H3

[RisingFury]

A probe mission is usually a one way trip so using an expensive drive on a probe would only be worth it for longer missions. An earth/moon transporter is not a use-once-throw-away ship so if there is enough demand for earth/moon transfers then yes for 10 billion dollars the thing would be built.
If you just look at the estimated constellation program costs an earth/moon transfer ship that gets 900tons of payload (or maybe just 500-700 accounting for ship mass) to the moon within 24 hours with just 1000tons of drive mass (H2 or even Water would do) for just 10 billion dollars would be something they would be VERY happy to build.

The point is that this would be a craft much more suited to flying long distance missions - like a grand tour of the solar system or even on a voyage to other stars. A single high thrust burst of low Isp propellant will not do it, or will do it only if certain geometry conditions are met - as they were for the Voyager mission. If a low Isp, high thrust propulsion system would get the job done, believe me, we'd be on Mars by now.

The burntime is not 3 days but 2.78 hours for the proposal in my post above. You don't need to spiral out with that acceleration..

Three hours, sorry.

But still you have to spread the burn through several orbits before you get ejected.

But oh well if thats not working take 400kg/s massflow. Then you have only ~5000m/s total deltav but 1.4 m/s^2 acceleration so that would be ~41 minutes total burntime, thats roughly a half orbit in LEO so definately no spiraling there.

Yea, unless you wanna burn for one third of the orbit, you're gonna have to split your burn over several orbits.

Ok then lets take the Saturn example. Saturn is how far, 8-9 AU ? For simplicity lets take 10AU and calculate how long it would take us to go half the way with constant acceleration for the 3 different setups proposed:

5 AU are roughly 750e9 m

Given the acceleration we can calculate the time it takes to fly the leg as

Assuming you fly in a straight line from Earth to Saturn and that the Sun doesn't exist to pull you in. With that, the error is such that the following calculation is worthless.


Furthermore...

Finally we have the setup with 2000tons with 100ton reactor and 1000ton drive mass:
i figured out an optimal mass flow of 51.7g/s for this mission so lets see..

exhaust velocity
v = sqrt(10GW * 2 / 0.0517kg/s) = 621970 m/s

thrust
F = v * 0.0517kg/s = 32156N

acceleration
a = 32156N / 2000000kg = 0.0161 m/s^2

t = sqrt(750e9m * 2 / 0.0161 m/s^2) = 9652342s =~ 112days
at the fuel massflow of 0.0517kg/s we use
0.0517kg/s * 9652342s = 499026kg of fuel to go the 5AU so half of the fuel on board.. as already noted if we had used the rocket equation here things would even look better for this setup as the acceleration would double towards the end of the mission.

You're using an "optimal" mass flow of ~50 g/s, which will, of course, provide much better results then your suggested 100 kg/s.


For this simple calculation, using a mass flow of ~50 g/s is roughly in between 100 kg/s and 0.0284 g/s, however, your oversimplification doesn't do it justice, because a real voyage between Earth and Saturn would not follow a straight line. In fact, you need roughly 7 km/s of Delta-V for a most efficient transfer, without slinging around other planets.

Obviously a real journey would use an optimized mass flow for shortest transfer, but it would be far closer to 0.03 g/s then to 100 kg/s, which was my original point. You'd probably produce enough thrust just by cooling the reactor.


There is one more aspect to adding mass that you should take into account:
Whatever the substance you're going to add, be it water or hydrogen, will drain certain amount of power, just by introducing mass. The reason is that you'll need to overcome the binding energy, holding the molecules together and the binding energy, holding electrons within the molecule. The inefficiency will increase with the added mass flow, effectively reducing the power output of the reactor.


If I have some spare time, I'll write you the complete calculation taking into account the orbit around the Sun, the distance of the voyage, optimal mass, fuel flow and so on.

 

[Mindblast]

The point is that this would be a craft much more suited to flying long distance missions - like a grand tour of the solar system or even on a voyage to other stars. A single high thrust burst of low Isp propellant will not do it, or will do it only if certain geometry conditions are met - as they were for the Voyager mission. If a low Isp, high thrust propulsion system would get the job done, believe me, we'd be on Mars by now.

The problem we have with chemical thrusters is not the low ISP high Thrust but the low chemical energy in the fuel. To get 10GW out of LH2+LOX you'd have to burn 630kg of fuel. That leaves you with no other choice than very low isp high thrust. With fusion as an energy source we don't have this problem and can choose what isp and thrust suites the mission best.

Three hours, sorry.

But still you have to spread the burn through several orbits before you get ejected.

You'd have Hohmann transfer velocity after 30-40 minutes at 0.7m/s^2. Of course its not the most energy efficient way to burn so far from perigree but who cares..

Yea, unless you wanna burn for one third of the orbit, you're gonna have to split your burn over several orbits.

With 1.4m/s^2 you'd even have Hohmann transfer velocity after 15-16minutes burntime. Really no need to split the burn over several orbits here.

Assuming you fly in a straight line from Earth to Saturn and that the Sun doesn't exist to pull you in. With that, the error is such that the following calculation is worthless.

Even with the lowest thrust setup (1000tons 100ton reactor) you have a speed of 33km/s after accelerating for 5 AU... adding the initial speed of the earth in its sun orbit which is 29.8km/s you get > 60km/s. That may not be a straight line but it is not far from it. Of course to reach the Hohmann velocity (7km/s by your word) would require about 107days already so this setup has a problem in the initial acceleration phase. Which only shows that the high thrust setup with a = 0.0161 is even more superior as this would be at 7000m/s after 5 days already and would have a top speed of 155km/s at the 5AU point and that IS almost a straight line transfer.
Seeing that, it would probably be the best approach to use even higher massflow for high thrust in the initial acceleration within the gravity well of the starting planet and then lower the thrust once the orbit was brought to a higher eccentricity.

You're using an "optimal" mass flow of ~50 g/s, which will, of course, provide much better results then your suggested 100 kg/s.

Well of course you wouldn't go to saturn throwing out 100kg/s. That massflow was chosen for an efficient LEO/LLO transfer.

Obviously a real journey would use an optimized mass flow for shortest transfer, but it would be far closer to 0.03 g/s then to 100 kg/s, which was my original point. You'd probably produce enough thrust just by cooling the reactor.

Well using 51.7g/s would be a mixing ratio of 1815 : 1 and if i remember correctly your original point was "Why add additional mass at all ?" which i think i have shown.

There is one more aspect to adding mass that you should take into account:
Whatever the substance you're going to add, be it water or hydrogen, will drain certain amount of power, just by introducing mass. The reason is that you'll need to overcome the binding energy, holding the molecules together and the binding energy, holding electrons within the molecule. The inefficiency will increase with the added mass flow, effectively reducing the power output of the reactor.

All true.. thats why i wrote:

Assuming we can magically convert all the energy to kinetic energy...

If I have some spare time, I'll write you the complete calculation taking into account the orbit around the Sun, the distance of the voyage, optimal mass, fuel flow and so on.

Yep do that..

 

[RisingFury]

The numbers you're using now don't mean anything. You're assuming a flight of 5 AU... where the minimum distance between Earth and Saturn would be some 8 AU. Your voyage would then be longer then that because you're traveling around the Sun as well as outward.

But the biggest blunder is that you're not taking into account the change of mass over time and you're changing initial conditions.

If you're gonna do any meaningful comparison, set a ship mass, set the reactor mass and number of reactors and work out the propellant each setup will need according to a set mass flow or set the same amount of mass for each setup. Obviously, there will be an optimal setup - which should get used in a real world application, don't get me wrong - all I'm saying is that it will be far closer to the high Isp, then to the low.


And I don't think you understood what I meant with adding mass making the reactor inefficient...

Even if only 30% of the energy extracted from nuclear reaction goes towards propulsion, adding mass will further decrease the efficiency.

In both cases you have a reactor with 30% efficiency which provides power, but injecting more mass into the stream will reduce the efficiency further. The reason is that you're storing H2 or H2O or whatever you want... when you inject the dead mass into the stream, it some of the energy in the stream will be used to break the molecule apart and ionizing it. The more mass you inject, the lower your efficiency falls because you need to turn more of it to plasma. It's like trying to boil water while adding more cold water and taking the same amount of water at higher temperature away.

---------- Post added at 06:07 PM ---------- Previous post was at 05:50 PM ----------

Yea... one more thing.

The reason I'm against adding dead mass is because it's more efficient to design a larger reactor. By doubling thrust, the biggest mass penalty would be an increase by the mass of the reactor, however, I think it would be possible to design a reactor that would be able to handle a far larger mass flow without increasing the mass by a lot. VASIMR is quite capable of doing that.

 

[Mindblast]

The numbers you're using now don't mean anything. You're assuming a flight of 5 AU... where the minimum distance between Earth and Saturn would be some 8 AU. Your voyage would then be longer then that because you're traveling around the Sun as well as outward.

Have you even read the post ? I assumed covering a distance of 10AU and only calculated the initial 5AU acceleration phase of the flight, showing that the setup adding propellant mass covers the distance by far in the shortest time. Obviously the remaining 5AU to complete the 10AU ride is the deceleration which calculates exactly the same way unless the rocket equation is used which even shifts things more in favor of the drive with added propellant mass.

But the biggest blunder is that you're not taking into account the change of mass over time and you're changing initial conditions.

As said above taking the change in mass over time into account (rocket equation) will show even more benefit for the design that uses more drive mass during the trip (setup 3).

If you're gonna do any meaningful comparison, set a ship mass, set the reactor mass and number of reactors and work out the propellant each setup will need according to a set mass flow or set the same amount of mass for each setup. Obviously, there will be an optimal setup - which should get used in a real world application, don't get me wrong - all I'm saying is that it will be far closer to the high Isp, then to the low.

And thats what i did... compare setups 2 and 3.. both are 2000tons initial mass, 2 uses 11 reactors of 100 tons each, 3 uses 1 reactor of 100tons but 1000tons of additional drive mass.

Sure the ISP of ~70km/s for setup 3 is rather high compared to chemical engines but compared to the 26537km/s ISP of setup 2 it is rather low.

And I don't think you understood what I meant with adding mass making the reactor inefficient...

Even if only 30% of the energy extracted from nuclear reaction goes towards propulsion, adding mass will further decrease the efficiency.

In both cases you have a reactor with 30% efficiency which provides power, but injecting more mass into the stream will reduce the efficiency further. The reason is that you're storing H2 or H2O or whatever you want... when you inject the dead mass into the stream, it some of the energy in the stream will be used to break the molecule apart and ionizing it. The more mass you inject, the lower your efficiency falls because you need to turn more of it to plasma. It's like trying to boil water while adding more cold water and taking the same amount of water at higher temperature away.

Thats hardly a good metaphor, we are not trying to boil something here.. in fact we don't care much about the temperature of the exhaust gas but look at isp and thrust.
And about the ionizing part.. ionization energy of H2 is 1312kJ/mol so with 50g/s massflow that is about 65MW of energy going into ionization, thats not even 1% of our 10GW reactor power.
For the dissociation of H2 to 2H its even less.. 435kJ/mol so not much of a problem.

Yea... one more thing.

The reason I'm against adding dead mass is because it's more efficient to design a larger reactor. By doubling thrust, the biggest mass penalty would be an increase by the mass of the reactor, however, I think it would be possible to design a reactor that would be able to handle a far larger mass flow without increasing the mass by a lot. VASIMR is quite capable of doing that.

VASIMR is miles away from handling 10GW power though..
And if you compare my proposed engine setups 2 and 3 again you'll see that to get the same thrust of setup 3 without adding additional mass you'd have to raise the power output from 10GW to about 450GW.

Oh well i guess i can't convince you anyway, i invite you to do the math yourself and also read some of the papers on askmar i mentioned earlier (for example http://www.askmar.com/Fusion_files/QED Space Transportation.pdf)

I will close for today with my favorite xkcd link for threads like this one:
http://xkcd.com/386/