Advice needed about rocket performances

[Dr Wu]

I am writing a science fiction novel featuring a manned exploration into the Oort Cloud. So to keep things simple as possible, my question is this: is it reasonable to suppose an antimatter-powered spacecraft could travel from Earth space out to a distance of (say) 2,000 AU* within a time-period of around ten months? This would be under a continuous thrust (including deceleration) of 1.6 m/s2 - about the same as our Moon's surface gravity.

The one bedevilling problem in all this has been my long-running inability to crack the Tsiolkovsky rocket equation, and do so in ways that would resolve the above issue. And why is this important? To satisfy the demands of the plot, I need to have a clear idea what the ship's mass ratio would be for such a sub-interstellar mission, plus some understanding about the efficiency of an antimatter reactor (beam-core or an antihydrogen-catalysed fusion drive?) Also, there's the question about the quantity of fuel needed for the return trip back to Earth. The plot has its eye on that fuel, which is another way of saying that a large question mark hangs over the quantity issue.

The spacecraft , by the way - despite comprising for the most part of supremely lightweight materials - still masses at some 5,000 tonnes, and includes its own 'foldable' revolving space station: the crew are in the Oort Cloud for the long haul.

Thanks in advance.

*This is somewhat short of the Oort Cloud's inner margins, I agree, but, well. . . stuff happens en route.

 

[mfb]

1.6m/s^2 for 5 months gives you a speed of 20000km/s or ~7% the speed of light. if you want to slow down and come back again in the same way later that needs 28% the speed of light as delta-v capability. That looks possible if you have huge amounts of antimatter available. The amount will depend on the efficiency of the drive, but you'll probably burn some 5-digit number of tons of antimatter.

Note that accelerating with 1g for about two weeks gives the same travel time, but half the final velocity (which reduces the required antimatter by some significant factor).

 

[Dr Wu]

Many thanks for your response. Actually, the journey time each way is ten months, not five. On another point I'm a bit concerned about the quantity of antimatter needed. I wasn't banking on 100% efficiency, more like 60 -70% as a rough guesstimate. That admitted, I'd be interested on your take about the Edward Muller website. I was rather hoping the fuel - at least the antimatter half of it - might be two-digits (each way) rather than the five, as you propose. On a related point, yes, the ship does return to Earth, but I http://www.edwardmuller.com/index.php?Page=calculator

Oh, dear, I must have hit the wrong key! So where was I? Ah, yes: the ship does return to Earth, but the assumption was that it would do so at the same 1.6m/s2 rate. Could you clarify? Many thanks.

 

[mfb]

You can edit your post with the "edit" button, I merged the two now.

Actually, the journey time each way is ten months, not five.

That's what I used for the calculations. 5 month acceleration, 5 months deceleration, and the same back again.

Even with 100% efficiency (and there is no known way to reach that) you need roughly 32% fuel to get there and back again, which means 16% antimatter - 800 tons. With the other approach (accelerate for 1g for a while, then coast, decelerate again, same for the return trip) you just need about 400 tons.
If you want to save more fuel, reduce the speed or the mass. Everything that is not directly needed for humans on the way there can be sent slower and in advance, everything that is not needed for the humans during the return trip can be left there, or sent back at a lower speed.

That webpage shows the incredible amount of energy needed to produce 800 tons of antimatter - well, you have a large ship and want to accelerate it to some percent the speed of light.

 

[Dr Wu]

Many thanks again for your helpful (and timely) advice. After your first comments, I did some back-of-the-envelope calculations and came up with a total energy outlay of 5,300 exajoules - enough, it would appear, to shift 5,000 tonnes (including fuel) a total distance of 4,000 AU at 1.6 m/s2. This tops out at about 1,200 tonnes of 'ambimatter' fuel. Unfortunately, I don't trust my mathematics. Neither, for that matter, do I trust some of the webpage calculators. I am moreover trying to keep within the bounds of scientific feasibility, not to mention my take on human nature itself. So the prospect of an expeditionary spacecraft setting off from Earth space with enough fuel to cause a global catastrophe is one I find unconvincing, at least given the context of this novel. Therefore, if I were to adopt your approach - accelerating for two weeks at 1g then coasting for much for the way thereafter - how much do you think I would save in terms of energy/fuel mass?

Regards

 

[Ryan_m_b]

If you want to work with the Tsiolkovsky Rocket Equation (and I'm not sure why you wouldn't) you can use Wolfram Alpha to work out any of the variables given the others. If you want to go 2000AU (3e14 metres) in 10 months (2.63e7 seconds) you'll need to be traveling at 1.14e7mps, or to put it another way 40 million kilometres per hour. I don't know if there are any reputable figures for what the exhaust velocity of an antimatter rocket would be, a quick google brings up a few figures, the biggest being 1e8mps.

Plugging all that into Wolfram Alpha (plus your final mass of 5e6kg) and solving for initial mass gives us: 5604 metric tonnes. In other words you'll need 604 tonnes of fuel (half of which is antimatter) to get up to that speed. That's just a fly by though! If you want slow down at the destination that number increases to 1281 tonnes of fuel and if you want the crew to come back 2889 tonnes.

Using that last figure and good old e=mc² that much fuel can release a total of 2.59e23 joules of energy, which is about how much solar energy hits the Earth in 4 weeks. That's the problem with a single stage rocket, the amount of energy needed to go interstellar in a reasonable time is horrific. Given all that: do you need your crew to get there so quickly and/or does the destination have to be so far? Bringing the destination closer (say 100au) and the timeline longer (perhaps with suspended animation) the insane fuel requirements will come down massively.

 

[mheslep]

Couple ideas:
o Manufacturer the anti-matter at some distance from earth, a distance that satisfies both safety concerns and the feasibility of repeated ~short trips out and back to prepare for the long haul.

o Beam coherent EM power to the craft in route, with the beam source as large and powerful as you like, driven by solar collection, nuclear, etc. Resolves energy needs if not propellant (Tsiolkovsky) mass.

o Cut the outbound acceleration energy/mass needs by boosting locally with high g's, and to which the ship and crew are made immune by
some kind space-time warp.

o Dump Tsiolkovsky propellant and push against some invented quantum vacuum thing. Still requires mv^2 energy, again perhaps from beamed power.

 

[mfb]

So the prospect of an expeditionary spacecraft setting off from Earth space with enough fuel to cause a global catastrophe is one I find unconvincing, at least given the context of this novel.

That's how the universe works. Nearly every realistic and powerful propulsion system is a potential weapon of mass destruction.

Therefore, if I were to adopt your approach - accelerating for two weeks at 1g then coasting for much for the way thereafter - how much do you think I would save in terms of energy/fuel mass?

See post 4.
With the short acceleration phase and the hypothetical 100% efficiency of the antimatter drive, the required fuel scales (nearly) linearly with inverse time - increase travel time from 10 to 20 months and you reduce the fuel needed by another factor of 2.
And fuel needed is proportional to mass - reduce the mass from 5000 to 1000 tons and you save another factor of 5. And so on.

 

[Ryan_m_b]

Beamed propulsion is not a bad idea. A station in orbit of the sun could fire a laser or a stream of charged particles at a light/magnetic sail attached to the vessel. That way you get propulsion without the huge fuel requirements. Might need a bit of hand waving and assume future developments will allow for reasonable accelerations but most readers would probably accept that.

 

[mheslep]

If the wiki is correct and the solar power flux at 1 AU (1366W/m^2) provides force 9e-6 N/m^2 for a perfect reflector, then the sail needs to collect 1.2 PW for the 10 month duration to provide the 8000kN required for +/-0.16g on a 5000t craft. Conjure a sail material that can reflect 1GW/m^2, then the sail is 1.2 sq km. Round-trip energy 3e22 Joules, delivered to the spacecraft , or 167t rest mass. Beam divergence is an inverse function of wavelength, so conjure up whatever gamma and up wavelength is required for some square km spot sizes at ~100AU.

If Ernst Stavro Blofeld / Dr Evil / Hugo Drax, etc should acquire control of the beam source and redirect it at things he doesn't like there may be a problem, though typically such interference is resolved shortly after someone yells, "lets get out of here", and an application of rising theme music.

 

[mfb]

1GW/m^2? Even tiny losses (good luck reflecting gamma rays) would vaporize the reflector, so we should look for larger reflectors. And it is supposed to be light-weight, right? To stay below 1000 tons at 1km^2, we have at most 1kg/m^2 or a layer with a thickness of the order of 1mm - which thins out significantly if we go to larger sail sizes.

 

[Ryan_m_b]

If a charged particle beam is used rather than a laser then a magnetic sail can be used, the advantage there is that such a sail is a static magnetic field and not a physical object. Obviously the equipment generating the field will have mass but it could potentially weigh a lot less than a physical laser sail. Apparently it may be possible to enhance such a device with plasma surrounding the rocket:

http://en.m.wikipedia.org/wiki/Magnetic_sail

 

[mheslep]

1GW/m^2? Even tiny losses (good luck reflecting gamma rays) would vaporize the reflector, so we should look for larger reflectors. And it is supposed to be light-weight, right? To stay below 1000 tons at 1km^2, we have at most 1kg/m^2 or a layer with a thickness of the order of 1mm - which thins out significantly if we go to larger sail sizes.

Kitchen Al foil is 50 gm/m^2. So a 1000t Al foil sail allows 20 km^2 not counting supports for 8000 kN. But as this is sci fi conjure a sheet of carbon nano something with less density, high thermal conductivity.

 

[mfb]

Thermal conductivity is not the point (where do you want to conduct it to?), it has to be emitted as blackbody radiation.
I underestimated the quality of dielectric mirrors: >99.999% for a narrow wavelength window according to Wikipedia without a specific source, so 99.9999% is realistic. That gives 1kW/m^2 of heating for our 1GW/m^2 sail, Assuming it is a perfect blackbody everywhere outside the laser range, and including ~1kW/m^2 solar power at ~1 AU, we get an equilibrium temperature of 370 K. Okay, certainly possible, assuming we use a laser to drive the spacecraft (and we have to adjust its frequency over some range to account for the Doppler effect).

 

[Dr Wu]

Again, thanks for all these extremely helpful and thought-provoking suggestions. Unfortunately, I cannot (as yet) make the Wolfram Alpha calculator work for me. The parameters keep reverting to their default values in ways I don't quite understand . . . although this is far from being the end of the matter!

Unfortunately too, given that my own work is a sequel to a previously published SF novel (by the inestimable Robert L Forward), the basic setting cannot be altered. My expedition has to cover a distance of some 2,000 AU and there's an end to it. Moreover, the spacecraft must be powered by antimatter. This is because a crisis occurs later in the story - a terrorist-inspired 'flashpoint' - involving human xenophobia and a large quantity of explosive material: hence the requirement for antimatter. Now I do want a big bang, a seriously big bang - one big enough if possible to be detected back on Earth twelve days later (?) Yet even I baulk at the idea of 604 tonnes of matter/antimatter making hay in the outer suburbs of the solar system. I have NO idea what the resulting gamma-ray burst would be; but if it's equal to a month's worth of solar radiation striking the Earth's surface, then clearly it must be an explosion of cataclysmic proportions - one that I imagine would be observed across several light years? Also, I don't want the ship's crew, plus other characters, reduced to radioactive waste, if I can possibly help it.

With all this in mind, I'm willing to engage in some strenuous hand-waving - anything to reduce the antimatter fuel to more manageable quantities. A voyage up to 20 months is certainly feasible, as is using super-lightweight nano-like composite materials to bring down the mass of the ship to (say) between 800 - 500 tonnes, including reactor, forward shield and fuel? The 9.8 m/s2 acceleration is problematic in that I do have Mars-based settlers among the ship's personnel. They wouldn't be able to take such a fierce acceleration for very long, I'm sure. Could I give them their marching orders, if push came to shove? Yes, but it would mean a serious rewrite of existing material. It's not a deal-breaker, though.

Hibernation is already integrated into the story, so that's not an issue. The spacecraft itself is based upon the one (reputedly) featured in the film 'Avatar' - or so I'm led to believe: motor in the front towing everything behind it like a goods train. I really do like the concept, although I gather from those who know more about these things that a tether-based configuration might present all kinds of manoeuvring problems, especially near gravity wells etc. . .

So the ingredients are these: a spacecraft so light it could take off in a stiff breeze; one moreover capable of covering 2,000 AU inside twenty months, and do so without bequeathing preposterous quantities of frozen antimatter fuel to the storyline. This fuel then is the main problem. A sudden thought. This antimatter fuel is intended for the return leg of the mission, but since the ship would be approaching Sol during the latter stages of the voyage, could the deceleration stage be achieved in part by a light sail of some kind, using it as a braking mechanism, in other words? If so, the only antimatter fuel needed - or at least the Lion's share of it - would be used to accelerate the ship essentially from rest at the start of the return leg of the voyage.

Does any of this make the remotest sense? And again many thanks.

Regards

 

[mfb]

Wait, you want the antimatter/matter fuel to explode at a distance of 2000 AU, but the crew in the spacecraft is supposed to survive?

The 9.8 m/s2 acceleration is problematic in that I do have Mars-based settlers among the ship's personnel.

There are good indications they could survive longer exposure to 1g as long as they don't have to walk around all the time. Experimental data is just based on humans on Earth and accelerations beyond 1g, of course: NASA study. If that is not sufficient: suspend them in water. That shouldn't be an issue.

500 tons with the slow acceleration? Then we are at ~80 tons antimatter using the theoretical 100% efficiency, or a few hundred tons with a more realistic value. That is equivalent to 1.4*10²² J or the energy of the sunlight hitting Earth in a day, which is also the total energy the sun emits in 40 microseconds.
In terms of visiblity: at a distance of 2000 AU, only a fraction of 10^-16 hits earth, equivalent to the solar radiation within a few picoseconds. Integrated over ~50ms in the eye (and assuming the explosion happens on a shorter timescale) it would be 10 orders of magnitude dimmer than the sun, or about the brightness of a bright star, but just as a very brief flash. Visible to the naked eye, but you have to look in the right direction at night or you will miss it.

It is certainly an event telescopes can detect from light years away if they look in the right direction, but the explosion will appear dimmer than the sun - and very short.

Divide all explosion numbers by 2 because the ship will have used half its antimatter storage when it is at a distance of 2000 AU and I forgot to include that.
Divide all numbers by 2 again if you want to travel for 20 months.
Divide all numbers by 2 again if you use the 1g acceleration scheme.
Still visible, just a bit dimmer.

Braking and accelerating are the same thing in space. You can include the solar sail with its exawatt laser beam, it might reduce the amount of antimatter a bit more (at most a factor of 2 if you just need it to reach the Oort cloud and accelerate back again).

 

[mheslep]

Thermal conductivity is not the point (where do you want to conduct it to?), it has to be emitted as blackbody radiation.

Yes I know BB is only way to reject heat off the spacecraft ; the point was to conduct the heat load off the necessarily thin and possibly fragile sail material to a structure designed for the purpose of radiating heat, in particular a structure i) facing space at a couple degree kelvin and not the sun, and ii) thermally rugged.

I underestimated the quality of dielectric mirrors: >99.999% for a narrow wavelength window according to Wikipedia without a specific source, so 99.9999% is realistic. That gives 1kW/m^2 of heating for our 1GW/m^2 sail, Assuming it is a perfect blackbody everywhere outside the laser range, and including ~1kW/m^2 solar power at ~1 AU, we get an equilibrium temperature of 370 K. Okay, certainly possible, assuming we use a laser to drive the spacecraft (and we have to adjust its frequency over some range to account for the Doppler effect).

Nice.

 

[mfb]

A square kilometer sail looks like a very good radiator. You don't want to have another even larger sail hanging around, I guess.

 

[Dr Wu]

Yes, about the antimatter-fuel explosion: I should have mentioned that the ship's crew - indeed, the ship itself, apart from the return drive section, including the fuel itself - are well away from the source of the explosion (20 million km?) when it occurs. My apologies. Aside from my own writing concerns, but regarding the lightness of materials needed for any manned (or even unmanned) interstellar missions that may occur in the distant future, I'm struck by the lightweight construction of the Solar Impulse aeroplane, currently flying around the world. It looks shockingly fragile, little better it seems to me than a solar-powered kite, but one with a larger wingspan than a Boeing 747 and massing no more than 2.3 tonnes. Of course, there are limits to the parallels Solar Impulse and its kin offer for extended space flight. Still, it's an interesting concept and one that may present new insights into the development of lightweight materials suitable for astronautics. The other thought that springs to mind about the possibility of humankind spreading beyond the heliopause is an observation Carl Sagan made thirty-five years ago. His contention, as I recall, was that whatever form spacecraft may take in the future, they will be as different to the ones in use today as modern aircraft are to Leonardo de Vinci's helicopter. Clearly, all the energies harvested even from antimatter will be hopelessly inadequate when it comes to envisioning a manned mission to the nearer stars. I guess challenges of this order will require for their success new discoveries in physics, unlocking the hidden potential that may or not be lurking in so-called 'vacuum energy' or dark energy - or is that the same thing?

I take onboard the encouraging remarks about my Mars-based crew members being able to tolerate 1g conditions. That at least is one rewrite I won't have to do now :)

 

[mfb]

Okay, 20 months, 1g acceleration scheme (note that .5 g for twice the time is also possible, just takes about one or two weeks longer then, or a tiny bit more fuel for the same time), so the explosion energy is down to ~1.8*10²¹ J.
At a distance of 20 million km, that is about 1J/m². Completely unproblematic, some shielding against gamma rays could be interesting but it is not required.

 

[Dr Wu]

In consideration of everything, I’ve roughed out the following scheme:

@ 1g acceleration:

V1 = 0

V2 = 6,250 km/s

t = 7.5 days (acceleration period)

d = 13.3 AU x 2 = 26.6 AU (includes deceleration perod).

(NB: the deceleration period is also 7.5 days @ 1g: total 15 days)

2,120 AU – 26.6 AU = 2,093.4 AU (coasting period)

t = 580 days (coasting period) + 15 days = 19.8 months

Dry mass of spacecraft = 500 tonnes.

Fuel (matter/antimatter) = 160 tonnes*

Total mass: 560 Tonnes + an unknown quantity of matter/antimatter fuel for the return leg of the voyage.Just one other thought: since the mission’s (orbital) destination is a ‘dwarf’ neutron star (mass 9.945e29kg), I wonder if the spacecraft could use the star to assist in both its deceleration and acceleration, this by means of a mag-sail? The neutron star’s magnetic field is almost a 100 million Tesla, and as such it would seem almost criminal not to make use of it. *This is at 100% efficiency, therefore the total fuel mass would need to be somewhat greater than this figure. The total fuel mass, however, would depend on whether the spacecraft can harness the neutron star's magnetic energies, as described above.

Regards

 

[Dr Wu]

A correction: total mass of the spaceship should read: 660 tonnes, not 560 tonnes as described above.

 

[mfb]

There is an "edit" button to change your posts.

The fuel requirement seems to be a bit on the high side for 100% efficiency.

The field of neutron stars is strong very close to the neutron star only - something like tens of thousands of kilometers. You have to be very slow to use this magnetic field for a longer time, and then there is not much speed left you could get rid of. Let's say 1 g again (ignoring the question how to achieve that), then you can approach it with ~20km/s, or .3% of your cruise speed. Probably not worth the effort.

 

[Dr Wu]

Yes, I see. Finally. . . (I'm beginning to sound like Lt Columbo), mheslep suggested the use of a lightsail, or a fixed particle-beam accelerator as a possible workaround to the Tsiolkovsky rocket equation. Here, I wonder if such a solar-powered energy source could be used during the outward part of the voyage, and have the ship's onboard matter/antimatter fusion drive applied as a braking mechanism. Or would this result in painfully slow acceleration rates, even allowing for whatever energies that could be obtained from the Sun itself via an orbiting beamer array? I realize that the ISV Venture Star in 'Avatar' uses the same hybrid drive system. I also note in passing that details about the ship's tonnage are conspicuous by their absence in the stats section of the film's website, although it's clearly no flyweight. Even so, an acceleration of 1.5g is mighty impressive. Do the numbers add up, though?

 

[mfb]

The required power values are in this thread already. And the sail does not look completely impossible. It requires enormous amounts of power, but so does the antimatter drive. Actually, the solar sail is more efficient if you manage to confine your beam to the sail (which will be really tricky over large distances).

 

[Dr Wu]

Many thanks, mfb. I'll be sure to heed your latest advice about the solar sail, plus your warning concerning the need to keep the beam trained on the sail over large distances. In the meantime, I shall now give you some peace, certainly for the present. I am extremely grateful for all the help I've received from your good self (and your colleagues) on this thread, and although I'm acutely aware of my scientific limitations, as well as being a 'new face' to this forum, I shall do my best to contribute whenever the opportunity avails.

Regards

 

[mheslep]

YHere, I wonder if such a solar-powered energy source could be used during the outward part of the voyage

Man-made, coherent beamed energy, not natural solar. For a square-km sized sail, 1.5g, and 5000t ship, the sail power density requirement is on the order of a GW/square-meter. So, even at 1 AU, the sail has to be 10⁹ times larger using just solar flux, growing larger as the ship moves out.

 

[Ryan_m_b]

A laser, firing continually at a small tatget over hundreds of light years, is more believable than the production and storage of hundreds of tonnes of antimatter. Especially given the social consequences of such a world.

 

[Dr Wu]

Ah, yes, a "man-made, coherent beamed energy" propulsion system is actually what I meant, although I failed to make this clear in my previous post. Incidentally, the spacecraft is now much reduced in mass and I was thinking of an acceleration range between 1.0 and 0.5g, rather than 1.5g (as in 'Avatar').

On a related point: would it be possible to send ship-to-ship radio/laser messages across a distance of 2,000 AU? If so, would there be enough bandwidth available to include video? Or is this too much of a stretch?

 

[mfb]

Voyager 1 sends ~1kbit/s over a distance of 130 AU with 260 W of power. If you want 1 MBit over 2000 AU with the same receiver (70m radio telescopes), you would need 200,000 times this power, or ~50 MW. You can save a lot if you switch to laser communication. Compared to the power requirement of the antimatter drive, this is probably no issue.
The other direction is even easier. If you can use exawatt lasers for propulsion, a gigawatt laser for data transmission should be trivial. Alternatively, modify the power of the exawatt laser.

 

[mheslep]

you would need 200,000 times this power

Dish size on Wu's spacecraft is also a factor in that multiple. Though as you point out, if the craft is powered by laser it can certainly communicate far more efficiently. Without googling, I wonder if NASA is considering such for future deep space spacecraft . Maybe the improvements in solid state laser power make this a possibility, or not.

 

[mfb]

The factor 200,000 times is for spacecraft -> inner solar system only (and you can reduce it with a larger dish for the spacecraft ). For the other direction, you probably want a smaller dish and a larger sender power - if you increase power by a factor of 1000, you can reduce the dish size by a factor of 1000, reducing the 70m dish to a 2m dish (ignoring issues with angular resolution here).
And this is for radio waves. I did not find numbers (apart from the data transmission rate) for NASA's test, but apparently it gives better data rates with lower power.