Using atmosphere as propellant

Discuss the technical details of an "open source" community-driven design of a polywell reactor.

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rjaypeters
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Post by rjaypeters »

DeltaV, such a good post! For convenience, I'm going to call your concept the "Sexy Beast".

I'm trying to (notionally) design a spaceship (hereinafter the "Truck") which won't be spending much time in the atmosphere except for fueling and loading. I'm also trying to reduce development cost by not including features found in the Sexy Beast (e.g. Holbach array fans, electric turbines, REB for supersonic flight, etc.) and using a big helicopter.

In every respect (except for two) I expect the Sexy Beast will be a superior vehicle compared to the Truck. I'd also expect the Truck to take less time and money to develop. Otherwise, the Sexy Beast will probably be the winner in whatever category you name.
DeltaV wrote:Hope your rocket consumes less than the SSME.
SSME is not the example to use. The Sexy Beast and the Truck use the same rockets powered by a Bussard. The Truck makes the transition to rocket flight a lot earlier than the Sexy Beast. So, if
DeltaV wrote: Polywell should have power to spare before orbit boost.
We can wait while the rotor stops and stows. It won't take that long.
rjaypeters wrote:Before re-entry, we have the choice of lifting the blades away from the body and aligning them above the hub before starting their rotation or just leaving them along the body. I'd prefer to leave the blades along the body and use the sink rate airflow to help lift and auto-rotate them.
DeltaV wrote:Deploying them before reentry guarantees they melt or break off.
No, it doesn't. The Truck will not be using a ballistic reentry, but a semi-ballistic and powered one (so, slower). And as I wrote, I don't prefer lifting the blades above the hub and behind the body (wrt to local airflow) before re-entry.

Further on the subject of powered re-entry, the Truck won't need as much TPS because it will be moving slower through the atmosphere.
rjaypeters wrote:I'm not saying VTOL fans won't work. I am saying for the equivalent lift, helicopter works better and is lighter.
DeltaV wrote:Polywell should have power to spare before orbit boost. Lots of lift fans if needed. Two helo rotors can't lift that much, and only give one level of redundancy, assuming they're cross-connected. Eight lift fans can tolerate losing two or three. Don't forget the complexity of rotor heads, gearboxes and cross shafts compared to Halbach rim-drive motors.

I really like the Halbach rim-drive motors. I like better that helicopter technology is well understood.
DeltaV wrote:Jumping from helicopter to rocket means you'll need to carry a lot more reaction mass, especially with the hover time needed for blade stowage.
Now, we're just going to have to run the numbers.
rjaypeters wrote:The helicopter removes the weight of the REB equipment
DeltaV wrote:Huh?
The Truck doesn't carry the REB.
rjaypeters wrote:and lets us carry (in fact, requires) more reaction mass.
Carry more, no. Sikorsky Skycrane payload is 20,000 lb. Think you're going to go orders of magnitude beyond that?

Yes, what is this project about if not going far beyond what has been done before?
rjaypeters wrote:On another point, these vehicles are going to be heavy. I'm guessing around one million pounds. We're still going to need landing pads, but flame buckets won't be required.
DeltaV wrote:So the low disk loading of helo blades becomes moot.
No. A concrete landing pad is a lot easier to build than a flame bucket.
rjaypeters wrote:I don't see loiter or atmospheric cruise as requirements which should drive the design of the first generation Polywell SSTO. IMO, high speed and/or extended flight through the atmosphere is not what we should be designing for in the first generation Polywell SSTO.
DeltaV wrote:That's trivial compared to getting to orbit. Atmospheric cruise lets you pick your orbit and your takeoff/landing locations. So you want to limit yourself to a few orbit inclinations and one or two launch/landing sites, like Shuttle?
I don't think high-speed flight through the atmosphere is trivial.

No. Pointing the Truck in the direction you want before rocket boost changes your orbital inclination. Orbital changes are orbital maneuvers. Making a big change in landing site is an orbital and powered re-entry manuever for the Truck.
rjaypeters wrote:Once we understand the Bussard better (and can make it better), follow-on vehicles should have more difficult to satisfy requirements. Else, what would the engineers do?
DeltaV wrote:Go for broke. Before the daggum gubmint regulates it all away.
You mean like the X-33 program? Sorry, that was a cheap shot and not at you DeltaV, but at the (I'm trying to nice, here) people who spent millions on that waste of a program. [end of rant]
"Aqaba! By Land!" T. E. Lawrence

R. Peters

rjaypeters
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Post by rjaypeters »

Never mind.

As nice as these notional designs are, they are too expensive to develop without some real money. Who will pay for the Sexy Beast (see my previous post), let alone the Truck?

I was wrong in my previous posts, the first Bussard-powered SSTO should be a steam rocket that looks like a scaled-up Delta Clipper.

I'm going hate giving up backyard landings, but we have the flame buckets built for liftoffs and the (much lighter usually) returning steam rocket will be able to land on a good-sized concrete pad.

Interact with the atmosphere for (edit: thrust and) reaction mass? Sure, if you have the requirements, time and money to build what you want. Otherwise, use the Bussard power to ascend as slowly through the atmosphere as you please and then pour on the coal for orbit.

edit: I should have said: "... then pour on the boron for orbit."

Thanks for your time.

"Power corrupts but wealth stupefies."
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93143
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Post by 93143 »

rjaypeters wrote:I was wrong in my previous posts, the first Bussard-powered SSTO should be a steam rocket that looks like a scaled-up Delta Clipper.
Water is a lousy SSTO propellant. The jet efficiency is terrible due to the expansion behaviour, and achieving a high coolant temperature (necessary for decent Isp in ARC mode) is difficult because ultra-high-temperature steam is corrosive. With the high average molecular weight, chamber temperatures for good values of Isp are preposterously high, meaning your magnetic shielding has to be much better than with hydrogen. Plus you can't do LOX augmentation because water doesn't react with LOX (CTF is hypergolic with water, but you might not want to mess with that stuff), so you're stuck with whatever power you can get out of the fusion reactor (for reference, the three Space Shuttle Main Engines put out almost 10 GW of jet power at sea level, or over 15 GW in vacuum, which is a lot of power for a Polywell and is still insufficient to supply more than about 18% of the launch thrust).

Also, even with liquid hydrogen, and LOX injection for thrust augmentation early in the trajectory, you still end up with a preposterously small and powerful reactor being required just to get to orbit - never mind doing a powered descent afterwards...

No, I think airbreathing is the only way.

GIThruster
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Post by GIThruster »

93143 wrote:Plus you can't do LOX augmentation because water doesn't react with LOX.
Why would it need to react?
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GIThruster
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Post by GIThruster »

93143 wrote:No, I think airbreathing is the only way.
So lets go with that for a moment? What if you diamond chemical vapor deposit on all the critical systems? Can you then use any sort of "air" or atmosphere we find on any planetoid in our system? That would be handy. . .
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93143
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Post by 93143 »

GIThruster wrote:
93143 wrote:Plus you can't do LOX augmentation because water doesn't react with LOX.
Why would it need to react?
...because otherwise the LOX is just reaction mass and it might as well be more water.

The point of LOX augmentation is to increase the available power in the regime where thrust is paramount, so you can operate at a half-decent Isp and thus don't have to use horrifying amounts of propellant getting off the pad.

Follow the link in my post, take a look at the graphs. Try to figure out where the Isp plot would intercept the y-axis if it weren't for LOX injection (hint: check out the engine efficiency plot)...
No, I think airbreathing is the only way.
So lets go with that for a moment? What if you diamond chemical vapor deposit on all the critical systems? Can you then use any sort of "air" or atmosphere we find on any planetoid in our system? That would be handy. . .
I don't know about diamond specifically - but with a hypothetical coating capable of taking the required temperatures and chemical environments, I don't see why not. (Engine design would be interesting, since you can't just design to a single flight path or even a single value of gamma...) You'll need an impervious coating on the radiators too, of course, if you want a ZMO cruise mode...

...what "planetoids" are we talking about? Earth, Venus, Mars, Titan...? The gas giants require too much speed to orbit; I'd stay the hell out of their atmospheres if I were you...

(Unless you have M-E thrusters. Funny story - the gravity at the 1 atm point on Saturn is about a gee, and Uranus and Neptune aren't far out either... Now, if I were me I'd still stay away; gas giants scare me. I like solid ground under my feet...)

My old attempt at an SSTA was pretty heavy and not very capable, because I used (loose) R^7 scaling for the cores. Using B^4R^3 with pegged superconductors favours smaller cores, so if you can fit the rest of the equipment into the form factor without arcing troubles and cooling issues and such, you should be able to get down to quite a reasonable size. (Actually, in the multi-GW range, alpha beam spreading probably starts to favour a compact collector system, which might interact with arcing and pumping issues to produce a maximum feasible power level...) The trouble is that the design problem is quite steep with respect to the reactor characteristics, and it's hard to tell what's a reasonable starting assumption and what isn't... on nasaspaceflight, I came up with a (rather optimistic) notional 10 GW reactor with a 1 m coil bore, that weighed ~20 mT with shadow shielding and 90 mT with full shielding, based on extrapolation from Bussard's component mass estimates. A reactor like that could conceivably power an all-rocket SSTO like the one I presented in the other thread, but even the shadow-shielded version wouldn't be enough for a fully-powered descent, not with engine and tankage masses taken into account...

WizWom
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Post by WizWom »

True, the ISP of water is lower than H2.

But, thrust is related to the molecular mass of the resultant; that is, the thrust for a water resistojet should be as good as the thrust for a LH2/LOX exhaust.

If you really want high thrust in a heated exhaust then go with Xenon or some other High Z noble gas. Oh, wait, that is what is planned for initial low-power resistojet and ion rockets.

Getting to orbit is not (much) about ISP - as the study of RP1 vs H2 fuels shows. It's a multi-variate equation set.

And providing power without using the fuel for it is a BIG step.

With "unlimited" power, you can take water, dissociate it, heat the gases, then push them into a reaction chamber to get back the energy of dissociation as thrust. - in addition to the energy of heating.

The whole point of a rocket is to turn potential energy into kinetic energy.
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93143
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Post by 93143 »

WizWom wrote:True, the ISP of water is lower than H2.
It's more complicated than that. Isp depends on energy per unit mass of the propellant(s), modified by expansion parameters and suchlike. Pump lots of energy into water and less into H2, and the Isp for water will be higher. (And its peak temperature will be a lot higher.)

The relationship with molecular weight is actually dependent on temperature being the limiting parameter. For a given chamber temperature, water has much lower Isp than H2, because its specific heat is lower, so at the same temperature there's less energy in it. With a magnetically-shielded engine, temperature is no longer important except as a design parameter for the magnetic shielding, and all that matters Isp-wise is energy per unit mass (and of course second-order effects like expansion chemistry). The massive advantage of H2 disappears, and all that's left are the second-order effects (a lot of which still favour H2, though tank size and deep cryogen handling favour water...).

This is why water and CO2 are not seriously considered as propellants in nuclear thermal rockets; NTRs are strictly temperature-limited. CO2 in particular is really, really bad in an NTR; you would literally get higher Isp out of a V2...
But, thrust is related to the molecular mass of the resultant; that is, the thrust for a water resistojet should be as good as the thrust for a LH2/LOX exhaust.
Thrust is only strongly related to molecular weight if the design limiting parameter is temperature.

For constant jet power, Isp and thrust are inversely proportional, and can be controlled by varying the mass flow rate. Higher mass flow rate = higher thrust and lower Isp. In a real electric rocket, the efficiency will not be constant, so it's a bit more complicated than that, but that's the general idea.
If you really want high thrust in a heated exhaust then go with Xenon or some other High Z noble gas. Oh, wait, that is what is planned for initial low-power resistojet and ion rockets.
Modern electric propulsion is focused on getting high Isp at good efficiency. Xenon is used because it has a high mass-to-ionization-energy ratio and doesn't contaminate the vehicle, not primarily for thrust reasons.
Getting to orbit is not (much) about ISP - as the study of RP1 vs H2 fuels shows. It's a multi-variate equation set.
Did you take a look at my other post? Admittedly it's only one data point, but it's interesting to note that the propellant load is 72% LOX...
And providing power without using the fuel for it is a BIG step.
Yep. It definitely helps. Mostly by increasing the available Isp. Thrust we can do already.
With "unlimited" power, you can take water, dissociate it, heat the gases, then push them into a reaction chamber to get back the energy of dissociation as thrust. - in addition to the energy of heating.
*facepalm* Why the hell would you bother doing that? Just take the energy you would have spent on cracking the water, skip the middleman and inject it into the chamber as heat. You'll avoid any inefficiencies involved in the cracking step, and you won't have to carry the equipment associated with it.

Conservation of Energy. It's not just a good idea - it's the Law...

More importantly, how did you get the idea that Polywell represents "unlimited" power? Rocket engines are very, very powerful. My notional all-rocket SSTO uses (or rather, turned out to require) an over-optimistically small and powerful reactor, and it only supplies about 20% of the engine power during the boost phase - the rest is LOX/LH2 combustion...

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Post by WizWom »

93143 wrote:
WizWom wrote:And providing power without using the fuel for it is a BIG step.
Yep. It definitely helps. Mostly by increasing the available Isp. Thrust we can do already.
Let's say I want to add 10,000 m/s to a mass of 1,000,000 kg - no matter which way I slice it, I have to add 10 Gigajoules to the mix. If I have a mass ratio of 2.5, that means I have to spend 25 GJ to do this work. Now, in a chemical rocket, that power comes from the chemical potential of the reactants. In a nuclear or fusion rocket, it comes from the power plant.

In sheer joules available, nuclear has a huge advantage; the problem is that everything nuclear but Orion has a very limited energy flow rate. If I can only put out 100 MW from a small polywell, a Space Shuttle assembly that can put out 1000 MW will seem more powerful. - even though that space shuttle can only run for 25 seconds, and my nuclear plant can run for a year.

And THAT is the reason nuclear space travel has bogged down; designing a fast reactor that's not going to melt is tough.

As for the NERVA: dumb idea, was a dumb idea from the start. The materials for making a nuclear core have to deal with the physics of fission materials, which, generally, suck. Thorium has wondrous high-temp stability, but isn't fissionable, and the oxides have poor thermal conductivity. The answer is probably to suck it up, deal with the annoyance of electrical generation, and make a high temperature heating chamber that has nothing to do with nuclear material. Separate the problems.
93143 wrote:
WizWom wrote:With "unlimited" power, you can take water, dissociate it, heat the gases, then push them into a reaction chamber to get back the energy of dissociation as thrust. - in addition to the energy of heating.
*facepalm* Why the hell would you bother doing that? Just take the energy you would have spent on cracking the water, skip the middleman and inject it into the chamber as heat.
Because it is already assumed that we are running the heating chamber at its limits, of course. So, lighter materials get to a higher speed. Plus, we get the energy we used to crack it back out - after the heating chamber.

So, we get all the thrust of the equivalent Hydrox rocket, and we get additional thrust from the electrical or nuclear heating. And all with compact and safe water.

The problem for nuclear has been and will continue to be heat rejection for the electrical cycle. Not a problem while we are using huge amounts of mass for thrust during launch - we can use the thrust mass as a heat sink, and throw the waste heat out the back. But a VERY big problem once we hit orbit and are thinking more in terms of adding a LOT of energy to a tiny amount of mass than a moderate amount to a lot of mass.
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rjaypeters
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Post by rjaypeters »

WizWom wrote:The problem for nuclear has been and will continue to be heat rejection for the electrical cycle. Not a problem while we are using huge amounts of mass for thrust during launch - we can use the thrust mass as a heat sink, and throw the waste heat out the back. But a VERY big problem once we hit orbit and are thinking more in terms of adding a LOT of energy to a tiny amount of mass than a moderate amount to a lot of mass.
The TRITON shown here:

http://www.engineeringatboeing.com/data ... 4-3863.pdf

includes a radiator for dumping the waste energy (among other things). Yeah, just _another_ thing to carry just when we are trying to remove mass...
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93143
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Post by 93143 »

WizWom wrote:Let's say I want to add 10,000 m/s to a mass of 1,000,000 kg - no matter which way I slice it, I have to add 10 Gigajoules to the mix.
50 TJ, actually.

Also, you aren't taking the energy of the ejected propellant into account.
If I have a mass ratio of 2.5, that means I have to spend 25 GJ to do this work.
No, that's not how that works.
If I can only put out 100 MW from a small polywell, a Space Shuttle assembly that can put out 1000 MW will seem more powerful. - even though that space shuttle can only run for 25 seconds, and my nuclear plant can run for a year.
You're making up numbers on the fly. Your principle is correct, but your numbers are horribly wrong.

Also, since "powerful" refers to power output, not time-integrated energy output, the Shuttle doesn't just "seem" vastly more powerful than a nuclear power plant - it is vastly more powerful than a nuclear power plant.

The Shuttle stack's power output at liftoff is 43 GW. (It would need to be higher for pure hydrolox, but the SRBs have lousy Isp to go with their great thrust.) After a couple of minutes it drops the SRBs, and before long the SSMEs are at vacuum efficiency and putting out 15 GW in total. I estimate that the vehicle averages somewhere in the vicinity of 20 GW over the entire eight-minute climb to orbit.

If you want to launch something in that size range under pure rocket thrust, you need power in the tens of GW just to get it off the ground. If you want super high Isp, you need even more power, because now the exhaust carries more energy per unit mass, meaning less thrust for each watt of power (linear vs. quadratic).
And THAT is the reason nuclear space travel has bogged down; designing a fast reactor that's not going to melt is tough.
It's not that bad. Dumbo looked pretty good; much better than Timberwind for flow uniformity, and T/W at least as good.
As for the NERVA: dumb idea, was a dumb idea from the start. The materials for making a nuclear core have to deal with the physics of fission materials, which, generally, suck. Thorium has wondrous high-temp stability, but isn't fissionable, and the oxides have poor thermal conductivity.
Again, it's not all that bad. NERVA was indeed (IMO) a worse idea than Dumbo, but for an upperstage engine it was decent.

Dumbo gets around the issues with heat transfer by simply making the fuel elements and flow channels thinner and more numerous. Laminar flow through a stack of corrugated foils/plates into a central bore; a single engine would have had several stacks like this. One of the options for the fuel elements was to use a cermet fuel layer sandwiched between two layers of tungsten foil; this would likely (it seems to me) have solved the problems with erosion/corrosion that plagued earlier NTR designs before a recent NERVA-type study settled on W-UO2 cermet with tungsten cladding. Very good high-temperature performance too.
The answer is probably to suck it up, deal with the annoyance of electrical generation, and make a high temperature heating chamber that has nothing to do with nuclear material. Separate the problems.
Bad suggestion. Do you have any idea how much extra weight you'd be adding?
93143 wrote:
WizWom wrote:With "unlimited" power, you can take water, dissociate it, heat the gases, then push them into a reaction chamber to get back the energy of dissociation as thrust. - in addition to the energy of heating.
*facepalm* Why the hell would you bother doing that? Just take the energy you would have spent on cracking the water, skip the middleman and inject it into the chamber as heat.
Because it is already assumed that we are running the heating chamber at its limits, of course. So, lighter materials get to a higher speed. Plus, we get the energy we used to crack it back out - after the heating chamber.

So, we get all the thrust of the equivalent Hydrox rocket, and we get additional thrust from the electrical or nuclear heating. And all with compact and safe water.
Your scheme:

0) Given a tank of water and a fusion reactor capable of X GW,
1) flow the water through a cooling loop, absorbing (1-E)X GW of heat,
2) crack the warm water into warm/hot H2 and O2 with a large, complex, heavy cracking plant, using Y GW of fusion power to supply Z GW of endothermic chemical power and Y-Z GW of thermal power,
3) add EX-Y GW of fusion power to the H2 and O2 as thermal energy in a preheat chamber,
4) burn the hot H2 and O2 in a combustion chamber, releasing Z GW.

Net power input into the reaction mass: (1-E)X+(Y-Z)+(EX-Y)+Z = X GW.

My scheme:

0) Given a tank of water and a fusion reactor capable of X GW,
1) flow the water through a cooling loop, absorbing (1-E)X GW of heat,
2) run the warm water straight into the 'combustion' chamber and heat it with the electrical output of EX GW.

Net power input into the reaction mass: (1-E)X+EX = X GW.

Advantages:
- No cracking plant or preheating chamber (= far lighter, cheaper, and easier to design), less potential for losses due to fewer stages.
- Doesn't require the fusion reactor to be capable of putting out enough power to crack the entire mass flow rate of water, which would set a (fairly high) lower limit on Isp and a (far too low) upper limit on thrust.

Disadvantages:
- The 'combustion' chamber has to support electric heating. This shouldn't be a big deal. Peak temperature is the same in both cases.

...

Neither scheme is capable of producing an SSTO with any halfway plausible assumption about the reactor's power-to-mass ratio. But mine's probably closer.

...

Now, it's true that your scheme might (I need to study the problem in great detail to figure this one out) have some advantages in terms of ion recombination. But you can get those advantages more surely and safely without the cracking plant, and in any case the extra energy from actually carrying hydrogen and oxygen instead of water is enormously helpful in getting enough thrust early in the burn.

Not that even that can produce a reasonable SSTO design, unless multi-GW cores come in a lot smaller and lighter than I expect (the absence of gamma rays would sure help, but not necessarily enough)...

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Post by Stoney3K »

93143 wrote:- The 'combustion' chamber has to support electric heating. This shouldn't be a big deal. Peak temperature is the same in both cases.
So, basically, you just want to build a fusion-powered kettle? ;)

You do seem to be working on the assumption that direct conversion is going to work for Polywell and we won't need to go the thermal route to generate electrical power.

Otherwise, a thermal-first, electrical next path through the engine (dump all of the Polywell's heat into the water, then bleed off a portion of the steam to spin a turbine) would be a good way to consider.
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Post by WizWom »

93143 wrote:Disadvantages:
- The 'combustion' chamber has to support electric heating. This shouldn't be a big deal. Peak temperature is the same in both cases.
It should be clear that If you heat the reactants to your maximum chamber temperature, and then get additional chemical energy from them afterwards, that your final temperature will be higher afterward than if you heat the resultant.
Stoney3K wrote:Otherwise, a thermal-first, electrical next path through the engine (dump all of the Polywell's heat into the water, then bleed off a portion of the steam to spin a turbine) would be a good way to consider.
No, that's a poor choice. What you need is a bimodal reactor; once you get out of a gravity well, you can do much better in total mission mass with high ISP; for that, you need to stop playing games with huge mass, and instead go to the v side of the momentum equation - that is, Ion propulsion.

Oh, and the actual energy for a shuttle launch:
2x Booster rockets, ISP 316, 12.5 MN each; total 39 GW @ 100%, 99.7 burn seconds, 3.9 TJ energy
3x SSME, ISP 412 avg, 1.78 MN each; 7.2 GW @ 100%, 440 burn seconds, 3.2 TJ
Thus, the engines have 7.1 TJ of energy to impart.
Orbital energy is 6.6 TJ. The rest is lost to drag.

To have a fusion rocket with any decent capacity, you are going to be talking Terajoules and Gigawatts. A 100 MW Polywell which weighs 10 tons WON'T get off the ground - except possibly as a very clumsy plane.

A reasonable Polywell for SSTO will need to provide 10 GWe in about 10,000 kg.
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Post by Stoney3K »

WizWom wrote:It should be clear that If you heat the reactants to your maximum chamber temperature, and then get additional chemical energy from them afterwards, that your final temperature will be higher afterward than if you heat the resultant...
The point is that cracking the water into separate reactants (H2 and O2) will cost you energy, which will be released afterwards when you burn the reactants. Net gain (when compared to adding thermal energy directly) is zero.
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Post by 93143 »

Stoney3K wrote:You do seem to be working on the assumption that direct conversion is going to work for Polywell and we won't need to go the thermal route to generate electrical power.
Yep. Otherwise any significant electrical generation capability is going to be very heavy, and the Isp will be limited to the same range as that of a fission NTR... I doubt a Polywell could be made anywhere near as light as a Dumbo core of the same power output, and without aneutronic fusion the major advantage is gone.
WizWom wrote:
93143 wrote:Disadvantages:
- The 'combustion' chamber has to support electric heating. This shouldn't be a big deal. Peak temperature is the same in both cases.
It should be clear that If you heat the reactants to your maximum chamber temperature, and then get additional chemical energy from them afterwards, that your final temperature will be higher afterward than if you heat the resultant.
Like Stoney3K said (and I already told you before): Conservation of Energy.

You have to add energy to water to crack it, and that energy doesn't show up as heat (inefficiencies in the process do show up as heat, but the necessary chemical energy won't). Burning the result just gets that energy back into the thermal domain; it isn't "extra" energy.

The available fusion power cannot be varied on a whim. If you have X GW available for your scheme, I have X GW available for my scheme. (Except that your engine is way way way heavier, so I can probably afford to have more.) Neither scheme provides any chemical power that isn't subtracted from the fusion power first. And you'll notice that the "heating chamber" in my scheme is the same as the combustion chamber in your scheme, so they do have to take the same temperature...
Oh, and the actual energy for a shuttle launch:
2x Booster rockets, ISP 316, 12.5 MN each; total 39 GW @ 100%, 99.7 burn seconds, 3.9 TJ energy
3x SSME, ISP 412 avg, 1.78 MN each; 7.2 GW @ 100%, 440 burn seconds, 3.2 TJ
Thus, the engines have 7.1 TJ of energy to impart.
Orbital energy is 6.6 TJ. The rest is lost to drag.
Where are you getting your numbers?

The SRB vacuum Isp is 269 seconds. Sea level is 237 seconds. Burn time is 124 seconds.

The SSME vacuum Isp is 452 seconds, sea level is 361 seconds. Most of the flight is in vacuum or near-vacuum; a flight average of 412 seconds sounds too low. Burn time is 480 seconds.

Also, at 412 seconds, 1.78 MN is 3.6 GW. Multiply by 3 and you have 10.8 GW. Plus that's roughly the sea-level thrust, so it's too low.

Total orbital energy of the Orbiter, payload, and ET is about 4 TJ. Most of the remaining ~6 TJ goes into the high-velocity exhaust gases.
To have a fusion rocket with any decent capacity, you are going to be talking Terajoules and Gigawatts. A 100 MW Polywell which weighs 10 tons WON'T get off the ground - except possibly as a very clumsy plane.

A reasonable Polywell for SSTO will need to provide 10 GWe in about 10,000 kg.
For all-rocket SSTO, yeah, it does need to be pretty light. Not necessarily quite that light, but if the engine performance I assumed can't be achieved due to ionization effects, that ~250-tonne structure+payload mass drops substantially. And you can forget about a powered descent...

I'm thinking airbreathing SSTO will work out a bit better. 100 MW is still useless, of course...

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