4.6 Power Level Calculations

The warp engines are fuelled by plasmas, energized from energy created in quantite\fusion reactions in the warp core. The fuel for these reactions is stored in the primary deuterium tank in the ship's stardrive section. The tanks are loaded with deuterium at 140,000 PSI. The supply is held in compartmentalized tanks within the main body tank to prevent loss due to damage. The total internal volume is some 120,200 m3 but is more normally loaded to a volume of 118,500 m3. These tanks have a rated loss below 0.0000002 kg/day.

Though we know the volume, for fusion reactions we need an approximation of the total mass. Given that the deuterium is in a compressed gaseous state we can use an approximation of its density as:

25.2 gram per cubic centimeter

For the creation of energies the matter reactant is forced in to a side fusion reaction through an injector from the primary deuterium tank to meet in the reaction chamber with helium-3 from the primary he3 tank in the stardrive section. Here they are fused in a gravimagnetic tokamak, with muon-beam enhancement, to produce a high-energy plasma with a temperature on the order of 10^8 degrees Celsius.

In the core injectors bring in pellets of pure quantite ore and the plasma inside of a pinched-spheroid gravitic field to create a maximized reaction. When bringing the reaction chamber up to levels for warp flight a ratio of reactant (plasma) to reactant (quantite) is about 5:1. Though one would expect the annihilation ratio to be 1:1 there is some degree of plasma loss that is not involved in the reaction. When breaking the warp one limit this loss drops to 3.2:1. The plasma-quantite ratio changes to increasingly more efficient values up to warp 5 where the ratio stabilizes at 1:1 and remains at this level for all speeds above warp 5. Engine efficiency of the starship and the resultant energies from quantite annihilation is very high of the order of 97%.

Pendragon Class fuel storage for five-year missions disregarding refueling, Bussard collector usage or quantite mining:

15000 m (469,500,000 kg, 469,500 tons) of quantite and

118,500 m3 of deuterium

118,500 m3 of helium-3

Given a loss rate of 0.0000002 kg/day of deuterium over the 5 year mission

365.256*8 = 2922

2922 * 0.0000002 = 0.0005844 kg

Calculations show quantite to be the limiting factor on mission length. The Pendragon Class project was designed to have an operational life of five years at warp six before fuel exhaustion. This means that after five years the fuel will be consumed, given the nature of reactions, to mean that the quantite will be depleted first with the possibility of redundant deuterium left.

To calculate the energy released during the mission aiming for fuel exhaustion in five years we must estimate fuel mass.

Total mass of deuterium:

118,500,000,000 * 25.2 = 2,986,200,000,000 grams

2,986,200,000 Kg

The loss of deuterium over the 5-year period is insignificant, so it can be ignored for the sake of ease.

Given that there are

86,164.0905 (seconds) * 1826.25 (days)

157,357,170.275 seconds in the five-year period

Quantite is a quantum-stressed material; meaning that whatever catastrophe formed it imparted a massive potential energy dosage to the superstrings that make up every particle of that substance. Unstable quantum materials such as quantite have several unique properties. For example, the electrons and protons that make up quantite cannot be exchanged with those of another object, as one might experience with static electricity. The physical state of quantite cannot be altered easily and, due to the fundamental binding forces of the atoms being unstable on a multidimensional plane, any massive alteration of the movement of quantite molecules will result in a massive detonation.

Upon the discovery of Quantite, scientists found that by radically altering the atomic movement within Quantite atoms, specifically via the use of heat, they could produce a massive energy release. An increase in temperature would cause the molecules of Quantite to move about more quickly, just like heated air in a balloon and when the molecules reached a specific state of excited movement the superstrings binding the atom together at the quantum level would completely destabilize and a detonation would occur.

By combining fusion technology with Quantite, Starfleet has been able to abandon matter/anti-matter and nuclear fusion as their primary means of power generation for the following reason:

Unlike matter/anti-matter reactors, Quantite does not require complex electromagnetic fields, or expensive methods of containment that can easily be breached. Refined Quantite is stable at temperatures as low as -500° C and as high as 11000° C, which means it can be stored at room temperature with practically no extraneous containment system, while matter/anti-matter requires a massive cryogenic super-cooling system to maintain safe storage. Quantite can be mined off of a planet, while production of matter/anti-matter is a negative-result venture, as it required more power to produce an given amount of anti-matter, then the potential energy the produced anti-matter was capable of generating. Quantite can be used to produce a massive amount of energy with a minimal amount of resources. Matter/anti-matter requires an extremely complex and unreliable M/AM injector system prone to catastrophic system failure.

One of the key problems in using Quantite was the fact that not all Quantite reached detonation at the same temperatures. Quantite from one planet could be ignited at temperatures as low as 2000° C, while Quantite from another planet would require temperatures as high as 20,000° C... it all depended on how close the planetoid was to whatever catastrophic event that created it. Consequently fusion power is often used in conjunction with Quantite. Fusion reactor plasma has a temperature of 5*10^7° K, several thousand degrees above the maximum ignition point of any known grade of Quantite, thus negating this problem.

Now, Quantite`s energy release is approximately 1500 times more than total matter conversion, as the superstrings act as 'springs', storing vast amounts of energy in their multidimensional coiling. The ratio for plasma to quantite is 2:1.

Matter reacting is: 10 + 5 = 15 Kg

(Assuming 1 part matter 1 part helium-3 for the fusion reaction, that cuts down deuterium use in half. Also, there will be deuterium waste, in the form of fusion plasma that does not react with quantite. However, given that we started with such an excess of deuterium and that the level of reactants can run higher than the ratio 1:1, we can ignore the imbalance, also as discussed below should deuterium run low, there exists a supply of liquid deuterium approximating, 297,600 Kg [9,300*32] of liquid fuel that can be fed into the reactor)

Also note: there are thirty-two cryo tanks in the saucer section module. These function as auxiliary fuel supplies, however the fuel is not in the same physical state. The auxiliary tanks store deuterium in a liquid state. The Volume of each tank is 113 cubic meters and each is capable of storing 9.3 metric tonnes of fuel. This means that the density in these pods must be far lower than in the PDT, specifically 9,300 Kg / 113 = 82.3 kg/m3 or 0.0823 gram per cubic centimeter. This is over 303 times less than the density of the main PDT tank, and is very much more than the typical Density of liquid deuterium, which is around 0.1630 grams per cubic centimeter but does closely approximate with the liquid density of hydrogen 0.07099 g/cm3. The only feasible explanation is that the material has a density comparable to liquid deuterium but the tanks are not filled to capacity. This is similar to the PDT which have an internal volume of 120,200 m3 but which are more normally loaded to a volume of 118,500 m3. This ratio of volume to load is far higher than for the secondary tanks and might suggest the need for more safety measures in the primary hull.

Using the Matter from the Primary fuel supply only we can calculate the energy output of the warp core.

By E=mc2, factoring in 1500

E(joules) = 15 (kg) * (299 792 500 )2 (ms-1) * 1500

E(joules) = 2,022,199,718,765,625

2.022 petajoules per second

2.022 petawatts (3 decimal places)

Given the loss of energy of 2% (100-98% efficiency) this gives:

A loss of .08 petawatts.

1.9 petawatts (3 d.p.) Total useable power created in the Quantite\fusion reactor.

Targanide accelerators at the beginning of each power transfer conduit leading from the core enhance the energy of the plasma flow by 18%, leading to a total energy boost of 72%.

2,022,199,718,765,625 * .72 = 1,455,983,797,511,250

3.4 petawatts - total output of core with enhancement.

It could be argued that an integral is required to take account of the effect reduced mass has on the ship, in that as the mission continues the ship will become lighter and more easily propelled. The mass of fuel is negligible compared to the overall space frame and the vectored impulse field reduces apparent starship mass to avoid relativistic effects.