# Where do Federation vessels get all that energy, and how much would it cost today?

Reading about how gravity is generated in a Federation vessel, this questions came to my mind:

If we use the Enterprise D as an example, we know these items consume energy:

• Gravitational force
• Lights
• Transporter
• Replicator
• Holodecks
• Computer (massive A.I.)
• Tractor beam
• Force fields
• Phasers
• Turbolifts
• Shields

It seems like a lot of resources!

• What generates this amount of energy?
• How much energy does a ship consume?
• How much would it cost nowadays in US dollars?
• I'm not a Trekkie so I may have it all wrong, but don't those vessels traverse interstellar distances at multiples of the speed of light? So isn't propulsion a big enough energy cost to show up on your list? – user14111 Jul 13 '16 at 17:47

``````>>>What generates this amount of energy?
``````

Star Trek ships use antimatter as main source of of energy + some complicated technology to maintain a stable reaction and transfer power around the ship.

``````>>> How much energy does a ship consume?
``````

From the Technical Manual, paraphrased: (The Galaxy Class has thirty antimatter storage pods), each having a volume capacity of 1,000 cubic meters. now, going from the antihydrogen having the same mass as hydrogen, therefore weight, and using a standard of storing it at -257.87 at 1 atmospheric pressure... the weight of hydrogen in just one pod is 70,796 kilograms

and later

And the tech manual says this: the galaxy class uses it all in about three years... meaning that, taken literally, it would burn through about 1,940 kilograms of anti-matter... per day.

1940 kilograms of anti-matter per day can generate A LOT of energy. To be precise this is equal to 3880 kilograms of annihilated matter which equals to

``````3.492 x 10^20 joules
``````

As a comparison the explosion of the Little Boy atomic bomb generated:

``````4.184 × 10^12  joules
``````

So every day a Galaxy class ship consumes the same energy equal to about 83 millions Little Boy atomic bombs.

(a better question would be - what does the ship do with the energy when sitting "idle" i.e. not at warp ... most probably they have a system to reduce the energy production and actually going and running at wrap consumes much more energy than the "average" one)

``````>>> How much would it cost nowadays in US dollars?
``````

A lot :)

Depends how you calculate the price - prices for gas, for electricity or for gasoline. Also is it retail price or production price.

If we take electricity retail price then as per http://www.statista.com/statistics/183700/us-average-retail-electricity-price-since-1990/ it was about 10 cents per kilowatt hour.

One kilowatt hour is equal to

``````3.6 x 10^6 joules
``````

For one day a Galaxy class star ship generates (and consumes) about

``````9.7 x 10^15 kilowatt hours
``````

Taking the above price this is about

``````9 700 000 000 000 000 dollars
``````

OR

``````9 700 000 000 million dollars
``````

OR

``````9 700 trillion dollars
``````

As a comparison again - an estimation of the World Bank is that the world GPD for 2013 is about 75.59 trillion dollars.

Of course this comparison is irrelevant.

Q1. Federation vessels are fueled by Anti-matter and matter with dilithium acting as conduit (control valve) that governs how much matter and anti-matter interacts with each other and directs it into the system. Matter is everywhere and easy to get obviously so we don't need to talk about that. Dilithium as it is in the Star Trek universe is more or less just a magic crystal to do what is needed...also called a mcguffin. Antimatter... We're never told how they get it... but a small bit of a matter/anti-matter interaction can power lots and lots and lots of things for a long time. Just think of how much energy is in a Nuclear Bomb, realize that the containment for the anti-matter is more than 20 times larger than the entire bomb, and matter/anti-matter interaction will produce more than 1000x more energy between equivilent masses.

Nuclear bombs use a small fraction of e = mc^2. Matter/anti-matter is 100% conversion of mc^2 to e.

Q2. Not much relatively to the amount produced. A very small fraction of the energy produced by the ship is used in the majority of the systems. The largest proportion of energy, almost all of it, goes to the warp drive.

This is speculative as it isn't ever directly said in amounts and is contradicted by what's in various episodes. This is done for drama, not realism and makes no sense in most cases, because you can drain off 99+% of a Federation vessel's energy reserves and almost all the energy costs of the things we know of in reality would still have power for a very long time.

The warp core, which houses the ship's antimatter is the equivalent size of 5 fatmans at the very least. Assuming they have similar densities, Fatman is 4,670 kg. Five times that is 23,350 kg. The price for the anti-matter in a fed vessel would cost in the range of \$1,459,375,000,000,000,000,000 minimally. I don't know how to even say that number off the top of my head.

• Where do you get the prices for antihydrogen? – Catija Jul 13 '16 at 19:31
• Google seach, first answer for how much does anti-matter cost, sourced from NASA's estimation. – Durakken Jul 13 '16 at 19:35
• So link to it? Right now it looks as if you just pulled it out of thin air :D – Catija Jul 13 '16 at 19:36
• Also, the fuel (matter and anti-matter) are not housed in the warp core. They're stored in containment pods at the top and bottom of the warp core. I don't believe they're ever seen on screen. – Xantec Jul 13 '16 at 19:48
• @xantec got a volumetric estimation for that so that I can give an adjusted extrapolated answer? – Durakken Jul 13 '16 at 19:53

It's basically magic. The in-universe explanation is that matter-antimatter interactions are used to power starships. This is the most efficient method known to current physics to release energy. The amount of antimatter needed to provide the energy estimated (in The Physics of Star Trek) to be used by a starship is far more than the mass of a starship itself.

Update: a few tidbits from The Physics of Star Trek.

• Impulse uses nuclear fusion, not matter-antimatter reactions. However, it would require approximately 81 times the mass of the ship itself in hydrogen to accelerate to 0.5c. (It would only be twice the mass if you used antimatter instead.)
• You need to decelerate at the end of your journey, which means 81 times the mass of the ship again. But if the ship were carrying that with it, you would need to accelerate it at the beginning of the trip, increasing the amount of fuel needed at the beginning of the trip by another factor of 81.
• To collect hydrogen en route instead would require a collector 25 miles in diameter to collect one gram of hydrogen per second, which is only 0.0001% of the hydrogen you would need for propulsion alone.

As you can see, it is neither feasible nor plausible to actually power a starship with anything resembling our current understanding of physics.

• How do they estimate the energy needed to go millions of times faster than light, when going faster than light is thoroughly impossible? – Ross Presser Jul 14 '16 at 7:05
• The estimate didn't even need to include warp; impulse alone is implausible given the amount of energy needed to accelerate something as massive as a starship to the fractions of c under consideration. I'll try to find some of the relevant passages later this evening. – chepner Jul 14 '16 at 15:14
• Impulse is not supposed to be based only on our current understanding of physics--The TNG Technical Manual says on p. 75 that they supplement the fusion engine with a "compact space-time driver coil, similar to those standard in warp engine nacelles, that would perform a low-level continuum distortion without driving the vehicle across the warp threshold." And p. 77 elaborates that the effects of the coil are that it "(1) reduces the apparent mass of the spacecraft at its inner surface, and (2) facilitates the slippage of the continuum past the spacecraft at its outer surface." – Hypnosifl Jul 15 '16 at 5:28
• Also, p. 21 of the U.S.S. Enterprise Owner's Workshop Manual says "The fusion reaction generated superheated plasma, which was then channeled through subspace compression coils, which increased the apparent mass of the plasma exhaust products, so the resulting forward propulsion of the vessel was as if a much greater mass of plasma had been expelled. This greatly reduced the fuel (and mass) requirements for impulse propulsion." – Hypnosifl Jul 15 '16 at 5:29
• And out of curiosity, what basis does The Physics of Star Trek have for saying "The amount of antimatter needed to provide the energy estimated (in The Physics of Star Trek) to be used by a starship is far more than the mass of a starship itself", given that antimatter is used for warp rather than impulse, and as @Ross Presser said Trek warp is imaginary physics whose energy requirements are unknown? – Hypnosifl Jul 15 '16 at 5:31