Advanced Solar-Electric Energy: Part I

[PB666]

7 hours ago, YNM said:

@PB666 Would be an interesting spacecraft shape I see...

So in the future, all spacecraft will be streptococci ?  

 

Also, I don't see they'd be making for the solar concentrator @MatterBeam mentioned.

IMHO "rocket equation" applies whatever it is you're using. You have to trade things off to get something else in real life.

If only things would grow in space and make solar panels. But at least this design is modular enough the side pieces could be assembled in a space factory, drawn into space, inflated and attached.

The problem is that the design is surface inefficient.

[MatterBeam]

23 hours ago, YNM said:

@MatterBeam

You need them still in "large quantities" right ?

So how would you make the stiff trusses ?

Also, it's space. You don't have ground anchors. You'll need something like triangular elements or such.

Those are just... visual aids. Not actual examples...

21 hours ago, PB666 said:

The inflatable version would work if it was filled with aerogel that way if there was a micrometeorite collision it would hold its form. You could drag them safely behind the ship via a long stand-out and a tether.

But you are not going to be able to conduct megawatts of power that easily. You could locally feed current to the center of the sphere, but once you collect it you are now talking about 10,000s of volts traveling down two conductors and they are still going to be very hot. The largest number of spheres per cross-sectional area would be 3, this means our 10 to 100 MW is traveling down a maximum of 3 wires for 3 to 30 Megawatts per wire.

I have done some calculations. The wire I have choose is Grosbeak (26/7), its1.3 kg/meter and has an electrical resistance of 8.97E-5 per meter, a flow limit of 798 A at STP it has a strength of  <1211 kN. The power output of a wire is given by Amps²*Ohms. The Temperature of the wire is given as Q_emitted = P/A = sT⁴ where Q is the rate of emission, P/A is power over area, E is the emissivity constant of a metal  (aluminum = 0.11), s is the  Stefan's constant (5.97E-8 m²/K⁴ and T is the temperature in kelvin.  The outside of Grosbeak is 10 aluminum wires of approximate AWG 6.5 and has a emission area (one half the surface of each strand) of 0.1 m² per meter of length.

As a consequence we can determine the temperature of the surface of the wire in cold dark space. Aluminum wire in normal operation is not suppose to exceed 333'K and the maximum tolerance of 363'K, with a prefered operating temperature below 293'C. For a 10 MW feed (where plus and minus strand are separated) in unlit space, the preferred voltage on grosbeak is 62 kV, the nominal minimum voltage is 51 kV and brief minimum voltage of 45 kv.
Power loss along the conductor is not substantial even over a kilometer (0.005%) at 62 kV. The greatest risk is overheating of the wire. You can give the wire a coating that allows greater emission, aluminum being a great reflector is also a poor emitter. It should be noted that the highest amperage in atmosphere is higher than it is in space, this is because air can flow between strands cooling them, in space there is no air for to cool.

This is something to keep in mind as we are thinking about electric powered space craft. The two cables themselves suffice as the tether, the problem is that there needs to be a high voltage transformer (and its thermal radiator) somewhere near the power source, probably embedded in the power source itself. For example in an inflated sphere, power is traveling from the outside of the sphere to the center, presumably the tether travels to several spheres.The voltage is best converted on the surface where the heat can be released as small as possible amperage load going to the transmission cable/tether. 

I should point out that if you needed less force to hold the wire you could use a hollow carbon fiber core with a single large diameter shell of aluminum wire, in this case transmission only occurs at the surface of the cable where heat is generated over large areas. This would give structural rigidity of the wire and prevent the wire from twisting (+ and - making contact, a very bad thing, linemen may take a month to reach Puerto Rico, they don't make calls in deep space).

I must insist, the wiring we have today is not relevant for a multi-megawatts solar electric craft. The wires will not be bare, so the emissive constant you'll use is that of the insulating layers. They can be actively cooled through jackets of circulating fluid, and even kept at cryogenic, down to superconducting temperatures, by keeping them in shadow and a liquid helium/hydrogen cooling system. High-temp superconductors can even be cooled by liquid nitrogen (70K) and would allow for massive currents at low voltage. 

Also, the shapes you are referring to are for the reflectors. The reflectors don't have wires running out of them, as they don't generate electricity. 

Because the wires are so lightweight, it is likely that the spacecraft can afford to keep several kilometers of wiring as a backup.

 

[YNM]

1 minute ago, MatterBeam said:

Those are just... visual aids. Not actual examples...

Well, so is most diagrams, unless they are worthy to have a price tag on it.

Seriously, I question heavily the trusses etc. , would they ever be soo light ? (mind you that the trusses would be under compressional stress, not tensile stress.)

[MatterBeam]

21 minutes ago, YNM said:

Well, so is most diagrams, unless they are worthy to have a price tag on it.

Seriously, I question heavily the trusses etc. , would they ever be soo light ? (mind you that the trusses would be under compressional stress, not tensile stress.)

The forces involved are what matters, and they're quite low when you're accelerating at 0.01g. The trusses might end up being decently massive, but they would still contribute little to the overall mass per m^2 of reflectors, and even less to the kW/kg rating of the solar electric system. 

[PB666]

37 minutes ago, MatterBeam said:

Those are just... visual aids. Not actual examples...

I must insist, the wiring we have today is not relevant for a multi-megawatts solar electric craft. The wires will not be bare, so the emissive constant you'll use is that of the insulating layers. They can be actively cooled through jackets of circulating fluid, and even kept at cryogenic, down to superconducting temperatures, by keeping them in shadow and a liquid helium/hydrogen cooling system. High-temp superconductors can even be cooled by liquid nitrogen (70K) and would allow for massive currents at low voltage. 

Also, the shapes you are referring to are for the reflectors. The reflectors don't have wires running out of them, as they don't generate electricity. 

Because the wires are so lightweight, it is likely that the spacecraft can afford to keep several kilometers of wiring as a backup.

 

When you insulate the wire you make matters worse, insulation traps heat, take a look at the heat stability characteristics for resistance in the conductors. Active cooling systems needs someplace to dump that heat and the longer the wire the less effective that cooling will be. I agree that aluminum wire is not choice, but liquid helium cooling in long wire, this wont work, helium boils at very low temperatures after which you have vapor lock in the lines, and whatever heat you generate has to be lost somewhere else. You really need to study the problem of heat dissipation more carefully. You are making assumptions about heat dissipation in space that with study you will find not to be true.

 

[MatterBeam]

13 hours ago, PB666 said:

When you insulate the wire you make matters worse, insulation traps heat, take a look at the heat stability characteristics for resistance in the conductors. Active cooling systems needs someplace to dump that heat and the longer the wire the less effective that cooling will be. I agree that aluminum wire is not choice, but liquid helium cooling in long wire, this wont work, helium boils at very low temperatures after which you have vapor lock in the lines, and whatever heat you generate has to be lost somewhere else. You really need to study the problem of heat dissipation more carefully. You are making assumptions about heat dissipation in space that with study you will find not to be true.

 

For superconducting wires, there is no internal resistance, so no heat generated when current runs through the wire. All heat will come from external sources, primarily sunlight. Insulation reduces the amount of sunlight absorbed and reduces the rate at which that heat reaches the wire itself. 

Even for non-superconductors, like a thick length of aluminium, heating should be minimal. What helps is that many solar cells in series produce a high voltage, while the distance to be traversed from the solar cell to the engine doesn't have to be very long (a dozen or so meters at most) because as I've said, the solar collectors are not directly connected to the solar cells. 

Let's say we have a 100MW to deal with. We'll set the voltage to a modest 100V, stepped up to 10kV. The current is therefore 10kA. What combined thickness of aluminium wires should we use to carry this current over a distance of ten meters without suffering more than a certain rate of heating, matched by the cooling capacity?

Let's imagine passive cooling fins attached to the wires. Four fins of 20cm width would have an area of 8m^2, but only 5.6m^2 effective after interreflection. At 300K, it radiates 2.44kW. This means that with a current of 10kA allows for a resistance of 24.4microOhms. This means wires as thin as 0.01m^2 are possible. 

Using better cooling allows for thinner wires. 

The liquid helium/hydrogen comment was with aluminium superconductivity in mind, which requires 1.2K temperatures. I should have clarified. 

[PB666]

1 minute ago, MatterBeam said:

For superconducting wires, there is no internal resistance, so no heat generated when current runs through the wire. All heat will come from external sources, primarily sunlight. Insulation reduces the amount of sunlight absorbed and reduces the rate at which that heat reaches the wire itself.

Superconductors need a huge amount of refrigeration and heat conductance for that refrigeration system. In space the sun will be striking the outside of the conductor it will transmit heat into the interior which will need to be cooled. The second issue is superconductors may not be structural, so you need to add structural weight on top of that. Third problem is that your refrigerant lines are on you ship, your power source is up to a km away, that refrigerant needs to be cycled over a 2 km stretch and you have 2 wires you have to do this. You are making a grand assumption that superconduction, low boiling point gases and cooling systems will be applicable without any aforementioned knowledge that they will work under these circumstances.

 

4 minutes ago, MatterBeam said:

Even for non-superconductors, like a thick length of aluminium, heating should be minimal. What helps is that many solar cells in series produce a high voltage, while the distance to be traversed from the solar cell to the engine doesn't have to be very long (a dozen or so meters at most) because as I've said, the solar collectors are not directly connected to the solar cells.

Wrong, there is the skin effect. In any large gauge electrical wire running at high tension electrons tend to move at the surface of the wire. Increasing the cross-sectional area of a wire by 2 increases the maximum conductance of the wire by SQRT(2). Secondarily the surface is the coolest part of the wire, resistance increases with heat, and so larger wires have higher internal temperatures. This is the reason grosbeak  and other similar wires have low conductance high thermal stability steel at their centers and that they break the conductor into many strands at the surface to reduce eddy formation in the wire. These wires are primarily aluminum structural but have steel assist, this is for periods of peak demand and peak stress. On a cold winters night where demand is very high but winds are blowing hard, the line gets hot it stretches and one line makes contact with the next, hard blow . . . . power is out for the next day. 

Here is the heat related resistance of aluminum.  The temperature coefficient (a= alpha for electrical resistance is 3.9x10-3/degree C).  R = R₀ (1 + a * (T - T₀)  http://hyperphysics.phy-astr.gsu.edu/hbase/electric/restmp.html

Electrical connections need to be close to cells. You can only step of voltage on the panel itself so much before you get arcing between two opposing voltages. Therefore from the cell cluster to the main you need to step up voltage and then step up voltage again (and alternate) for transmission over the wire. The higher the frequency the more information that is carried in hv and less in the form of amperage.

29 minutes ago, MatterBeam said:

Let's say we have a 100MW to deal with. We'll set the voltage to a modest 100V, stepped up to 10kV. The current is therefore 10kA. What combined thickness of aluminium wires should we use to carry this current over a distance of ten meters without suffering more than a certain rate of heating, matched by the cooling capacity?

Let's imagine passive cooling fins attached to the wires. Four fins of 20cm width would have an area of 8m^2, but only 5.6m^2 effective after interreflection. At 300K, it radiates 2.44kW. This means that with a current of 10kA allows for a resistance of 24.4micro Ohms. This means wires as thin as 0.01m^2 are possible. 

 

But the cooling fins are not structural and they add mass and create opportunity to ionize the gases of space resulting in losses. Secondarily for peak performance you need contact heat transfer between the wire to the fins and for reduced weight you need good emitters. The problem with good emitters is they are also good light (hv) absorbents so you need now to unidirectionally shield your wires from the sun.

The whole point of this exercise is to bring together technologies that exist, not fantasies within some range of reasoning. If you are going to have to create a whole new variety of conductor just to move electricity then we are in the realm of vapor-ware. I don't mean this to impinge on creativity, but there is also the law of unintended consequences and you should be prepared to accept these until technologies designed to resolve these come about.

Several problems you have been presented you have discounted in a hand waving manner, for example the critiques of structural stability. There have been experiments to see how things behave in space, the results have been rather unexpected. Piping, which I am very fond of, even without significant static load tends to become unstable without bracing with length and has a high tendency to want to bend and deform at the center. Things in space need to be cross-braced more frequently than you think.

Carbon fiber is very nice, but its not aluminum piping and connectors that you can buy off the shelf (which I am very fond of in my spacecraft builds). Most carbon fiber applications are custom and such large solar collectors require either assembly in space or manufacturing the carbon-fiber in space. In the future these things may be widely available.

 

[KG3]

Hello, I've been wondering if large solar sail type objects could be spun to give them some rigidity via centripetal force.  Also, could they be held taught somehow by using static electricity?  I mean if there were objects imbedded in the sail that repelled each other via a strong static charge.    

[MatterBeam]

3 hours ago, KG3 said:

Hello, I've been wondering if large solar sail type objects could be spun to give them some rigidity via centripetal force.  Also, could they be held taught somehow by using static electricity?  I mean if there were objects imbedded in the sail that repelled each other via a strong static charge.    

Hi!

Rigidity through centripetal force is definitely an option, but you will have difficulty preventing the sails from bending under the slightest acceleration. This is because the sails are so thin that they are not very strong. That means they cannot support a large centripetal force which would come from spinning the sails more rapidly to prevent bending. 

Static electricity is another option, but remember that space is not empty. Solar winds and the interplanetary medium would interact with this charge, causing electric arcing and a lot of damage to the sails. If you reduce the charge, the repulsion between same-charged-surfaces becomes weaker and less effective. 

So yeah, these options are doable for a solar sail, but for a solar reflector that accelerates much more quickly than a solar sail, you'll have trouble.

[wumpus]

Light itself exerts a force via momentum, which is likely what would be used to focus a mirror (perhaps of mylar) or angle a sail to exert a force in specific direction (I'm less sure about the sails, I suspect the light will be working against you).  The catch is that with a mirror and electric propulsion, the efficiency of the electrical system more or less exerts an acceleration on the entire spacecraft (thus warping the mirrors).

On 11/19/2017 at 12:25 PM, PB666 said:

Superconductors need a huge amount of refrigeration and heat conductance for that refrigeration system. In space the sun will be striking the outside of the conductor it will transmit heat into the interior which will need to be cooled. The second issue is superconductors may not be structural, so you need to add structural weight on top of that. Third problem is that your refrigerant lines are on you ship, your power source is up to a km away, that refrigerant needs to be cycled over a 2 km stretch and you have 2 wires you have to do this. You are making a grand assumption that superconduction, low boiling point gases and cooling systems will be applicable without any aforementioned knowledge that they will work under these circumstances.

 

Wrong, there is the skin effect. In any large gauge electrical wire running at high tension electrons tend to move at the surface of the wire. Increasing the cross-sectional area of a wire by 2 increases the maximum conductance of the wire by SQRT(2). Secondarily the surface is the coolest part of the wire, resistance increases with heat, and so larger wires have higher internal temperatures. This is the reason grosbeak  and other similar wires have low conductance high thermal stability steel at their centers and that they break the conductor into many strands at the surface to reduce eddy formation in the wire. These wires are primarily aluminum structural but have steel assist, this is for periods of peak demand and peak stress. On a cold winters night where demand is very high but winds are blowing hard, the line gets hot it stretches and one line makes contact with the next, hard blow . . . . power is out for the next day. 

Here is the heat related resistance of aluminum.  The temperature coefficient (a= alpha for electrical resistance is 3.9x10-3/degree C).  R = R₀ (1 + a * (T - T₀)  http://hyperphysics.phy-astr.gsu.edu/hbase/electric/restmp.html

Electrical connections need to be close to cells. You can only step of voltage on the panel itself so much before you get arcing between two opposing voltages. Therefore from the cell cluster to the main you need to step up voltage and then step up voltage again (and alternate) for transmission over the wire. The higher the frequency the more information that is carried in hv and less in the form of amperage.

But the cooling fins are not structural and they add mass and create opportunity to ionize the gases of space resulting in losses. Secondarily for peak performance you need contact heat transfer between the wire to the fins and for reduced weight you need good emitters. The problem with good emitters is they are also good light (hv) absorbents so you need now to unidirectionally shield your wires from the sun.

The whole point of this exercise is to bring together technologies that exist, not fantasies within some range of reasoning. If you are going to have to create a whole new variety of conductor just to move electricity then we are in the realm of vapor-ware. I don't mean this to impinge on creativity, but there is also the law of unintended consequences and you should be prepared to accept these until technologies designed to resolve these come about.

Several problems you have been presented you have discounted in a hand waving manner, for example the critiques of structural stability. There have been experiments to see how things behave in space, the results have been rather unexpected. Piping, which I am very fond of, even without significant static load tends to become unstable without bracing with length and has a high tendency to want to bend and deform at the center. Things in space need to be cross-braced more frequently than you think.

Carbon fiber is very nice, but its not aluminum piping and connectors that you can buy off the shelf (which I am very fond of in my spacecraft builds). Most carbon fiber applications are custom and such large solar collectors require either assembly in space or manufacturing the carbon-fiber in space. In the future these things may be widely available.

 

Some thoughts:
Superconductors:  There are two issues here.  First is that high temperature superconductors tend to be ceramic which is extremely unlikely  to be a useful material for high surface area - low mass structures.  Rigidity is not your friend.  The second is that even high temperature superconductors in the "shade" are likely to be heated by the radiators to non-cryogenic levels, so as PB666 says, the refridgeration system will be worse than the I**2R losses.

Skin effect: skin effect is largely a function of frequency, which shouldn't be an issue for transmitting power between solar panels and spacecraft.  I do wonder if multiple strands of tiny wire (which wouldn't be effected by the skin effect anyway) would transmit electricity better than a single thicker wire.  The only time I've *ever* seen this done on Earth is for lighting protection: this can be done with a thin mesh of uninsulated wire (lighting will simply ignore any realistic insulation), so I might be missing something (it may also have to do with rounding and quality assumptions for wire gauge, I don't bother with where the amperage limits came from, I just use them.)

Electrical connections need to be close to the cells.  I have trouble following this.  My vision for a highpower space solar array would be the smallest possible solar EV cells spaced as far as possible apart (mostly to give the radiators the room they need).  Mylar mirrors would concentrate sunlight to the EV cells, and the arrays would transmit power in a daisy chain back to the spacecraft.  Now that you mention it, a certain length of the wire will likely require insulation in order to avoid arcing and similarly require thicker copper to reduce heating.

I wouldn't assume that the cooling isn't structural, expect anything that can do multiple duty to do multiple duty.  I'd also expect radiators to be similar to the mylar mirrors, possibly with coatings that conduct heat along the surface or dye the thing black to radiate better.  Still, the level of concentration will likely involve a heat pipe to transmit heat to the radiators at temperatures they can handle.  I'd expect these (the piping used for the heatpipes) to drive the scale of the design, along with the temperature tolerance for the radiators.  As far as "structural radiators" I would assume that solar cells would be held in place by 2 power lines, one hot (going out) heat pipe, and one cold (going in) heat pipe (expect some rare connections to include dampening).  On the other hand this assumes that the mirrors all have adjustments allowing them to focus on the fixed cell array.  It may be much easier to move the cells underneath the mirrors.  Also expect the mirrors to be made like a Cassegrain telescope (a primary mirror collecting light and shining it on a secondary mirror, which then transmits the light through a hole in the center of the primary).  This is to allow the radiators to be in the shade of the mirrors.  Further expect the array to be placed in three dimensions so the radiators don't heat each other up.  Hopefully this means the power lines can still hide in the shade (at a cost of being 40% or so longer thanks to following diagonals and such).

To be honest, I suspect a large scale "solar thermal" system based on the Cassegrain idea would work better.  No ideas on how you make the "combustion [energy transfer] chamber", that looks like a nasty problem.

And yes, this is a decades out idea (permanent bases on Mars is likely to happen first).  Most current designs that remotely resemble this type of thing have to unfold out of a fairing (and suffer all the "shake and bake" effects of a launch).  This type of thing screams "assemble in space" and is nothing like the macroscale assembly of the ISS.  It would take a massive load of research to switch to a "fragile, gossamer" spacecraft design (probably needed for efficient use of solar power.  Or we could go nuclear, or stay on Earth).

 

[KG3]

So your reflector needs to be pointing towards the sun.  Does that mean your engine will always point toward or away from the sun too?  Is there a design that allows you to fire your engine prograde or retrograde in respect to your orbit around the sun or whichever direction you might need?  How difficult will it be to keep such a large nebulous object pointed at the sun?       

[Guest]

6 minutes ago, KG3 said:

So your reflector needs to be pointing towards the sun.  Does that mean your engine will always point toward or away from the sun too?  Is there a design that allows you to fire your engine prograde or retrograde in respect to your orbit around the sun or whichever direction you might need?  How difficult will it be to keep such a large nebulous object pointed at the sun?       

The reflector and receiver can be on a rotating platform. Place them dorsally and ventrally in relation to the Sun in terms of general craft orientation so they always have maximum exposure to the Sun. You can then point your engine in pretty much any direction and control exposure through rotation of the reflectors and frames. This may complicate the structure of the reflector but it is much more desirable than a fixed reflector. 

[wumpus]

19 hours ago, KG3 said:

So your reflector needs to be pointing towards the sun.  Does that mean your engine will always point toward or away from the sun too?  Is there a design that allows you to fire your engine prograde or retrograde in respect to your orbit around the sun or whichever direction you might need?  How difficult will it be to keep such a large nebulous object pointed at the sun?       

As Regex says, you should be able to point it in arbitrary directions (this makes solar thermal more difficult).  I wouldn't be too surprised if it is actually fixed to 90 degrees from the Sun, and only allow prograde, retrograde, normal and antinormal (and degrees in between), at least if solar thermal.  This would greatly reduce the complexity of all the controls, but might require an additional form of thrust for radial in/out (possibly deliberately miss-aligning the mirrors (for minimal power) slapping a heat engine in the thermal chamber and using electric propulsion).

It might have a limited ability to sweep fore and aft, but you certainly don't want the exhaust from the thermal rocket anywhere near the radiators.

[PB666]

Just a few notes, This reactor is 1/2 the scale of the Wendelstein 7-A (which is a test reactor), and makes broad assumptions. That fusion will someday work, that it will work on smaller scales and if not that we could launch a 500t fusion reactor into orbit and then craft the rest of the power plant around it.
1. To initiate a stellenator requires more battery power than I have provided.
2. The assumption is that about 1/4th of the volume is metal and the average density is of aluminum.(the magnets are made of heavy metal so. . . )
3. The side branches can be made much more efficiently with carbon fiber single piece backbone.
4. Core I brought to orbit with a double up of the russian Soyuz-5 using asparagas and 1 extra booster on stage one. Its 200t of payload to orbit. The xenon can be fueled in orbit.
5. Core design is a tug, active payload is ore.
6. The drives are based of 35 kW but on a larger scale, each drive has six subdrives and each subdrive pulls about 523 kw of power. Therefore the assumption is power is fed in multiple kv feeds from the reactor to drive along high voltage lines. This allows some scalability in the ISP, but the default ISP is 9000 sec. (89,000 m/s). This allows for a power kick during the last oberth manuever at earth of 4 times higher acceleration.
7. Each blue triangle is generating 9.49 N of thrust over a surface of 0.2 m^2 this is roughly 15 times the output per surface area of the HiPEP thruster. (Just to let you know that I am not exaggerating the area required).
8. Obviously a fusion reactor would need tons of radiators, and this vessel has none. For steam generated power the radiators are essential, there is no mass provided for turbine or power handling.
9. Xenon or argon is immaterial the assumption is that Argon tanks made of carbon fiber would reduce the mass required for storage and storage can be provided in the branch carbon fiber construct.

This post is provided to basically tell that fusion reactors are not the cure-all to space problems. Solar panels may still be superior in space where they can be used and small scale fission reactors where they cannot be.

 

 

[MatterBeam]

23 hours ago, wumpus said:

Light itself exerts a force via momentum, which is likely what would be used to focus a mirror (perhaps of mylar) or angle a sail to exert a force in specific direction (I'm less sure about the sails, I suspect the light will be working against you).  The catch is that with a mirror and electric propulsion, the efficiency of the electrical system more or less exerts an acceleration on the entire spacecraft (thus warping the mirrors).

Some thoughts:
Superconductors:  There are two issues here.  First is that high temperature superconductors tend to be ceramic which is extremely unlikely  to be a useful material for high surface area - low mass structures.  Rigidity is not your friend.  The second is that even high temperature superconductors in the "shade" are likely to be heated by the radiators to non-cryogenic levels, so as PB666 says, the refridgeration system will be worse than the I**2R losses.

Skin effect: skin effect is largely a function of frequency, which shouldn't be an issue for transmitting power between solar panels and spacecraft.  I do wonder if multiple strands of tiny wire (which wouldn't be effected by the skin effect anyway) would transmit electricity better than a single thicker wire.  The only time I've *ever* seen this done on Earth is for lighting protection: this can be done with a thin mesh of uninsulated wire (lighting will simply ignore any realistic insulation), so I might be missing something (it may also have to do with rounding and quality assumptions for wire gauge, I don't bother with where the amperage limits came from, I just use them.)

Electrical connections need to be close to the cells.  I have trouble following this.  My vision for a highpower space solar array would be the smallest possible solar EV cells spaced as far as possible apart (mostly to give the radiators the room they need).  Mylar mirrors would concentrate sunlight to the EV cells, and the arrays would transmit power in a daisy chain back to the spacecraft.  Now that you mention it, a certain length of the wire will likely require insulation in order to avoid arcing and similarly require thicker copper to reduce heating.

I wouldn't assume that the cooling isn't structural, expect anything that can do multiple duty to do multiple duty.  I'd also expect radiators to be similar to the mylar mirrors, possibly with coatings that conduct heat along the surface or dye the thing black to radiate better.  Still, the level of concentration will likely involve a heat pipe to transmit heat to the radiators at temperatures they can handle.  I'd expect these (the piping used for the heatpipes) to drive the scale of the design, along with the temperature tolerance for the radiators.  As far as "structural radiators" I would assume that solar cells would be held in place by 2 power lines, one hot (going out) heat pipe, and one cold (going in) heat pipe (expect some rare connections to include dampening).  On the other hand this assumes that the mirrors all have adjustments allowing them to focus on the fixed cell array.  It may be much easier to move the cells underneath the mirrors.  Also expect the mirrors to be made like a Cassegrain telescope (a primary mirror collecting light and shining it on a secondary mirror, which then transmits the light through a hole in the center of the primary).  This is to allow the radiators to be in the shade of the mirrors.  Further expect the array to be placed in three dimensions so the radiators don't heat each other up.  Hopefully this means the power lines can still hide in the shade (at a cost of being 40% or so longer thanks to following diagonals and such).

To be honest, I suspect a large scale "solar thermal" system based on the Cassegrain idea would work better.  No ideas on how you make the "combustion [energy transfer] chamber", that looks like a nasty problem.

And yes, this is a decades out idea (permanent bases on Mars is likely to happen first).  Most current designs that remotely resemble this type of thing have to unfold out of a fairing (and suffer all the "shake and bake" effects of a launch).  This type of thing screams "assemble in space" and is nothing like the macroscale assembly of the ISS.  It would take a massive load of research to switch to a "fragile, gossamer" spacecraft design (probably needed for efficient use of solar power.  Or we could go nuclear, or stay on Earth)

Solar pressure on a 1000m^2 reflector would be at most 0.018N. If the reflector massed just 7kg, an acceleration of 0.01g would impose a force of 0.67N, which is about 38 times greater. As the reflectors get lighter and lighter and acceleration lower, solar pressure plays a bigger role. 

You can create a sunshade to cover the wires, at the cost of blocking out part of their radiative surfaces. Or just accept the inefficiency and increase the cooling capacity. Either way, why would you have superconducting wires dangling in space?! In both designs I described, the photovoltaics are embedded deep within a structure inside the spacecraft. Only the reflectors and the optics are exposed to space. 

I promise you all, in Part 3, I will propose a detailed design of a solar-powered spacecraft meant to travel from Earth to Jupiter. 

The 'telescope-like' design I have in mind is closer to the Newtonian telescope. Using an non-imaging surface, I can get even get light to be focused coming in from the sun at an angle, so that the secondary mirror does not block any of the sunlight. 

Look at type (h).

We definitely need to build these things in space. As I said in the blog post, the key to the performance of future solar systems is to maximize on the thinnest reflectors possible and minimize the solar panel area required. 

22 hours ago, KG3 said:

So your reflector needs to be pointing towards the sun.  Does that mean your engine will always point toward or away from the sun too?  Is there a design that allows you to fire your engine prograde or retrograde in respect to your orbit around the sun or whichever direction you might need?  How difficult will it be to keep such a large nebulous object pointed at the sun?       

The engine just needs to point through your center of gravity in the direction of acceleration you need. If you put your propellant tanks and engine in the middle, solar reflector on one side and payload on the other, you can create a spaceship where aligning these things doesn't matter. 

Examples of sideways-on-a-stick designs:

21 hours ago, regex said:

The reflector and receiver can be on a rotating platform. Place them dorsally and ventrally in relation to the Sun in terms of general craft orientation so they always have maximum exposure to the Sun. You can then point your engine in pretty much any direction and control exposure through rotation of the reflectors and frames. This may complicate the structure of the reflector but it is much more desirable than a fixed reflector. 

Exactly this. 

2 hours ago, wumpus said:

As Regex says, you should be able to point it in arbitrary directions (this makes solar thermal more difficult).  I wouldn't be too surprised if it is actually fixed to 90 degrees from the Sun, and only allow prograde, retrograde, normal and antinormal (and degrees in between), at least if solar thermal.  This would greatly reduce the complexity of all the controls, but might require an additional form of thrust for radial in/out (possibly deliberately miss-aligning the mirrors (for minimal power) slapping a heat engine in the thermal chamber and using electric propulsion).

It might have a limited ability to sweep fore and aft, but you certainly don't want the exhaust from the thermal rocket anywhere near the radiators.

 

1 hour ago, PB666 said:

Just a few notes, This reactor is 1/2 the scale of the Wendelstein 7-A (which is a test reactor), and makes broad assumptions. That fusion will someday work, that it will work on smaller scales and if not that we could launch a 500t fusion reactor into orbit and then craft the rest of the power plant around it.
1. To initiate a stellenator requires more battery power than I have provided.
2. The assumption is that about 1/4th of the volume is metal and the average density is of aluminum.(the magnets are made of heavy metal so. . . )
3. The side branches can be made much more efficiently with carbon fiber single piece backbone.
4. Core I brought to orbit with a double up of the russian Soyuz-5 using asparagas and 1 extra booster on stage one. Its 200t of payload to orbit. The xenon can be fueled in orbit.
5. Core design is a tug, active payload is ore.
6. The drives are based of 35 kW but on a larger scale, each drive has six subdrives and each subdrive pulls about 523 kw of power. Therefore the assumption is power is fed in multiple kv feeds from the reactor to drive along high voltage lines. This allows some scalability in the ISP, but the default ISP is 9000 sec. (89,000 m/s). This allows for a power kick during the last oberth manuever at earth of 4 times higher acceleration.
7. Each blue triangle is generating 9.49 N of thrust over a surface of 0.2 m^2 this is roughly 15 times the output per surface area of the HiPEP thruster. (Just to let you know that I am not exaggerating the area required).
8. Obviously a fusion reactor would need tons of radiators, and this vessel has none. For steam generated power the radiators are essential, there is no mass provided for turbine or power handling.
9. Xenon or argon is immaterial the assumption is that Argon tanks made of carbon fiber would reduce the mass required for storage and storage can be provided in the branch carbon fiber construct.

This post is provided to basically tell that fusion reactors are not the cure-all to space problems. Solar panels may still be superior in space where they can be used and small scale fission reactors where they cannot be.

It all boils down to the power density.

[wumpus]

Note 1:  While "The Martian" may be the most accurate SF this decade on the movie screen (a low bar I know), that doesn't mean that it is all that accurate (the dust storm was admitted to be forced).  Any rotation has to keep the radiators pointing normal to the Sun, likewise you can assume that solar arrays will be pointing at the Sun (if using ions*) [note we can generally assume that this vehicle isn't going past Mars: forcing an "outer planets" ship would justify nuclear fuel, but the radiators still would take up a similar amount of space that the solar panels should have.

Note 2: You certainly *can* place the collector between the mirrors and the Sun, but that leaves you with the radiators in front of the mirrors.  Since they are going to be at right angles (roughly) to each other, it will certainly work.  You still will require roughly similar amounts of mirror and radiator surface area, and all the radiators will be in front of the mirrors.  Also assume that any material not absolutely flat (things holding the radiators in place, any heat pipes,. etc) will all be hit with the full force of the Sun.  Not my first choice.

* don't expect to use ions to move crewed voyages.  PB666 has crunched the numbers in several threads and shows just how slowly any such craft has to go.  I still have great hopes for ions, but not directly moving people.

[MatterBeam]

Just now, wumpus said:

Note 1:  While "The Martian" may be the most accurate SF this decade on the movie screen (a low bar I know), that doesn't mean that it is all that accurate (the dust storm was admitted to be forced).  Any rotation has to keep the radiators pointing normal to the Sun, likewise you can assume that solar arrays will be pointing at the Sun (if using ions*) [note we can generally assume that this vehicle isn't going past Mars: forcing an "outer planets" ship would justify nuclear fuel, but the radiators still would take up a similar amount of space that the solar panels should have.

Note 2: You certainly *can* place the collector between the mirrors and the Sun, but that leaves you with the radiators in front of the mirrors.  Since they are going to be at right angles (roughly) to each other, it will certainly work.  You still will require roughly similar amounts of mirror and radiator surface area, and all the radiators will be in front of the mirrors.  Also assume that any material not absolutely flat (things holding the radiators in place, any heat pipes,. etc) will all be hit with the full force of the Sun.  Not my first choice.

* don't expect to use ions to move crewed voyages.  PB666 has crunched the numbers in several threads and shows just how slowly any such craft has to go.  I still have great hopes for ions, but not directly moving people.

Those are just illustrations to show how the various components are arranged in relation to each other and the direction of travel. Don't take everything so literally, don't read too much into pictures!

Mirrors, radiators? Please clarify your second point. Just to be sure, the mirrors do not have anything to do with radiators. 

Ions can definitely be used for fast interplanetary travel. In fact, if you can travel several times faster than the biggest chemical rockets even if your acceleration is measured in milligees (1/1000 of a g).

This is because although the departure from Earth takes weeks instead of minus, you can keep accelerating to higher velocities. Use the trip calculator provided here: http://www.rocketpunk-manifesto.com/2011/08/mission-to-mars.html

You will notice that even if you input modest figures, such as 1kW/kg, 25% of dry mass dedicated to propulsion, 3500s Isp and so on, you'll end up with a 289 ton spacecraft that sends 100 tons of payload to Mars in just 85 days. This is departure from Earth and insertion in low Mars orbit. It has a mass ratio of 1. A 450s Isp chemical rocket with a similar mass would put only 80 tons around Mars, and will take 8.6 months to do so. 

[PB666]

1 hour ago, MatterBeam said:

Those are just illustrations to show how the various components are arranged in relation to each other and the direction of travel. Don't take everything so literally, don't read too much into pictures!

Mirrors, radiators? Please clarify your second point. Just to be sure, the mirrors do not have anything to do with radiators. 

Ions can definitely be used for fast interplanetary travel. In fact, if you can travel several times faster than the biggest chemical rockets even if your acceleration is measured in milligees (1/1000 of a g).

This is because although the departure from Earth takes weeks instead of minus, you can keep accelerating to higher velocities. Use the trip calculator provided here: http://www.rocketpunk-manifesto.com/2011/08/mission-to-mars.html

You will notice that even if you input modest figures, such as 1kW/kg, 25% of dry mass dedicated to propulsion, 3500s Isp and so on, you'll end up with a 289 ton spacecraft that sends 100 tons of payload to Mars in just 85 days. This is departure from Earth and insertion in low Mars orbit. It has a mass ratio of 1. A 450s Isp chemical rocket with a similar mass would put only 80 tons around Mars, and will take 8.6 months to do so. 

Yeah but in reality his numbers are all based on a set of what ifs all of which pretty much don't exist. He has no power supply, the only power supply that could do it is fusion. The problem is that its  NOT just the weight of the reactor, its also the weight of the cooling radiators (steam generation will not work without heat transfer . . .it is just a bomb without heat transfer). I was very generous in the ION drives, very; the reality is they would likely occupy 10 times the area and the infrastructure required would be prohibitive.

The trip is if I had a power supply that could generate 50 MW and not weigh  >1/3rd the weight of the total ship then I could get to Mars. The smallest operational 'maybe someday a fusion reactor'  is 5.5 meters across about 2 meters high and made up of aluminum and magnets made of rare earth minerals. >100 t of weight probably 150 to 200t. This does not include the steam generator components in the reactor, the turbine, the radiators . . . . . . . . .

The reason I showed the fusion reactor is to basically argue, look fusion is great if you need lots of power, but its not physics-less power, these things have alot of mass and supporting infrastructure, and its not clear that long-term steam-power is a viable thing in space. Lots of mass and supporting structure mean . . .very hard to move from place to place.

Here is a 1MW system of solar panel (10 x 100 feet) at 32% efficiency (432 w/sq.meter) is 432,000 kW, one on each side, one to the front and two on the back. 1t per panel at 4 panels. 1.73 MW for 4 tons at earth not at Mars (0.69 MW) . This ship is chosen because it minimizes the specific infrastructure devoted to panels, which becomes really problematic for very long panels. I want to say that 1000 sq. meter retractable solar panels are a fantasy, they do not exist.
Here is a reality check. https://www.nasa.gov/content/solar-arrays-on-the-international-space-station.  The solar panels on ISS generate total 120 kw of electricity from 8 @ 35 meters x 12 meters. That is just 36 watts per meter, that is really happens and we are planning based on solar power densities a magnitude higher. Each solar array and truss weight 15.8 t and thus 62.4 T are required for 120 kw of electricity ~2000 watts per ton. https://en.wikipedia.org/wiki/Integrated_Truss_Structure#Truss_subsystems

So when I start with 400,000 watts per ton it means I am provisioning power at 200 fold higher density than the current most reliable application (that is to say an application used to support the lives of humans in space over a prolonged period of habitation).

Next we look at ION drives. Here is the highest TWR drive in existence. " The pre-prototype HiPEP produced 670 mN of thrust at a power level of 39.3 kW using 7.0 mg/s of fuel giving a specific impulse of 9620 s.^[2][4] Downrated to 24.4 kW, the HiPEP used 5.6 mg/s of fuel giving a specific impulse of 8270 s and 460 mN of thrust." wikipedia.

Here are the structural statistics. .41m x .93m x 0.15m means the unit is 0.3831 sq. meters (estimated weight between 10 and 20 kg). This gives a rated thrust density of 1.2007 newtons sq.meter. The weight per square meter is between 0.026 and 0.052 kg per sq.meter disregarding framing. The power is 63 kw per sq.meter.

In the above we have 1.73 'handwaving' megawatts. this requires 27.5 sq meters of thruster or a circle of trusters 3 meters in radius (very doable) [that is to say 1.6 larger cross-sectional area of the largest engine in stock KSP. The engines will weigh ~1.5 tons with adequate trussing. The force production is 33N. So if we had an ounce of fuel (and all the controls were physics-less) we could generate a TWR of 0.000611. This is 6 ma of acceleration.

So on our bare bones Mars mission  (we carried a quart of earthworms living in a 1 kg container) we need 2 @ 5760 = 11520 dV to go and return. In this situation you will need 0.92t of fuel and 0.093t of tank. The TWR drops to 0.000523. Fuel and fuel tank are now 15.9% of ships weight (you thought the ISP was too generous). To break earth orbit would require  30 days minimum using efficient kicks.

So the next thing is we need a minimal computer control module. Lets say we need a decent battery - 1 ton (we do, burning between AtP of 160 and 020 requires a battery, even when using kicks),  Command and control, communication, rcs, reaction wheels 1 ton. So now we are up to a base weight of 7.5 tons. The amount of fuel&tank is 1.23 tons. TWR = 0.000383. 50 days to escape earth.

So now we want to go to mars in 89 days and return in doing so we need 58k (m/s) dV of fuel on this very simple earthworm ship. Lets see what this very efficient ship offers up:  Fuel is now 60% of the weight (remember you complaining about ISP being to high!).fuel&tank are now  9.86 tons. (5kg/8000 USD means 15.7 million USD to get that quart of earthworms to mars and back). TWR = 0.000204 Days to escape earth assuming thrust is on 25% of the time . . . . 75 days to escape Earth.

We move onto humans. . .that is to say Elon Musk. The ISS weight 419 tons, but we only need on section of it. So lets at 41.9 tons of weight and recalculate. This allows the transport of 1 human (On ISS 6 humans live in 10 livable modules so . . . . ). So here we go . . . . . Weight = 100t. . . TWR = 0.000031. 59.5 t of xenon used (~100M USD). Assuming a quarter of each orbit burning to escape earth or Mars (3398 dV/(.25*.00031))about 500 days to exit Earths gravitational influence. You are not going to Mars in 89 days. ISP of 9000 is not too high, to get to Mars in 89 days and return you need alot of power and a very high ISP thruster

Lets now replace those solar panels with an 1.724 Megawattage of ISS panels. 62t * 1.724/.120 - 4  = 886.333 t. TWR =0.0000013, Xenon used is 1119 t (1.8B USD). Total weight is 2kT. Elon died of old age before reaching Mars.

Its like this, getting to Mars in 89 days ranges from practically impossible to theoretically impossible. To leave in earths SOI in 50 days would require a 17.24 MW ship. To leave in 5 days would require a 172.4 MW ship and 400,000 square meters of '1kg/sq.meter' solar panels, and that is with panels we do not have (and dont BS that they exist, until they have been applied to a human ship, as far as we are concerned they do not exist). Fusion we do not have . . . . Fission cannot produce anything near the power required. Radioisotopic thermal generators are too small . . . .We have only to consider making solar panels much more efficient, structurally sound at a lower weight.

THis group is old, we have seen the 39 days to Mars (of VASIMR) which has been debunked, we have seen other claims, mostly debunked, this claim is not exceptional. Electric power is great, but only if you can get the electric power/weight ratio up by magnitudes over what it is now, and even so its spells worlds of trouble with wiring and cooling systems.

 

 

 

 

 

[MatterBeam]

@PB666: You are a very engaging read, but in many of your posts, you get lost in a storm of assumptions and successive conclusions. Above is one of them.

Here's what I have to note:
-I presented the trip calculator (an excel file) on that link. The maths works out, whatever the set of numbers you put in. And I'm not defending the author's numbers.
-Your argument about the potential of fusion vs the weight of the components.... is just another way of saying kW/kg. If your fusion reactor has 0.1kW/kg, it loses out to existing solar panels at 0.3kW/kg, before other complications are included (fusion fuel availability, sunlight intensity, ect). 
-Propulsion power density should include the mass of all the systems that create, convert and use power, as well as the waste heat management systems. Using further subdivisions of the components (reactor, radiators, engines) is much less useful, and rather pointless as they will all be mostly proportional, so they can all be brought into the same kg sum per kW of output. 
-Area and volume has nearly zero relevance in space. Space is free, mass is not. The volume of the engines will have nearly zero effect on the mission performance, only their mass does. 
-Solar panel power density is usually rated by output, not input.
-1MW of input corresponds to 8.55x85.5m with 1367W/m^2 of sunlight. 10x100feet corresponds to 127kW of sunlight. This is why everyone hates imperial.
-At 32% efficiency, you's produce 320kW, so I think that's a typo.
-Where did you get '1 ton' from? If we look at current developments, the triple-junction solar cells that can get 32% efficiency mass about 0.85kg/m^2. That 1MW input array would mass 621kg in total. The structural mass you'd need on top of that figure would be about 1kg/m^2 for 731kg, but it can also be ~3000 times lower than that for any solar panel lifted up from Earth. If it is meant to only stay in space and handle the gentle accelerations of a milligee craft, it will never need to structural support to survive the 3g+ peak accelerations and vibrations of a launch vehicle. 
-If we work only with the power density figure, we can easily work out that an advanced multi-junction solar panel would produce roughly 320/(621+731): ~236W/kg. A bit better than what is being achieved today (150W/kg).
-Why would the panels on a solar electric craft have to be retractable?
-The ISS solar panels are a terrible example. They're old, use old technology, are built for sturdiness and reliability and to be easily replaced by an astronaut in EVA, and only produce 27W/kg. 
-If the ion drive matches the power density of the solar panels, then you're halving the system power density. If they provide a better power density, then you're approaching the power density of the solar panels. If they're lower, then you're losing system power density. The relationship is 1/x = 1/y + 1/z. X System Power Density, Y Panel Power Density, Z Engine Power Density.  VASIMR by Ad Astra published 200kW/620kg including radiators and other sub-systems, or 0.32kW/kg.
Put together, we get 1/236+1/320: 1/136. The overall system power density would be 136W/kg. 
From here, we can calculate all the mission parameters. It is a much simpler approach than calculating truss diameters and the N/m^2 rating of ion engines. 
-The acceleration figures you ended up with are purely the result of the assumptions you came up with yourself. 
-Extremely high Isp is not a good thing. The savings on propellant are inversely proportional. If you halve your propellant load by increasing Isp from 1000s to 2000s, you'll get less savings by doubling again from 2000s to 4000s and so on. Propellant is the cheapest part of a spaceship. Lowering the Isp until a decent balance between mass ratio and average acceleration is what actual rocket design should do. It is an iterative process though, and real world designs are subject to constraints outside of the scope of this discussion (what the year's NASA budget is, what the diameter of the fairing is, what are the current president's preferred space objectives and so on).
-Getting to Mars in 89 days requires about 25km/s of deltaV. With a 3500s Isp engine, that's a mass ratio of 2.04. I don't see where the physically/practically impossible part is. 

[PB666]

So i have been tinkering with the numbers. I was going to model the problem but unfortunately I could not get emissives to work in Unity 5 due to the increased number of steps now needed to do so (and the fact the versions of Unity 5 im using appears to be glitched). I was a matter of luck that this happened.

What I have determined is that for kicking using low acceleration is that the time required in days is 260 days /(acceleration * theta) where theta (degrees) is the time aloted per orbit (degrees converted to time) for burning ones engines. For example if A = 0.01 and theta is 10' (5 degrees before Pe to 5 degrees after) then its 2600 days to reach a point where the engines can be continously fired. If we fired over period of 100' that time would be cut to 260 days but the cost in fuel would increase due to spiralling away from the planet. The typical burn starts at 15dV/degree*a 

Because we need about 3000 dV  the 1 to 1.5 dV per burn (burn dV decreases because orbital speed increases at Pe). it translates to >2698 orbits, during the last burn the engines are fire about 50 seconds before Pe and fire continuously until transfer-planet intercepting orbit is achieved.

Here is the setup.

200 MegaWatt nuclear reactor 50t (can be turn on and off when needed)
3040 square meter of HiPEP at 26 kg per meter 80t
Payload 200t
Fuel 38.4 t
Fuel tank 3.84 t

This fuel is 10% more then the fuel need to get to Mars and return assuming that 200t of payload is delivered in LMO and 20t is returned to LEO.
Total weight leaving earth is 372,295 kg total returned to Earth 153,895 kg. even if the power of the FNR increases 2 fold you do not get the full benefit because the HiPEP weight would increase by 80t. The critical issue is power output on the ION thrusters, that needs to go up by a factor of 2 or more. Whereas with electro solar the ION thruster mass it trivial compared to the weight of the solar panels becuase of the presumptive power density of Fusion electric the reactor weight becomes less of a concern relative to the thruster weight. 

Starting orbit was alt = 140,000.
Here are the value for different starting orbits.

Altitude
200000    255.6 days/(acceleration * theta).
400000    244.8 days/(acceleration * theta)
800000    234.4 days/(acceleration * theta)
1,600,000  206.9 days/(acceleration * theta)
1.5 Earth radius (3185000 alt)  170.6 days/(acceleration * theta)
2 Earth radius 186.6 days/(acceleration * theta)
GTO 46.6 days/ " "

Some other things are learned by this excercise. Approach Jovian inner satellites is not recommended with ION drive systems, Although it could deliver a rocket that might do so, the time requirements to correct orbit near a large gas giant would be prohibitive.

 

GTO 47.7 days/" "

And it makes really no sense to bring a bus down to LEO if the majority of its weight is not-expendable when loads can be delivered rapidly to GTO despite the loss of dV associated with LfOX based systems versus ION drives. THe drag alone created by AoA crossectional area of 3040 m² suffices as a good enough reason not to go below 200,000 meters.

Anyway ION drive bases 39 or 89 days to MARS will not work, the output density to weight ratios to the drives are two low. These slow accelerating space tugs need to stay away from the depths of gravity wells. It may be possible to create a fusion ION drive that has alot higher thrust and power output that circumvents the problem.

 

 

[MatterBeam]

@PB666

I think you are approaching the concept of not being able to to continuously accelerate away from a planet incorrectly. 

You must first break down the interplanetary trip into three parts: the acceleration to escape velocity, the transit, and the insertion.

For Earth, you can handle the climb from 7.8km/s to 11.2km/s by itself. All you have to make sure of is that the angle you leave from Earth from roughly points you at your target planet.

During transit, you can further accelerate to first raise your apohelion to actually reach Mars, then shorten the trip with further acceleration above the lowest-energy trajectory that is the Hohmann trajectory. Since the transit times are measured in months, while the 'further acceleration' will be a week at most, this is not a complicated thing to optimize.

Insertion just requires that the craft start decelerating early enough so that its velocity relative to the target planet falls below the planet's escape velocity. It needs enough distance and time to accomplish this. 

The part with which you seem to have an issue with is the first acceleration to escape velocity. You suppose that a craft can only accelerate along a tiny portion of its orbital period/angle. This is not the case! Solar-electric trajectories are notoriously hard to optimize, but they all use a continuous acceleration over the entire orbital period. They disregard the small benefit of the Oberth effect, but gain in the time it takes to reach the escape velocity.

A good calculator is the General Mission Analysis Tool (http://gmatcentral.org/) that is free to download and has a tutorial to handle low-thrust missions between planets. 

The numbers you used for your reactor and engines are pretty good! 4kW/kg for the reactor, 2.5kW/kg for the engines. Assuming no other equipment, that's 1.53kW/kg for propulsion. 
Let me run your numbers (130t propulsion, 200t payload, mass ratio 1.115...) against a more ideal scenario. You did not define an exhaust velocity or Isp for the engines, so I'll assume it is 6000s, which has been demonstrated by HiPEP and would give enough deltaV for a Hohmann (minimum energy, 8.6 month) trajectory to Mars. 

You can accelerate at a rate of 0.0183m/s^2 initially (1.86 milligee), rising to 0.0204m/s^2. Let's take the average of 0.019m/s^2. 

What I got in GMAT. Continuous acceleration up to escape velocity.
To climb from 7.8km/s to 11km/s (escape velocity at 140km altitude), you need to accelerate for 1.95 days. 
To reach Mars, you add another 300m/s, which is an additional 4.4 hours.

For a Solar-Electric craft, you'll start only being able to accelerate on the sunny side of the orbit. As your altitude increases, less and less of the Earth's shadow blocks your orbit. It is known as the beta angle, and it becomes negligible to nil at high altitude.

[PB666]

1 hour ago, MatterBeam said:

@PB666

I think you are approaching the concept of not being able to to continuously accelerate away from a planet incorrectly. 

You must first break down the interplanetary trip into three parts: the acceleration to escape velocity, the transit, and the insertion.

For Earth, you can handle the climb from 7.8km/s to 11.2km/s by itself. All you have to make sure of is that the angle you leave from Earth from roughly points you at your target planet.

During transit, you can further accelerate to first raise your apohelion to actually reach Mars, then shorten the trip with further acceleration above the lowest-energy trajectory that is the Hohmann trajectory. Since the transit times are measured in months, while the 'further acceleration' will be a week at most, this is not a complicated thing to optimize.

Insertion just requires that the craft start decelerating early enough so that its velocity relative to the target planet falls below the planet's escape velocity. It needs enough distance and time to accomplish this. 

The part with which you seem to have an issue with is the first acceleration to escape velocity. You suppose that a craft can only accelerate along a tiny portion of its orbital period/angle. This is not the case! Solar-electric trajectories are notoriously hard to optimize, but they all use a continuous acceleration over the entire orbital period. They disregard the small benefit of the Oberth effect, but gain in the time it takes to reach the escape velocity.

A good calculator is the General Mission Analysis Tool (http://gmatcentral.org/) that is free to download and has a tutorial to handle low-thrust missions between planets. 

The numbers you used for your reactor and engines are pretty good! 4kW/kg for the reactor, 2.5kW/kg for the engines. Assuming no other equipment, that's 1.53kW/kg for propulsion. 
Let me run your numbers (130t propulsion, 200t payload, mass ratio 1.115...) against a more ideal scenario. You did not define an exhaust velocity or Isp for the engines, so I'll assume it is 6000s, which has been demonstrated by HiPEP and would give enough deltaV for a Hohmann (minimum energy, 8.6 month) trajectory to Mars. 

You can accelerate at a rate of 0.0183m/s^2 initially (1.86 milligee), rising to 0.0204m/s^2. Let's take the average of 0.019m/s^2. 

What I got in GMAT. Continuous acceleration up to escape velocity.
To climb from 7.8km/s to 11km/s (escape velocity at 140km altitude), you need to accelerate for 1.95 days. 
To reach Mars, you add another 300m/s, which is an additional 4.4 hours.

For a Solar-Electric craft, you'll start only being able to accelerate on the sunny side of the orbit. As your altitude increases, less and less of the Earth's shadow blocks your orbit. It is known as the beta angle, and it becomes negligible to nil at high altitude.

The standard ISP for HiPEP is 8900 sec. In addition I ran your numbers, to develope the 5600 spiralling dV you need to escape, requires 3 days using the acceleration you gave, but since you wasted half your fuel by using a spiralling path and lower ISP, your net load went from 180,000 PL to 140,000 PL (200,000 to 160,000 if exchanging at Mars). Congradulations you just discovered the payload efficiency tradeoff for ION drives. Unfortunately the head of the space tug company your work for just fired you.

This has been tested are revealed many times. If you use your thrust to circularize (make more circular) then you have to pay an additional cost to circularize, you cannot keep that energy when you leave, it goes into the planetary system.

[MatterBeam]

2 hours ago, PB666 said:

The standard ISP for HiPEP is 8900 sec. In addition I ran your numbers, to develope the 5600 spiralling dV you need to escape, requires 3 days using the acceleration you gave, but since you wasted half your fuel by using a spiralling path and lower ISP, your net load went from 180,000 PL to 140,000 PL (200,000 to 160,000 if exchanging at Mars). Congradulations you just discovered the payload efficiency tradeoff for ION drives. Unfortunately the head of the space tug company your work for just fired you.

This has been tested are revealed many times. If you use your thrust to circularize (make more circular) then you have to pay an additional cost to circularize, you cannot keep that energy when you leave, it goes into the planetary system.

The HiPEP produced a range of ISPs, 6000-9000s. I used 6000s because it is the only way it matched the numbers you came up with. A more sensible design would have a much lower Isp anyway, and a much better tank mass to propellant mass ratio. 
The 5600m/s... is for the entire mission. From Earth departure (3500m/s) to Mars arrival (2100m/s). I am concentrating on the first part. 
I have demonstrated that 'spiralling out' is not 'wasting' fuel.
A spiralling trajectory does not circularize, it just reaches escape velocity and straight lines away from the planet

[PB666]

1 minute ago, MatterBeam said:

The HiPEP produced a range of ISPs, 6000-9000s. I used 6000s because it is the only way it matched the numbers you came up with. A more sensible design would have a much lower Isp anyway, and a much better tank mass to propellant mass ratio. 
The 5600m/s... is for the entire mission. From Earth departure (3500m/s) to Mars arrival (2100m/s). I am concentrating on the first part. 
I have demonstrated that 'spiralling out' is not 'wasting' fuel.
A spiralling trajectory does not circularize, it just reaches escape velocity and straight lines away from the planet

No, No, No....5760 dV is for a very specific model, its a launch that places the outbound burn at completion that intercepts Mars without the need for a plane change burn and then with minor correction places the craft to LMO were it burns to circularlize without any system entry slowing burn. Specifically you leave earth and try in orbit to intercept mars LMO at its orbital apo. To achieve the 5760 you have to launch from a particular time of day, +/- 10 degrees achieve minimum orbit at 140,000 then make your escape burn average to a certain time of day something like 135 Atp, preferable at as high a g-force as possible with no spiraling. If you spiral out of orbit or spiral into Mars orbit the dV goes up markedly. You can achieve the same with an ION drive as long as you estimate how many kicks you need, the backtrack that number of days alterning the place of the launch and burn by 0.985 degrees per day. Its not the best way but the model allows you do kick with no increase in cost, spiralling cost extra dV. Noting that a kick is a spiral but a spiral that preserves pE as closely as possible with constant burning you loose dV.

Correcting an error of a previous post because its demonstrates your misunderstanding in these matters.
At SOI you get to (Must keep) any specific kinetic energy that you gained during our burn but that you did not loose to specific potential energy. (See thread on this, it was specifically put out because of misunderstandings that you have). SKE = V²/2 SPE = u/r (for any radius). For any circular orbit SKE = u/r and SPE = (1.4142 * V)^2/2. Consequently burning to a planet at LEO along a optimal vector can both add dV (in terms of post scape velocity) and inclination velocity in excess of what is added at LEO.

If you for instance burned to barely escape earth and then at mars burn to reach HMO and then burned again to circularize mars these are your DV assuming we nailed the plane change at liftoff window and

dv1 - 3240.  Burn to escape Earths SOI and no more (spiralling cost even more)
dv2 - 3663. Burn to Mars and no more
combining dv1&2 into a single burn with associated plane change - 3884 (you saved 3019 dV)
dv3 - 1986. Burn to match velocity just inside Mars SOI
dv4 - 1499. Circularize at Mars LMO. (Spiralling in costs more)
combining dv3&4 into a single - 1877 (you saved  1608 dV).

You said using the r_min "Oberth" did not result in any remarkable savings . . . you are wrong. . . . .by converting all but a mid-trip correction burn (which is usually only a couple dV) you save 45% of the dV required to get to Mars, if you are a space tug hauling non-perishable items to mars you just cost your money (xenon gas is very expensive) and you reduced his PL by 40% and in addition you just earned your competitor business. To put it otherwise you increased the companies variable cost by 81% over what it might have been if you planned your burns carefully.

The last burn you make to Mars from a spiralling orbit is for-all-intents and purposes is dV2, this means that you have already spent at least dV1 to get to that point, whereas by repeatedly kicking at say 150-300 km I am basically emulating a model orbit exit by using the elliptical nature of orbits to give more optimal burn time.

I should mention that if you watch You-tube videos of KSP long time players you will see that they make burns along multiple axis in order to maximize the burn and avoid waste. You will find many posts here about players complaining that the trip to Moho cost alot more than stated on the dV map of the Kerbol system. This is the reason why. The dV map assumes that Hohmann transfer are made with only 2 burns. For planetary systems like Jool the process is more complicated because achieving LMO may not be desirous unless it can intersect a given planets orbit.

https://en.wikipedia.org/wiki/Specific_orbital_energy

 

 

 

 

 

[MatterBeam]

What is SKE? What is SPE? What is HMO? How much is 'markedly'? 

Why should we spend months using periapsis kicks when the deltaV penalty for doing a spiralling orbit is small for a Hohmann trajectory and tiny for an accelerated transit?

Is the incredibly long mission time worth taking along a few percent more propellant?