Power to mass ratios, ion engines, FTL, et cetera.

[Jedi Master Spock]

Just throwing some figures out there. Most of these are on my website, but they get ignored a lot there.

Power required for a current generation ion engine per unit of thrust: ~25 kW/N.
Efficiency of a modern ion engine: High enough that differences in efficiency are insignificant for these calculations.
Primary determining factor, thrust/power ratio: Exhaust velocity.
Relationship: Linear.
Is it plausible that SW ion engines have similar exhaust velocities, and therefore thrust/power ratios? Yes. Could it be otherwise? Of course.
Top thrust of a SW fighter: Somewhere around 200 g (median estimate.)
Expected power consumption, SW fighter engine, under the above assumptions: 50 MW/kg. If a heavy SW fighter has a mass of 20 tons, this would be 1 TW.
Estimated acceleraton of capital ships in SW: Generously, ~50g.
Expected power consumption, SW capital ship engine, under the above assumptions: 12 MW/kg. If a SW capital ship has a mass of 50 million tons (5e10 kg) this would be 600 PW.
Gravitational potential, R=850,000 km, 1 solar mass: -160 GJ/kg
Gravitational potential, R=100,000,000 km, 1 solar mass: -1.3 GJ/kg.
Minimum wattage required to go from R=850,000 km to R=100,000,000 km in 100 seconds (stationary): 1.6 GW/kg. ("Relics") If a Galaxy class is 10 million tons, this would be 16 EW.
Time required to travel this distance using a terawatt engine pushing a million ton starship, i.e., a KW/kg engine: Years.
Gravitational potential, R=6400 km, 1 terran mass: -62 MJ/kg.
Gravitational potential, R=19200 km, 1 terran mass: -21 MJ/kg.
Gravitational potential, R=83200 km, 1 terran mass: -5 MJ/kg.
Change in energy, surface to 1-6.5 planetary diameters: 49+/-8 MJ/kg.
Average power, ship using 100% efficient non-inertial anti-gravity drive going from surface to hyper limit in ~1 minute: ~800 KW/kg.
With an inertial drive and a final velocity of 2 Earth diameters per minute: 380 MW/kg.
Rate of change of gravitational potential, ship displacing "magically" with no actual kinetic energy away from a large mass at an "effective velocity" of v[i.e., as in an freely interruptable FTL, such as warp drive, Enchenach drive, et cetera]: (v dot g)m, where g is the local gravitational field and v is the velocity.
Local value of g close to the Sun: 274 m/s.
Power for a "lightspeed" drive directly fleeing the Sun at an "effective velocity" of c: 82 GW/kg. If a GCS is 10 million tons, this is 800 EW.
Power for a "lightspeed" drive directly fleeing the Earth at an "effective velocity" of c: 3 GW/kg. If an ICS is 700,000 tons, this is 2 EW.
Power for a 1000 times lightspeed drive in an orbital 1 m/s g field: 300 GW/kg. If a GCS is 10 million tons, this is 3,000 EW.
Gravitational potential, R=19200 km, 1 terran mass, R=150,000,000 km, 1 solar mass: -910 MJ/kg.
Gravitational potential, R=4,500,000,000 km, 1 solar mass: -30 MJ/kg.
Change in energy, fairly low Earth orbit to Neptune, "lightspeed" drive: 880 MJ/kg.
Average rate of power, 3 minute trip one-way: 5 MW/kg. If the NX-01 is ~200,000 tons, this would be 100 TW.
Time required to travel this distance using a terawatt engine pushing a million ton starship, i.e., a KW/kg engine: Days.

[Roondar]

Interesting figures.

A note here would be that we have no way of knowing if ship engines actually have to do all the work to push the ships in question. Then again, wouldn't a mass lightening field require the exact difference in power anyway?

For instance, take a peek at the first episode of DS9, where a runabout uses a tractor beam to pull in a much larger vessel than itself (albeit a willing vessel). Can we actually say anything of the required power of the engine to do this, or is the fact a tractor beam is used (which lowers the apperant mass of what you are towing, as more or less verified in that episode where Q becomes human) enough to make it imposibble to quantify.

In essence I suppose my real question boils down to this: how do we know the ST/SW ships don't use mass lightening tech to require less power to move their ships? And if they do, can we say anything about the effective work done (as in power) by the mass lightening device or is that completely out of the question?

[Mr. Oragahn]

Well, if I don't got things wrong, because that's just a sort of layman view on this, here's how I understand it;
Within the premise of conservation of energy, by reducing the (effective) mass linearily, you'd increase the speed, but slower than the factors applied to mass, since the speed in the equation is squared, so in the end, you need to square root it back.

That would be, of course, assuming that the energy necessary to decrease mass would be inferior to the energy you'd need to spend to push the ship via simple newtonian physics.

With E=1/2 m v²
Say m = 4 kg, and v = 5 m/s.

0.5 x 4 x 5² = 50 J

0.5 x 1 x 10² = 50 J

If we decrease the mass by four (goes from 4 to 1), the speed will only double (2 x 5 = 10).

But if you try to obtain the same speed (10 m/s) only by increasing energy, and keeping a mass of 4 kg, you have to multiply the energy by four (200 J).

Assuming your engine is stuck at 50 J, the system you use to decrease mass, I think, should require much less the 150 J of energy.

Which puts a problem and requires massive technobabble, breaks a good load of laws, and that's to fiddle with what is known as invariant mass. Looks like it would require to put a portion of the particles that compose anything into some sort of stasis, another dimension or whatever bla bla.

That's a bit the trouble with advanced SF, faked gravities, gravitational maniupulation devices, repulsors and supposed mass lightening, you don't really get solid figures.

You get, at best, top figures based on zero help by special gizmos.

[Jedi Master Spock]

Well, if I don't got things wrong, because that's just a sort of layman view on this, here's how I understand it;
Within the premise of conservation of energy, by reducing the (effective) mass linearily, you'd increase the speed, but slower than the factors applied to mass, since the speed in the equation is squared, so in the end, you need to square root it back.

Well, here's my basic take: Fundamentally, you need to converse both energy and momentum, at least locally, for things to make any sense. That means that if you're reducing mass (in isolation) you're having to supply the extra energy through your mass lightening field to make up for the apparent acceleration.

[Jedi Master Spock]

Interesting figures.

A note here would be that we have no way of knowing if ship engines actually have to do all the work to push the ships in question. Then again, wouldn't a mass lightening field require the exact difference in power anyway?

The difference in energy is the same regardless of how you got there. However, mass lightening has the additional complication of reducing the magnitude of the gravitational potential relative all objects [in a neighborhood expanding outward at lightspeed], whether or not you move relative to them. If you lighten your mass by 99+% parked outside a Sun-like star, you're coming up with a hundred gigajoules per kilogram somehow even if you don't budge an inch.

It makes a very real difference, though, talking about inertial vs non-inertial drives, because final kinetic energy can be quite significant - as can the kinetic energy of drive exhaust.

And if they do, can we say anything about the effective work done (as in power) by the mass lightening device or is that completely out of the question?

Yes, we can. We still have differences in energy and times, which do let us ballpark "minimal" - or "effective" - power. For Star Trek, for example, the moment the warp field comes apart or turns off, the ship goes back to "normal" behavior - i.e., sitting there with full mass - which means it really ought to conserve energy in the fashion I outlined when I initially published my website.

Anything else would mean Trek ships have a free conservation-violating energy source in the production of warp fields.

[SailorSaturn13]

There is an interesting point: under Relativity mechanics, you conserve the momentum, but not the mass center. If a tractor beam changes the targets coordinates WITHOUT giving velocity, the ship doesn't have to move

[Jedi Master Spock]

There is an interesting point: under Relativity mechanics, you conserve the momentum, but not the mass center. If a tractor beam changes the targets coordinates WITHOUT giving velocity, the ship doesn't have to move

In spite of the inertia dodging we do when momentum has no meaning, changing position at a rate of c is so remarkably high that it tends to be the peak power requirement. Even at the furthest hyper limit suggested (6 planetary diameters from the surface) you need 17 MW/kg to flee straight away, and if you use 1 planetary diameter, you're up to several hundred MW/kg.

Which reminds me, an ISD's density should be around 1, not 1,000. *corrects initial post*

[Roondar]

Ok, lets see if I got this straight.

The effective work done by a mass lightening device would require more power than you'd use by simply having bigger trusters. Since ST/SW both clearly use mass lightening tech* to obtain better-than-expected performance of their engines this probably means that the effective work done by said devices is not actually the amount of work really done.

*) Or other similar ideas such as gravity drives, warp or gravity fields, etc. You know, technobabble/magic.

In other words, for mass lightening/gravity/warp field based ships to make sense, the technology in question must have an effective efficiency over 100%. Far over 100% even.

Fascinating.

I suppose that in ST this problem is solved because of subspace. We know from the episode in which Q turned human that a subspace field projected around an asteroid lowers its mass (albeit slightly because of limits on what size of field the Enterprise-D could muster). The assumption on my part is that projecting a subspace field (which requires energy) does not so much do work as it does 'change the rules', or specifically it affects whatever gives particles mass.

This would fit in with conversation of energy quite neatly, since you are not actually doing the work which you appear to be doing and generating your subspace field does cost energy, which you supply, so no rules are broken.

However, assuming mass lightening to use the energy we'd expect is clearly not an option - we'd require more energy to lower the mass enough to gain the speed increase we desire than we do by just supplying more thrust. No one would be stupid enough to build a drive system like that ;)

[2046]

For a poor-but-useful analogy, think of those little toys that magnetically levitate something. Obviously, this effect of magnetism is not actually cheating physics in any way, but for the purpose of the analogy you basically are getting a free lunch, suspending something in mid-air without having to expend energy to do so.

Now imagine being able to turn that on and off at the flick of a switch. This is similar to the maglev train concept, for which power requirements are available. Just doing some quickie research (I'm low on time), the Russian MPV supposedly takes a mere "0.01Kilowatt per Metric Ton" to achieve/sustain levitation, meaning a 600lb mass could be held inches aloft with an input into the system of 2.7 watts.

Obviously just putting some concrete blocks under the maglev train would achieve the same effect with no continuing power requirement . . . no doubt Trip's family probably had such a display in their yard . . . but it certainly beats an alternative of having some sort of thrusters beneath the train providing a constant acceleration of one g.

Imagine something similar, but on a grander scale, and you have the basic idea of antigravs in sci-fi.