Foundationverse power generation: Foundation's Fear evidence

Murazor · Post by **Murazor** » 2006-02-13 01:44pm

Rereading the Second Foundation trilogy books for future threads with commented quotes from the Foundation series, I found a decent incident that allows us to calculate possible power generation figures for Imperial spaceships.

The relevant pieces of information are:

Sark had seven wormholes. One was dying. It hung a light-hour away, spitting out wild worms that ranged from a hand’s-width size, up to several meters.

From Foundation's Fear, Part 7 'Stars like grains', Chapter 3.

Four hours later, closing at high velocity with the big wormhole complex, he saw her side of it.

From Foundation's Fear, Part 7 'Stars like grains', Chapter 4.

***

This allows us to calculate the speed reached by Dors and Seldon's ship. It crosses a light hour in slightly over four hours, so its average speed in this journey is of roughly 0.25c or 75,000 km/second.
Supposing a constant acceleration during the aforementioned four hours, we can calculate:

Final speed = Average speed * 2 = 150,000 km/second.

Speed/time = Acceleration => 150,000/14,400 = 10,41 km/s^2 (roughly 1000 gravities).

Using the following information...

The kinetic power of a ship pushed by a relativistic particle stream is approximately P = F c, where F is the thrust (force, in Newtons) and c is the speed of light. If the mass of the ship plus its fuel is m and the acceleration is a then we simply have F = m a, which is familiar to students of Newtonian physics.

From Dr. Saxton's Star Wars Technical Commentaries, Power Technologies.

... I have calculated that the result is P = 1 * ~1E4 * 3E8 = ~3E12 w/kg. The engines must generate roughly three terawatts of power per kilogram during this trip.

Comments? Flames? Gross mistakes spotted?

Nyrath · Post by **Nyrath** » 2006-02-13 04:26pm

I get a final speed of 140,000 km/s and an acceleration of 9.7 km/s (980 gravities), which is close enough for government work to your figures.
( using D = 1/2 AT^2 )

After burning at 980 gs for four hours, each kilogram of ship will have a kinetic energy of K= 1/2 MV^2 or about 9.8E15 joules per kilogram (approximately 2.3 megatons per kilogram).

Watts = Joules/second. The trip is 4 hours or 14,400 seconds. 9.8E15 joules / 14,400 seconds = 6.8E11 watts/kilogram. Which is within an order of magnitude of your 3E12 w/kg.

In Asimov's THE STARS, LIKE DUST (which takes place centuries before the establishment of the galactic empire), the ships are fueled by total conversion:

'It must take an awful lot of power to keep an artificial gravity going.'

'Enough to power a small town.'

'There isn't any danger of our running short of fuel, is there?'

'Don't worry about that. Ships are fueled by the total conversion of mass to energy. Fuel is the last thing we'll run out of. The outer hull will wear away first.'

In Asimov's SECOND FOUNDATION, the ships have different fuel:

There is nothing, never has been anything, quite like a busy spaceport on the outskirts of a capital city of a populous planet. There are the huge machines resting mightily in their cradles. If you choose your time properly, there is the impressive sight of the sinking giant dropping to rest or, more hair-raising still, the swiftening departure of a bubble of steel. All processes involved are nearly noiseless. The motive power is the silent surge of nucleons shifting into more compact arrangements.

Batman · Post by **Batman** » 2006-02-13 05:02pm

Actually for a halfpoint turnover trip I get slightly more than 21 kps squared.
s=1/2 at^2 (with s being distance, a accelleration, and t time)
s and t are given (.5 lighthours and 7,200 seconds, respectively) so we try to solve for a.
5.4E11m = 1/2a m/sec^2 x5.329E7 sec^2
10,416,666e m =1/2 a m/sec^2 x 1 sec^2, so
a=21,33333333e kps^2.
Somebody else to figure out what that means for power generation.

Batman · Post by **Batman** » 2006-02-13 05:04pm

Ghetto edit:

Batman wrote: Somebody else has to figure out what that means for power generation.

Blerg.

Nyrath · Post by **Nyrath** » 2006-02-13 07:58pm

Batman wrote:Actually for a halfpoint turnover trip I get slightly more than 21 kps squared.

I get an acceleration of 9.7 kps^2 because I read "closing at high velocity with the big wormhole complex", and assumed this was a "accelerate all the way and hit the wormhole like a bat out of you-know-where", NOT a Heinlein torchship "accelerate halfway - skew flip - decelerate to stop" trajectory.

But with your acceleration, the ship is changing velocity for 14,400 seconds (half of it negative, but that doesn't count with regards to expending power) for a delta V of 302,000 km/s. Plugging it into K=1/2 MV^2 gives 4.7E16 joules. Divided by 14,400 seconds gives 3.2E12 watts/kg, which is a perfect match for Murazor's figures.

Batman · Post by **Batman** » 2006-02-13 08:23pm

Nyrath wrote: But with your acceleration, the ship is changing velocity for 14,400 seconds (half of it negative, but that doesn't count with regards to expending power) for a delta V of 302,000 km/s. Plugging it into K=1/2 MV^2 gives 4.7E16 joules. Divided by 14,400 seconds gives 3.2E12 watts/kg, which is a perfect match for Murazor's figures.

Something doesn't compute here. My figure has the ship accelerate a twice Murazor's rate so how can the power consumption be the same?

Post by **Surlethe** » 2006-02-13 08:31pm

Nyrath wrote:In Asimov's SECOND FOUNDATION, the ships have different fuel:
There is nothing, never has been anything, quite like a busy spaceport on the outskirts of a capital city of a populous planet. There are the huge machines resting mightily in their cradles. If you choose your time properly, there is the impressive sight of the sinking giant dropping to rest or, more hair-raising still, the swiftening departure of a bubble of steel. All processes involved are nearly noiseless. The motive power is the silent surge of nucleons shifting into more compact arrangements.

I seem to recall the Foundation used gravitic propulsion during Second Foundation.

Batman · Post by **Batman** » 2006-02-13 08:34pm

Surlethe wrote: I seem to recall the Foundation used gravitic propulsion during Second Foundation.

Not that I recall, especially as 'Foundation's Edge' toted gravitic drive as a completely new invention.

Post by **Surlethe** » 2006-02-13 08:38pm

Batman wrote:
Surlethe wrote: I seem to recall the Foundation used gravitic propulsion during Second Foundation.
Not that I recall, especially as 'Foundation's Edge' toted gravitic drive as a completely new invention.

My mistake; thanks for the correction. It's been a few years since I read them.

Eframepilot · Post by **Eframepilot** » 2006-02-14 01:50am

Technology in the Foundationverse is highly inconsistent. The original Foundation has the breakaway star-nation of Anacreon reverting to fossil fuel power after seceding from the Galactic Empire, a rather silly development for any interstellar power. The weapons in the original Foundation trilogy are some sort of exotic nuclear disintegrators that work by mysterious unknown nuclear reactions similar to Trek phasers, but the weapon of the hero in Foundation's Edge is a simple microwave gun.

The total mass/energy conversion in The Stars, Like Dust mentioned above would be the pinnacle of all power sources (short of a zero-point energy tap that gets energy for free) and so the later references to "nuclear" and "atomic" power in Foundation books are a backslide in technological development.

Murazor · Post by **Murazor** » 2006-02-14 05:17am

Nyrath- Thank you for checking my lousy math. Yesterday I was in a hurry and couldn't elaborate on the post.
About the Second Foundation quote, the ships mentioned are the civilian vessels in the Kalganian spaceport, aren't they? Even if they are fusion powered (strongly implied in this quote) this still doesn't rule out more advanced forms of power generation for warships.

Batman- Nyrath uses a different approach. Using Saxton's formula, the power result for your acceleration figure is 6.39E12 watts/kg. You calculate that the ship spends half the trip accelerating to reach 0.5c and the other half slowing down. The peak kinetic energy at the mid point if of 1.12E16 joules per kilogram, meaning 1.56E12 watts/kg generated for the whole trip. BTW, for those interested, the main site's relativity calculator provides the non-Newtonian KE for objects moving near c (the results are order of magnitude above those obtained with Newtonian formulas).

Eframepilot-
1) Anacreon returned to chemical energy, because they just didn't know how to operate or maintain (never mind replace) Imperial technology. Seldon claimed that the primary purpose of the Foundation was the compilation of the Encyclopedia Galactica to fight the growing ignorance.

2) All the phaser-like weapons are hand-held models (the ship mounted weapons are completely different from the one instance they are seen in action). There are descriptions of Imperial and Pre-Imperial DET hand-held weapons as destructive (if notmore) than Trevize's blaster.

3) Oddly enough, in all fields where a comparison is possible, the starships seen in The Stars, Like Dust are more primitive than later models. A technological backslide in a single, particular area of knowledge? Not bloody likely, IMHO.