Limits

[PB666]

We have been having a running discussion in this subforum for the last year or more concerning a type of energy that does not require an apparent mass to generate momentum. Although energy can be converted into light which has momentum it has very little momentum given the energy contained within, and so finding something that has a magnitude more momentum per input energy created alot of discussion. In the end here I hope to show that it really matters little. 

To start off this analysis lets imagine the settlers of the mid 19th century American west.  To accomplish their journey they had wagons with supplies and draft animals to pull the supply, this carried them across an expanse that was devoid of trade goods to either feed themselves or their livestock. Along the way the live stock feed, and because high energy foods spoiled they would kill animals and butcher them for meat and fat. There was a thing called winter, at which point unless you had settled in, it would not be a good thing to be in space. Conceptually speaking all major exploratory journeys are like this, if we imagine the discovery ships, they had to have supplies to last them several weeks, they might stop at islands to pick up water and supplies, and they would not want to be caught in a hurricane. Therefore the concept of expanse, resource management and risk have been dealt with.

So now lets consider the trip to or any planet. Our Mississippi river is the LOE, we first have to get our ship up across the problem of drag and its desire to fight orbits. During this phase of the journey we cannot rely on any space resource and so it is a given that the initial state provides the energy and mass to create momentum. Once we have a semi-stable orbit we then can examine the problem of space.

Space is a name, it has a sort of implicit meaning that it has no stuff in it. Actually space has alot of stuff, at least our local space, relative to the vast expanses of emptiness between galaxies. The stuff in space however tends to get concentrated into inertially defined bodies. Between these bodies are gases and for a traveler these gases are always in motion and because the gases are almost always charged (that means gas is a mixture of plasma and gas), the gas is maintained in a rarefied state by momentum and electromagnetic energy from the sun, as a consequence it can at times be non-inertial. To be clear here, the density of gas, even in the atmosphere of the sun, is so dilute it is of little practical use. That is to say in the time frame of our journey their is neither the time or a relevant volume of space to collect this an use it. The material state of vacuum space is more than an annoyance if anything, in LOE it creates drag and in interplanetary space it carries ions that can damage equipment or injure travelers.

The bodies in our space fall basically into three categories. The smallest of these are asteroids and comets. Asteroids are the left overs from planetary genesis, the gas from our sun slows down and hits things out in the outer system, cools, and gases and dust that did not form large bodies eventually coalesce into dirty ice balls that get tugged by our planets and burn up, eventually. The planets clear orbits and thus are clearly inertially defined in their motion, since they are no longer colliding. Finally you have the bodies in which atomic conversion is a major character of the bodies visible appearance, at high enough energy these also emit gases. To our traveler these are the resources of space, so lets define these as such

1. Asteroids and Comets. Resources - Mass (Carbon, Oxygen, Hydrogen, Nickle, Silica, Aluminum): sub resources (metal for building, water for drinking or fuel cells, carbon for food or electronics, all for momentum), trivial amount of inertia, and transitory or impermanent destination.
2. Planets and Moons. - Inertia (as in they warp space), destinations, and the resources of #1. 
3. Stars - Electromagnetism, Inertia, trivial emission of Gas and Plasma (as such also a source of electric charge)
4. Not 1 to 3 above - Quantum space - Non-zero rest energy of fields that permeate our universe (which of yet we are not fully aware or know how to exploit).

 So basically above we can define space as a list of virtual items, in this we can then rank them to our Space traveler. My ranking may shock but . . . 

A. [Quantum] space - this is the most important resource of space because it permits long distance travel and because its fields make it possible to establish travel strategies. The physical distance between destinations is in the >10⁹ meters, traveling in drag affords speeds of 100s of meter per second, therefore matter just slows down the process. Matter also creates lots of other problems like gravitational collapses and complex body problems.
B. Destinations (virtual and physical) - travelers will eventually need resources or a travel interest.
C. Electromagnetic radiation - discussed below. Essentially EM is the purest source of energy, that is not to say it is the sole source of energy, but rest mass as an energy source has an investiment cost (in space this translates into mass).
D. Inertially derived warping of space time - for the occasional Oberth effect.
E. Mass     -     E = mc^2,    p = m * v

These are the resources what are their costs.
A. Space - Not suitable for biota, no push-off mass, all* momentum must be derived within (*the status of the rf resonance cavity thruster goes undefined), energy required to reach space and return, energy taken by contamination within vacuum space.
B. Destinations represent almost always a non-inertial logic, a dV required to reach them, we talk about space-time, we also have to consider dT. Destinations may have other problems like too much or too little of some other resource (Namely light).
C. EM - heat dissipation with too much, energy conversion for use in propulsion and systems.
D. Oberth masses - Friction or obstructions, space-time (see B).
E. Mass - collection, landing, mining, conversion (not to mention cooling equipment)

So basically we have a list of issues for our traveler. Breaking this down much of traveler concerns are non-inertial movements in space-time which require energy and for the most part momentum derived from mass ejection. The above is not the intent of the article, it simply breaking things down into abstractions that the next part can deal with.

So what is the problem of traveling (not the traveler). If you are not going to something that cross the same space-time (in some relevant timescale) point dV needs to be applied somewhere.

We derive dV
Light - almost never used, but requires no mass (we have to assume at this point that the rf resonance cavity thruster is not this type of drive)
Chemical - the fuel becomes the ejection mass - limited to bond breaking partial bond formation energy of the fuel. Basically at high temperature unfavorable bonds break the most stable reform as the cool. There is a finite limit on how much energy can be obtained from a chemical bond, it is defined in calories per mole and typically is in the form of O-O, H-H, N-O, N=O, C-C, C-H, C-N, C=C, C=N.
Electrodynamic - the mass becomes energized by the input of energy and accelerates. (Ion, plasma, VASIMR, Hall effect, rf resonance*)
Atomic - a source of heat is used to rarefy gas or liquid which then expands like chemical energy drive. 

We can see we need energy to produce light, we need to carry mass to produce chemical energy, we need to carry a nuclear reactor or we need to accelerate ions. Unless you want to carry all the energy with the craft there is a limitation of space, right now its solar power, (given the high mass issues with nuclear and cooling issues)

Space gives effectively about 1N of thrust for every 233kg of solar panels (C). This gives a maximum 4.2 mm/s² of acceleration (0.0004g), with that one needs about 233 meters of space. You can assume that a manned spacecraft this will be 10% of the mass so you are effectively limited to about 0.04g. I have created new ion drives and panels in the game to reflect this (HiPep design thrusters). The major problem is orbiting, this designed requires another source of accelation and is not suitable around low hv objects. Nuclear is worse, the reactors cost as much as the panels in terms of weight but much more in terms of cooling.

if we argue that solar is kg per sqm then any means of reducing this improves the portability of the system.

Modern age silicon lens are light weight and can focus light on a panel of much lower size and weight. This type of system works great in interplanetary flight, however only at a tangent to orbit, so inefficient transfers are not optimal unless the lens are placed on tracks that can move their positions. They also do not work well in non-inertial manuevers close to inertial bodies, this is because the incident angle shift with prograde motion.

The mass of the ion drive is trivial (the most efficient drives of a few kilograms will easily consume all the energy we can currently produce), at 9000 dV the mass of the fuel becomes trivial (because you cant produce enough energy to eject it), the mass of energy production facility is just about everything. Find a way to lower the mass of energy production and Manned missions to (but not landing on) are possible.

 

 
 

 

 

[K^2]

E² = p²c² + (mc²)²

This is the mass shell. It is a requirement for a particle that can propagate as a free (non-virtual) particle. We are interested in how much the energy changes as we change momentum. In other words, we wish to compute ∂E/∂p.

∂E/∂p = pc²/E

Which tells you that to propel yourself efficiently, you want reaction mass with high E at low p. If you can come up with something other than increasing m in the equation for energy to achieve that, please, let me know. Otherwise, that's all there is to the limits.

Note that in the limit of the photon drive, m = 0, the above reads ∂E/∂p = c. In other words, you need almost exactly 300MW of power for every 1N of thrust if you don't have reaction mass.

The most important fact to keep in mind is that vacuum fields are taken into the account with above. In order for a quantum field to absorb momentum, you must create an excitation in it. For that excitation to propagate, it must have a mass pole. That mass pole is on the shell and obeys E² = p²c² + (mc²)². Like any other excitation that can propagate in space.

There's your limit.

[PB666]

2 hours ago, K^2 said:

E² = p²c² + (mc²)²

This is the mass shell. It is a requirement for a particle that can propagate as a free (non-virtual) particle. We are interested in how much the energy changes as we change momentum. In other words, we wish to compute ∂E/∂p.

∂E/∂p = pc²/E

Which tells you that to propel yourself efficiently, you want reaction mass with high E at low p. If you can come up with something other than increasing m in the equation for energy to achieve that, please, let me know. Otherwise, that's all there is to the limits.

Note that in the limit of the photon drive, m = 0, the above reads ∂E/∂p = c. In other words, you need almost exactly 300MW of power for every 1N of thrust if you don't have reaction mass.

The most important fact to keep in mind is that vacuum fields are taken into the account with above. In order for a quantum field to absorb momentum, you must create an excitation in it. For that excitation to propagate, it must have a mass pole. That mass pole is on the shell and obeys E² = p²c² + (mc²)². Like any other excitation that can propagate in space.

There's your limit.

Thanks for responding, I forgot to tabulate this

So basically the current

particle acceleration drive is 70 Kw/N (This number comes from NASA 35 kW/500 milli newton)
cannae  drive is ~30 Mw/N (30000Kw/N)
photon drive is 300 Mw/N

The problem is immediately evident:

A meter of sunlight is 1.1 kw however at a 25% efficiency it pans out to about 0.3 kw per meter. To get one newton of power then you need 70/.3 = 233 sqm/Newton, This is the best.
If we look at the Cannae drive its advantage, even for clearing space junk becomes evident 30,000/0.3 = 100,000 meters of solar per N. If we go by mass then this is 100000 kg, and that results in an acceleration of 10 uN or 1 ug of force. the photon drive is then 1 uN and its relative force is 0.1 ug.

To make this more clear, we could improve the efficiency of the ION drive by a few percentage (14% maximum and the efficency of the solar panels 200% maximum and you still have no less than sqM/N. I have to remined everyone that the tiniest chemical thrusters are in kN of thrust, we are talking about 75 sq.meters of area to provide 1000th of that. You could lower the weight of the solar panels to 10 meters per kilogram, but you still have 1w per meter max to deal with, you still have to spread panels over wider space, not a problem if you have a very heavy load, but if the intent is to accelerate or you are using them in close orbits, you will have a stability problem that needs to undergo reinforcement problem. I solve this in the game by crafting new poles and joints, but there are practical limits. A stabilize wire structure has a problem with solar panels in that panels need space to track the sun. This is the limit I am refering to, for ION drives the efficiency limit basically sets the downstream limits (how many Kw needed, theoretically nuclear is limited by the heat exchange problem, unless there is a cheap way of direct charging; solar is limited by solar irradiation per unit meter of space and the technical mass requirements of reaching and filling that space) so this is the limit, the practical limit, it is the Mars problem. How do you get a fully fueled land and return vehicle to mars.

What you came up with is an impractical limit, because it does not take into account the technological limitations. We cannot increase much the efficiency of ION drives, there is only so many Kw to begin in any unit area of space at any radius from the sun. We can lower the weight required, but that can only be done to a practical limit. For example suppose you use silicon Fresnel lenses to refract light, there is a limit on how thin the material can be (basically determined by the wavelength of green light) before you start causing it to do something else, like diffract. I will summarize at the end.

In terms of manipulating the vacuum of space, again cannae might interplay in some unknown way, but currently we do nothing extraordinary to achieve this, but if we knew more about the field it might be possible to manipulate them to our advantage, I don't see it but the possibility exists. My point is this, it hardly matters, for deep space flight the problem is not momentum per say, its energy, and the cannae drive is not immune, if anything its magnitudes more vulnerable than ion drive.

Priority should be finding better power sources for the ION drive,
The cannae drive cannot compete with current ION drives, the reason is this:
1. The small amount of thrust it produces
2. The weight of the drive
3. The weight of the solar panels required to power the drive.
4. The force of drag acting in LEO
5. The fact that even junk would be difficult to catch with such low acceleration, or to state more precisely you could catch objects in geostationary orbit, but everything else is subject to variable forces

So we can currently ignore both the Cannae and Photon drives.

Our example is this, lets say we accelerate a kilogram of xenon and accelerate it to a 1 and the ship weighs 10000 kilogram

m1v1 = m2v2 1/10000 = v2  ∂E1 = 1/2 ∂E2 = trivial
2 ∂E1 = 2 ∂E2 = trivial
4 ∂E1 = 8 ∂E2 = trivial
8 ∂E1 = 32 ∂E2 = trivial
16 ∂E1 = 128 ∂E2 = trivial

Higher ISP result from higher momentum ejecta but at a much larger expense of energy required to generate it. The energy sources used to accelerate the mass are not even adequate for current transfer requirements from earth to mars for manned space craft, more ISP is not the problem, the problem is critically the supply of energy.

This HiPep that they created is 31 x 46 cm, it requires 35 Kw, thats 245 times the solar radiance for that and produces 0.5N.

ug here means 10E-6 earth surface gravities.

Again we have here the practical limitations, so the equation is this. I will set a current of 50 ug of acceleration for a people carrying space craft, this is not practical for many space applications. The mass and the area of the ION drive is immaterial, find ways of increasing energy production of the spacecraft without raising the weight, it can include better construction materials, lighter solar panels, more efficient solar panels. I am not contradicting what you are saying, but when you say "Which tells you that to propel yourself efficiently, you want reaction mass with high E at low p." means that you energy production is not rate limiting, I completely agree that you want to limit p derived from m, BUT this means that you have available a relevant energy source to create a level of E that will achieve a desired dV/t

My example here is that I have a craft with 38 2x6 meter solar panels (to be realistic I need 40 more) and 4N of ion drive and a _modest_ 1 human carrying 12000 kg space craft, it has F = 0.3333 mN at 9000S you can sit down and calculate how long it will take to realize the 30,000 dV available, then you understand the limit that you should be thinking about.

 

 

 

[K^2]

You are missing the point. In order to improve efficiency, you have to bring reaction mass. It's the only way to reduce ∂E/∂p. Ion drive brings very little reaction mass and is limited primarily by energy supply. Chemical drive brings a lot of reaction mass and that's your only limitation. Photon drive has no reaction mass and is purely energy-limited. Cannae drive is non-physical, and is limited by suspension of disbelief. It's entirely your call on which of these you want to be your limiting factors for a particular mission. They all fit along the same curve of the energy vs mass, give or take a chunk for efficiency.

Up to a point, we can play around energy limits with a nuclear reactor. But mass defect of ~1% fundamentally limits you to a rocket with effective I_SP of ~0.1c/g. For Solar System, that is plenty. For interstellar, it might as well be useless. Your next step up is an antimatter or a black hole drive. Again, your call on where the limitations of that are going to be, but you're still a prisoner of E² = p²c² + (mc²)². You can't get around that with a reaction drive. It's fundamentally impossible.

The only way to go further in any reasonable time frame is to alter the geometry of space-time. It's wormholes, warp drives, or bust.

[PB666]

You are talking about physics way beyond scope here, lets bring it closer to earth

With chemical energy we want to improve ISP because the reaction masses momemtum is derived from energy bond breaking and formation and if it is not utilized for generating thrust it is wasted therefore we don't really care that our E to p ratio is great, the limit to this is internally controlled. The reaction has a certain amount of mass and that mass has a certain about of O-O, C-H, C-N, etc bond energies that can generate N-O, C-O and O-H bonds of lower energy. Once you have converted all that reaction energy to craft and gas energy your ISP cannot go any higher.

Not the case with an ION drive, in the ION drive xenon has no bond energy to be derived from lower energy states and we are adding energy to strip electrons from the outer orbital. Consequently we can continually add as much energy as we want, 9000 ISP seems to be great, but then where does that energy come from, and then if we compare the kW of power generated in a unit space by chemical versus kW of power in unit space by solar or fission reactors on board space craft, then thats were the rate limitation creeps in.  If we begin our mission at venus and travel to mercury the problem is much less severe (except for the low efficiency of solar cells and high radiation levels essentially fry them if they are not turned at an angle), but our mission begins at 1.1 kw/M (1.361 actually but measures the entire spectrum) and goes to 0.432 the earth value. If above earth we get 0.3 kw/M on mars we get 0.12 kw/M. The weight of xenon that you have on earth will not help you on mars, because you will need 2.5 the mass of solar panels to drive what ever ISP you decide on (as long as the power loss is minimal). Again I repeat the point, the problem is not mass, though if you have the luxury of having reaction mass to dispose of it helps. the problem is power, energy, juice, hv, amps*volts whatever you want to call it. He's arguing in the other thread that a post LEO mars mission needs 19,000 dV, ok so if your craft begins to saturate dV with a certain mass of Xenon and you are kicking out just double the E/m ratio, you are going to pour through that mass in a hurry but for no good reason, because the excess momentum per energy you obtain (with more ion drives and its associated mass) has to push more Xenon mass around. You don't win.

The only win scenario that I see is to make use of static orbits like Earth L2 and Mars L1 to park gas and pick up, therefore not carrying the weight. A better Idea might be to park permanent bulky solar carraiges in space, made of less efficiency light weight panels that have masses of 0.1 or 0.05 kg per meter squared that a ship can dock into once in 'safe space' such as at L2 or L1 of mars. and then use that energy carriage to carry it back and forth.

another 300 dV due to the non-perigee burn losses.

 

 

Edited February 2, 2016 by PB666
Many errors - 100000 meters of panel on 5t payload unreasonable