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Now, obviously I love my LV-N as much as anyone. But fundamentally, the tyranny of the rocket equation can not be escaped by providing amazing energy density, because it is mostly not about energy density.
Fundamentally, rocket engines are characterized by two quantities: their thrust -- how much force they can deliver -- and their effective exhaust velocity (or specific impulse), which basically states how efficient they are at converting reaction mass into thrust. v_e is one of the factors which goes into the rocket equation for the delta v budget, the other being the logarithm of the initial and final mass quotient. If you want more delta v, trying to get to a higher v_e seems obvious.
For vanilla chemical rockets, the energy for accelerating the exhaust gas comes from having a fuel and an oxidizer react thermally. This puts some limitations on the exhaust velocity because chemical reactions will only yield so much energy per unit mass (especially as more exotic reagents like FOOF would have their own problems).
The nuclear thermal rocket avoids this energy bottleneck. The problem is that with hot gasses, the next bottleneck is right around the corner: you need materials to withstand the temperature. Energetically, you could just heat your reactor to 10000K (if your reactor can use fast neutrons, at least) and get an amazing exhaust velocity. [^1] Too bad your tungsten pipes will melt at 3700K, though.
The other thing you might do is just to forsake using thermal exhaust. You simply build an ion accelerator open at the downstream end (at least vaccum will not be a problem) and point it into the direction you do not want to go. If you have energy, there is no limit on how high your v_e can go.
Of course, the downside of ion drives is that their thrust is very tiny. This is a problem if you want to get somewhere before you die of old age. [^2] And using nuclear power over solar is not going to fix that -- even particle accelerators which we build on Earth, where we can just take power from a socket have abyssal thrust to weight ratios.
In conclusion, the use of nuclear energy (either fusion or fission) might help a bit, but it will not help you to escape from the tyranny of the rocket equation.
[^1]: Of course, what you get is the exhaust velocity, but what you pay for in energy is proportional to the exhaust velocity squared. This unfair business practice lead to a class-action suit against physics which was settled in 1905. Now as your exhaust velocities approach c, you the energy costs of marginal momentum get constant. Consumer advocates claim that this is a bad compromise because most households have exhaust velocities much lower than c and do not benefit from this at all. Attempts to lower c have been met by resistance of both high school students (who prefer Newtonian physics for real world problems) and gamers (who fear their ping times will increase).
[^2]: Additionally, in KSP, you can not speed up the simulation while you are accelerating. This makes missions which rely on ion drives rather cumbersome. (Though they would be even more cumbersome if the devs had not increased the thrust of the Dawn engine by a factor of 2000 over their Earthly counterparts.)
You have made several serious errors that invalidate your point.
a) The facts that you need high temperature to achieve high exhaust velocity, and that there are limits to the temperature of solids, do not imply that high exhaust velocity is impossible. All you need to do is ensure that your rocket motor is not in thermal equilibrium with your propellant or your fuel. The obvious way to do this is to have low thrust, as that allows your cooling system to keep up. Making your fuel also your propellant, and limiting its ability to thermalise before leaving the ship, also help (the limit is still proportional to F*Ve, but you can raise the proportionality constant). It helps a lot that plasma can be contained magnetically.
b) Thrust doesn't matter all that much except for takeoff. The time taken on a brachistochrone trajectory goes roughly as the inverse square root of your thrust (1), so a millionth the thrust is only a thousand times the travel time. 1 mG could get you the distance to Pluto in about a year and a half. What really matters for transit time is the delta-V needed to achieve brachistochrone at all, and that means nuclear.
c) Speaking of which, yes, nuclear has staggeringly-higher Isp than chemical, to the point that the rocket equation is generally in the linear rather than exponential regime for interplanetary flight and, hence, its "tyranny" is indeed "escaped" (interstellar's a different beast; if you want to go relativistic you're generally looking at antimatter fuel or external drives like light sails). "800 seconds" is a fucking joke compared to what nuclear's capable of - in the highest-Isp version of fission, the fission-fragment rocket, it's capable of millions.
I made the point about exhaust velocities mostly wrt fission engines using thermal gas as a propellant. If you have a fission reactor as an energy source, getting a heating your propellant to a much higher temperature than your fuel elements seems challenging.
The length of your brachistochrone would depend on your available acceleration. If you have unlimited thrust, the fastest path is a straight line (relativity aside). If your thrust is very limited, I would expect that you will spend a lot of time orbiting the Earth while prograding until you escape it eventually, and then you will spend a lot of time circling the sun until your intercept.
However, I agree that 10mm/s^2 is still a usable amount of thrust within the solar system. The Dawn spacecraft got around with much weaker engines, but it definitely increased the transition time.
I am more skeptical about fission fragment engines. Sure, the exhaust velocity -- a few percent of c -- is amazing. But for every fragment which escapes and generates thrust, another one (or three) will hit your spacecraft. Because energy scales with v^2, if you want a decent thrust, that will mean an ungodly amount of energy. 1kN times 0.01c is something like a few Gigawatts of thermal power, similar to what a large commercial nuclear reactor might have. Cooling this away in space would be challenging. And if you add a reaction gas to get more momentum per energy (at lower exhaust velocities), you still have to confine that gas magnetically, which also adds overhead.
Right. So you run open-cycle. You mix your fuel with your propellant, stick it into your nozzle, and burn it at plasma temperatures (remember, while terrestrial nuclear reactors burn up their fuel over the course of years, this is not actually required; a nuclear bomb burns its fuel to reasonable completion inside a microsecond). You will need cooling systems for the nozzle, of course, but the temperature gradients are all in the right direction.
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Why would we need to escape the rocket equation? It's like going from horses to cars. Both need fuel and both have limits in speed and transport capacity. But cars are so much better than horses. The range of a car is much greater than the range of a horse.
I know that fusion rocketry is very difficult, getting a magnetic nozzle or similar advancements has not been achieved. Fusion (besides Orion-style) has not been achieved. But that should be what we aim for.
Neither horses nor cars are propelled by the physics of the rocket equation. The rocket equation is an exponential (or a logarithm, depending on which way you arrange it). It provides a hard limit on performance that cannot be hand-waved away. You say, rightly, that future technologies can perform better. This is true. How much better? What are the numbers that we can plug into the rocket equation in order to compare to the other numbers that we can plug into the rocket equation? It is only then that we can really get a sense for the scale of how much better future technologies can be.
Ironically enough quiet_NaN doesn't actually do that, he just gives general exposition about the difficulties of spaceflight. Misleading, in my view, since energy density is vital, that's the fundamental essence of the entirety of rocketry. Nuclear fusion based rocketry would not just 'help a bit' but provide enormously greater capabilities.
We all agree that nuclear rockets are far more effective. Trying to plug in numbers to the equation is useless at this phase because we don't know how heavy a fusion rocket will be, nor what kind of exhaust velocity can be achieved. We don't have any such rockets. But we do know that chemical rockets are extremely slow and inefficient. They're unsuitable for serious space colonization (as are human bodies in my view).
Stepping back and taking a very broad view, there are several steps to the research, development, and engineering of a system. Generally, one begins with physical principles. With those physical principles, one can compute theoretical limits. One can also sketch a concept of operation based on those physical principles. Often times, at that point, one can still handwave away many practical concerns and compute how close a concept could, in theory, get to the raw theoretical limits. As one progresses, one may include an increasing number of more real-world difficulties.
For nuclear rocketry, we are not building on a blank slate, as though no one has ever started down this path at all, as though we simply have no idea what the theoretical limits are or what the concept-based performance could look like (still handwaving away many practical considerations). People have been doing this work and publishing it for half a century.
Do you agree or disagree with this general picture?
I'm not agreeing or disagreeing, it's just not relevant.
I am saying these things:
Quiet_Nan was saying
Neither point matters in relation to my argument. I think we all know that fusion rocketry is difficult.
You are asking in response:
But that also doesn't really matter to my point. As long as it's significantly better than chemical rocketry, which it is, then that makes it a better option for long-range spaceflight, since it can do the work and chemical rockets can't.
I don't understand your somewhat patronizing approach of asking about concept-based performance. I don't need to cite a specific fusion design to know that fusion designs can provide much more capable rocketry. That's inherent given the nature of fusion vs chemical rocketry. We already know this. There is plenty of variance between designs and some may just not end up being workable.
Trying to explain specific impulse, thrust vs delta v to me is wholly irrelevant to the substance of what I'm saying!
Lets use another one of your examples. Cars are much better than horses. Does that imply that cars are a better option for long-range spaceflight? If you think this statement doesn't quite make sense, try to explain without reference to any first principles, conceptual designs, concepts like specific impulse, thrust, and delta-v, etc.
Alternatively, to hone in really narrow:
How do you know that it can do the particular type of work you're asking it to do? Wouldn't it be nice if you had some reasoning, from first principles and/or conceptually, which could inform you as to whether it is plausibly up to the type of task you're asking of it? Some sort of check to see if you're accidentally expecting a car to go to the moon, just because it's better than a horse?
You know what's even better than first principles reasoning? Already knowing the answer. I already know that fusion rocketry designs can perform long-range spaceflight, to the edge of the solar system at least without being restricted to tiny payloads. You can do a quick internet search if this is new information to you.
Ah, so you think that there is something to be looked at in terms of designs, and at least something about distances/payloads, yes? And you think that this information can be found and understood with just a quick internet search? You just think that these internet sources don't use first principles reasoning, conceptual designs, concepts like specific impulse, thrust, and delta-v, etc., I guess. Those things are wholly irrelevant to your point. Am I understanding you correctly?
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Fuck it, build Orión. I want a nuclear warhead fueled torch ship.
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