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This is for a sci-fi universe depicting an interplanetary civilisation using fusion torch-ships. Think "1G for days".

For a run to Neptune at 1G the peak velocity at turnover works out to about 2.2%C or about 6,650 km/s, although plugging the more optimistic values from this table of fusion exhaust velocities into the rocket equation suggests you could theoretically have a total delta-V in your tank much higher than that.

The interplanetary medium is pretty diffuse compared to air at sea level, but you would still have to contend with particles from the solar wind, gas molecules and the (hopefully) very occasional dust grain.

The question is, at what speed do these things start to become a practical problem? The issues I've seen suggested include heating of the leading edges of the ship, abrasion of the same and at very high speeds, actual nuclear fusion.

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    $\begingroup$ I point out that in stories by Robert A. Heinlein "torch ships" used total conversins of matter into energy for their drives and could accclerated to almost the speed of light and then decelerate. Has some more recent work of science fiction used the term "torch ship" for spacecraft with merely fusion drives? And if so, which use is the more fmous and should be preferred by science ficiton fans? $\endgroup$ Jul 8 at 19:33
  • $\begingroup$ Your peak velocity might be a bit off. I get 0.043c, given an acceleration time of ~.66^6s and a total journey time of ~1.3^6s. $\endgroup$ Jul 11 at 11:11
  • $\begingroup$ I went purely by SUVAT to get that 2.2%C figure. Assuming a trip to Neptune of 30 AU with a turnover at the midpoint, that means the ship accelerates for 15 AU and then decelerates to a relative stop after another 15AU. I took 1 AU as 150,000,000,000 m and plugged those values into v^2 = u^2 + 2AS. u^2 is zero of course, so that term could be ignored. That left v^2 = 2 * 9.81 x (15 AU * 150,000,000,000 m) = 44,145,000,000,000 m/s, so v = 6,644,170 m/s. Assuming a rough value for C of 300,000,000 m/s that makes our peak velocity at turnover just over 2.2% of the speed limit. $\endgroup$
    – RogerC
    Jul 12 at 12:41

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G-forces are the limiting factor.

Assuming your civilization attained the incredible energy densities necessary to go up to these ludicrous speeds, the fact is that any ship containing humans still can't accelerate faster than a few g's without killing everyone on board. And if you want to accelerate constantly for several days (which is what it would take to cross the solar system), you'll get major health risks above 1g - good ol' Earth gravity.

The Expanse (book/TV series) is notable for its vertical ships, oriented like multi-story buildings that accelerate at 1g, providing artificial gravity and fast transport in one fell swoop. I recommend it as a good example of hard sci-fi at the limits of plausible interplanetary travel (and great storytelling to boot).

The maximum speed in your setting will simply be the midpoint speed of the longest journey you can take through the solar system, accelerating at 1g for the first half and decelerating for the second half (nobody will ever go much faster than this since it would leave the solar system). Some simple math, plugging in Pluto's mean orbit for the rough size of the solar system, gives a maximum travel time of about 15 days, at which point the ship has reached 0.04 c.

So hopefully that makes it clear that, for interplanetary travel with humans on board at least, nobody will be moving at especially high relativistic speeds.

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Use dimensional analysis

Let's say that you are trying to travel through the solar wind at 0.2 times the speed of light. You said "interplanetary," so you're pushing through the solar wind. The solar wind has 4 hydrogen atoms per cubic centimeter. We wish to know the mass per second of hydrogen atoms that we are hitting.

Let's say that the spaceship has a frontal area of 100 m^2.

So the calculation is:

mass of hydrogen atoms hit per second = 4 (hydrogen atoms/cubic centimeter) * 0.2 * (speed of light) * 100 m^2 * (10^(-27) kg)/(hydrogen atom)

WolframAlpha will do unit conversions automatically, so you can just plug it in here and you get

= 4 * 10^(-11) kg/s

Now, that's not a lot of mass, but we are hitting the atoms at 0.2c.

This post suggests the collision speed required for fusion is in the area of 0.05c, so the atoms will be fusing with the hull. Fusion releases around 0.7% of the mass of the hydrogen as energy. So that means in one second it releases this much energy:

0.007 * 4 * 10^(-11) kg * c^2

= 25,000 joules

The more significant factor is the kinetic energy of the hydrogen atoms. Relativistic kinetic energy is (1/sqrt(1 - v^2/c^2) - 1) * mc^2. m is the amount of mass, which we'll take to be the mass in one second, 10^(-11) kg. So, the kinetic energy from collisions in one second is:

(1 / sqrt(1 - (0.2 c)^2 / c^2) - 1) * 4 * 10^(-11) kg * c^2

which WolframAlpha tells us is:

= 74,000 Joules

(74,000 Joules + 25,000 Joules) per second is 99 kilowatts. It's as if you had a heating element on the front of your spaceship drawing 99 kilowatts. Your spaceship is going to have to get rid of 99 kilowatts of heat.

That's probably possible, with powerful refrigeration units to conduct the heat to radiators and get rid of it. Projecting a magnetic field ahead to push the atoms out of the way might be an alternative.

Of course, this assumes you do not hit a pebble. Hit a pebble at 0.2c and that's probably game over.

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  • $\begingroup$ Orders of magnitude (power) tells us that 99 kW is on a par with a truck engine, while International Space Station tells us that it's about what the ISS's solar panels produce. You'll need to include radiators to deal with the heat, but it's no big deal. $\endgroup$
    – Mark
    Jul 9 at 18:53
  • $\begingroup$ @Mark Generating 99 kW of heat is not hard (think 99 electric space heaters running at once), but cooling that much heat is a very different story. Put a toaster in a freezer, and the toaster wins by a very wide margin. Space is an excellent insulator, and unless you are carrying a lot of extra mass for venting, your only way to vent the heat is radiative cooling. $\endgroup$
    – causative
    Jul 9 at 19:00
  • $\begingroup$ @Mark Also consider that the ISS is in Earth's shadow half the time, where it's very cold, helping it to vent heat. An interplanetary spaceship would be in sunlight all the time, plus the 99 kW of heat from the solar wind. I agree that it should be possible to vent that heat with enough radiators and refrigerant coils, but it's a significant engineering challenge. Although, if your torchship has a 1 GW or more power plant, that's by far a more challenging heat source to cool. $\endgroup$
    – causative
    Jul 9 at 21:28
  • $\begingroup$ Another concern is the radiation. All those protons are ionizing radiation. Your ship has to have very thick shielding if it has any crew. $\endgroup$
    – causative
    Jul 9 at 21:30
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    $\begingroup$ Thanks, that's exactly what I was looking for! It looks like the ship's drive would be a far more significant problem than the solar wind. $\endgroup$
    – RogerC
    Jul 10 at 19:39
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Practical speed limit for any ship is limited by energy

You will want to read up on the initiative called Breakthrough Starshot which has several of he most wealthy people on earth trying to get us close-up pictures of Proxima Centauri within a generation.

Their goal is to send a “starChip” probe of only a couple grams mass at a speed of 0.2c on a trip to our nearest star by a 20-30 year trip through 45,000,000,000,000 miles of space, snap a selfie, and radio it home.

The practical limits of this adventure have been deeply explored, and the interstellar medium is incredibly hostile to small things. The shielding on this craft, by NASA calculations, can withstand several impacts with interstellar molecules of hydrogen or helium which they expect, but they calculated that impact with a grain of dust the diameter of a human hair would completely vaporize the probe at that velocity. NASA also calculated that the ship would only survive if the density of interstellar dust were below a certain fraction (it is among those many papers in the Breakthrough page, I could not find it), and unfortunately the calculated interstellar dust is significantly higher than wht is needed. If you want to consider interplanetary dust, even Star Trek admits you can’t go to warp inside the solar system. You WILL hit something big, and enough small things to burn you up.

But the energy to drive this can’t possibly fit onboard theprobe, so they are using sails. And a 100 Gigawatt laser system. Yes, 100 Gigawatts to get a raisin up to 0.2c, which it is hoped to reach within 6 months of acceleration.

So the solution is to obviously build a bigger ship with bigger shields. This means more mass, and that means more energy. How many raisins does your scifi ship weigh? Multiply 100GW times that, and decide if this is practical. But, you need energy to accelerate AND to decelerate. Twice, if you want to come home. So one round-trip excursion anywhere is the energy of acceleration x4.

But with unlimited energy (like every respectable sci-fi author invents), all you need to do is accelerate faster and trips between Earth and Neptune can be done in a day,right? As long as you don’t have any squishy organisms onboard, that is fine. But I think in the hard-science sorting machine’s calculations, G’s matter. Even The Expanse gets this right.

The hard science answer today is that it is simply not practical to produce the energy required to make a massive object accelerate and decelerate for an interstellar trip at high-fractional light speeds. Yes, fusion particles reach high-fractional light speed. The hard science sorting machine puts sub-atomic particles and spaceships into different boxes, however, because mass matters. A lot. And doing this inside the tiny space of a solar system is up against the hard science of inertial momentum.

Please determine what scientist you want to embarrass before attempting this story. It’s a necessary evil of the genre.

Your science fiction story needs to decide what part of hard science it wants to break, because you absolutely have to make some scientists do a face-palm to make your world work.

Don’t fret. Every sci-fi author has done this already. It was much easier back in Jules Verne’s day when we didn’t know what was out there.

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  • $\begingroup$ +1 for "raisins". :-) Pushed with laser from earth. Is there a way to also decelerate remotely (pull?). $\endgroup$
    – Pablo H
    Jul 9 at 19:29
  • $\begingroup$ Nope. It's a one-way trip for the most expensive selfie in human history. They haven't decided where the lasers will be but Earth is a bad idea. We spin around a lot, and have birds, clouds, airplanes, etc. that don't go well with lasers. $\endgroup$
    – Vogon Poet
    Jul 9 at 21:44
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    $\begingroup$ @PabloH Deceleration is possible if you can aim everything accurately enough. The sail comes apart into two pieces, the big one is boosted even further but bounces the beam back on the small one that then decelerates. Your engineering had better be very, very, very good. You also need big sails to even consider this--not an option for Starshot. $\endgroup$ Jul 9 at 21:55
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I'm not sure where, but you've definitely made an error with your math. Going by that table from atomic rockets, it gives the most optimistic figure of .117c. With a mass ration of 10 (90% fuel) then you're talking about an effective delta-v of around .26c. Even if we go by a less optimistic value like the space shuttle's mass ratio of 16 then we're talking about something around .32c. It's not called the tyranny of the rocket equation for nothing, as much of the extra fuel is wasted by the mass of carrying extra fuel, which is why you probably want staging for something at this scale. I will note that even this .26c value only includes the total delta-v, as your useful speed is half that unless you want to collide with the destination at full speed.

That is also proton-proton fusion, which has a pretty good chance of not even being possible outside of a sun. Considering how hard even dirtier De-T fusion is on Earth, sustaining that reaction in space is rather unlikely. Going by a more realistic figure of .087c for duterium-helium3, this gives you a delta-v of .2c instead.

Something else you're missing is that exhaust velocity and effective exhaust velocity are not the same. So while the fusion rocket might have an exhaust velocity of .3c, the effective exhaust velocity is even lower. Orion drives for example were only 25% efficient, while a modern rocket bell is somewhere in the 90%+ range. Fusion power could never be this efficient because a truly efficient rocket design would melt due to the extreme heat without any good way to dissipate it in space. You're left relying on magnetic nozzles which are less efficient. Somewhere in the 50-60% range is all you're likely going to get. At that level your .26c max velocity is now down to around .16c with an effective max velocity of .08c. If you want the kinds of speeds you're suggesting then you need some version of antimatter, which is almost certainly impossible to store at the scale required in a safe fashion.

As for mitigation, streamlining will help slightly, but it also makes your frontal armor less efficient, so that it requires more surface area to cover the same volume of ship. Most hypothetical design's I've seen use umbrella style shields. At the lower practical values, streamlining is almost entirely pointless.

Magnetic sails just plain won't work, because in order for it to push particles out of the way they will also slow the ship down due to conservation of momentum. There is some debate about whether a Bussard Ramjet would produce more drag than it does thrust. The upside is that you can use this conservation of momentum to slow down like an interstellar parachute. The best use for a magnetic sail is that you can use it to slow down and so can burn up nearly all of your fuel on the way there. A fairly plausible mission profile for an unmanned ship with such a design can be found here. I will note that it has a mass ratio of 35 because it is using D-D fusion.

EVAs are a bad idea any way you shake it. While an umbrella shield would help with physical impacts, the biggest problem is radiation that there is no practical way to shield against. The ISS is only relatively safe because it is in LEO and is still under Earth's magnetic field, while astronauts still have shortened lifespans. Space suits just can't do it without becoming extremely impractical unless you have something better than Iron Man level powered armor.

There is also another problem with fast ideas like this. Unless there is already infrastructure in the destination star system, then you'll need to bring along essentially a self contained society a la a generation ship. If you're doing this, then there is less reason not to just go slower in the first place and just use the greater payload to carry more stuff. If you're talking about these kinds of speeds within the solar system, see the discussion of The Expanse.

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Didn't want to answer this one under hard-science tag, but considering present answer and danger of the q being closed, I can't keep silence, so on the softish side.

Practical is defined by what you have and what you want and can achieve, so, in a sense if you can 0.9c it practical in some sense as it saves time for people onboard of the craft, and it not so much practical to fly at 0.1c even to proxima (maybe practical if there is such neccessity) and even less practical and more difficult to fly at that speed to more distant stars.

But torch ship won't be able to get close to 0.9c(it can but...), and more resonable balance is indeed so often used 0.1c, and it potencially (close so) what a torch ship can do. So it your practical speed, due limitations of rocket equation

As ISM it does not have such an impact on speed limits, as sure a dust particle colliding at anything with more than 1000km/s may be problematic, but it also worth noticing that even more so it is for a dust paticle to collide with another dust particle at such speeds.

So making shield in front of the ship, by "saturating" (1-10-100x of ISM density) a cloud in front of a ship(by torch exchaust as an example, which then moves at about the speed of the ship) may be an effective mean to destroy all small particles into a plasma before ship arrives and bring that plasma to speeds closer to speed of the ship. Project orion(if I remenber correctly, or someone in reference to that project at that time) or something were proposing use of foil shreds for that - may work as well, cloud of paticles - ice grains of somehing may work as well. It should provide protection from lobe collisions so as side collisions. And it can be done in more than few ways - but it all is the same sacrificial material vs ISM, which you can constantly recycle, in that sense water ice as shield, water ice and sand, gas cloud, etc whatever it is easy to fix/deploy in the flight)

So potencially there are ways to protect caft from particles, and create warning sytem to detect things by hours ahead for big chunks which can not be destroyed by this cloud. And speed does not matter here 0.1c-0.9c it is not of much difference.

So practical velocity is defined by spacecraft capacities, what a practical space craft can achieve as a max velocity. In a sense torch ship and fusion ships are not practical for intertellar travel, but good stuff for interplanetary one. So as technologies which do not have self healing self repair properties(aka nanobots of some kind 1-2-3D nano) are not that suitable for interstellar travel.

As EVA - depends on approach, if it is a cloud infont of the ship, then space next to the ship, is quite safe and protected as km's around it

PS

  • Not downvoting because there have been scientific studies of spray, gas, and cloud shielding of spacecraft, but not upvoting because you haven't cited any of them. – @Mark

True, true. For same reason I can't comment, old browser and pad to write an answer, for same reason I didn't want to write an answerto this one, because finding links is very inconvinient on this setup.

You can edit the q and add few links, I would like to read it myself as well, maybe. As the q and a discussion of dust particles problem is not new in public discourse, and I do not see those solutions to be mentions as often as they should. I have impression that at some point it was only me pushing that idea on WB at least. I mean - I first come up with the idea writing answer or something, and then some time later I found(while researching material for some answer) a short cite mentioning proposal/connection between shred of foil and orion(or something) it was not a research work but a mentioning, I remembered it, then I even lost a link to that mentioning(I do remember as I did try years ago to find it again but without a success). I mean those solution should be 101 of space travel discourse, not forcing ppl to reinvent weels as it happened to me, but clearly they aren't, still.

So I literally forced myself to write an answer to the q, considering how not well discussed the problem and its solutions are, to which current answers are another demonstration - at time of writing a guy started to talk about energy limitations, as if the fuel does not provide enough energy, and problems of project starshot, forcing OP to invent/handwave unlimited energy sources in a hard science answer, as it fusion alone is not enough.

Further answers didn't do much better and q is about to close, so there won't be a single answer which adresses OP's clearly stated worries. @cuasative answer is somewhat exception, but his crew dies from pebble and can resist only hydrogen of ISM. For reasons I can not comment(broken javascrip for my browser) I can not upvote or downvote, or all of them would get you understand what.

So, save the planet, edit the answer or write your own if you have a chance, and add links to solutions. I hope you do not wavered once The expanse was used as an example, source, lol.

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    $\begingroup$ Not downvoting because there have been scientific studies of spray, gas, and cloud shielding of spacecraft, but not upvoting because you haven't cited any of them. $\endgroup$
    – Mark
    Jul 9 at 18:55

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