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Thread: Fusion RAIR is worthless!

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    Fusion RAIR is worthless!

    Since I had a hard time finding the formulas for determining the efficiency Ram-Augmented Interstellar Rocket propulsion, I thought I'd derive it's performance on a theoretical basis.

    For those of you who aren't familiar, a Ram-Augmented Interstellar Rocket (or RAIR) is kind-of like a Bussard interstellar ramscoop, except instead of using the scooped-up interstellar medium for fuel it uses it only for reaction mass. This gets around the Bussard fusion-fuel ramscoop's main problem: if you want to inject the incoming interstellar hydrogen into your fusion reactor, you have to slow it down (relative to your spacecraft). You can't expect to shoot it into your fusion chamber at 1/10 of the speed of light and not run into insurmountable problems. By slowing the incoming material down, though, you're causing drag. Your spacecraft's top speed could never exceed its own exhaust velocity! So, by using the scooped-up matter ONLY as reaction mass to push against, you no longer need to slow it down, and you could hypothetically use it as extra reaction mass to make your engines more efficient.

    Or ... could you? Would it actually help?

    My main (optimistic) assumption was that you had a perfectly efficient nuclear fusion engine, which could fuse all of your onboard hydrogen fuel into helium, and allocate all the energy from this burning process in any ratio you desire between your helium fusion products and the incoming ram-scooped reaction mass.

    You immediately run into two big problems:

    1. The interstellar medium is extremely thin. In the "local fluff" in which the sun and a few neighboring stars are embedded, the density of the interstellar medium is only about 1 atom of hydrogen for every 10 cubic centimeters. (Outside the local fluff it's even worse.) This means that if your starship had a ridiculously huge 1000 km radius scooping field, at 10% of the speed of light you'd only be scooping up 15 grams of hydrogen per second. Even a modest spacecraft would have to weigh in at at least 100 tonnes empty to carry anything even remotely interesting, and that's the empty mass, before the mass of your unexpended fuel is added in. Even with perfect hydrogen-to-helium nuclear fusion (assuming no ram-assist), you'd be burning about an ounce of fuel (28 grams) every second to accelerate that 100 tonne spacecraft at 1g. That's nearly twice the mass of material you're scooping in for "reaction mass". And realistically, if your mission calls for you to go significantly faster than 10% of light speed, your fuel load at 10% of light speed is going to at least double your spacecraft's mass, so you'd actually have to burn at least twice this much fuel.

    2. The reaction mass isn't standing still when you scoop it in. It's zipping down your gullet at 30,000 kilometers per second. What does this mean from the standpoint of the Conservation of Energy, and the Conservation of Momentum? It means it's going to take a hell of a lot more energy to impart a given amount of momentum to 15 grams of this matter, than it will to impart the same amount of momentum to the spent fuel products (which at the moment of burning are travelling along with you at the same speed as your spacecraft).

    This second one is the big killer. How much more energy does it take? Well, for your normal exhaust, the kinetic energy you'll have to add to get a mass m up to a speed v is:

    E = 0.5 m v2

    ... because it starts out with a velocity of 0. But, the ram-scooped material starts out with a velocity of 30,000,000 meters per second. So if the same energy E were applied to it, the formula to determine how much faster it's going afterward (dv) becomes:

    E = 0.5 m (30,000,000 m/s + dv)2 - 0.5 m (30,000,000 m/s)2

    Note that the magnitide difference between v and dv is independent of the size of m. It would not matter even if interstellar space were filled with bowling balls. That second equation will always be less efficient than the first. Convert it to momentum in a variety of cases, and see for yourself!

    And this is even assuming that you've completely overcome the drag problem and that the incoming material can be scooped up with no drag at all.




    Bottom line: With perfect nuclear fusion, where the energy released can be routed entirely into kinetic energy of your fusion products or the ram-scooped mass or both, RAIR buys you nothing.

    It might be useful for braking and refuelling near the end of the voyage, but as an acceleration trick it's worthless.

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    Quote Originally Posted by tracer View Post
    This second one is the big killer. How much more energy does it take? Well, for your normal exhaust, the kinetic energy you'll have to add to get a mass m up to a speed v is:

    E = 0.5 m v2

    ... because it starts out with a velocity of 0. But, the ram-scooped material starts out with a velocity of 30,000,000 meters per second. So if the same energy E were applied to it, the formula to determine how much faster it's going afterward (dv) becomes:

    E = 0.5 m (30,000,000 m/s + dv)2 - 0.5 m (30,000,000 m/s)2
    You're making a pointless comparison. You get no points for dumping a certain amount of energy into the exhaust. What matters ultimately is how much speed your starship gets. In the ideal situation, the exhaust ends up with zero kinetic energy, while the starship ends up with all of the kinetic energy. So you don't want dv to be high. In fact, the lower, the better! In the ideal case, the "road" has a total mass so much greater than the vehicle that pushing on it produces practically no "recoil" on the road. That way, 100% of the kinetic energy pumped into the system goes into the vehicle.

    You do note, correctly, that this "road" is extremely thin, so you'd need to be moving very fast before the "road" is massive enough to be useful.

    I had long ago given up on the idea of RAIR using the natural interstellar medium, but I have since considered ideas involving artificial "runways" of reaction mass pellets in place of the ISM.

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    Quote Originally Posted by IsaacKuo View Post
    You're making a pointless comparison. You get no points for dumping a certain amount of energy into the exhaust. What matters ultimately is how much speed your starship gets. In the ideal situation, the exhaust ends up with zero kinetic energy, while the starship ends up with all of the kinetic energy. So you don't want dv to be high. In fact, the lower, the better! In the ideal case, the "road" has a total mass so much greater than the vehicle that pushing on it produces practically no "recoil" on the road. That way, 100% of the kinetic energy pumped into the system goes into the vehicle.
    From my computation, this only works if the mass of the accelerated material is significantly larger than the spacecraft itself. (Conservation of momentum between the accelerated scooped-up mass and the accelerated spacecraft, don'tcha know.)

    How did you propose pushing against the "road" without dumping energy into it?

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    Quote Originally Posted by tracer View Post
    From my computation, this only works if the mass of the accelerated material is significantly larger than the spacecraft itself.
    That is correct.
    How did you propose pushing against the "road" without dumping energy into it?
    Assuming the "road" starts off at zero velocity, you manage to dump less energy into it the more massive it is (in comparison to the starship).

    But if the "road" starts off with some velocity going in the desired direction, then you can actually get away with dumping all of the kinetic energy into the starship.

    For example, suppose the "road" and the starship both have a total mass of 1kg (not realistic, of course, but it makes the mass easier). You start by using, say, a lunar mass driver to accelerate the "road" to 1000km/s and then the starship to 1000km/s. This requires the mass driver to pump in 1E12J of kinetic energy.

    Next, the starship accelerates down the "road", pushing each bit of road rearward by 1000km/s. Overall, this requires pushing both the road and starship by 1000km/s, so it requires the starship to pump in 1E12J of kinetic energy.

    In the end, the starship ends up moving at 2000km/s, with a total kinetic energy of 2E12J--in other words, the starship ends up with 100% of the kinetic energy which was originally pumped into the system. The "road" ends up moving at 0km/s, with a total kinetic energy of 0J.

    The general principle is for the road to be pushed rearward by exactly as much as its original forward velocity was. This way, kinetic energy isn't pumped into the road--instead, kinetic energy is "stolen" from the road. It's like pushing off of a moving platform. You get an extra boost from the fact that the platform is moving.

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    Of course, if you don't slow the incoming material down on its way through your ship, your argument falls down.

    If you use the fusion energy to accelerate the incoming gas to a higher velocity than it entered, you are gaining velocity. This is what a jet engine, ram jet or scram jet does in the atmosphere.

    I think the way you are looking at it is fundamentally flawed. If you speed up the passage of the gas through your engine, so that it is exiting the exhaust faster than it entered the intake, you will gain velocity. I don't see the need "in principle" why it needs to be slowed down to zero first.

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    I'm not saying the ram scoop idea is actually feasible by the way, in fact I'm sure it's not, I'm just talking about the principle.

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    Quote Originally Posted by kzb View Post
    Of course, if you don't slow the incoming material down on its way through your ship, your argument falls down.
    That isn't the place where his argument falters. In his equation, he gives the propulsion system the benefit of the doubt, assuming that 100% of the incoming material's kinetic energy is either recovered or never lost.

    He notes that the velocity change of the ISM material will always be less than the exhaust velocity you'd get from just a plain old fusion rocket (ignoring the ISM material). This is true, but it misses the point. What matters is the velocity change of the starship rather than the velocity change of the reaction mass.

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    Yeh OK. I thought we were slowing the incoming gas to zero velocity relative to the ship then speeding it up again. But given that we are not, and also since we are assuming 100% efficiency, I would expect that the two would be equal in terms of momentum change.

    From memory, hydrogen fusion should result in products travelling at 12%c. But that kinetic energy could also be used to do work on a secondary reaction mass, and given 100% efficiency, the two should have the same result.

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    Quote Originally Posted by kzb View Post
    I think the way you are looking at it is fundamentally flawed. If you speed up the passage of the gas through your engine, so that it is exiting the exhaust faster than it entered the intake, you will gain velocity. I don't see the need "in principle" why it needs to be slowed down to zero first.
    I was talking about a "true" Bussard fusion ramscoop when I said the incoming material would have to be slowed down, not a RAIR. Obviously, in a RAIR the incoming material would not need to be slowed down.

    In Bussard's original design, the incoming material is used as fusion fuel. There's no known way to fuse hydrogen into helium while it's zipping through your gut at 10-90% of the speed of light rearward. Every piece of fusion technology on the table or on the drawing board requires the reactants to be injected into the fusion chamber at about the same speed that the fusion chamber is travelling.

    If you know of a "scramjet" design that induces proton fusion while the protons are zipping past at nearly the speed of light, I'd like to hear about it!

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    Quote Originally Posted by kzb View Post
    Yeh OK. I thought we were slowing the incoming gas to zero velocity relative to the ship then speeding it up again. But given that we are not, and also since we are assuming 100% efficiency, I would expect that the two would be equal in terms of momentum change.

    From memory, hydrogen fusion should result in products travelling at 12%c. But that kinetic energy could also be used to do work on a secondary reaction mass, and given 100% efficiency, the two should have the same result.
    Okay, let's say you have 1000 Joules of kinetic energy.

    You have a choice of adding this 1000 Joules to either a 1 gram mass, or a 100 gram mass.

    KE = 1/2 m v2 , right?
    That means v = SQRT (2 * KE / m)

    If you give 1000 Joules of KE to the 1 gram mass, it'll be travelling at v = 1410 m/s
    If you give 1000 Joules of KE to the 100 gram mass, it'll be travelling at v = 141 m/s


    Now, how much momentum is this?

    p = mv , right?

    For a 1 gram mass at 1410 m/s, p = 1.41 kg m/s
    For a 100 gram mass at 141 m/s, p = 14.1 kg m/s


    Same amount of kinetic energy.
    TEN TIMES the momentum.







    BUT, this analysis assumes that the 1 gram mass and the 100 gram mass both start out at velocity 0 (relative to you). If the 100 gram mass starts out at a velocity of 30,000,000 m/s, you're going to get a MUCH different result.

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    Quote Originally Posted by tracer View Post
    In Bussard's original design, the incoming material is used as fusion fuel. There's no known way to fuse hydrogen into helium while it's zipping through your gut at 10-90% of the speed of light rearward.
    That's okay because there's no known way to fuse hydrogen into helium while it's not zipping through your gut at 10-90% of the speed of light rearward. The reaction cross section of protium-protium fusion is terribly low. Even in the intense oven of stellar cores, it takes billions of years for a typical hydrogen to react.
    Every piece of fusion technology on the table or on the drawing board requires the reactants to be injected into the fusion chamber at about the same speed that the fusion chamber is travelling.
    That's not exactly true. The classic piece of fusion research equipment--the fuzor--uses reactants which are screaming toward the fusion chamber at high speeds. In fact, it is this speed which gives the nuclei enough "oomph" to hit each other forcefully enough to react.
    Quote Originally Posted by tracer View Post
    BUT, this analysis assumes that the 1 gram mass and the 100 gram mass both start out at velocity 0 (relative to you). If the 100 gram mass starts out at a velocity of 30,000,000 m/s, you're going to get a MUCH different result.
    One critical thing you're failing to consider is the amount of energy it took to accelerate a rocket's reaction mass up to its current velocity.

    In fact, both a rocket and a "runway" vehicle can have comparable efficiency. Neither has a big inherent advantage over the other. A rocket has to spend energy to accelerate the propellant it takes along with it, but it can recover this energy if its exhaust velocity matches its delta-v. A "runway" vehicle doesn't waste energy accelerating its propellant along with it, but as you note it takes a lot of energy to get a "push" off of a runway that's already moving rearward compared to you.

    These factors more or less even out. Ultimately, in both cases you end up with the starship with up to 100% of the kinetic energy pumped into the system, and the "exhaust" with as little as 0% of the kinetic energy pumped into the system.

    Where the "runway" system can win out is if the rocket's average exhaust velocity does not match the delta-v. If you want a cruise velocity which exceeds the average exhaust velocity of your rocket thruster, then the rocket equation implies exponential increases in the mass ratio as well as exponentially increasing losses in efficiency.

    A "runway" system, in contrast, can theoretically maintain a quadratic increase in mass ratio, and maintain a flat efficiency curve.

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    Quote Originally Posted by tracer View Post
    It might be useful for braking and refuelling near the end of the voyage, but as an acceleration trick it's worthless.
    As for most matter, I'm buying your explanation. Any way to rarify the incoming stream to limit it to particles which we can easily deal with at relativistic speeds?

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    Same amount of kinetic energy.
    TEN TIMES the momentum.

    I guess I just don't know what we are comparing so perhaps I should shut up. However, if you have 100X the mass, you also have 100X the energy, because we are fusing it all, and with 100% efficiency in both cases.

    If you fused 100X as much mass you would have 100X as much kinetic energy and also 100X as much momentum.

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    Quote Originally Posted by kzb View Post
    However, if you have 100X the mass, you also have 100X the energy, because we are fusing it all, and with 100% efficiency in both cases.

    If you fused 100X as much mass you would have 100X as much kinetic energy and also 100X as much momentum.
    The issue isn't "how much do we burn?".

    It's "now that we've burnt it, how much material do we impart that energy to?".

    The deal with a RAIR is that you don't fuse the incoming material -- you fuse the fuel in your fuel tanks, and use the energy to accelerate both the incoming material and the spent fuel mass.

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    Quote Originally Posted by tracer View Post
    The issue isn't "how much do we burn?".

    It's "now that we've burnt it, how much material do we impart that energy to?".

    The deal with a RAIR is that you don't fuse the incoming material -- you fuse the fuel in your fuel tanks, and use the energy to accelerate both the incoming material and the spent fuel mass.
    If the sole purpose of your "fuel" is to add energy to your reaction mass, then the best fuel is anti-protons, which you can then inject directly to the RAIR flow. MHD effects allow for control and the derivation of system power. Lacking this, onboard fusion (or even advanced fission designs, at least in the nearer term considerations) power generation and a microwave or EM induction energy transfer system might work well, the problem is getting your engine up to its effective operating velocity which generally means what, a few %c, before you start achieving significant impulse at any kind of real efficiency on pure RAIR?

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    Quote Originally Posted by Trakar View Post
    the problem is getting your engine up to its effective operating velocity which generally means what, a few %c, before you start achieving significant impulse at any kind of real efficiency on pure RAIR?
    The problem is also, as I mention in the OP above, the fact that in the case of a fusion-powered RAIR, you'll get significantly less momentum if you transfer the thermal energy into the scooped-up material than if you just leave the thermal energy in your fusion fuel products.

    This is assuming that (A) the material you scoop up is more-or-less stationary with respect to your launching site (i.e. relative to your spacecraft it's zipping rearward at your current speed), and (B) the amount of material you can scoop up is tiny, on the order of a few grams per second even with a 1000-km diameter scoop.

    Neither of those assumptions needs to hold if you "seed the runway" with material before you take off (i.e. if you use Earth-based launchers to throw material out along the trajectory you'll be following) -- but I was interested in a straight RAIR that used the interstellar medium as-is with no "seeding".

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    Quote Originally Posted by tracer View Post
    The problem is also, as I mention in the OP above, the fact that in the case of a fusion-powered RAIR, you'll get significantly less momentum if you transfer the thermal energy into the scooped-up material than if you just leave the thermal energy in your fusion fuel products.
    This is wrong. You noted correctly that the delta-v change in velocity of the exhaust products is lower. But it's spread over more mass, so the momentum is greater.
    This is assuming that (A) the material you scoop up is more-or-less stationary with respect to your launching site (i.e. relative to your spacecraft it's zipping rearward at your current speed), and (B) the amount of material you can scoop up is tiny, on the order of a few grams per second even with a 1000-km diameter scoop.
    Yes, but even in this case the scooped material plus the fusion fuel will still have a (slightly) greater mass than the mass of the fusion fuel alone.

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    Quote Originally Posted by IsaacKuo View Post
    This is wrong. You noted correctly that the delta-v change in velocity of the exhaust products is lower. But it's spread over more mass, so the momentum is greater.
    I've done the arithmetic. At 10% of the speed of light, assuming the scooped-up material is stationary with respect to the Earth -- remember, I'm talking about a RAIR that uses the interstellar medium as-is, not a pre-seeded runway -- you will ALWAYS get less momentum from shunting the energy into the scooped up material instead of into your burnt-fuel products, even if the amount of scooped up material is larger.

    For a stationary mass m accelerated to speed dv, the energy you'd have to add is:

    Eq. 1: E = 1/2 m (dv)2

    For a moving mass m with an initial velocity of v, accelerated so that it's going dv faster, the energy you'd have to add is:

    Eq. 2: E = 1/2 m (v + dv)2 - 1/2 m v2

    Let's say you have a 1000 km radius scoop that sweeps up 15 grams per second. (This is what you'd get in the Local Fluff out past the heliopause.) You burn ONE gram of fusion fuel. This gives you 6.3 x 1011 Joules.

    If you applied all 6.3 x 1011 Joules to your one (1) gram of stationaryspent fuel products, you'd increase its velocity from 0 to:

    dv = SQRT (2E / m) = 35,496,479 m/s
    INCREASE IN MOMENTUM = dv * m = 35,496 kg m/s

    If you instead applied all 6.3 x 1011 Joules to your fifteen (15) gram of moving scooped-up reaction mass, you'd increase its velocity from v to:

    dv = (-2*v*m + SQRT (4*v2m2 + 8*m*E)) / (2*m)
    (This is what you get when you apply the quadratic formula to Eq. 2 above. Check it out, it works.)
    dv = 1,368,774 m/s
    INCREASE IN MOMENTUM = dv * m = 20,532 kg m/s


    LESS OF AN INCREASE IN MOMENTUM, even though the energy was tranferred to a larger amount of material!
    Last edited by tracer; 2010-Mar-26 at 06:33 AM.

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    Quote Originally Posted by tracer View Post
    I've done the arithmetic. At 10% of the speed of light, assuming the scooped-up material is stationary with respect to the Earth -- remember, I'm talking about a RAIR that uses the interstellar medium as-is, not a pre-seeded runway -- you will ALWAYS get less momentum from shunting the energy into the scooped up material instead of into your burnt-fuel products, even if the amount of scooped up material is larger.
    Are you remembering to add the mass of the burnt-fuel products to the exhaust? Or are you assuming the burnt-fuel is simply dumped overboard?
    For a stationary mass m accelerated to speed dv, the energy you'd have to add is:

    Eq. 1: E = 1/2 m (dv)2

    For a moving mass m with an initial velocity of v, accelerated so that it's going dv faster, the energy you'd have to add is:

    Eq. 2: E = 1/2 m (v + dv)2 - 1/2 m v2

    Let's say you have a 1000 km radius scoop that sweeps up 15 grams per second. (This is what you'd get in the Local Fluff out past the heliopause.) You burn ONE gram of fusion fuel. This gives you 6.3 x 1011 Joules.

    If you applied all 6.3 x 1011 Joules to your one (1) gram of stationaryspent fuel products, you'd increase its velocity from 0 to:

    dv = SQRT (2E / m) = 35,496,479 m/s
    INCREASE IN MOMENTUM = dv * m = 35,496 kg m/s

    If you instead applied all 6.3 x 1011 Joules to your fifteen (15) gram of moving scooped-up reaction mass, you'd increase its velocity from v to:

    dv = (-2*v*m + SQRT (4*v^2(m)^2 + 8*m*E)) / (2*m)
    (This is what you get when you apply the quadratic formula to Eq. 2 above. Check it out, it works.)
    dv = 1,368,774 m/s
    INCREASE IN MOMENTUM = dv * m = 20,532 kg m/s


    LESS OF AN INCREASE IN MOMENTUM, even though the energy was tranferred to a larger amount of material!
    It sure looks like you're assuming the only thing in the exhaust is the mass of the incoming material. But this isn't how a ramjet works. A ramjet adds the mass of the burnt fuel into the exhaust in addition to the intake mass.

    This is a critical difference. It is, in fact, possible for a ramjet to accelerate a starship using nothing but inert propellant. This is a highly counterintuitive concept, so I do not expect you to believe it without detailed explanation...I'm not up for providing this explanation at the moment. Leaving that aside...

    Your calculation essentially assumes the fusion fuel is dumped overboard after it is burnt. This is always a bad idea, whether it be a ramjet or a rocket. It totally kills the performance of any propulsion system, so your result is not surprising.

    What you really should be doing is mixing the burnt fuel into the exhaust stream. The total energy input is now 6.3E11J from the fusion reaction plus 6.75E12J from the incoming stream. This gives us a total of 7.38E12J over 16g, or an exhaust velocity of 30,373km/s.

    This gives you a momentum gain of 35,968kg m/s, which is greater than 35,496 kg m/s.

    Not a big improvement, since we're indeed operating in a speed regime where the rocket is pretty efficient. But in principle, you don't have anything to lose by getting extra reaction mass to push against (assuming you can do it efficiently, of course).

    Like I said, there isn't in theory a big advantage for either the rocket or ramjet approach, unless you want a delta-v which greatly exceeds your rocket's maximum exhaust velocity.

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    Anyway, this is all assuming "all things equal", which is of course not plausible. As I see it, the main appeal of RAIR has little to do with any potential efficiency improvement and more to do with potential mechanisms for inducing fusion.

    One RAIR concept is to use boron propellant which reacts with interstellar hydrogen--or to invert this, using on board hydrogen to react with a "runway" of boron pellets. While this reaction is energetic and aneutronic, it's really hard to induce. The hope is that the violence of relativistic collisions will be sufficient to induce efficient fusion. So, even if it may be practically impossible to have a "fusion reactor" or fusion rocket, it may still be possible to have a workable fusion ramjet.

    Personally, I've gone off the entire idea of using fusion for propulsion. Relativistic impacts might be a way toward a practical fusion propulsion system, but it turns out kinetic impactors without fusion are far better still.

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    Quote Originally Posted by IsaacKuo View Post
    What you really should be doing is mixing the burnt fuel into the exhaust stream. The total energy input is now 6.3E11J from the fusion reaction plus 6.75E12J from the incoming stream. This gives us a total of 7.38E12J over 16g, or an exhaust velocity of 30,373km/s.

    This gives you a momentum gain of 35,968kg m/s, which is greater than 35,496 kg m/s.
    Ah, I see you're arriving at that 35,968 kg m/s figure by taking the momentum of all the outgoing exhaust (485,968 kg m/s), and subtracting the momentum the incoming stream (450,000 kg m/s).

    I thought I'd get the same result if I allocated, say, 99% of the energy released in the burnt fuel to accelerating the burnt fuel, and the remaining 1% of the energy to accelerationg the incoming stream, but to no avail -- I end up with the same momentum gain as, or ever-so-slightly less than, what I get if I put 100% of the energy into the burnt fuel.

    Is it because in the mixed-stream example, the incoming material is physically transferring some of its momentum to the burnt fuel, by banging into it?

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    Quote Originally Posted by tracer View Post
    I thought I'd get the same result if I allocated, say, 99% of the energy released in the burnt fuel to accelerating the burnt fuel, and the remaining 1% of the energy to accelerationg the incoming stream, but to no avail -- I end up with the same momentum gain as, or ever-so-slightly less than, what I get if I put 100% of the energy into the burnt fuel.

    Is it because in the mixed-stream example, the incoming material is physically transferring some of its momentum to the burnt fuel, by banging into it?
    It has to do with energy. The general principle applies to both jets and rockets. Basically, the issue is that having two exhaust streams with different speeds represents wasted energy. It's energy that you could have used, but instead let it go to waste.

    You're using some energy to accelerate the burnt fuel to velocity V1, and using the rest of the energy to accelerate the intake stream to velocity V2. Consider what happens if you "cross the streams". Unless V1=V2, then the result is an "explosion"...well, maybe not an explosion, necessarily, but some sort of energetic interaction as the stream particles violently collide with each other.

    If you surround this "explosion" zone with some sort of bell nozzle, then that violent interaction is converted into more thrust.

    Here's the really crazy thing--this kinetic impact effect alone is sufficient to provide a ramjet starship acceleration (after having first been given some forward velocity by another method, or by having the "runway" shoved down its throat). Instead of burning fusion fuel and mixing the burnt fuel with the intake stream, you simply mix inert propellant with the intake stream.

    Sounds stupid, doesn't it? But the end result is indeed acceleration of the starship. Your starship doesn't actually gain kinetic energy, of course. Nothing is pumping extra energy into the system. Instead, the starship keeps almost the same kinetic energy while losing mass.

    I'll show this calculation without relativistic effects for simplicity, to show the general principle:

    Let's assume a starship moving at 33%c, mixing in 1kg of propellant with 100kg of intake stream.

    Intake stream of 100kg, 1E8m/s velocity gives a kinetic energy of:

    E = 1/2 * 100kg * (1E8m/s)2 = 5E17J

    Mixing with 1kg of inert propellant implies an exhaust velocity of:

    V = sqrt(2E/M) = sqrt(2*5E17J/101kg) = 9.95E7m/s

    The momentum difference is:

    101*9.95E7m/s - 100*1E8m/s = 4.99E7Ns

    That's a pretty good acceleration impulse, considering the "fuel" was just inert propellant!

    What if we wanted to get the same performance out of a rocket? This means providing an impulse of 4.99E7Ns with 1kg of propellant. This implies an exhaust velocity of:

    V = 4.99E7Ns / 1kg = 4.99E7m/s = 0.17c

    So, at a speed of 33%c, this ramjet has the equivalent performance of a rocket with an exhaust velocity of 17%c. This is seven times more energetic than the 6.3%c of a hypothetical fusion rocket! In other words, a fusion rocket can't even come close to matching the performance of a ramjet which uses inert propellant instead of fuel. Not at this speed, and not at faster speeds.

    Using inert propellant may offer a number of advantages over using fusion fuel. It can be cheaper and denser, and it can be something that doesn't need to be cryogenically cooled. You don't have to worry about fusion reaction cross sections--indeed, it's not at all clear that practical fusion reactions are to be had at all. But the interactions of relativistic atomic collisions are already well understood and 100% "reaction" cross sections are easy.

    That said, once you get comfortable with the idea of using relativistic kinetic impacts for propulsion rather than fusion, the ramjet concept isn't necessarily the best way to go about it. One issue, of course, is how to get up to speed. You can be pushed by a relativistic particle beam or a stream of tiny relativistic impactors, but these things are good enough to bring you up to full speed anyway.

    A more troubling issue is that this ramjet only really works if the exhaust nozzle is very efficient. If you add in, say, an efficiency factor of 90% between the intake kinetic energy and the exhaust kinetic energy then the whole thing falls apart. If you consider the plausible sources of loss ranging from thermal x-rays to longitudinal exhaust speed variations, it's uncertain whether the a ramjet can really function effectively in practice.

  23. #23
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    Quote Originally Posted by IsaacKuo View Post
    What you really should be doing is mixing the burnt fuel into the exhaust stream. The total energy input is now 6.3E11J from the fusion reaction plus 6.75E12J from the incoming stream. This gives us a total of 7.38E12J over 16g, or an exhaust velocity of 30,373km/s.

    This gives you a momentum gain of 35,968kg m/s, which is greater than 35,496 kg m/s.
    I tried this at 33% of the speed of light (at which point you'd be scooping in 45 grams of material per second), with 1 gram of burnt fuel, and got an impressive momentum gain of 55,122 kg m/s -- much more than the 35,496 kg m/s I would have gotten by burning that 1 gram of fuel in a perfect fusion rocket.

    Oddly, though, when I tried it at 11.8% of the speed of light -- the same speed as the exhaust velocity of a perfect fusion rocket -- the momentum gain I got from the RAIR was exactly the same as what I got from the pure rocket. It's like the formula has a "minimum" right there.

  24. #24
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    Quote Originally Posted by tracer View Post
    Oddly, though, when I tried it at 11.8% of the speed of light -- the same speed as the exhaust velocity of a perfect fusion rocket -- the momentum gain I got from the RAIR was exactly the same as what I got from the pure rocket. It's like the formula has a "minimum" right there.
    Right. The minimum is when the exhaust velocity of the rocket equals the starship's speed. In this case, 100% of the kinetic energy pumped into the system ends up going to the starship, and 0% of the kinetic energy ends up in the exhaust. Obviously, you can't do any better than 100% efficiency.

    No matter how much or how little intake mass is mixed in with the fusion fuel, the specific energy remains the same--because the specific energy of the incoming mass is equal to the specific energy of the fusion fuel. As such, the exhaust velocity remains the same regardless of the mixture.

    Of course, this is all assuming unrealistic 100% efficiencies all around, with no waste and no losses. When you factor in realistic assumptions, you end up with a far more complex situation where things can end up...well, it's more complicated.

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    It seems to me that the ram scoop type concepts has exactly the same limitations as we see in atmospheric ram jet's you need to get up to a very high speed before they start to gain you anything at all.
    How does the calculus look if instead of just showing mass into the matter stream at 33% of light-speed one was to inject a small amount of antimatter. would antimatter increase the performance compared to using purely kinetic processes?

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    Quote Originally Posted by Antice View Post
    How does the calculus look if instead of just showing mass into the matter stream at 33% of light-speed one was to inject a small amount of antimatter. would antimatter increase the performance compared to using purely kinetic processes?
    Everything's better with antimatter!

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    Quote Originally Posted by Antice View Post
    It seems to me that the ram scoop type concepts has exactly the same limitations as we see in atmospheric ram jet's you need to get up to a very high speed before they start to gain you anything at all.
    Yes, unless you start doing things which get further and further away from what's normally thought of as a ram scoop type concept.
    How does the calculus look if instead of just showing mass into the matter stream at 33% of light-speed one was to inject a small amount of antimatter. would antimatter increase the performance compared to using purely kinetic processes?
    A small amount of antimatter would only make a small amount of difference. A large amount of antimatter might make a big difference, but you would likely do better with an antimatter rocket than an antimatter ramjet. The benefits of the ramjet concept would only kick in after your desired delta-v greatly exceeds the average exhaust velocity, and an antimatter rocket could have quite a good exhaust velocity.

    However, antimatter is...stupidly expensive to produce, and antimatter reactions would be problematic to exploit--lots of energy wasted into high energy radiation and neutrinos and you only get effective thrust if you deflect the very short-lived and short-ranged charged particles while you get the chance.

    A more potent and less problematic potential "store" of energy is the kinetic energy of relativistic impactors. Up until recently, I favored the idea of using near-c relativistic impactors to power a "relativistic kinetic impact powered rocket". The rocket puffs on-board inert propellant which is converted into explosions of plasma by the impactors. This gives you even better performance than an anti-matter rocket, but with doable technology.

    Earlier this year, I came up with a variant I call "double stream propulsion". Instead of one stream of near-c impactors, there are two streams of impactors moving at different speeds. The starship only holds a very small on board store of inert gas to ionize the impactors just before reaching the starship. The ionized impactor puffs then collide with each other, to produce the desired explosions of plasma to propel the starship. Compared to the earlier concept, this one no longer requires the starship to carry a significant mass of on board propellant.

    The key aspect to using relativistic impactors to "store" energy is that by its very nature you can't "store" them in a fuel tank. So you're never going to have something like an anti-matter rocket where you've got a honking huge fuel tank of volatile energetic stuff. Instead, you've got a vast formation of spacecraft working in some sort of coordinated fashion. One of those spacecraft is a big starship, but the rest are tiny little sacrificial bots.

  28. #28
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    Quote Originally Posted by IsaacKuo View Post
    A small amount of antimatter would only make a small amount of difference. A large amount of antimatter might make a big difference, but you would likely do better with an antimatter rocket than an antimatter ramjet. The benefits of the ramjet concept would only kick in after your desired delta-v greatly exceeds the average exhaust velocity, and an antimatter rocket could have quite a good exhaust velocity.
    There's one HUGE way in which an antimatter ramjet could outperform an antimatter rocket:

    If your antimatter consists of antihydrogen, you wouldn't need to carry any normal-matter annihilation material with you!

    (Well, okay, you'd need a little to get up to speed. But after that, you get 50% of your energy for free!)

  29. #29
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    Quote Originally Posted by tracer View Post
    There's one HUGE way in which an antimatter ramjet could outperform an antimatter rocket:

    If your antimatter consists of antihydrogen, you wouldn't need to carry any normal-matter annihilation material with you!

    (Well, okay, you'd need a little to get up to speed. But after that, you get 50% of your energy for free!)
    above and beyond that, you may be able to use the antimatter to catalyze some secondary p-p fusion in the ram-stream, its not going to be a huge contributor, but every little bit helps to offset the drag your collection field is establishing and contributes to net thrust. The primary issue is in wedding your energy expenditure to the reaction mass your ship is interacting with.

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    Quote Originally Posted by Trakar View Post
    above and beyond that, you may be able to use the antimatter to catalyze some secondary p-p fusion in the ram-stream, its not going to be a huge contributor,
    It's not going to be a contributor at all. Proton-proton fusion has a ridiculously low cross section.
    Quote Originally Posted by tracer View Post
    There's one HUGE way in which an antimatter ramjet could outperform an antimatter rocket:

    If your antimatter consists of antihydrogen, you wouldn't need to carry any normal-matter annihilation material with you!

    (Well, okay, you'd need a little to get up to speed. But after that, you get 50% of your energy for free!)
    This isn't a win, unless your delta-v greatly exceeds the average exhaust velocity. Assuming an efficient anti-matter rocket, this effective exhaust velocity is perhaps a third of the speed of light (lots of loss to neutrinos).

    Up until then, you do just as well bringing the hydrogen with you--or really, it doesn't have to be hydrogen. It could be something more convenient to store. The drive efficiency is about the same, but you don't have to deal with the ridiculously thin interstellar medium. You don't have to deal with trying to scoop it up--no overhead on the mass of the scoop, and so on.

    Of course, this is all assuming you even have all this anti-matter in the first place. It's so ridiculously expensive to generate, and then you get to have the "fun" of trying to store the stuff. Current state of the art lets us store anti-hydrogen atoms on the order of tens of SECONDS. Heck, we can't even store normal hydrogen in a spacecraft fuel tank for long enough for an interplanetary journey--much less anti-hydrogen.

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