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Old March 30 2014, 12:17 AM   #6
zDarby
Lieutenant
 
Location: NorCal
Re: Warp-power-scaling data point

Sorry it's taken so long to respond. I wanted to prepare the table below and make it presentable. This took some time, especially since I made a mistake and had to recalculate everything from scratch. Also my personal life has been rather full of late: teenage daughter drama, 20yr-old daughter drama and girlfriend drama, all feeding of each other.

EmperorTiberius:
There might be tactical and other considerations that make having a large, ungainly ship undesirable. What kind of difference in volume when heavy hydrogen is stored in a chemical are we talking about?
I've only really studied three chemicals in any detail: heavy water (D2O), duterated methane (CD4) and deuterated propane (C3D8). The largest, most obvious difference is between liquid deuterium and deuterated propane: propane has twice the energy for the same volume but three times LESS energy for the same mass. This is because carbon makes up 2/3s the mass of deuterated propane and contributes nothing to the energy released in all the reactions except the final, most difficult reaction, where the fuel is completely converted to Nickel.

Robert: I will reply to your questions ASAP. As always, you ask interesting questions that require involved answers... Just the way I like 'em! But it takes time to compose those answers. Hopefully, they'll be worth the wait.

I have come to the opinion that the NX-01 used the deuterium-deuterium reaction (DD), 1701 used the Catalyzed-Deuterium reaction (CatDD), 1701-A,B used the Proton-Catalyzed-Deuterium reaction (pCatD), 1701-C,D converted deuterium to carbon (D->C). This is an opinion.

[The energy output of these reactions and their relationship with the fuel is detailed in the table below, though I've not detailed the reactions themselves. If you would like me to detail each reaction, I will. I think I have them all written out somewhere. And if not, figuring them out again shouldn't be hard.]

I also opine that the Romulans used the (DD) until near the end of the Earth-Romulan war, where they engineered (CatDD) reactors, which were still not powerful enough to compete with M/AM; and by the TOS era, they had either (pCatD) or (D->C) reactors powering their ships. By TMP I speculate they used the final reaction calculated here, which converts the whole of the fuel to Nickel. (I notate it as "(*->Ni)" because it is the only reaction that actually burns up *all* the fuel and not just the deuterium within the fuel, which makes this notation more universal in this instance.) I further speculate Romulans stored ultradense deuterium by TMP. Sometime in the TMY era, IMHO, they succeed in building and artificial quantum singularity. (I've got plenty of speculation on this one as well.)

Finally, I speculate that Romulans rely on the interstellar medium more intensely than the Federation does. Some of this speculation can be found in the Let's Talk About the Rom Bop thread linked earlier. I hope to expound on this idea sometime later.

In the mean time, I hope the following table is understandable. Ask about what is not understandable and I'll give a go at explaining.

Code:
______________________________________________________
|Fuel (Liquid)      |deuterium| water |methane|propane|
|(1 atm pressure)   |    D    | D2O*  | CD4   |C3D8   |
|-------------------|---------|-------|-------|-------|
|Density    (kg/kL) |  165.6  | 1107  | 542   | 925   |
|Temp         (K)   |   20    | 277   | 112   | 100   |
|-------------------|---------|-------|-------|-------|
|D by mass        % |  100%   |20.11% |40.17% | 30.92%|
|eff. D dens.(kg/kL)|  165.6  | 223   | 218   |  268  |
|===================|=========|=======|=======|=======|
|d(M) DD reacton    | 973 e-6 |196 e-6|390 e-6|300 e-6|
|Dens by mass (J/kg)|.874 e12 |.176e12|.35 e12|.27 e12|
|Dens by vol  (J/kL)|.144 e15 |.195e15|.19 e15|.249e15|
|-------------------|---------|-------|-------|-------|
|d(M) CatD reaction | 3.48e-3 |722 e-6|1.54e-3|1.19e-3|
|Dens by mass (J/kg)| 3.45e12 |.694e12|1.38e12|1.07e12|
|Dens by vol  (J/kL)| .571e15 |.768e15|.750e15|.249e15|
|-------------------|---------|-------|-------|-------|
|d(M) pCatD reaction| 6.34e-3 |1.27e-3|2.55e-3|1.96e-3|
|Dens by mass (J/kg)| 5.70e12 |1.14e12|2.29e12|1.76e12|
|Dens by vol  (J/kL)| .943e15 |1.26e15|1.24e15|1.63e15|
|-------------------|---------|-------|-------|-------|
|d(M) D->C reaction | 7.00e-3 |1.41e-3|2.81e-3|2.16e-3|
|Dens by mass (J/kg)| 6.29e12 |1.26e12|2.53e12|1.94e12|
|Dens by vol  (J/kL)| .144e15 |1.40e15|1.37e15|1.80e15|
|-------------------|---------|-------|-------|-------|
|d(M) *->Ni reaction| 8.03e-3 |1.61e-3|3.84e-3|3.2 e-3|
|Dens by mass (J/kg)| 7.22e12 |1.45e12|3.45e12|2.88e12|
|Dens by vol  (J/kL)| 1.19e15 |1.60e15|1.87e15|2.66e15|
|=====================================================|
|EntD 62,500 kL (kg)| 10.3e6  |69.2e6 |33.9e6 |57.8e6 |
|-------------------|---------|-------|-------|-------|
|fuse E tot DD   (J)|0.905e21 |1.22e21|1.19e21|1.56e21|
|fuse E tot CatD (J)|3.57 e21 |2.29e21|4.69e21|6.18e21|
|fuse E tot pCatD(J)|5.90 e21 |7.90e21|7.76e21|10.1e21|
|fuse E tot D->C (J)|6.51 e21 |8.77e21|8.55e21|11.2e21|
|fuse E tot *->Ni(J)|7.46 e21 |10.0e21|11.7e21|16.6e21|
|===================|=========|=======|=======|=======|
|(wet:dry)mass  R **|1.00208  |1.0141 |1.00688|1.0118 |
|-------------------|---------|-------|-------|-------|
|Delta V  DD    (%c)|0.00916% |0.027 %|0.0191%|0.0287%|
|Delta V  CatD  (%c)|0.0173 % |0.0532%|0.038 %|0.0572%|
|Delta V  pCatD (%c)|0.0234 % |0.0706%|0.049 %|0.0734%|
|Delta V  D->C  (%c)|0.0245 % |0.0743%|0.0514%|0.0772%|
|Delta V  *->Ni (%c)|0.0264 % |0.0795%|0.0601%|0.094 %|
|-------------------|---------|-------|-------|-------|
|Ve/c DD        (%c)|    4.41%|  1.93%|  2.79%|  2.45%|
|Ve/c CatD      (%c)|    8.35%|  3.80%|  5.55%|  4.88%|
|Ve/c pCatD     (%c)|   11.3 %|  5.04%|  7.15%|  6.26%|
|Ve/c D->C      (%c)|   11.8 %|  5.31%|  7.50%|  6.58%|
|Ve/c *->Ni     (%c)|   12.7 %|  5.68%|  8.77%|  8.01%|
-------------------------------------------------------
Notes:
"d(M)" = amount of mass changed to energy in reaction, normalized.
"R" = rocket mass ratio: fully dry mass divided by fully fueled mass.
"Delta_V" = total possible change in momentum if used as rocket.
"Ve/c" = exhaust velocity if used as rocket reaction.

*Calculations for heavy water do not include burning of the oxygen. This is an oversight for time-saving reasons. (IE, I'm lazy.) This only effects the (*->Ni) reaction calculations. However, the effect is probably large and so this set numbers should not be taken very seriously.
**The assumed wet mass of Enterprise D is 4.96e9 kg. This comes from the TNG:TM. The numbers are similar but smaller if this is the assumed dry mass.

Hope that makes sense.
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