TOS Rom BOP as a pure fusion rocket
Before I begin, I had to transfer the previous gif animation of the BOP and the Miranda
here.
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This conversation made me reconsider the difference in energy intake between Warp Drive and Newtonian Drive, aka Rocket Propulsion, aka Impulse. (This latter is an assumption I adhere to. See my previous post on this thread concerning my assumptions.)
Calculating the energy requirements of a Star Trek warp drive needs quite a few assumptions. And I will get into this in a later post, when I feel more comfortable with my calculations. But we *have* the equations to predict how a fusion rocket will act, even under the influence of special relativity, and it requires fewer assumptions.
To understand what I'm talking about below, you need to look at "
BOP-Rocket_Tables.txt". It has a short introduction to why rockets have the specific limitation they do. But more importantly, it itemizes the results of a series of calculations I did to get a grasp the limitations of a BOP fusion rocket. To view the tables in the file you'll need a text editor that allows you to turn off word-wrap and that has a monospaced font. Your browser might display it well in a new tab. My firefox does, but who knows... Please don't attack my opinions without looking through and understanding the tables in this text file. Below are my speculations from those calculations.
With some google searchers and some approximations, I have learned that military sea vessels have densities on the order of 100 kg/KL --some are much more, some are a little less, but this is a good average. A compared to jumbo jets which are around 50 kg/kL --again, some more, some less. I therefore speculate the density of a Rom Bop is between 50 kg/kL and 100 kg/kL. Let's say 75 kg/kL. [Scenario D in the "empty masses of a BOP" table.] (Remember that a kilo-liter is the same as a cubic meter. I use "kL" because it's an easier abbreviation than m^3.)
Given the (R) ratio table, a BOP rocket will likely use the nacelles, wings and the hull's bottom curvature for fuel storage, giving a fuel-to-total volume-ratio of about 1/3. [Scenario 4 in the fuel volume table.] (It is perfectly possible a "real" BOP-rocket would dedicate more of its volume to fuel. I did not calculate for this, however.)
So, cross-referencing scenario [D4] with the d(V) table and the best fuel-density/fusion-cycle combinations, from better to worse, appear to be:
1) Deuterated Propane / (D->Ni56) > 13%c
2) Hydrated Propane / (p->Ni56) > 12%c
3) Liquid Deuterium / (pCatD) > 4.6%c
4) Liquid Deuterium / (CatDD) > 3.5%c
5) Liquid Deuterium+Tritium / (DT) > 3.5%c
5) Liquid Hydrogen / ppI > 2.7%c
6) Liquid Helium / (He3) < 2.7%c
7) Liquid Deuterium / (DD) > 1.8%c
However, in order of difficulty, hardest to easiest, the fusion cycles can be listed as follows:
1) (p->Ni56)
2) (D->Ni56)
3) (ppI)
4) (pCatD)
5) (CatDD)
6) (He3)
7) (DD)
8) (DT)
Thus the reaction (ppI) doesn't have what it takes: if you can do (ppI), you'd probably be able to do (pCatD) and you wouldn't bother. (At least not for a rocket. I've yet to find out what Warp has to say.) I should also mention that (DT) fusion, by far the easiest of the fusion cycles, puts most of its released energy into the momentum of a chargeless neutron, which is difficult to get energy from if all you have the electric fields which a burgeoning technology is likely to be limited to.
Thus, (IMHO) the likely evolution of fusion rockets in fuel and cycles is:
1st) L(D)/(DD)
2nd) L(He3)/(He3)
3rd) L(D)/(CatDD)
4th) L(D)/(pCatD)
5th) L(D)/(D->Ni56)
6th) (C3D8)/(D->Ni56)
For my money, the (pCatD) reaction is my bet for a TOS Rom BOP rocket. If you factor in efficiencies less than 100% as well as some energy being syphoned off for other things, you get a total d(V) between 2 and 3%c, which is pretty damned good. But it's not the best of the best, giving the Romulans further fusion fuel combinations to research.
If she were powered by deuterized propane, however, she could have a total d(V) of around 10%c, even factoring in inefficiencies and other power drains. But I see this as a final step before the introduction of artificial quantum singularities.
It should be noted that the (D->Ni56) cycle is the same cycle as the (p->Ni56) cycle save the first step, which turns protons into deuterium. (The multi-staged fusion cycles are not expounded upon in the tables. It seemed an unnecessary step, more likely to bore than edify.) In the process of turning deuterium into nickel, Carbon must be created and burned. Thus the carbon in the hydrocarbon fuels are also fused into Ni56 in these fuel cycles. This means not only that all the fuel is burned but that, by creating carbon from hydrogen, it is possible to create the storage hydrocarbon through nuclear and chemical processes. This hydrogen could be from the interstellar medium.
Also note that though the total energy output of carbon burning is much less than hydrogen burning, carbon helps to make the fuel more dense, giving it higher energy densities than hydrogen alone --be it protium or deuterium. There are, of course, heavier hydrocarbons than propane and a cursory glance at the d(V) table should demonstrate that there is an eigenvalue that balances higher energy-densities of large hydrocarbons with their lower d(M). Indeed, I know room temperature RP-1, with an average chemical component of about (C12H24), has already crossed this balance compared to 100K propane. None the less, I really can't be bolloxed to find the exact balance point, as finding it would entail calculating densities by first principals instead of looking them up in text books. And I'm just too lazy for this.
Another thing I have not gone to the trouble of calculating is the outcome of storing one's hydrogen fuel in "ultra dense" form. The announcement in 2009 and 2010 of discovering hydrogen --both light and heavy, aka protium and deuterium-- in its "Rydburg matter" forms indentured quite a bit of speculation about the ability to store hydrogen at densities on the order 100e6 kg/kL. This would drastically increase the calculated abilities and therefore drastically change any conclusions made.
However, I did not calculate for ultra dense hydrogen for several reasons. First, while I was doing the calcs I didn't think of it. Second, after I thought of it, I realized I'd have to do half again as much work as I'd already done to include it in the tables. Thirdly, we know neither Ent-D nor Voyager used ultra-dense Rydburg states to store their deuterium. They used liquid deuterium. And though there are no information about how the Romulans store their fuel during TOS, that the Federation doesn't use this method during TNG despite it's obvious advantages indicates it's not easy to make it work. So, I'm using this third reason as an excuse not to have do the work to include it in the tables.
In any case, I'd guess a TOS Rom BOP Rocket would use liquid deuterium as fuel, burn the fuel in the (pCatD) fusion cycle and have a d(V) of on the order of 2%c. Certainly other possibilities exist, this is just what I would choose from a story-telling perspective. However, her d(V) is not likely to be more than 20%c. (Calculating for 100% efficiency, using deuterated propane as fuel, 1100 tonnes as an empty weight and everything but the "Fin" and "Bridge" filled with fuel, the outcome was 22.8%c. However, this calculation left no room for an engines in the main hull, just tankage and is therefore unlikely in the extreme.)
My final statement on this subject is that I find it unlikely the TOS Rom BOP was a pure Fusion rocket. She's just too slow compared to a warp vessel; just too limited. She might stil be STL, meaning that "impulse" is not fusion rocketry but a kind of reactionless STL drive. But she's probably not a pure fusion rocket.
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I hope to post similar calculations I've done concerning a fusion powered warp BOP soon.
(In fact, I have a long boring speech I give to all those I tutor in math about it being a language. No one ever listens.) .... 
