship and that the crew is trained to withstand high g situations, we can estimate that the crew could withstand almost 50g of constant pressure, while it would feel like 1.5g inside the liquid. A quick back of the envelope math suggests that the acceleration and de-acellaration would both take around 17 hours. If an extra 2 hours is required for both launching and receiving the pods, the whole operation might take around 72 hours or 3 days whist not causing any physical damage to the crew.

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  • $\begingroup$ This is a very interesting alternative, I think maybe a hybrid of the two would be ideal. The enormous mass of the tug + barge on deployment or recovery would make a 50G acceleration incomprehensible. However, to turn the tug around during the A$_2$ acceleration, when only the mass of the tug is involved , I could see them getting into the tank and jacking the engines up for 5g at the turn-around and cutting that 60-day segment down to only two weeks in the fish tank. There are variations on the theme that can get us to three trips per year and still have down-time. Good find! $\endgroup$
    – Vogon Poet
    Feb 22 at 14:18
  • $\begingroup$ These are called perfluorocarbons. There is also a hydrostatic suit, the Libelle G- Multiplus Selfcontained Anti-G Ensemble (SAGE), which can take pilots to safe operation at 10g. $\endgroup$
    – Vogon Poet
    Feb 22 at 23:42
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If you fall back to Newton, then $t_0-t_1=t_2-t_f$ ((de)acceleration) = 30 days, $t_2-t_1$ (reverse) = 55-60 days (60 hours of +0.8g would not save much time, but can be used to correct interception course). Total is about 4 month (we need time for manuvering and rest). Since max gamma factor is only $\sqrt{1-0.01} = 1-0.005$, relativistic effects would give you less then a half of a day dilation and we can keep to this classical numbers - the error would be less than approximations we took.

So you can do up to 3 jobs in a year

1g is a huge acceleration!

P.S. at low relativistic speeds it is sometimes simpler to calculate in classic and then bring relativistic corrections. Wich can be easely calculated using approximation formula $\sqrt{1-x} = 1-x/2$

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  • $\begingroup$ 1G is a perfectly normal acceleration, we are subject to it all the time. I'd just make the crew cabins tiltable so they can swing in the direction they need to be. Saves the whole headache of "long term 0G" too. $\endgroup$
    – Borgh
    Nov 6, 2019 at 11:08
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    $\begingroup$ @Borgh, do not confuse force for acceleartion (change of speed). We are subject to force of "1G" all the time, but our accelaration is very very low (zero if you are sitting and not taking into account different types if slow stellar rotations your are paticipating in). Just imaging sitting in a traing, wich is accelerating with 10 m/s^2! $\endgroup$
    – ksbes
    Nov 6, 2019 at 11:27
  • $\begingroup$ No. You can do two missions per year. The poor buggers need some down time from slaving in a hot space tug. $\endgroup$
    – a4android
    Nov 6, 2019 at 11:52
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    $\begingroup$ @Borgh a rocket that can supply 1G continuously for months at a time, especially when pushing huge amounts of cargo, has an astonishing, terrifying level of power and complexity. It might involve lighting off thousands of tonnes of antimatter. That's what huge means in this context. $\endgroup$ Nov 6, 2019 at 11:55
  • $\begingroup$ @Borgh don't be silly. Just flip the whole ship. $\endgroup$ Nov 9, 2019 at 1:33
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ksbes answered the core part of the question, but I'd like to reframe it slightly to show how terrible the idea is.

Your tugs, mass $m_t$ need to push a barge, mass $m_b$ up to .1c, and decelerate a second barge down from .1c. They also need to reverse their velocity vector in between, slowing down their own mass to a velocity of 0 relative to their starting point and then back up to .1c again. If the tug did the trip on its own, it would need a $\Delta_v$ of 0.4c. Generally speaking, you don't want a $\Delta_v$ greatly in excess of your rocket's exhaust velocity, and the only thing with an exhaust velocity that high is a beam core antimatter rocket (we'll ignore the implausibility of such a rocket for now) with a $v_e$ of about 0.33c.

Working backwards, the braking $\Delta_v$ will be 0.1c, with a mass of $m_t + m_b$.

Now, A gentleman named Robert Frisbee did an interesting paper on beam-core driven starships (How to build an antimatter rocket for interstellar missions) where he observes that the normal delta-V equations don't apply to antimatter rockets, because a load of the mass involve simply up and vanishes (or rather, turns into deadly gamma rays, but one problem at a time). Instead you have to use a different equation to compute the mass ratio of your ship:

$$k_1 = \sqrt{(1-a)^2 + 4av_e^2 / c^2}$$ $$k_2 = (-2v_e*\Delta_v/c^2) + 1-a$$ $$R = \left(\frac{(k_2-k_1)(1-a+k_1)}{(k_2 + k_1)(1-a-k_1)}\right)^{\frac{1}{k_1}}$$

where $a$ is the proportion of mass flying out of the back of your rocket compared to that going into the reaction chamber... Frisbee's antimatter rocket had $a=0.22$. Anyway, this gives a mass ratio the boost and brake phases of 2.55 (eg. the fuel mass is 2.55 times the dry mass of the tug and barge). The non-beam-core mass ratio equation would give more like 1.35, so you can see already that things are starting to get awkward.

The braking phase needs a propellant mass of $m_{p3} = 1.55(m_t + m_b)$. The turnaround phase needs a $\Delta_v$ of 0.2c, and so a mass-ratio of 4.44. It needs to push the propellant used for the braking phase too, giving a a propellant mass of $m_{p2} = 3.44(m_t + m_{p3})$. The boost phase needs a $\Delta_v$ of 0.1c, and it needs to push the barge and the rest of its fuel, giving a propellant mass of $m_{p1} = 1.55(m_t + m_b + m_{p2})$. This gives a required initial mass ratio of $16.1466m_t + 10.8146m_b$. Lets say the tug is 100 times smaller than the barge. This means that for every tonne the barge weighs, you need nearly five and a half tonnes of pure antimatter. And that's not even per tonne of cargo, because there's the hull of the barge, the shielding, the navigation, the manoevering and docking systems and all the rest! Oh, and building a ship with a mass ratio that high is an additional tricky engineering task, especially when you're talking about antimatter confinement!

This is worse than simply strapping a suitable antimatter rocket to the barge and letting it boost and brake itself, because you're wasting fuel on your tug. The $\Delta_v$ for the barge alone would be just 0.2c, and with a mass ratio of 4.44 you'd need only about 1.72 tonnes of antimatter per tonne of barge!

If you used a single antimatter rocket to do the boosting, and a combination of magnetic parachute, solar sail, sail beam or other non-rocket-based braking system, you immediately reduce your propellant cost-per-launch to a little over a three quarters of a tonne of antimatter per tonne of barge, plus whatever the power requirements of the braking system are (which can be done with solar or fusion, as seems appropriate, which will be cheaper, simpler and safer). Hell, maybe now you can use your beam for the boost phase too, and avoid the whole dangerous business of mucking about with antimatter.

Now there's no tug, there's no need for human crews to spend months and months in a tiny tin box at dangerous speeds strapped to many, many tonnes of a hideously unstable propellant where any one of a thousand little problems will vapourise them in an instant. No maintenance of tugs. No need for rescue operations to retrieve the crew if anything goes wrong (you were gonna do that, right?).

Over seven times cheaper per launch (or more, if you have a beam launch), vastly safer, no miserable crew. What's not to like? And even if you don't like it, you risk someone else setting up this cheap safe alternative in your place, and then where will you be?

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  • $\begingroup$ Comments are not for extended discussion; this conversation has been moved to chat. $\endgroup$
    – Monty Wild
    Nov 9, 2019 at 6:14
  • $\begingroup$ I like this answer. But for a different question. It was an awfully lot of work to put into saying “Q: Can a crew handle it? A: Dont use humans.” I feel the need now to ask a question which justifies all this work. ((However, the antimatter engines in question will have an I$_{sp}=3.0e-10^7$s and an $a=0.5$ per research at Lawrence Livermore National Labararory (Moore, 1986)). Understand I can’t grant it the bounty here however. $\endgroup$
    – Vogon Poet
    Feb 22 at 23:21
  • $\begingroup$ @VogonPoet there's two reasons behind that... one is that I like to justify my answers... if people wanted arbitrary declarative statements without backing, they'd just go to quora or something. The other is that I tend to use my answers as a sort of notebook, because I have no ability to organize my own stuff. This was the first time I'd actually sat down and made use of Frisbee's modified rocket equation, so I wrote it all out for my future reference, even if no-one else was interested ;-) $\endgroup$ Feb 23 at 9:34

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