How much energy could the Enterprise-D produce?

Question

Just watched TNG: The Dauphin. In it the following exchange occurs when receiving a powerful transmission:

Data Sir, sensors indicate the communication originated from a tera-Watt source on the planet
Riker That's more power than our entire ship can generate!

This seems silly.

• There is currently a hydro power station that produces 22.5GW. 50 times that seems very large to us today, but when you consider the biggest nuclear weapons can release 0.5TWh, the numbers don't seem that extreme.
• Shields! Phasers! 150KW defensive laser systems exist. A 1PW laser accelerator is a thing. Those on the enterprise must —by virtue of needing to go much further and charge much faster— need more power.
• Transporters! Replicators! The holodeck! Surely the converstion of energy into matter and arranging that at distance, must pull a lot of power. And it's happening all over the ship, all the time.
• Impulse engines. Even in a vacuum, shifting 4.5 megatonnes must take serious power. To accelerate 1m/s over a second, you're looking at 45GW and they seem to do things much faster, all the way up to 75,000,000m/s. Full impulse seems to take a few seconds... That makes my calculator cry, with numbers around 8 ×10^24W... That's way over.
• Warp.
• Computer.

All of that, while keeping the lights on running other day-to-day things.

Was Riker just off by a unit, or is there something I'm not factoring into these points? How much energy could the USS Enterprise NCC-1701-D produce at peak output? Are there listed energy requirements for the components above that I've been guesstimating for?

Answer 1

Memory Alpha explains that

The warp core was one of the most powerful in Starfleet, generating approximately 12.75 billion gigawatts of power. (TNG: "True Q")

The exact quote is:

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 twelve point seven five billion gigawatts per (an alarm goes off)

(Source)

So, that's 12.75 million terrawats that the Enterprise-D warp core was capable of producing!

It also seems that's not the maximum amount. As per Relics:

SCOTT: Geordi, the shields will hold. Don't worry about that. I can get a few extra gigawatts out of these babies.

(Source)

Now, I know that's for the shields, but it does seem to indicate that the power output could be slightly more, but probably not a huge amount.

Regarding what Riker was on about:

In 2365, the command headquarters of Daled IV utilized a communication system that originated from a terawatt source, which was necessary to penetrate the planet's atmosphere. According to Commander William T. Riker, "that's more power than our entire ship could generate," meaning that they lacked the ability to respond to the communique. (TNG: "The Dauphin")

(Source)

That is, the communication system of the entire ship couldn't produce a terrawatt.

According to the excerpt from the script below, this seems to be confirmed:

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.

RIKER: Which means we lack the ability to respond, sir.

(Source)

Just judging by this quote which puts Riker's explanation into context, it does seem by 'entire ship' he meant 'the entire ship's communication system'. It would be pretty poor if a First Officer didn't know the energy output of the ship!

This site, citing the Star Trek: The Next Generation Technical Manual says the Galaxy Class had a

total output 50,000 TeraWatts

for the phasers. Now, that's a separate system with an upper limit nowhere near the total energy produced by the warp core.

As for the out of universe reason, as suggested by Stan's comment below, bear in mind that The Dauphin was well before True Q and the TNG Technical Manual had yet to be released, so, from an out-of-universe perspective, Riker probably was referring to the entire ship's output as being about a terawatt. From an in-universe perspective this is later contradicted in True Q with the more realistic figure of 12.75 billion gigawatts, so we resolve this contradiction by assuming that, in-universe, Riker was referring to the communication system alone.

Answer 2

This is not specifically an answer to the question but was going to be a comment to N_soong's wonderful answer but it ended up being too long and halfway to an answer itself.

Communications equipment is not something you can just throw more power at. If an antenna is not tuned to the power and frequency of the broadcast you will have some major issues due to what is known as reflected power.

When the antenna is not tuned to the transmitter then not all the power goes out the antenna. Any power that does not go out must come back at the transmitter. In the electronics world this is known as SWR and is a ratio of forward power (What makes it out of the antenna) and reflected power.

At lower levels you can get away with having a antenna that is not exactly tuned to the rest of the system but when you get higher up there in power you have to get a lot more narrow on what a specific antenna does. This is because of the fact that the transmitter can only take so much power coming back before it gets fried.

10% of 1 megawatt is 100 kilowatts. Star trek equipment could probably handle that although that is more than most FM radio stations put out in total. However 10% of 1 terawatt is 100 gigawatts. That is an astounding amount of energy to be feeding back into the system.

Answer 3

Here's another approach to this question:

From How long can a galaxy class starship last before it needs servicing?, the Enterprise-D can carry 3,000 m^3 of anti-deuterium (source: Rick Sternbach and Michael Okuda's Star Trek TNG Technical Manual).

Based on data from the Brookhaven National Laboratory, I'll estimate the maximum density of deuterium (in liquid or solid form) at ~ 0.2 g/cm^3 = 200 kg/m^3 (since it would be a liquid or solid, even vastly increasing the pressure wouldn't change the density much). Since anti-deuterium should have the same density:

200 kg/m^3 x 3,000 m^3 = 600,000 kg anti-deuterium

Now let's assume the Enterprise-D's engines could convert that anti-deuterium to energy with 90% efficiency (the manual specifies a minimum efficiency of 88% up to warp 7.0), by combining it with an equal amount of normal matter. Using E = m c², that would give us a total of:

1,200,000 kg x (3.0 x 10^8 m/sec)^2 x .9 = 1.0 x 10^23 kg m^2/s^2 = 1.0 x 10^23 J of energy

[J = joules]

And that total energy output, sustained over a 3-year period, would give us an average power output (for propulsion, which should be the main power consumer; total will be more, since they'll also be running the stereo and A/C) of:

1.0 x 10^23 J/(94,608,000 s) = 1.0 x 10^15 J/s = 1.0 x 10^15 watts = 1000 terawatts

[There are 94,608,000 seconds in 3 years.]

[By comparison, total current worldwide energy generation (all sources -- coal, gas, oil, nuclear, hydroelectric, wind, solar, geothermal, etc.) is about 15 terawatts = 2 kilowatts/person.]

We can compare this figure to one that can be estimated from the power usage chart for the engines (Fig. 5.1.1. p 55), and accompanying explanatory text, in the same Star Trek TNG Technical Manual. On p 57, Sternbach and Okuda say the Enterprise is able to cruise for an unlimited amount of time (until its fuel is depleted) at warp 6. So let's assume that's our average cruising speed. Now according to Fig. 5.1.1, the power usage (for propulsion) at warp 6 is 3 x 10^6 MJ/cochrane. Of course, those are the wrong units; since it's power, it should be MW/cochrane (MW = megawatts). So let's make that correction.

They further say that a warp 6 field bubble has a field strength of 392 cochranes. Thus the power required for propulsion at warp 6 is:

3 x 10^6 MW/cochrane x 10^6 W/MW x 392 cochranes = 1.2 x 10^15 watts = 1200 terawatts

This is nearly the same as the first value we calculated! [This is probably serendipitous :).] Of course, as mentioned above, there are other power consumers besides propulsion, but I'm assuming that's the big one, at least for sustained operation.

We can also use the graph and figures in the technical manual to estimate a maximum power output. At its maximum theoretical speed of warp 9.8, we have:

8 x 10^9 MW/cochrane x 10^6 W/MW x 2 x 10^3 cochranes = 1.6 x 10^19 watts = 16 million terawatts = 16 exawatts

This is very close to the 12.75 million terawatt (= 13 exawatts) figure quoted by Data (though I don't know how fast the ship was travelling at the time). At the same time, the 13 and 16 exawatt figures seem a little silly to me, even for 24th–century technology, since they're over 100 times the power the earth receives from the sun (174 petawatts)!

Furthermore, at a 90% conversion efficiency, the engines would need to dissipate 1 exawatt of heat, i.e., 10 times the power the earth receives from the sun! [Additionally, according to the tech manual, conversion efficiency tends to decrease at high warp speeds.] Though I suppose they could deal with this by saying the heat is dissipated into subspace...

Interestingly, the Wikipedia article referenced above says the Enterprise-D can maintain emergency warp, 9.6, for 12 hours. Using the same sort of estimates given above, that would require 11 exawatts of power. However, at that power output, the ship would use up its total fuel capacity in 3 hours. So clearly there's not perfect consistency among these different specifications.

Finally:

A 1PW laser accelerator is a thing. Those on the enterprise must —by virtue of needing to go much further and charge much faster— need more power.

It's important not to conflate peak power output capabilities (of things like lasers) with sustained power output. Today we are capable of building a pair of lasers with a combined peak power output of 20 petawatts = 20,000 terawatts. But this device will put out that power for only 150 femtoseconds = 1.5 x 10 ^-13 s, thus delivering a total energy of 3000 joules. It can do one shot/minute so, as impressive as its peak power output is, its sustained power output is only:

3000 J/min x 1 min/(60 s) = 50 J/s = 50 W

And remember that when we are talking about the power output of the Enterprise-D's warp engines, we're referring to sustained power output.

[Notably, the peak power output of these lasers is >1000x the current 15 terawatt sustained power output of human civilization!]