Warp Core Power Generation

(To be Updated)

In "True Q"[TNG6], we hear the following exchange occur in Engineering:

Amanda: "It's hard to imagine how much energy is being harnessed in there."
Data : "Imagination is not necessary; the scale is readily quantifiable. We are presently generating 12.75 billion gigawatts per . . . "

At that point, Data is cut off, leaving us hanging. Warsies contend that the quote is absolutely meaningless. As the basis of this, they point out the following facts:

1. Amanda refers to energy, but Data rattles off a figure in watts. Energy is measured in joules, with watts referring to power (energy over time).
2. "Gigawatts per" anything is a very peculiar phrasing, and watts per second would have to imply an increase in power.

The problem is that the above points do not render the entire quote meaningless. First, conversion of watts to joules and vice versa is a simple affair . . . a watt is a joule per second. Second, although "watts per" anything is a peculiar phrasing, it is not unheard of. A quick search through Yahoo provides numerous examples of this use where "anything" is a time unit, in a manner similar to the "kilowatt-hours" on most people's power bills. It does not imply an accelerating increase in energy. "Watts per X" is also used to denote intensity (watts per square meter), or power production per amount of fuel.

Opponents have then argued that I simply assumed that Data was about to offer a time unit. However, this is incorrect.

I am not assuming it is a unit of time. It is the only continuation of the sentence that makes sense (or, more correctly, "comes close to making sense") in the context. It is also (note well) the continuation that offers the smallest possible interpretation of the power figure given. Further, it also happens to correspond with the script (which, alas, is non-canon), where Data says "per second."

But, let's look at the other possibilities anyway:

Now, when Amanda says "in there" she referred to the warp core, so perhaps Data (being Data) was going to give her a power-by-unit-volume analysis. However, the largest volume he could logically use would be the warp core, so any smaller chunks of it would increase the total power.

It is possible, though less likely, that he was giving her a power-generation-by-fuel-consumption report, though this does not fit the context. Besides, proton/antiproton reactions liberate 90,000 gigajoules per gram of antimatter. To achieve 12.75 billion gigawatts, they would need something like 140 kilograms of antimatter per second, with an equal amount of matter, flowing through the reactor. (This assumes, of course, that there's no such thing as Trek uber-antimatter (which I don't think there is, but I thought it worthy of note here).)

If this 140kg of antimatter were somehow rigged at the same average density as a human being, this would be the equivalent of two rather chunky guys . . . say, Homer Simpson . . . slamming into each other each second.

There are problems with this idea.

1. There isn't room for two Homer Simpsons in the warp core. I'm not even sure he could fit down the pipes leading to the core, even if you buttered him. Seriously, though, two Homers per second is an awful lot of stuff to be in that core, even though it wouldn't be there all at once. I'm not even sure you could get each proton to react with each antiproton in such a situation (which would mean you would need even more than two Homers, compounding the problem).
1a. The dilithium crystals through which everything is channelled are awfully small to be dealing with two Homers per second.

Enterprise-D dilithium crystals

2. 140 kilograms per second would be 504,000 kilograms per hour, 84,672,000 kilograms per week, and 4,415,040,000 kilograms per year . . . and that's just the antimatter. Unless the Federation is full of antimatter gas stations, that isn't going to work.
2a. Using this reprint of a screen from "Contagion"[TNG] (which I use because it is similar to the MSD, but labelled), you can see that there isn't a lot of room devoted to antimatter containment. But, even if they were to somehow store antimatter with a density like that of iron, they'd need 630,720 m^3 for a year's supply. That would pretty much fill the entire volume of the engineering hull behind the warp core.
2b. Voyager went a long time without needing antimatter. In fact, I'm not sure they ever got any.

3. To power the Hathaway in "Peak Performance"[TNG], Wesley beamed over a small container of antimatter that he'd been using as a part of a science experiment. This not only gave the Hathaway sufficient power to engage in the wargames, but also gave her the energy necessary to engage warp drive.

Wesley's Antimatter (blue candle wax)

So, that just doesn't work (unless you go for Trek uber-antimatter). On the other hand, if the ship was only generating 12.75 billion gigawatts per day (as I suggested), that's "only" 147,000 gigajoules per second, or about 1.5 grams of antimatter (and an equal amount of matter) per second.

Given the size of Wesley's container, I'd call this a pretty fair guess, assuming the Hathaway didn't need as much power, and was on low-power mode anyway.

On the other hand, we have the following scene from "Revulsion"[VOY]:

Seven : "The optical assembly is properly aligned. I am ready to access the main power supply."
Kim : "After you."
(The pair climb down, and Seven begins to reach into a conduit)
Kim : "Wait! What are you doing, there are five million gigawatts running through there!"
Seven : "The exoskeleton on this limb can withstand it."

This gives a lower limit of 5,000,000 gigajoules (5,000 terajoules) per second for Voyager's power generation abilities, or 34 times my 147 terajoules/second figure for the Enterprise-D. This could either imply that the Enterprise-D was on a very low-power mode, or that my use of the term "day" is incorrect, and that something like "hour" (which, obviously, would result in a figure 24 times higher) would be more appropriate.

Some dispute such figures, pointing instead to "The Dauphin"[TNG]:

Data: "Sir, sensors indicate the communication originated from a terawatt source on the planet."
Riker: "That's more power than our entire ship can generate."
Data: "It is what is needed to penetrate the atmosphere."

However, there are several better things that can be done here than to throw out every other quote in favor of the quote from "The Dauphin". First, take a look at the context . . . they're talking about communications. We know from ST:TMP, et cetera, that starships carry not only subspace communications equipment, but also devices capable of transmitting via "primitive" radio frequencies, so one could argue that by "entire ship" Riker was employing a synecdoche. This can be reasonably well established, given that we know from "Who Watches the Watchers"[TNG] that a 4.2 gigawatt reactor can power a subspace relay station. It is likely, therefore, that the ship's entire complement of communications equipment can't send signals with a terawatt of power behind them, and that therefore Riker did not refer to the entire power generation capabilities of the starship Enterprise.

This allows us to fit the "Dauphin" quote into the numerous other examples, and not simply throw it away in light of the preponderance of evidence. It also provides a better solution than throwing away the preponderance of evidence in favor of a single quote.

Update:  An alert reader noticed a slip-up regarding the 140 kg figure.   The warp core only needs one Homer per second, not two.  I inadvertently doubled the proper figure.   I'll take care of that in the planned re-writing of the page.

Special thanks to Graham Kennedy of The Daystrom Institute Technical Library for the "Peak Performance" screenshot.

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