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

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Re: Rocket thrust

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


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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

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Postby MSimon » Thu Nov 05, 2009 9:43 am


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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


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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


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

Evil is evil, no matter how small

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Postby 93143 » Sat Nov 07, 2009 9:25 pm


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

To error is human... and I'm very human.

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


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



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