Recently I did the math to figure out how large a polywell fusion reactor would have to be to support the power requirements of a warp bubble, assuming the power requirements are always equal to those of the Ent-D. This is, of course, an invalid assumption but the Ent-D energy graph is all I have go on, so I'm sticking to this assumption. Turns out a 14 gigawatt polywell fusion reactor would have a magnetic grid on the order of three meters in diameter. Around that would then go the power grid and containment shell, making the whole thing on the order of 6 meters in diameter. This is larger than would fit in Cochrane's Pheonix. Indeed, all the fusion reactors I can calculate for simply would not scale to fit the physical dimensions of Pheonix while still putting out 14GW of power, which is the power requirements to overcome the Warp 1 hump for Ent-D. So that got me thinking. First off, there's more than enough power in the 3-6kg of plutonium found in a modern nuclear weapon to supply one to two hours of continuous 14GW, if all of it were fissioned, and that's at about 25% efficiency. (Six kilograms is enough, by itself, for a warhead but I don't know how much less can be gotten away with by using fusion tampers and U238 reflectors, etc. So I don't know how much plutonium Cochrane would have found in the ICBM. If it's a MERV --which is likely-- there shouldn't be a problem.) However, actually releasing the energy locked up in the plutonium is a major problem. Current methods release it all at once, and that's no good for obvious reasons. (Ka-BOOM!!) So, I did the math and you need about 1/5 gram of Pu239 to burn per second to get 14GW. This requires approximately 2^67 plutonium atoms to fission and, thus, approximately 2^67 neutrons to make them fission. Now, plutonium averages more than two neutrons released per fission --about 2.5, depending on circumstances. Assuming, on average, 0.5 neutrons per reaction are lost and 2 neutrons are absorbed to create more fissions, it would take (SURPRISE!!) 2^67 generations of neutron doubling to burn the needed plutonium. In case you were wondering, 2^67 is a rather large number of atoms and yet it's nowhere near enough for critical mass. In fact, it's not even a mol of atoms, 2^79. But there's a trick that can, theoretically, be done. If you hit a plutonium nucleus with an antiproton, the plutonium explodes in a shower of small fragments, including neutrons. As it turns out, you can probably produce from 2^4 (16) to 2^5 (32) neutrons in one interaction. (Plutonium239 has 93 protons and 145 neutrons. One proton will be destroyed. If the remaining protons are separate exactly into two nuclei, there will be two new palladium atoms of 46 protons each. The heaviest stable palladium atom has 64 neutrons, leaving 17 from the original plutonium that are not welcome in either of the new atoms. However, the amount of energy released by a proton-antiproton event should be enough to disintegrate the nucleus to small chunks, potentially releasing 52 neutrons.) For ease of calculation, let's assume the smaller number (2^4 = 16) is the average number of neutrons released per AM/Pu239 reaction. If you can get 23 generations of neutron duplication within the plutonium after the initial antimatter barrage, then you need 2^40 antiprotons to get the 2^67 total fissions you need. That many antiprotons is about 1.8 trillionths of a gram (1.8 picograms). Ok. Let's add some inefficiencies. Let's say 90% of the neutrons from the antiproton barrage are lost, 60% of the plutonium doesn't fission and 60% of the energy is lost before making it to the warp coils. That would mean the Pheonix would use up a gram of plutonium and a tenth a nanogram of antiprotons would be used up every second to excite the coils with 14GW. Again, 1 gram of Plutonium and 0.1 nanogram of antiprotons every second... In the movie, the Phoenix's engines are active for less than a minute. The exact amount of time depends on how you count the seconds between cuts. But, if we put an absolute maximum of 60 seconds travel time out and another 60 seconds back, and further assume 14GW is needed throughout this time, that will give an absolute maximum to the amount of plutonium and antimatter needed for this scenario: 120 grams Pu and 12 nanograms of antiprotons. Now, we can assume there's at least one kilogram of usable plutonium in the missile Phoenix was made from. But what about the antiprotons? Well, that's a problem. It's estimated there are about 160 nanograms of antiprotons in the Van Allen belt. Could collecting them be so efficient that Cochrane could get 7.5% of them? I suppose it's possible. But getting it down from orbit could be difficult depending on the condition of space infrastructure at the time. It seems likely it was pretty bad since he used an ICBM to launch his prototype. Still, maybe before their war with the Eastern Coalition, the United States had a small supply of antiprotons and Cochrane had access to what was left over... I don't know. [...Hrm... There is the distinct possibility that some nuclear weapons of the mid 21st century are fusion/antimatter hybrids, where chemically imploded fusion fuel converges onto a central container of antimatter. The resulting M/AM explosion would strike the implosion shockwave so hard that the fusion fuel would fuse completely, releasing several orders of magnitude more energy than the antimatter/matter explosion by itself. If these weapons are extent throughout the post-apocalyptic US, there might be enough in these weapons to use for the Pheonix. Or, maybe not. It depends on... all kinds of things actually... Anyway, continuing...] However, there's another problem: the design of the reactor. How do you get a gram of Plutonium and a tenth gram of antiprotons to interact correctly every time? Here's what I'm thinking: free nucleon lasers.... Let me explain. Free electron lasers take electrons, accelerate them in a linear accelerator and then make them go past a set of magnets whose poles alternate. The electrons wiggle and emit lased light in the process. But here's the important part: a stream of electrons, after being oscillated like that, stop being a stream and conglomerate into chunks, the size and separation depends on the frequency and amplitude of the oscillations. You can do the same thing with nucleons. The laser light that is emitted is in the x-ray range but as long as the path of the x-rays is away from the cockpit, you can engineer around them and there shouldn't be a problem. So, you have two nucleon accelerators, one for Pu239 and one for antiprotons. The soul reason for the tracks is to conglomerate and focus the nucleons into small clumps of, say, 1 milligram for Pu and 1 picogram for the antiprotons. Then you split the two streams into four and merge a stream set of Pu/AM in each nacelle, next to their warp coils at a frequency of 1 kilohertz and that will give 14GW of power to the warp coils --7GW per nacelle. You could even have a generator that produces electrical power that uses a pair of these clumps at 10 hertz, making 140 megawatts of power for the ship's other systems. Of course, if you could increase the efficiencies even a little bit, that would mean much less antimatter/plutonium would be used. With 100% efficiency, you would only need 0.2g of plutonium to fission per second for the 14GW we need. If Cochrane could get 30 generations of neutron doubling after the antimatter bombardment, then he'd only need 15 femtograms (15E-15) of antimatter (2^33 antiprotons) per second --while still assuming 16 neutrons per Pu/AM reaction-- to get the 2^67 fissions we're looking for. Again, this is at 100% efficiency. Furthermore, the assumption of 14GW throughout the flight is ludicrous. Far more likely, usage would peak at 14GW, and even that's an unlikely worst-case scenario based on Ent-D power usage --warp fields should scale in power usage depending on the size of the vessel and the materials of the warp coils. Still, I think it should be possible to find a way to strongly confine clumps of plutonium nuclei and smack them with clumps of antiprotons, producing both the power and the particles needed to charge Phoenix's warp coils. Now, I see yet another problem with this design. I've got little explosions going off inside the nacelles at 14 mega joules each. That's the equivalent of 3.3 kg of tnt, each. A second's worth (500 pulses) of these pulses, together, is equivalent to 1.6 tonnes of tnt in each necelle. Admittedly, that's spread out over their length. Still, that's a lot of force to be contained! Thoughts? What did I get wrong?
^ (1) The overwhelming majority of us who frequent TrekTech aren't physicists, and couldn't begin to tell you what you got wrong in your meticulous calculations. (2) This doesn't inhibit our enjoyment of the show or our fascination of the tech. (3) You are a skilled technical writer, though your material is a tad dry and needs more cowbell. (4) You spent a lot of time making unnecessary calculations, when EVeryone knows the way to make warp drive work is to point a finger and speak the word, "Engage"...
Dear zDarby, Will you please write a snappy synopsis that motivates me to actually read all that stuff you wrote in the OP? Thanks! --Alex
Best of luck in your aspirations to become a Star Trek technical adviser. However, you misspelled Phoenix at least twice.
Interesting read. My only thought is that Phoenix's warp field is considerably smaller than the 1701D's, plus it's much less mass (which I'd think would have some bearing on the equation), so I don't think you'd need anywhere near 14GW - and I'd bet you could get away with a lot less fuel than you've calculated above.
--Melakon, I'm not surprised about my spelling. I have a hard time spelling "spit" without getting a "p" or "h" in it. I'm lucky there are such things as spell checkers. Without it, that dissertation would have been unreadable. And thank you. --Albertese, I think I found a way to clear up the problem of the movie implying Pheonix used antimatter and the book saying it used plutonium. The answer is: it used both! Antiprotons were used to induce fission in plutonium chunks much smaller than critical mass. With only 120 grams of plutonium and 12 nanograms of antimatter, Pheonix could have sustained the warp 1 hump for 2 minutes and probably much more! And that's with all kinds of inefficiencies assumed. --SicOne, 1) I personally know very few who are up to my level of physics knowledge. And those that I do know are so far ahead of me they find talking with me about it tedious because I'm so damned ignorant. Basically, I've got nowhere to go but the internet to find people to talk to about the things I love: Trek and imagineering. There are a few here who have, in the past, been willing to lock slide rules with me and imagine, and I just LOVE that! So, when I have time, I come here. This place is GREAT! 2) Thank you. It's nice to be appreciated. 3) You're absolutely right! More cowbell, Mr. Ferrell! 4) I'm a tech Trekkie. Always have been. I don't care which captain was better. Blasphemous, I know. But was Geordi or Scotty the better engineer? Probably Scotty. But Geordi had the cooler toys! And Data was THE BOMB! (I probably just dated myself.) So, the "ENGAGE"-ing part is figuring out how treknology works. The more nerdy, the better. --drt, Absolutely! But it's the only warp 1 power point I have to use. I don't even have a rule-of-thumb scaling factor. I mean, does power increase it by warp bubble volume? By warp bubble area? By mass, subspace "hydrodynamics" (as it were) or just what? I don't know. (I'd love to hear some suggestions!) So I used the data point I had. And I think I've shown that even if it were 14GW, which I highly doubt, it could have been done this way.
I always had trouble remembering how to spell Phoenix too, until I moved out here over 20 years ago. One bank I was with out here sent me 200 checks with the city misspelled. That's bad when even the business can't get it right.
That is a damned fine question, Ithekro. One that I did not consider. Naturally, I don't know the answer. But, off the top of my head, i think we can eliminate a few possibilities. Naturally, it would have had to have happened sometime before 2063. (Which is only 69 years from now, by the way.) It does seem unlikely that the system would be a prototype specifically built for Phoenix. It's possible, but unlikely... However, if it were, there would be a demonstration set-up somewhere at Cochrane's compound. Again, this is possible but it doesn't seem likely. Far more likely is that it was a system used by the US military sometime during the war with the Eastern Coalition. This would mean, what? The 2050s? For what purpose, I'm not sure. It's use for energy production is of limited value: loads of energy for a short time. (Antiprotons are rare and, thus, expensive.) Do you have any suggestions?
Waitaminute! Are you writing to us from the year 1994?!?!? Don't worry, Deep Space Nine will get a lot better, but most people will think Voyager is a disappointment. Eventually another show called Enterprise will role around that pretty much kills the franchise. For the rest of us in 2014, 2063 is just 49 years off... --Alex
I'd just like to say that I would prefer a nacelle-based spacecraft like the Phoenix to the weird donut-based IXS Enterprise that NASA keeps speculating about. But whatever design works, would be great. I just hope that in the next 48 years we start to straighten out all the problems we're having here on Earth. We're just not ready yet to explore the Cosmos if we can't treat eat other in a civilized fashion. That's just me.
Well, when the Zombie apocalypse rolls around, we definitely won't eat each other in a civilized fashion.
--Albertese HA! And I'm asking you to believe I did my math right. Obviously a type-O. Although I don't know how I got 4 mixed up with 6. I was probably typing in a corner, unable to see the keyboard. Can't touch type numbers. --Wingsley I've been thinking about that. It seems to me a nacelle can be considered a long ring, or a set of rings. A large ring is probably made of several segments and a nacelle's segments are small rings. It's made me wonder why several rings in a line is a better design that a large segmented ring. The Vulcans seem to be the odd man out in preferring a single large ring and I've often wondered why. I've sometimes speculated that a single ring is more energy efficient but difficult to plumb with plasma; or perhaps more difficult to time. I like the latter better but find myself needing to invent reasons for it to be true: if we can time events in the nanosecond regime here and now, it would seem it should be trivial for the Vulcans. But, then, it's said it took the Vulcans a century or more to get into the Warp 2 regime. (Not sure where I heard that, actually, so take it with a grain of salt.)
Perhaps the rings are efficient, but are not combat capable. Or the warp coils that go around the ship are very costly. For the anime Space Battleship Yamato, during their third series in 1980, they had a interstellar craft that settled a small family on a planet around Barnard's Star five years before the start of the episode. In that universe, Earth gets its FTL drives from aliens in 2199. The episode was seemingly set in early 2205, but reconned to early 2203 by a later movie. The problem with both is that Earth doesn't seem to have the ability to made more than the first warp ship (Yamato) before the end of 2200, and those are mostly combat ships to defend Earth against possible invasion (they had been fighting a losing war for eight years without FLT drives prior to 2199). However, the ship that was used to get to Barnard's Star has a curious feature (which is entirely by accident as this was drawn in 1980). The ship has a ring around its aft drive section, as the ship is overall shaped sort of like an American football. When the remake series, Space Battleship Yamato 2199, came out the Earth still gets FTL drives from aliens from 2198 - 2199 to complete the first FLT warship (Yamato) so it can made the distance to the Large Magellenic Cloud and back in less than one Earth year (168,000 light years). The Earth fleet we see prior to this uses sublight engines. However, the football shaped ship with a ring gave me an idea if the remake series continues on to this same point again. What if the alien FTL engine was not the first Earth FTL drive. What if the warp drive NASA is working on did work sometime between now and the 2190s? It would be very limited. 10 times the speed of light is the current limit proposed. That would definately not be enough to get 168,000 light year and back in a year. Nor would it be all that useful against an alien race that has superior weaponry and FTL drives that can cover said distances in a year's time. A ring drive on Earth warships would likely be vulnerable to enemy positron beams (the weapons listed for the show). Thus the tactical advantage would be lost easily compared more heavily armored sublight ships (that still don't last very long in combat). But a ring ship could be sent in an escape attempt by a family to get away from a dying Earth. Their only trouble would be evading the enemy ships and sensors at faster than light speed and hope their FTL drives can't follow you easily (their superior drives act more like jump/wormhole drives that "instantly" jump the ship many light years in less than a minute rather than the Star Trek warp drives that cross space during the entire flight). 10 times the speed of light would get a warp ship to Barnard's Star (six light years away) in less than a year. There likely isn't any planets there, but back in 1980 it was suspected there were. The nearest potental habitable planet system would still be less than three years away at those speeds.
I will have to take the time to check your calculations and assumptions. Why assume Cochrane's group can get that much Pu versus using a fusion reactor? Inertial confinement fusion might be smaller in volume. Maybe they had access to antimatter if the group started before WW 3. What volume hoes into radiation shielding for any energy generation method? In all cases the energy requirements should be far lower than the E-D even assuming less efficiency.
--Ithekro Hrm... Ok. A ring is a bigger target but it would seem a nacelle would be easier to damage to the point of failure. Destroy the port strut, for example, and your half your warp coils are gone. But you could plumb a ring so that any part of the ring that still physically connected to the ship gets power. So I think the vulnerability point is arguable. A ring is probably way more expensive to build, yes. On the other hand, if it's more efficient, it will be less expensive to run. The question is, where is the right balance? The Vulcans seem to have abandoned the annular ring and gone for a more box-like ring, as seen in TNG Reunion #2. And if Daniel's future database is to be believed (from Enterprise) the Vulcans decide in the late 22nd century that three rings are better than one, at least for that one ship. This seems to imply some major advantage to the ring that's worth the expense. Your Space Battleship Yomato observations are cool. I want to encourage you to write more because I'd like to read more. I like where you're going with your retcon. I think you might be on to some interesting insights. Especially since some early NASA FTL pics include a ship similar to what you describe: an american football in the center of a ring. However, I humbly request that you publish further observations on Battleship Yamato elsewhere as it's tremendously off topic. But please do post a link here so that I (and others) can find it and read it. It's cool! --Ronald Held Yes! Please check my calculations! That would be great! Thank you! I wrote down my assumptions so that they would be challenged and a debate might break out. I'd especially appreciate you finding any assumptions I took for granted. (...Well, you know, other than "Star Trek has some basis in reality." I know it it doesn't, other than how it changes opinions in the real world. But without that assumption, what's there to talk about?) There are three basic reasons I went to fission instead of fusion. The first I stated already: The few fusion proposals I have any understanding of wont work. This includes: Polywell: Even with superconductor materials that superconduct at +500 Celsius and below (one can hope!) and using the inner hull as the outer casing, I don't see how it would be possible to shrink the mag-grid small enough that sparking wouldn't occur between the outer casing and the mag-grid. (The outer casing must be positively charged and the mag-grid, negatively charged, with tens to hundreds of kilovolts of potential between them. The amount of gas needed to be in the chamber for 14 GW would insure a discharge that would release containment and probably destroy the machine...As you can tell, I've thought about this one a lot.) Focus Fusion: These don't like to scale to power outputs larger than one megawatt. Out of the question. Magnetic Confinement, Inertial Ignition (General Fusion): This reactor doesn't like to scale to anything smaller than the size of a barn. Magnetic Confinement, Magnetic Ignition (Helion): This one is a possibility. Right now, a reactor that would fit in Phoenix would only produce power in the tens of megawatts. But if the magnetic fields were stronger, the pulse frequency higher and the power per pulse increased, it might have a shot. But those are quite a few, very difficult 'ifs'. I'm not even sure it's physically possible. But still: maybe. Magnetic Confinement, Thermal Ignition (TOKAMAK, Spheromak, Stellerator, etc, etc): Again, these don't like to scale to anything smaller than a barn. I mean, the required heat sinks alone would be orders of magnitude larger than Phoenix. Inertial Confinement with particle accelerators: Getting one of these to the size of a barn would make the Manhattan Project look like napkin doodles. Let alone making it fit into Pheonix. (...Of course, all that really means is that the field of particle accelerators is ready for some genius to revolutionize it with a new paradigm.) Inertial Confinement with lasers (NIF): Laser power density is increasing exponentially. I don't know by how much. But the NIF building is three (american) football fields in area and 10 stories in height. That's approximately 160,000 kL. (One kilo-liter is the same as one cubic meter, and kL easier to read than "m^3".) According to admittedly imperfect computer models I have, the volume of the main hull of Phoenix (which excludes cockpit, nacelles and rocket cones) was no larger than 200 kL. That's means at least ten doublings of laser power density (watts per liter) in the next 50 years. Probably a great deal more: Post ww3 seems post apocalyptic, plus NIF can't seem to produce any excess power and I'm asking for gigawatts. Still, is it possible? Perhaps. I just don't buy it. In all these cases, I'm not concerning myself with radiation shielding at all, just the equipment needed to make the fusion happen. Of course, none of this excludes the possibility of a new kind of fusion device that would work handily. Which brings me to my second point: Fusion is hard. I am not able to mathematically model fusion reactions at all well. So I have a hard time thinking up new ways of making a fusion reactor. This is, of course, entirely my own lack. Still, that's one more reason I looked at fission. Mind you, I have, in fact, proposed more than one method to build a fusion powered Phoenix. I think I even posted a couple here, somewhere on Trek BBS's Tech Trek forum. However, other posters have noted that the First Contact novelization seems to imply Phoenix used plutonium. Where as the movie seems to imply it used antimatter. The above is a proposal to make both implications true. What's more, I think it could be done. As to Phoenix needing less than the Ent-D's 14GW, I agree. I just don't know how much less. Again, the Ent-D power usage is the only thing I have to go on. So that's what I used. I'd be very happy to entertain any proposal for a rule of thumb power usage scaling factor. I have my own thoughts, of course. But this post is already too long. Suggestions?
Thanks for thinking of me, but I have almost no clue as to how the movie Phoenix was supposed to work. I say almost, because I didn't have any involvement in the design or commentary on the tech/script. Nada. I can make an informed guess, however, based on the technology level in the time of Cochrane and company, and that would be to react deuterium and antideuterium within the nacelles, to make the hot, hot plasma that juices the nacelle coils that makes the warp field that moves the ship that lives in the house that Jack built. I can accept that back in the day, they hadn't built a dedicated reactor. I can also accept that this method worked up through the TOS Enterprise, since we never saw a dedicated core until TMP. Cochrane and his gang could have managed the mag containment for a small amount of antimatter, not enough to actually go anywhere like alpha Centauri, but to at least do that proof-of-concept flight. I would say that an actual expedition to a Cent would have involved a Phoenix II. Rick
Then what was that big "boiler-looking" thing in the middle of the NX-01's engine room? I took that to be a M/AM reactor (i.e. a warp core).