Rocket thrust

If polywell fusion is developed, in what ways will the world change for better or worse? Discuss.

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Rocket thrust

Postby kunkmiester » Wed Nov 04, 2009 6:29 am

A slight discussion came up on another board about some of the ideas in this paper, specifically the supernova and hypernova class lifters:
http://techdigest.jhuapl.edu/td2703/mcNutt.pdf

Talk about trunk space! Anyway, I had the though that a polywell based rocket would cut the size down significantly, or at least do better as propulsion. I thought a bit, and looked up one of my sources:
http://www.ibiblio.org/lunar/school/Int ... stems.HTML
To see if I could figure some stuff out. I can't make heads or tails of how to get numbers for how much thrust per MW of reactor, per pound of propellant.

Say you decide to do four QED engines, running H2. You use 100 MW BFRs.

How much thrust will each engine produce, and how much fuel will be burned per second? They try to explain it in the second link, but it's all Greek to me.
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Re: Rocket thrust

Postby MSimon » Wed Nov 04, 2009 8:41 am

kunkmiester wrote:A slight discussion came up on another board about some of the ideas in this paper, specifically the supernova and hypernova class lifters:
http://techdigest.jhuapl.edu/td2703/mcNutt.pdf

Talk about trunk space! Anyway, I had the though that a polywell based rocket would cut the size down significantly, or at least do better as propulsion. I thought a bit, and looked up one of my sources:
http://www.ibiblio.org/lunar/school/Int ... stems.HTML
To see if I could figure some stuff out. I can't make heads or tails of how to get numbers for how much thrust per MW of reactor, per pound of propellant.

Say you decide to do four QED engines, running H2. You use 100 MW BFRs.

How much thrust will each engine produce, and how much fuel will be burned per second? They try to explain it in the second link, but it's all Greek to me.


You start with the temperature of the rocket chamber and the mass flow. It all falls out from that.
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Postby kunkmiester » Wed Nov 04, 2009 7:18 pm

That's not very helpful. :roll:
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Postby 93143 » Wed Nov 04, 2009 8:53 pm

It's true though. If you're in space and thus restricted to onboard propellant, the ratio between the power output and the propellant mass flow rate determines engine performance. So you optimize that depending on how much thrust you need and how hot the engine can get without self-destructing.

For a chemical rocket, engine performance is fixed, because the propellant is also the fuel, so the power-to-mass-flow ratio remains constant. The RS-25 is a high-thrust (2090 kN in vacuum) staged-combustion design with a regeneratively-cooled nozzle that's a compromise between sea level and vacuum efficiency, and it has an exhaust velocity of 4440 m/s in vacuum. The RL-10B-2 is a low-thrust (110 kN in vacuum) expander-cycle design with a regeneratively-cooled upper nozzle and a big ablative vacuum nozzle extension - but it uses the same propellant as the RS-25, so the exhaust velocity is about 4530 m/s in vacuum.

Note that you can simply multiply exhaust velocity by mass flow rate to get thrust.

For a fusion rocket, you can vary the mass flow rate independent of the power supply. This opens up options. Say you're using VASIMR. Jet power efficiency of 65%, 200 MW. At 50,000 m/s exhaust velocity, the mass flow rate required is about 100 g/s, and the thrust is about 5 kN. At 300,000 m/s exhaust velocity, the mass flow rate required is less than 3 g/s, and the thrust is below 900 N. Note that the thrust isn't dropping as fast as the mass flow rate, so with a given amount of propellant you can impart more overall kick to the vehicle with a high exhaust velocity (makes sense, right?), but if you need high thrust because you're in a hurry or a gravity well, you may have to compromise.

The fact that VASIMR's jet power efficiency is known (well, predicted, but the main point is it's available) makes the above a lot easier - you don't have to mess with ionization energies and specific heat ratios and expansion ratios and magnetic nozzle detachment efficiencies; you just use F_jet = mdot*v_exh and P_jet = 0.5*mdot*v_exh^2 (that's what I did above; I used P_jet = 130 MW and went from there). The temperatures involved in this case are very high, which is why VASIMR uses magnetic confinement - no material exists that could take the heat...

Also note that VASIMR has different quoted exhaust velocity ranges for different propellants - argon, for instance, has a limit of around 50,000 m/s, while 300,000 m/s is possible with hydrogen. This is probably due to temperature issues. For a given power input, if you want the particle energy (ie: temperature) to stay the same, you have to keep the number of particles per second the same, so if the particles are heavier the mass flow rate goes up. The difference between 50,000 m/s and 300,000 m/s is roughly the same as the square root of the mass ratio between argon and hydrogen, which supports this interpretation.

Specific impulse (Isp) is just exhaust velocity divided by g (scaling engine performance by propellant weight instead of mass). If exhaust velocity is in m/s, g = 9.80665 m/s^2, so the RS-25 gets 452.5 seconds of Isp and the RL-10B-2 gets 462 seconds. VASIMR gets a maximum of 5000 s with argon or 30,000 s with hydrogen. Dr. Bussard's CSR drives range between (IIRC) 800 s and 70,000 s, but require development.


If you're NOT in space, you can use air as propellant. The fun part about this is it's free - using more air with the same power input increases thrust, but it doesn't increase internal propellant expenditure, so the total impulse goes up as well. This is why the Boeing 777 has such huge fat ultra-high-bypass turbofans - more mass ejected slower gives you the thrust you want for less fuel, because of the fact that thrust scales with exhaust velocity but power scales with exhaust velocity squared.

If you're going for a Polywell-powered orbital launcher, you'll want a bit more than 400 MW... Bussard's notional ARC-QED SSTO spaceplane used a 6 GW reactor, which is roughly similar to the combustion power of one RS-25. Using only onboard hydrogen as propellant, at an Isp of 2000 s, thrust would be about 600 kN, or about 30% of an RS-25, even with very high jet power efficiency. For horizontal takeoff and winged flight this might be reasonable, though the challenge is getting the hydrogen coolant hot enough that you can cool the reactor with a mass flow rate that low (using a refrigeration cycle to get the coolant hotter doesn't waste energy because the extra power used for refrigeration all winds up in the exhaust anyway). With airbreathing, you can do much better; the thrust doesn't have to suffer even at high Isp, and you can dump (and burn!) more hydrogen coolant without losing so much performance - but this is still definitely not a Nova-class booster... though if the power-to-weight ratio of the reactor is high enough you could use a cluster for that... about 30 of them would match the power output of the Saturn V first stage, but the F-1 had a sea-level Isp of only 263 seconds, so you'd still either need to go airbreathing or lose thrust and thus overall vehicle weight (the Saturn V could barely lift itself; T/W at takeoff was about 1.14)...

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Postby kunkmiester » Thu Nov 05, 2009 6:30 am

That helped a lot more. I'm still not sure I have what I need to get the info I want.

Specific impulse has always seemed a mystery to me--an esoteric figure that talks a lot without saying much. With lbs/newtons/Kg of thrust, you can do your work over time equations, and the propellant flow rates tell you how long it can run. Nothing fancy.

Looking at the Saturn V wikipedia page, it says that the first stage had 7.6 million pounds of thrust, and ran for 150 seconds. I can work with those numbers. If I knew the flow rate for the propellant and oxidizer, I can calculate how much of each I need to make that run.

A watt is a joule per second. So, a 1000MW reactor pumps out 1000 Mj per second(for the QED engine, this is how much heat you're putting in the propellant, assuming 100% efficiency). An advantage to a fusion rocket like you said is that you're not limited to certain flow rates. Let's use H2 for an unrelated reason--you don't have to worry about that small neutron fraction irradiating it.

If I build a single stage to orbit, I'll probably throttle down the propellant feed as I get up higher, and efficiency becomes more important than raw thrust. So, I can look up the specific heat of hydrogen: 14.304 J/g•K. Heat in a gas is basically the average particle speed.

I can run the math to get the temp of a certain mass flow of propellant. What I don't know is how to get the thrust from that. To go back to the Saturn V anology, using those thrust/time weights would give the amount of propellant needed to get the same lift performance--200,000 lbs to LEO or 100,000 lbs to LO. It's crude, but it works. And it makes a lot more sense to a layman who can barely figure out what ISP is, let alone how to use it.
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Postby MSimon » Thu Nov 05, 2009 9:43 am

Here is a rocket engine simulator that might help:

http://www.grc.nasa.gov/WWW/K-12/rocket/ienzl.html

The math:

http://www.grc.nasa.gov/WWW/K-12/rocket/rktthsum.html

and a Joe Strout page:

http://www.strout.net/info/science/rocketsim/links.html

Maybe we can get Joe to chime in here.
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Postby taniwha » Thu Nov 05, 2009 10:02 am

Start from first principles...

Basic rocket equation:

F=Me*Ve

F = thrust in Newtons
Me = propellant mass rat (kg/s)
Ve = velocit of propellant (m/s)

E=M*V^2/2 (energy) (^ is power)
P=E/t (power)

Using dimensional analysis (sorry, don't know of a better way to show this):
E=kg*(m/s)^2/2 (I think constants are normally left out, but anyway...
P=kg*(m/s)^2/(2*s)
=kg*m^2/(2*s^3)
F=(kg/s)*(m/s)
=kg*m/s^2

Hmm, that's just a "m/(2*s)" [Ve/2] shy of power, so...
P=F*Ve/2
=(kg*m/s^2)*(m/(2*s))
= kg*m^2/(2*s^3)
This also means that
P=Me*Ve^2/2

This is just the power in the exhaust. Required engine power will be higher due to inefficiencies.

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Postby 93143 » Thu Nov 05, 2009 7:02 pm

The name "rocket equation" is usually used to refer to Tsiolkovsky's equation:

deltaV = v_exh*ln(m_initial/m_final)

where the exhaust velocity v_exh = g*Isp. This gives you the change in velocity resulting from a rocket burn with a given Isp, using the ratio of vehicle masses before and after the burn. Naturally if you're talking about a launch vehicle there are gravity losses and drag losses to account for, so the actual delta-V required is higher than the final velocity achieved.

kunkmiester wrote:Looking at the Saturn V wikipedia page, it says that the first stage had 7.6 million pounds of thrust, and ran for 150 seconds. I can work with those numbers. If I knew the flow rate for the propellant and oxidizer, I can calculate how much of each I need to make that run.


A good estimate can be had by using the quoted Isp of 263 s. With a thrust of 34,020 kN, we have

F_jet = mdot*v_exh

34,020,000 = mdot*(263*9.80665)

mdot = 13,190 kg/s

Some web pages mention 15 tons per second. If that's short tons (1 t = 2000 lbs), it makes sense. A metric tonne is 2204.6226 lbs.

Note that the thrust and Isp change during the burn, due to the drop in atmospheric pressure. But the fuel flow rate shouldn't change too much.


Isp isn't really that difficult. Impulse is thrust*time. Specific impulse is a measure of how much impulse in pound-seconds you can get from a pound of fuel. Or newton-seconds from a newton of fuel. The fact that weight of fuel is used rather than mass is a bit of a hack; it means you need to multiply the number by Earth's surface gravity to actually use it, which is pretty arbitrary and makes it not really a universal measure - but the result is that Isp is in seconds, and EVERYONE uses seconds, which makes it a universal measure in a different sense. If you say a particular nuclear thermal rocket has an Isp of 850 seconds, any rocket scientist anywhere in the world will immediately know exactly what you mean. No need to convert from ft/s to m/s...

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Air-breathing variants...

Postby Nik » Fri Nov 06, 2009 12:38 am

If you check out the technical PDFs referenced from Reaction Engines' site, you'll get an idea of how much reaction mass 'air breathing' saves.
http://www.reactionengines.co.uk/

IIRC, they also realised that it may be better to carry extra hydrogen as coolant and burn it *inefficiently* than to carry the extra turbo-machinery etc required to burn it efficiently...

Another thought: A pure, Polywell-fired system may dump too much ozone on the neighbours. That could mean the elegant, all-electric cycle becomes the afterburner / rocket phase of a vehicle with regular turbojet operation below ~10,000 feet...

Um, could your design take off and land on electric fans ? Analogy would be diesel-electric locos. Beyond smog risk, the electric 'afterburner' kicks in. I suppose the best analogy is ships with diesel cruise and turbine sprint...

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Postby 93143 » Fri Nov 06, 2009 2:50 am

Dr. Bussard's notional SSTO spaceplane used kerosene-fueled turbojets to get up to Mach 2, because they perform better at low speeds than the fusion drive does.

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Postby kunkmiester » Fri Nov 06, 2009 4:46 am

It looks like I might actually have enough to do the math to get the information I want.

I was looking at H2 for propellant not just for the ozone, which I'd not known about, but makes sense, but also for isotopes produced by the neutron flux. Running air will make a variety I'm sure. Also, the nozzles and other hardware can be optimized better for a single fluid, I'd imagine.

I've been told efficiency relies in part on how fast your exhaust stream is flowing, versus the airflow around the form. This is why turbofans are so much more efficient than tubojets--you have a supersonic exhaust stream from the jet, whereas the fan has it closer to the cruising speed of the airliner.

This is virtually impossible for some flight regimes--starting from 0 m/s on a launch pad means you'd need an impossible amount of propellant flow to actually lift. For Bussard's idea, you wouldn't necessarily need traditional turbojets, you'd just need to run your engine so that the exhaust velocity is closer to the airstream velocity. If he decided to use kerosene for this reason, it's because he didn't think that you could run the engine at the different flow rates. I find this hard to believe. throttling a pump isn't hard, and the fact that you'd be throttling at the upper end of the flight path anyway, as the high thrust isn't as necessary, means you might as well start out hard, and lean out the propellant feed as needed. Even easier if you're not limited to just onboard propellant, too.

I agree that the runway shuttle is a better design, but if you look at page eleven of the pdf I linked to, and check out the size of those rockets, you'll see what I saw--that kind of thing is ridiculous. that let to the thought of what you'd need to get the same specific impulse with QED rockets. Confusion of a variety of things led to the slightly easier process of duplicating the Saturn V performance, as an easier problem that can be checked easier.
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Postby 93143 » Sat Nov 07, 2009 9:25 pm

kunkmiester wrote:I was looking at H2 for propellant not just for the ozone, which I'd not known about, but makes sense, but also for isotopes produced by the neutron flux. Running air will make a variety I'm sure.


Not so much, I think.

(A) The neutron flux from a p-11B reactor is about one hundred millionth of the neutron flux from a neutronic reactor of comparable power. I wouldn't expect significant activation even of the reactor structure, never mind the propellant.

(B) If the reactor is fully shielded, the airflow won't even see that neutron flux. If it's only shadow-shielded, how does the propellant airflow see any more neutrons than the aerodynamic flow around the vehicle?

Also, the nozzles and other hardware can be optimized better for a single fluid, I'd imagine.


That depends on the engine design. De Laval nozzles are pretty universal. The rest of the engine does get substantially heavier and more complicated if you try to make it airbreathing, but even with chemical fuels it's possible to design an engine that makes it worthwhile. The potential improvement in capability from running airbreathing is not small, as you'll see below.

I've been told efficiency relies in part on how fast your exhaust stream is flowing, versus the airflow around the form. This is why turbofans are so much more efficient than tubojets--you have a supersonic exhaust stream from the jet, whereas the fan has it closer to the cruising speed of the airliner.


Not quite. Thrust-to-power ratio (which is a completely different efficiency measure from Isp, by the way) depends on the difference between initial and final propellant velocities (initial propellant velocity being the velocity of the ambient air for an airbreather, or the velocity of the vehicle for a rocket). So what you've said is true only for airbreathing engines.

The underlying reason is simple Newtonian mechanics - momentum is proportional to mass and velocity, but energy is proportional to mass and the square of the velocity. If you do the math, you find that an increase in mass flow rate combined with a proportionate decrease in propellant velocity change gives you the same thrust for less power.

Unfortunately, this means airbreathing engines tend to get less efficient at high speeds, all else being equal. Since the airflow initial velocity is higher, the energy required to induce a given change in velocity is also higher. And since the power requirement curve flattens as you approach final velocity=initial velocity, once you pass a certain airspeed you find that a straight rocket design would get more thrust than an airbreathing engine at the same power level no matter how high the airbreather's mass flow rate gets (the airspeed in question obviously depends on the Isp of the rocket being compared). Of course, the airbreather will still have higher Isp than the rocket because most of the propellant is still free...

With chemical engines all of this is heavily constrained by the coupling of power and internal propellant expenditure, in addition to various associated practical difficulties. Fusion power frees things up a bit, but you do eventually still run into practical difficulties (ozone, magnetic shielding requirements, minimum coolant mass flow rates, etc.).

For Bussard's idea, you wouldn't necessarily need traditional turbojets, you'd just need to run your engine so that the exhaust velocity is closer to the airstream velocity. If he decided to use kerosene for this reason, it's because he didn't think that you could run the engine at the different flow rates. I find this hard to believe. throttling a pump isn't hard, and the fact that you'd be throttling at the upper end of the flight path anyway, as the high thrust isn't as necessary, means you might as well start out hard, and lean out the propellant feed as needed.


There are two measures of engine performance. One is thrust-to-power ratio, which is a measure of how fast your vehicle can go with a given energy input. The other is specific impulse, which is a measure of how fast your vehicle can go by expending a given fraction of its internal mass as propellant.

For a jet engine, thrust-to-power ratio is directly proportional to specific impulse (roughly, since you're probably still expending some internally-carried propellant).

For a rocket engine, thrust-to-power ratio is INVERSELY proportional to specific impulse.

You can't just run a lot of propellant out the back of a rocket and expect high "efficiency". You'll get a lot of thrust, yes, but you'll run out of propellant in no time flat. Modern multistage chemical rockets actually do this - that's why they're multistage. The Saturn V used almost a tenth of its first stage propellant just clearing the launch umbilical tower.

Check out Figure 7 on page 5 of this pdf. Bussard has apparently done the analysis, and turbojets are just better than the ARC-QED rocket at low Mach numbers.

Even easier if you're not limited to just onboard propellant, too.


Yes. Much easier. But engine design gets... interesting, which may be why Bussard didn't go that route right away. More advanced SSTO designs are probably possible...

I agree that the runway shuttle is a better design, but if you look at page eleven of the pdf I linked to, and check out the size of those rockets, you'll see what I saw--that kind of thing is ridiculous. that let to the thought of what you'd need to get the same specific impulse with QED rockets. Confusion of a variety of things led to the slightly easier process of duplicating the Saturn V performance, as an easier problem that can be checked easier.


The payload mass fraction of that thing is below 5%. Even with relatively casual design, Bussard's spaceplane gets 14%, and I suspect it could do better with heavy optimization by a couple of competing teams of geniuses. It could also be scaled up - the Skylon D series is already bigger and heavier than Bussard's SSTO. Of course, all this only buys you maybe ~100 tonnes to orbit, unless you want to get really special with the runways and ground handling...

Also remember that Polywell would be useful for in-space propulsion as well, which would result in a substantial reduction in IMLEO requirements for missions anywhere in the solar system. Not necessarily two orders of magnitude substantial, but still...

VTOL SSTO could prove to be feasible with Polywell, if the power-to-weight ratio of the reactor and supporting equipment can get high enough. You could then make a heavy lifter as big as you wanted (subject to ground infrastructure and acoustic concerns). The enormous specific energy advantage from fusion power, combined with the large penalty in dry weight, might make airbreathing a good idea even for a VTOL - probably ram air in an RBCC configuration, accepting the penalty associated with a rocket liftoff and offsetting it with the advantage of much lower propellant usage in flight. Back in the optimistic '60s they tossed around ideas for air-augmented super heavy SSTOs - fusion might make something like that worthwhile. But I haven't looked into it in detail; the lack of hard numbers on all-up Polywell system masses makes it difficult...

One thing you'd have to watch is the power requirements for the rocket liftoff. If you could get the Polywell cluster to produce MUCH more power than would be developed by a kerolox cluster capable of lifting the vehicle, it might be possible to just do a Liberty-ship-type design with high-thrust rocket propulsion in the multi-thousand-second range for Isp (the chart in Bussard's paper is right around there, you'll recall), allowing partially propulsive descent and landing after a launch. Naturally this possibility is dependent on a sufficiently large achievable power-to-weight ratio for the Polywell and associated systems...

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Postby D Tibbets » Sat Nov 07, 2009 11:24 pm

Why worry about ozone? So long as there were not to many space planes flying, some more ozone may be a good thing (if you do most of your accelerating in the stratosphere). Heck takeoff from Chile and fly over Antartica in polar orbits to fill the ozone hole :wink: Of course that would be somewhat inconvient for trying to get something to an equatorial orbit.

As far as conventional takeoff space planes, do the constraints concider cheating by using strap on rocket boosters like many Air Force planes have used in the past (like B47, C-130, etc)?

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Postby 93143 » Sun Nov 08, 2009 12:33 am

D Tibbets wrote:Why worry about ozone? So long as there were not to many space planes flying, some more ozone may be a good thing (if you do most of your accelerating in the stratosphere). Heck takeoff from Chile and fly over Antartica in polar orbits to fill the ozone hole :wink: Of course that would be somewhat inconvient for trying to get something to an equatorial orbit.


The concern is ground-level ozone. Large amounts of it near populated areas. We don't need that.

As far as conventional takeoff space planes, do the constraints concider cheating by using strap on rocket boosters like many Air Force planes have used in the past (like B47, C-130, etc)?


...

I'll just link you to this previous rant of mine, lest I spend all evening on a massive broadside:

http://forum.nasaspaceflight.com/index. ... #msg427616

The immediately ensuing discussion provides some elaboration if you want it.

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Postby taniwha » Sun Nov 08, 2009 6:57 am

93143: Oops, so it is. "F=Me*Ve" is such a fundamental equation to the derivation of the rocket equation, I got the two confused.


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