Can a 100 MW give you 1g in space if your total weight is, say, 2000 tons? Don't know, and don't want to figure it out right now. Considering the title of Bussard's paper, I would think we'd at least be in the right ball park. If anybody wants to figure it out, please do so.
Absolutely not.
This takes some figuring, because power and thrust are not directly related. It all depends on the engine, and the
specific impulse, or how much momentum you gain per unit mass of fuel.
Thrust is related to momentum. From Newton's second law, the total force is equal to
d/
dt(
m v) = "m dot" v + m "v dot." If we assume the propellant escapes with a fixed exhaust velocity
ve, then "v dot" is zero, and we are left with thrust
T = "m dot"
ve. "m dot" is the rate at which we consume propellant.
Power, on the other hand, is the rate of
energy exertion. If we assume our engine, powered by the Bussard device, is 100% efficient, then all of this energy goes into the kinetic energy of the propellant -- the power is the rate of kinetic energy production. In other words,
P = 0.5 "m dot"
ve2.
So let's suppose we have a spacecraft of mass M = 2000 tons (a "ton" is hereby defined as 1000 kg; to hell with archaic units!) and 100 MW power generation. We also assume that the rate of propellant consumption is small compared to the mass of the spacecraft. We require it to accelerate at 1
g, or about 10 m/s.
Thrust, therefore, is equal to M
g = 2 x 10
7 N. Thus "m dot"
ve = 2 x 10
7 N.
Substituting this in for power, we get
P = 100 MW = 0.5 (2 x 10
7 N) (
ve). Rearranging, we get:
ve = 100 MW / 107 N = 10 m/s
That should be our first warning sign -- the exhaust gas speed is not very fast. Similarly, we find that the rate of propellant consumption needed is quite high, "m dot" = 2 x 10
6 kg / s. In other words, at such a low power level, the spacecraft will consume its entire mass in only one second to produce one
g. This spacecraft has a specific impulse
Isp =
T / ("m dot"
g) =
1 second.
This is math's way of telling you your idea will never work. At such a low power level, this engine cannot possibly produce 1
g usefully. It has no hope whatsoever to ever get off the ground.
---
In orbit, however, we don't need such high acceleration, and we can tolerate lower power consumption. A Bussard device is likely to be harnessed to an ion propulsion system of some kind. Rather than force an acceleration, let's instead pick an exhaust gas speed, and see what kind of acceleration we can expect.
Ion engines have exhaust speeds anywhere from about 3,000 m/s for traditional thrusters, up to 300,000 m/s for
VASIMIR, still under development. VASIMIR is a pretty good fit to our needs -- it is a variable specific impulse drive. For a given power level, you can trade whether you want lower thrust, but efficient use of propellant (a high
Isp), or if you need higher thrust and can afford to burn propellant (at low
Isp). This tradeoff exists because thrust is linear with exhaust velocity, but energy scales with the square of velocity, and in an ion engine it is the energy, usually electrically generated, that is the limiting factor.
Let's consider these two extremes of
ve. VASIMIR is about 60-80% efficient; let's keep it at 100% just to keep everything comparable to each other.
At 3,000 m/s, a power level of 100 MW gives us an "m dot" of about 22 kg/s, for a total thrust of 66.7 kN. This much thrust pushes our 2000 ton spacecraft at (66700 N) / (2,000,000 kg) = 0.033 m/s
2, or
0.033 g. That doesn't sound like much. However, the mass consumption rate is much more reasonable. If we suppose our spacecraft is 10% propellant, then we'd be able to keep up this acceleration for about 2.5 hours, for a total delta-V of about 3 km/s. That's respectable for an upper stage, particularly for a mere 10% propellant fraction.
The other extreme, 300,000 m/s, gives us an "m dot" that's 10,000 times smaller, or 0.0022 kg/s. But it also gives us a total thrust 100 times smaller, i.e. 667 N, or only
0.00033 g. That's not enough to notice.
But. We can keep up this rate of acceleration 10,000 times as long -- nearly three years! -- using the same assumptions as above. Now our total delta-V is over
three hundred kilometers per second, or about 1% the speed of light. Not bad at all.
Of course, if you're willing to launch a 2000 ton spacecraft, there are
other options you should consider. We also haven't solved how to get 2000 tons in orbit in the first place, which is going to be nearly insurmountable.
Rather than focus on 2000 ton spacecraft, this device would be much more useful if it could be scaled to, say, 20 tons, as in the reactor section of the
JIMO concept or enough to fit in the payload bay of the Shuttle. Scaling it even smaller, say 1 ton, would be better still. But it's not clear this can be done.
Like I said on the first page, miniaturization is the key. If it can't be shrunk, it's not going to be of much value to spaceflight.
(According to
http://www.frontiernet.net/~docbob/shuttle.htm, total weight at liftoff is 4.5 million pounds; subtract 1 million pounds of solid propellant, 603 tons liquid O2, 101 tons liquid hydrogen to get about 3 million pounds in outer space)
Your arithmetic is way off. The "dry weight" of the STS stack is about 215 tons, plus about 25 tons cargo and 10 tons consumables, such as fuel for maneuvering and re-entry and air. You've only counted the solid propellant in one SRB, and I think you substituted 1,000 pounds per ton.
Rockets in general have a "propellant fraction" of about 70-85%, i.e. 70-85% is fuel that gets burned just getting the rest to orbit. The Shuttle is high at about 88%, but it's not a fair comparison because the Shuttle also includes a highly complex re-entry system, something no dumb booster has.
To compare the above exercise to the Shuttle, each SRB burns through 49,900 kg of solid propellant in about 110 seconds, and the three SSME's burn about 735 tons of LOX and H
2 in 520 seconds. The Shuttle has an aggregate
Isp of about 300 seconds. At ~ 3 MJ/kg for the solid propellant and 15.9 MJ/kg for the liquids, the 2,000 ton STS exerts about 49.5 GW of power at liftoff, to generate about 1.5
g.
This is about 500 times as much power as the Bussard generator you proposed, for slightly higher acceleration, of a similarly sized vehicle. 100 MW just isn't going to cut it.
* a tour bus - maybe we've finally got a way to get rid of Gravy!
I strongly suggest that those who need so much help shouldn't make such obnoxious remarks. Rather than try to get rid of him, perhaps you should listen to what he has to say.
For additional reading, this
junior-high school level treatment may be of some interest, courtesy our friends at NASA Glenn. Happy learning.
