Advanced Solar-Electric Energy: Part I

[MatterBeam]

Hello! I share with you the recent post from here: http://toughsf.blogspot.com/2017/11/advanced-solar-energy-in-space-part-i.html I hope you will find it interesting and will have something to discuss!

Advanced Solar Energy in Space: Part I

Solar Thermal Rockets can be efficient and have high performance. However, they remain temperature-limited to an exhaust velocity of 12km/s.

How do we surpass this limit?

The limits
 

NASA's Suntower concept.

Solar Thermal Rockets have been shown to have great potential if we use modern materials technology - they can be as performant as Nuclear Thermal Rockets in the inner Solar System. 

 

With Liquid Rhenium Solar Thermal Rocket, we demonstrated that it could be possible to increase the maximum operating temperature from the 4500K of the most advanced solid heat exchangers to the 5900K of a liquid rhenium-based heat exchanger. However, despite these high temperatures, a Solar Thermal Rocket can never exceed an exhaust velocity of 12km/s. Due to the second law of thermodynamics (the heat exchanger cannot get hotter than the source), the heat exchanger in a Solar Thermal Rocket cannot get hotter than the surface of the sun. As exhaust velocity depends on temperature, we cannot obtain more than 12km/s exhaust velocity out of a rocket that uses the Sun as a heat source. 

 

Electric rockets

Solar Electric rockets are well known for powering propulsion systems with much higher exhaust velocities. The ion thruster on the Dawn probe was powered by 38m^2 of solar panels and achieved an exhaust velocity of 31.3km/s (3200s Isp).

A high exhaust velocity allows for the amount of propellant carried to be drastically reduced for any deltaV requirement. For example, if we wanted to go from Earth to Mars, the deltaV requirement is 6000m/s. A chemical-fuel rocket with an exhaust velocity of 3678m/s (375s Isp, like the Raptors on SpaceX's BFR) would need to consume 4.1kg of propellant for each 1kg of dry mass to fulfil the deltaV requirement. An ion thruster like Dawn's would only need 0.21kg for each 1kg of dry mass: a twenty-fold decrease.

In short, the main advantage of electric rocket is that they allow for very small spaceships that don't need a lot of propellant to go to further and faster. 

So what's the catch?

Electric rockets have two major downsides.
 

The first is the power source. So far, we have used solar energy in the form of solar panels, or nuclear energy in the form of RTGs, to power electric rockets. 

 

Solar panels have a fundamental efficiency limit called the Shockley–Queisser limit. It states that no more than 33.7% of the energy of sunlight can be extracted by a single solar cell. Most common solar cells have the potential to extract 32% of the Sun's energy using silicon band-gaps, while commercial versions manage an efficiency of only 24%. The world record for silicon solar panel efficiency is 26.3%.

An early Space-Based Solar Power concept.

Solar panels are rather heavy for their area and performance. They are usually several kilograms per square meter. Research into making solar panels lighter has produced designs such as thin-film solar cells with 0.2 or even 0.1kg/m^2.

 

Combining the efficiency of the most advanced solar panels with the sectional density of thin-films solar cells makes for a system with a power density of 1.5kW/kg at most. Modern advanced solar cells for spacecraft aim for 0.3kW/kg. 

 

Other power options rely on nuclear energy. The current form of nuclear energy of spacecraft, RTGs, has woefully poor performance. A power density of 1 to 10W/kg is to be expected. 

The SP100 nuclear reactor.

Nuclear reactors with a carnot heat cycle (Stirling heat engine, steam turbines and so on) have great potential, but currently they are limited by the low temperature difference between the reactor core and the radiators. This is the result of having to keep the fissile fuels inside the reactor core solid and safe (so a low maximum temperature) and the low performance of thermal radiators currently employed (so a high minimum temperature). Despite these limitations, nuclear reactors producing over 10kW/kg have been designed. They have a potential of over 100kW/kg or more.
 

Nuclear power has problems not related to its performance as well. For the foreseeable future, fissile fuels are expensive, dangerous to handle and a hot-button political and environmental topic. The radioactivity continuously degrades the power generating equipment and makes refurbishment or repairs a complicated affair. A lot of effort will have to be put into finding sources of fuels if we intend to exploit the Solar System, otherwise we'd have to wait for alternative nuclear technologies such as fusion reactors to mature.

Low power density means low acceleration. Spiralling trajectories are the result.

The second problem with electric rockets is their low propulsive power. 

One aspect is that the electrical power divided by the exhaust velocity leads to a very low thrust output. Another aspect is that the cryogenic magnets, the superconducting coils, the electrostatic chambers... are simply quite heavy. Current laboratory-tested concepts such as VASIMR are only expected to have about 1kW/kg, with most other designs struggling to reach ten times less specific power. 

Between the two, electric rockets end up having extremely low thrust. This prolongs the burns that chemical rockets can perform in minutes into weeks-long affairs that spend an inordinate amount of time in Earth's Van Allen belts. The benefits of the Oberth effect are completely lost and gravity losses that come from accelerating away from the optimal angle become significant. Reducing the duration of these burns requires dedicating most of the spacecraft's dry mass to power generation and propulsion, so as to increase the rate of accelerations. The propellant to payload ratio quickly drops to levels comparable to chemical propulsion.

 

Advanced Solar Electric Energy

We need to improve the performance of electric rockets. It is possible to do this without relying on problematic nuclear propulsion, limp solar panels or the massive amounts of chemical fuels needed for interplanetary travel.

What we need is advanced solar energy concepts with much higher power densities. We will now look at designs that allow the efficient use of sunlight to produce electricity out of compact and lightweight generators

They common key to these designs' performance is the use of solar collectors made of extremely lightweight materials, based on the technology developed for solar sails. These reflective surfaces of only a few grams per square meter can focus huge amounts of sunlight onto a small surface. Intense sunlight allows for higher performance and greater temperatures. 

Concentrated photovoltaics

Photovoltaics convert the light they absorb into electricity. By increasing the intensity of this light, more electricity can be produced from the same solar cell. This increases power density. Peak gains are obtained from x1000 -x3000 concentration.

Concentrated photovoltaics attempt to multiply the intensity of sunlight collected by a solar panel by adding a concentrator. A concentrator focuses sunlight onto the solar panel's surface. Since the concentrator only needs to be reflective, it can be much lighter than an equivalent surface area of solar panels. By maximizing the collector area (lightweight) and minimizing the solar cell area (heavy), a better power density can be achieved. 

On top of simple mass optimization, efficiency can be improved. Conventional solar cells use a single silicon p-n junction. The efficiency therefore capped by the the Shockley-Queisser limit. This is sufficient as the design is cheap and relatively lightweight, so higher output is achieved by adding more solar panel area.

Doped silicon solar cell.

Concentrated photovoltaics leads to a very small solar panel surface area. It becomes more reasonable to use more complex solar cells that improve efficiency. Multijunction solar cells use multiple p-n junctions on top of each other. Each p-n junction is tuned to a portion of the electromagnetic spectrum. Sunlight ranges from radiations in the infrared to X-rays. Only 47% of sunlight's energy is contained in the narrow portion of the electromagnetic spectrum called the visual spectrum, that corresponds to radiations of wavelengths 400 nanometers to 700 nanometers. Conventional solar cells only absorb a fraction of this small segment.

Red, green and blue p-n junctions capture energy from wavelengths that correspond to the low (infrared to red), middle (yellow and green) and high energy (blue to UV) sunlight. 

Triple junction solar cell. Up to 50% efficiency.

Quadruple junction solar cell extending into the deep IR wavelengths. Better suited for space use. Up to 56% efficiency.

By increasing the number of junction layers and dividing light received into small slices corresponding to each layer, a theoretical maximal efficiency of 86.8% is possible. The number of layers for each efficiency improvement increases exponentially.  Reaching 86.8% efficiency requires an infinite number of layers. By three layers, the efficiency cap is raised to 63%, which we will deem sufficient. Another concern is heating. The sunlight that is not converted into electricity becomes waste heat instead. Increasing the temperature of a solar cell lowers its efficiency. When concentrators are focusing sunlight to tens to hundreds of times its normal intensity, the heating can quickly become problematic. 

Active cooling is therefore required to keep concentrated photovoltaics cool and efficient for space applications. 

In the above graph, a solar cell under 1000x sunlight intensity is tested at a range of temperatures. At 400K, it is estimated that there is an efficiency loss of 11% of the value at 280K. Lower temperatures improve the rate at which photons are converted in the semiconductors, prevent losses from re-radiated energy and lessen the effect of other inefficiencies such as recombination.

Another study cooled down solar cells down to 50 Kelvins. The graph above is the theoretical maximal efficiency achieved at each temperature. We notice that at 50K, the peak efficiency (41%) is 37% higher than the peak efficiency at 300K (30%). 

Three-junction solar cells can have a mass of 0.85kg per square meter or less. In this book, 0.1kg/m^2 is cited for a concentrated solar cell array, although it cannot be determined if it is multi-junction. This recent NASA proposal for concentrator quadruple-junction solar cells designed to survive extreme environments cites 0.24kg/m^2 as the figure for solar cells without their concentrators. 

Let us now consider two designs for modern or advanced multi-junction concentrator solar energy systems. We note that waste heat management is a determinant factor in the potential performance of these designs. Refer to All the Radiators for more details. 

Modern concentrated photovoltaic example:

Different solar concentrator configurations.

We will use conservative figures. 0.85kg/m^2 for the solar cells, with quadruple junctions operating at room temperature (300K) to provide an efficiency of 40%. The concentrator is a parabolic dish of mass 7g/m^2 and a reflectivity 95%. The solar concentration is x1000. 

1.29MW of solar energy is focused by 1000m^2 of concentrator onto each 1m^2 of solar panel. It is converted into 519kW of electricity and 779kW of waste heat. 

The waste heat must be dealt with using a lightweight, low temperature radiator. 

A liquid droplet radiator is ideal for this task. 0.1mm wide droplets of mercury coated in black paint, spaced by 1mm and released at a velocity of 20m/s across a 1m wide gap would cool down from 300K to 5K before being captured as solid mercury balls. The radiators would remove 27kW of heat for every kilogram of droplets. Using multiple sheets of droplets multiplies this figure at the cost of a slight efficiency loss due to interreflection. 
The component masses for 1m^2 are 0.85kg of solar panels, 7kg of collectors and 28.9kg of radiators. It produces 519kW.

The system power density becomes 14.1kW/kg. A more realistic figure would include the mass of additional systems such as power converters, droplet radiator booms and pumps, solar tracking mechanisms for the collectors and so on, probably bringing down the system power density to 10kW/kg. 

Advanced concentrated photovoltaic example:

Graphene foam can form the basis for ultra-lightweight solar collectors.

We will use optimistic figures. 0.25kg/m^2 for quadruple junction solar cells operating at a 275K temperature. The efficiency is 60%. Micron-thick aluminium concentrators resting on graphene foam or tensed by Zylon wires have a mass of only 1 gram per square meter. Reflectivity is 95% and solar concentration is 10000x.

13MW of sunlight reach the solar cells. 7.79MW becomes electricity while 5.19MW becomes waste heat.

We will use a hybrid wire/droplet radiator.

The wires can have alternating hydrophobic and hydrophilic surfaces.

Small droplets of water are held by charged surfaces, alternating hydrophobic/hydrophobic patches or simple surface tension, on a thin wire. The wire drags the droplets along like a conveyor belt. Ink turns the water black and improves emissivity. Each 1m^2 of radiator area is composed of 1000 parallel wires holding 1 million droplets of 1mm diameter each, moving along at 10m/s. The passage through the vacuum cools the droplets from 275K to 64K. The high heat capacity of water and its high heat of fusion (energy needed to freeze it) means that more than 1.5MW of heat can be removed by 1kg of water and wires.

The component masses are 0.25kg of solar panels, 10kg of concentrators and 3.5kg of radiators. System power density can approach 500kW/kg. 

Even more advanced designs that use thinner reflectors, faster wire/droplet radiators and lower temperature (higher efficiency) solar cells can probably reach 1MW/kg. 

High temperature thermophotovoltaics

Photovoltaics are most efficient when converting light composed of wavelength exactly matching the band-gap of the n-p junction materials they are composed of. 

This is what allows laser-to-electrical conversion to achieve very high efficiencies. The wavelength of the laser exactly matches the band-gap of the converter.

We cannot expect such efficiencies using the Sun's broad spectrum of radiations. Even multi-junction solar cells can only cover part of the spectrum, at the cost of greater complexity, cost and mass per square meter. 

Using different receiver/emitter materials helps specify which wavelengths reach the PV cell

There is a solution in tuned thermo-photovoltaics. In this design, the Sun's rays are focused on a heat exchanger. The heat exchanger absorbs the entire solar spectrum and radiates it back in a narrower range of wavelengths. Selective filters reflect anything outside of an even narrower selection of wavelengths back to the heat exchanger so that the energy is not wasted.

A heat exchanger combined with efficient filters allows us to reduce the solar spectrum to emissions exactly matching the band-gap of a solar cell. Efficiencies of 98% of the maximum thermodynamic efficiency are possible using a single n-p junction. 

TPV system with optical concentrator.

Currently, thermophotovoltaics are limited by the stability of the heat exchanger, the loss of re-radiated energy, the lack of cooling systems and simple lack of development when compared to traditional photovoltaics. For example, most designs tested today focus on Silicon Carbide or Tungsten heated to 1500K, while the thermophotovoltaic cells reach 350K or more. The maximal thermal efficiency becomes 76%. From this amount, 20 to 50% of the radiations from the heat exchanger are lost or simply go in the wrong direction in typical flat heat exchanger designs. Solar cells operating at high temperature, losing efficiency compared to their counterparts at 300 or 270K. The radiations outside the band gap range of wavelengths are not always efficiently recycled back into the heat exchanger too. Finally, the low temperature emitters cannot achieve the high emission intensities (MW/m^2) that have helped the efficiency of concentrated solar photovoltaics.

A solution to these problems can be found.

Hot tungsten coils.

Using higher-temperature heat exchanger materials is a start. Carbon is ideal, with a melting temperature of over 4000K. Tungsten can reach 3000K temperatures without a problem.  

Instead of using small band-gap p-n junctions such as Gallium Arsenide, Silicon with a band gap of 1.1eV, which corresponds to wavelengths of 1100nm, can be selected. This corresponds to the peak emissions of an emitter at 2660K. Active cooling can handle the heat load to reduce the cold end temperature to 270K. The thermal efficiency of system with a 2660K hot end and 270K cold end is 89%. This is an immediate 13% improvement over current systems.

A photonic crystal composed of layers of gallium arsenide and air with an otherwise impossible band gap.

Even more recent research focusing on artificial band-gaps created by using photonic crystals permits efficiencies greater than 40%. 

The configuration of a cylindrical heat exchanger absorbing sunlight from surfaces on the ends.

The heat exchanger can be shaped into a very long cylinder inserted into a closed chamber. The chamber's inner walls are coated with TPV cells. Sunlight concentrators focus sunlight onto the exposed top and bottom of the cylinder. The cylinder then re-radiates this heat from the enclosed lateral walls onto the TPV cells. It is called a 'thermal well'. The large exposed to enclosed surface area ratio of the cylindrical heat exchanger means that very little of the heat exchanger's radiations are lost. This is another 20-50% improvement over current designs.

A good optical filter is needed. For silicon, a filter would need to only allow wavelengths longer than about 800nm or shorter than 1100nm. This is possible today with developments in nano-structured metamaterials and photonic crystals. 

Finally, as demonstrated in the previous section, it is possible to gain a 20% increase in efficiency or more by cooling the solar cells.

Together, these optimizations can achieve the 50% efficiency purported in recent research, or approach 70 to 80% efficiency as dictated by theoretical limits. 

We will now look at a modern, then advanced, design for a solar TPV system.

Modern thermophotovoltaic example:
We will only use figures available in today's research. 

High temperature thermo-photovoltaic device.

We use a tungsten heat exchanger, heated to 3000K. The thermophotovoltaics are indium-gallium-arsenide-phosphide cells with a bandgap tuned exactly to the peak emissions of the heat exchanger, for an efficiency of 61%. The n-p junction is only 50 nanometers thick and backed by a silver plate to reflect unabsorbed wavelengths back to the heat exchanger. 

Blackbody emission spectrums for various temperatures.

The heat exchanger will be a carbon-coated cylinder. Sunlight is focused onto its flat ends. The light is absorbed and heats up the tungsten. Heat conducts down the cylinder and is re-radiated out of the lateral surfaces. A shell of solar cells intercepts these radiations. At 3000K, the tungsten is emitting at 4.1MW/m^2 but only 1.15MW/m^2 reaches the solar cells. This means that for each square meter of tungsten, there will be 3.56 square meters of solar cells.

The thinner the heat exchanger, the lighter it can be. A 10cm wide, 1m long tungsten cylinder would mass 153.8kg and have a lateral surface area of 0.31m^2. It will be able to illuminate 1.1m^2 of solar cells. The mass of tungsten per square meter of solar cell becomes 139.8kg. If we use a 1cm wide cylinder instead, we calculate a tungsten mass of just 14 kg per square meter of solar cells. We will use the latter figure. Another benefit is that the radiations lost from the cylinder ends amount to only 0.25% of the total radiations.

The full radiation of the heat exchanger's lateral surfaces will have be matched by an equivalent input from its top and bottom surfaces. For a 1cm wide rod, this means that 0.031m^2 of lateral surface area are supplied by 1.57cm^2 of illuminated area; a ratio of 395:1. The solar concentrators are therefore heating the tungsten at an intensity of 1632MW/m^2.

95% reflective solar concentrators would be achieving a concentration of x628399. If the tungsten rod is I-shaped, with larger absorbing surfaces at the top and bottom, the radiative efficiency is lessened but the concentration factor becomes more manageable. If a 10% radiative loss is acceptable, the a concentration factor of 'only' x15710 is needed. At 7g/m^2, about 0.68kg of reflective concentrator surfaces would be needed to heat a 1cm and 1m long wide tungsten rod. This represents about 0.61kg per square meter of solar cells.

Plasmonic light-trapping nanoparticles help very thin solar cells capture as much light as thick solar cells.

As this is a single-layer solar cell, we can use the masses of thin-film solar cell arrays as a basis for our power density calculation. This means 0.2kg/m^2 or less. A silver backing plate and a denser semiconductor mix might mean an area density closer to 1kg/m^2. They convert the radiations into 631.3kW of electricity and 403.7kW of heat.

The solar cells must be kept at 300K. Cooling will rely on the mercury droplet radiator mentioned above. 14.9kg of droplets are required to remove the waste heat. 

Component masses come out as 1kg for the solar cells, 14kg for the heat exchanger, 0.61kg for the solar concentrator and 14.9kg for the droplets. 

System power density is 20.6kW/kg, although other components we have not considered might lower this somewhat.

Advanced thermophotovoltaic example:
Advanced materials technology and miniaturization techniques can drastically increase the system power density of thermo-photovoltaics. 

Photoluminescent emitters allow short wavelength radiations without the need for high temperatures.

Indium gallium phosphide, typically used as the 'blue cell' in a multi-junction solar panel, will be our only layer. It operates best when it receives 545nm wavelength light. This light will be supplied by a 5317 Kelvin blackbody, with metamaterials filtering out wavelengths too long to be efficiently converted by the solar cell. The solar cells have an 80% conversion efficiency of light at 10MW/m^2 intensity, while massing only 0.1kg/m^2. 

The lightbulb structure needed to contain the liquid rhenium.

The heat exchanger will be liquid rhenium, held inside a transparent tube of fused quartz. The tube walls are actively cooled by circulating hydrogen gas in a manner similar to what was proposed for Closed-Cycle Gaseous-Core Nuclear Thermal Rockets, or 'nuclear lightbulbs'. An alternative would be electromagnetically contained plasma, such as cesium ions. 

Non-imaging optics allow for extreme solar concentration ratios with sub-1% radiative losses. 

Parabolic compound troughs can also reduce the sun-tracking requirements of the solar collectors.

The liquid rhenium heat exchanging cylinder will be 2mm wide. It masses only 66 grams per meter length. Heat is absorbed from end-caps 6.3mm wide, giving it an I-shape. The tube radiates at 40.78MW/m^2 and receives 4078MW/m^2 through the end caps. Each tube shines on 0.0256m^2 of solar cells, so it adds 2.57kg per square meter of solar cells.

Sunlight is supplied by 197m^2 of 95% reflective solar collectors. At 1g/m^2, the solar collectors would mass about 0.2kg.

Each square meter of solar cells produces 8MW of electricity but also 2MW of waste heat. We use the water and wire arrangement of radiators from the advanced version of the concentrated sunlight generator to handle this. It would require 1.33kg.

Component masses are 0.1kg for the solar cells, 2.57kg for the heat exchanger, 0.2kg for the solar collectors and 1.33kg for the radiators. System power density should be close to 1.9MW/kg, though realistically it will be lower.  

Part II

In the second part of this series, we will look at power generation options that do not rely on photovoltaics.

[Scotius]

Very educational. But also complicated. While promising, this technology still seems to have a long way to go before being ready to be deployed in space.

[YNM]

Doesn't change the fact that you're theoretically limited to 1.4 kW of power for each m2 of "catching" equipments.

They can be lightweight and easy to use, sure, but I wonder you can say the same around Neptune, for instance.

I could only imagine they're useful for the rocky planets around the Sun (potentially also for other stars). Outside of that, in the reigns of gas and ice planets, they're quite lacking.

Edited November 16, 2017 by YNM

[Bill Phil]

1 hour ago, YNM said:

Doesn't change the fact that you're theoretically limited to 1.4 kW of power for each m2 of "catching" equipments.

They can be lightweight and easy to use, sure, but I wonder you can say the same around Neptune, for instance.

I could only imagine they're useful for the rocky planets around the Sun (potentially also for other stars). Outside of that, in the reigns of gas and ice planets, they're quite lacking.

I wouldn't be surprised if concentrated solar energy was used out at Neptune. Just needs to be larger. And for a power station, that's not necessarily an issue. You get less power to mass, but that's only important if you're worrying about mass. If we get to a point where we need a power station at Neptune, then shaving off the grams likely wouldn't be a serious concern, since we'd probably have advanced propulsion tech that could actually put useful payloads there with high efficiency.

Of course there are alternatives. What gets used would depend on the circumstances of the situation. 

[MatterBeam]

13 hours ago, Scotius said:

Very educational. But also complicated. While promising, this technology still seems to have a long way to go before being ready to be deployed in space.

Technically, all the technologies I mention have already been deployed in space or have real-life working demonstrators. Concentrator solar panels have been used on Deep Space 1: https://en.wikipedia.org/wiki/Deep_Space_1 and thermophotovoltaics are a well-understood technology.

4 hours ago, YNM said:

Doesn't change the fact that you're theoretically limited to 1.4 kW of power for each m2 of "catching" equipments.

They can be lightweight and easy to use, sure, but I wonder you can say the same around Neptune, for instance.

I could only imagine they're useful for the rocky planets around the Sun (potentially also for other stars). Outside of that, in the reigns of gas and ice planets, they're quite lacking.

The collector equipment is usually the component with the lightest mass per square meter: only a few grams or less. The more collector area we use (and higher solar concentration), the lower the average mass per square meter of the entire system. 

Around Jupiter, we would be receiving 10% of the sunlight around Earth, around Saturn 1% and 0.1%. 
1kW/kg is generally accepted as the minimum needed for rapid interplanetary travel. It is the performance required of a generator to power a VASIMR rocket to Mars in 39 days. This means a power and propulsion system can travel quickly around Jupiter if it had 10kW/kg, around Saturn at 100kW/kg and Neptune at 1MW/kg. Currently, solar electric systems are unable to produce this level of power density, so they would become incredibly underpowered in the outer solar system. With the designs I suggest, travel around Saturn and even Neptune under solar power is possible using the advanced designs I described.

The reason solar-electric power is considered weak today is because it struggles to reach 100 to 300W/kg.

2 hours ago, Bill Phil said:

I wouldn't be surprised if concentrated solar energy was used out at Neptune. Just needs to be larger. And for a power station, that's not necessarily an issue. You get less power to mass, but that's only important if you're worrying about mass. If we get to a point where we need a power station at Neptune, then shaving off the grams likely wouldn't be a serious concern, since we'd probably have advanced propulsion tech that could actually put useful payloads there with high efficiency.

Of course there are alternatives. What gets used would depend on the circumstances of the situation. 

Quite right!
Making the solar collectors larger should not be a big problem, as they mass only a few grams per square meter while the rest of the system (solar cells, cooling ect) does not have to get more massive. 

One application I will talk about in Part 2 is beamed power. Towering structures holding together several km^2 of parabolic reflectors can collect a lot of sunlight even in the outer solar system. It is converted into electricity by the solar-electric systems I am describing. This electricity can be used to power lasers to transmit that energy to other spacecraft. This means that you only need one big collector while all the rest of the spacecraft only uses a tiny laser dish to power its rockets. 

[YNM]

1 hour ago, MatterBeam said:

The collector equipment is usually the component with the lightest mass per square meter: only a few grams or less. The more collector area we use (and higher solar concentration), the lower the average mass per square meter of the entire system.

Do you have any data on what they'd be made of ? What acceleration they're going to have ?

[MatterBeam]

11 minutes ago, YNM said:

Do you have any data on what they'd be made of ? What acceleration they're going to have ?

The solar collectors are made of the same materials, structures and general configurations as solar sails. Solar sails today can be made of Mylar, averaging 7 grams per square meter. In the future, thinner sheets of aluminum and lighter structural materials, such as graphene foam, can allow for reflective surfaces of only 0.1 grams per square meter. If you really get down to it, nanometers-thick metals such as silver with a silica coating can mass as little as a few milligrams per square meter.

I will work out a full example spaceship in Part III to demonstrate the level of performance possible with Advanced Solar-Electric power and propulsion schemes. 

[NSEP]

Very interesting. I now see greater potential for solar than before! Amazing!

[YNM]

1 hour ago, MatterBeam said:

The solar collectors are made of the same materials, structures and general configurations as solar sails. Solar sails today can be made of Mylar, averaging 7 grams per square meter. In the future, thinner sheets of aluminum and lighter structural materials, such as graphene foam, can allow for reflective surfaces of only 0.1 grams per square meter. If you really get down to it, nanometers-thick metals such as silver with a silica coating can mass as little as a few milligrams per square meter.

I tried doing it with mylar. Apparently you'll have problems keeping this flat, they'll have to flail around I think. Also, they're sliightly different than solar sails because solar sails work on pressure - they bend away from the Sun (towards where you're going), the electric contraption will bend towards the Sun (or away from where you're travelling to).

I haven't figured doing the pulling forces though. There's some possibility they're fine up to thousands of metres, but I'm not sure for something like a few kms.

Edited November 16, 2017 by YNM

[PB666]

As you are limited by 3.25E25 W/m²*r.

There is no limit to the ISP to solar thermal since at high temperatures gas becomes ionized. At such temperatures uv lasers and rf can be used to accelerated the heated gas. The issue is stabilizing the mess before it glows white hot.

Its nice to see the theory, but the reality currently for application solar panels is about 40% efficiency, this I don't see as the major concern. I can simplify the problem like this.

1. We need light weight frames that can be deployed that are huge. I don't mean 10x bigger than current, but 100x or 1000x bigger than current frames (such as ISS).
I was thinking for example a device that is 40 meter long or more (2, 1 on boths sides of ship). IN reaching orbit it unfolds like pocket knife. The end the travel to the center on piece grabbing the second, then the pieces move away as the center brace telescopes outward in both direction to 200 or 300 meters and pulling a then solar film that is 400 x 40 meters = 16000 sq. meters. Getting efficiency over 50% is not necessary if the weight can be reduced to 0.1 kg per m²

2. In the example above panels are producing 50% eff x 16000 x 1400 w = 11.2 MW of power, the power density at the ends 280 kilowatts per meter. if the voltage is 12 then the amperage is 20,000 amp per meter on the pickup bar. This is way too high for the conductors to efficiently conduct. The voltage needs to be raised to around 600 volts this drops the amperage on the pickup bar to around 500 amps, this amounts to several bulky wires. And alternative is a pickup wire on the side. But again this has to step up the voltage to 5000V range in order to get the amperage down.

3. In the above example there is a ship with 32000 sq. meter of panel at 22.4 MW of power and at 0.1 kg per sq. meter. the panels weigh 3.2 tons. This is not too bad for a ship that weight 20 to 50 tons but lets see how bad. 

Suppose a 10 kg ION thruster produce a maximum of 35 kw but we can use them most efficiently at 20 kw and have an ISP of 9000 (exhaust velocity of 89,000 m/s). 22.4 mw/0.02 Mw per thruster is 1120 drives. Each drive occupies a quarter of a meter, the ION drive foot print is gong to be 250 m² (a 9 meter radius, this would be between factor 12 and 16 KSP rocket in diameter). The drives themselves would add 11.2 tons. Not to bad.  But for all of that what are we going to get in terms of thrust. N= 2 * 22.4 * 0.8/9000  = 3982 N. If the weight is 50 to 60 tons then the acceleration is 0.0724 a with a maximum TWR of 0.1297 inside the orbit of venus.

Not adequate for oberth maneuvers but lets look at total performance. Lets say 1/3 of the ship was devoted to fuel, what types of dV are we looking at. A 55 ton ion driven solar electric would loose 16.5 Ton and gain 31,500 m/s of dV. Such a ship has 11.2 tons of thrusters 3.2 tons of panel, 16.5 tons of fuel, a few tons of electrical (converting 22.4 MW of power safely into thruster usable form). At 80 percent efficiency those thrusters total will generate  4.48 MW of heat (which we wave our hands and pretend we have dealt with all the while knowing the ship melted), We need another 3.2 tons of ultralight radiator. Oh and BTW the waste heat is 500 times more power than the fission based reactors! This leaves a payload of 17.9  tons.

However, outside planetary systems, this amount of thrust and dV is more than enough to do anything you want to do in our solar system. If you kick heliocentric retro down to mercury and perform an oberth around mercury you can be leaving the solar system at 50,000 or more m/s with 17.9 tons of payload. Fat chance stopping at pluto though, its still too little sunlight.

 17.9 Tons is still to small to transfer colony ships or earth return landers. 17.9 ton payload, however is an excellent size for an interplanetary tug than can cycle back and forth to mars several times on a single load of fuel, or increase payload for one round trip.

48 minutes ago, YNM said:

I tried doing it with mylar. Apparently you'll have problems keeping this flat, they'll have to flail around I think. Also, they're sliightly different than solar sails because solar sails work on pressure - they bend away from the Sun (towards where you're going), the electric contraption will bend towards the Sun (or away from where you're travelling to).

I haven't figured doing the pulling forces though. There's some possibility they're fine up to thousands of metres, but I'm not sure for something like a few kms.

Films need to be pulled from both ends, this is why I mentioned framing. The frames need to stretch from two opposing sides of a rectangular film. What MB is not considering however is that with very large film solar panels there is a large wattage flowing over the ends, unless the voltage has been stepped up into the kV range there is going to be alot of heat at the interface.

 

[MatterBeam]

6 hours ago, NSEP said:

Very interesting. I now see greater potential for solar than before! Amazing!

Thanks! There's more to come.

5 hours ago, YNM said:

I tried doing it with mylar. Apparently you'll have problems keeping this flat, they'll have to flail around I think. Also, they're sliightly different than solar sails because solar sails work on pressure - they bend away from the Sun (towards where you're going), the electric contraption will bend towards the Sun (or away from where you're travelling to).

I haven't figured doing the pulling forces though. There's some possibility they're fine up to thousands of metres, but I'm not sure for something like a few kms.

A tension-wire structure should be decent. The wires can pass in front of the parabolic disk without a problem, so you can form a 3D pyramid-like structure where the reflective films are pulled by each corner of the pyramid. Another option is inflatable rims. 

4 hours ago, PB666 said:

As you are limited by 3.25E25 W/m²*r.

There is no limit to the ISP to solar thermal since at high temperatures gas becomes ionized. At such temperatures uv lasers and rf can be used to accelerated the heated gas. The issue is stabilizing the mess before it glows white hot.

Its nice to see the theory, but the reality currently for application solar panels is about 40% efficiency, this I don't see as the major concern. I can simplify the problem like this.

1. We need light weight frames that can be deployed that are huge. I don't mean 10x bigger than current, but 100x or 1000x bigger than current frames (such as ISS).
I was thinking for example a device that is 40 meter long or more (2, 1 on boths sides of ship). IN reaching orbit it unfolds like pocket knife. The end the travel to the center on piece grabbing the second, then the pieces move away as the center brace telescopes outward in both direction to 200 or 300 meters and pulling a then solar film that is 400 x 40 meters = 16000 sq. meters. Getting efficiency over 50% is not necessary if the weight can be reduced to 0.1 kg per m²

2. In the example above panels are producing 50% eff x 16000 x 1400 w = 11.2 MW of power, the power density at the ends 280 kilowatts per meter. if the voltage is 12 then the amperage is 20,000 amp per meter on the pickup bar. This is way too high for the conductors to efficiently conduct. The voltage needs to be raised to around 600 volts this drops the amperage on the pickup bar to around 500 amps, this amounts to several bulky wires. And alternative is a pickup wire on the side. But again this has to step up the voltage to 5000V range in order to get the amperage down.

3. In the above example there is a ship with 32000 sq. meter of panel at 22.4 MW of power and at 0.1 kg per sq. meter. the panels weigh 3.2 tons. This is not too bad for a ship that weight 20 to 50 tons but lets see how bad. 

Suppose a 10 kg ION thruster produce a maximum of 35 kw but we can use them most efficiently at 20 kw and have an ISP of 9000 (exhaust velocity of 89,000 m/s). 22.4 mw/0.02 Mw per thruster is 1120 drives. Each drive occupies a quarter of a meter, the ION drive foot print is gong to be 250 m² (a 9 meter radius, this would be between factor 12 and 16 KSP rocket in diameter). The drives themselves would add 11.2 tons. Not to bad.  But for all of that what are we going to get in terms of thrust. N= 2 * 22.4 * 0.8/9000  = 3982 N. If the weight is 50 to 60 tons then the acceleration is 0.0724 a with a maximum TWR of 0.1297 inside the orbit of venus.

Not adequate for oberth maneuvers but lets look at total performance. Lets say 1/3 of the ship was devoted to fuel, what types of dV are we looking at. A 55 ton ion driven solar electric would loose 16.5 Ton and gain 31,500 m/s of dV. Such a ship has 11.2 tons of thrusters 3.2 tons of panel, 16.5 tons of fuel, a few tons of electrical (converting 22.4 MW of power safely into thruster usable form). At 80 percent efficiency those thrusters total will generate  4.48 MW of heat (which we wave our hands and pretend we have dealt with all the while knowing the ship melted), We need another 3.2 tons of ultralight radiator. Oh and BTW the waste heat is 500 times more power than the fission based reactors! This leaves a payload of 17.9  tons.

However, outside planetary systems, this amount of thrust and dV is more than enough to do anything you want to do in our solar system. If you kick heliocentric retro down to mercury and perform an oberth around mercury you can be leaving the solar system at 50,000 or more m/s with 17.9 tons of payload. Fat chance stopping at pluto though, its still too little sunlight.

 17.9 Tons is still to small to transfer colony ships or earth return landers. 17.9 ton payload, however is an excellent size for an interplanetary tug than can cycle back and forth to mars several times on a single load of fuel, or increase payload for one round trip.

Films need to be pulled from both ends, this is why I mentioned framing. The frames need to stretch from two opposing sides of a rectangular film. What MB is not considering however is that with very large film solar panels there is a large wattage flowing over the ends, unless the voltage has been stepped up into the kV range there is going to be alot of heat at the interface.

I think you should take a more step by step approach. Some of the limitations you mention are self-imposed.

Due to the second law of thermodynamics, the heat exchanger in a solar thermal rocket cannot be hotter than the Sun. Heat flows from a hotter source to a colder sink.

1. Current frames are built out of aluminium and designed to survive the 3g+ accelerations and vibrations during a launch from Earth. Much lower masses can be achieved by in-space construction. 
50% efficiency with 0.1kg/m^2 means a power density of 6.8kW/kg using sunlight at Earth orbit. Impressive when compared to today's 300W/kg, but still lower than what is potentially possible with concentrated sunlight. Without concentrated sunlight, you would find it very difficult to reach that efficiency anyway.

2. Voltage/Amperage are not things I mentioned because they are mostly engineering problems. Superconductivity, for example, makes ultra-high amperages a non-issue for example. 

3. Why would you use an ion thruster with such an extreme Isp? Such Isp becomes wasteful for interplanetary trajectories because your propellant savings are inversely proportional to your deltaV requirement. Each increase in exhaust velocity saves less and less propellant, until you're negotiating kilograms on a multi-ton ship. Suppose we use an electrodeless plasma thruster. Let's set the Isp to a more reasonable 2000s. Per megawatt, the engine produces 102kN before efficiency losses. 

If you have a 50 ton dry mass rocket and want to go to Mars, you need a deltaV of 6km/s. That's a mass ratio of 1.36, or 18 tons of propellant. Wet mass is 68 tons. If we have access to just 10MW of power, the initial acceleration is 0.015m/s^2, with the average acceleration at 0.017m/s^2. The departure burn to Mars will require a departure burn duration of 56 hours, which is tiny compared to the 8.6 month travel time to Mars.

Let's go big. Let's dedicate an entire 50 tons to power and propulsion, averaging 10kW/kg. That gives us 500MW of propulsive power to push a 100 ton dry mass rocket. With an engine Isp bumped up to 4000s, thrust is 25.5kN. We want to cut the Earth-Mars trip down to 2 months. This is an impulse-2 trajectory that requires 52.9km/s of deltaV. The mass ratio requires is 3.85, so now our fully loaded rocket masses 385 tons. It starts accelerating at a low rate of  0.066m/s^2, but it averages 0.1m/s^2. 

This 2-months to mars rocket spends roughly 3 days accelerating away from Earth. Decent, no? This is without even using the 'advanced' designs mentioned in the blog, at 1MW to 2MW/kg. Payload should be 30 to 40 tons.

For the designs I proposed, there are no large films. There are large solar collectors, but they're just reflective dishes that only bounce sunlight. The actual solar panels are a much smaller surface embedded in the rocket, surrounded by cooling equipment and wires as thick as necessary to carry away the current. 

Edited November 16, 2017 by MatterBeam

[PB666]

1 hour ago, MatterBeam said:

Thanks! There's more to come.

A tension-wire structure should be decent. The wires can pass in front of the parabolic disk without a problem, so you can form a 3D pyramid-like structure where the reflective films are pulled by each corner of the pyramid. Another option is inflatable rims. 

I think you should take a more step by step approach. Some of the limitations you mention are self-imposed.

Due to the second law of thermodynamics, the heat exchanger in a solar thermal rocket cannot be hotter than the Sun. Heat flows from a hotter source to a colder sink.

1. Current frames are built out of aluminium and designed to survive the 3g+ accelerations and vibrations during a launch from Earth. Much lower masses can be achieved by in-space construction. 
50% efficiency with 0.1kg/m^2 means a power density of 6.8kW/kg using sunlight at Earth orbit. Impressive when compared to today's 300W/kg, but still lower than what is potentially possible with concentrated sunlight. Without concentrated sunlight, you would find it very difficult to reach that efficiency anyway.

2. Voltage/Amperage are not things I mentioned because they are mostly engineering problems. Superconductivity, for example, makes ultra-high amperages a non-issue for example. 

3. Why would you use an ion thruster with such an extreme Isp? Such Isp becomes wasteful for interplanetary trajectories because your propellant savings are inversely proportional to your deltaV requirement. Each increase in exhaust velocity saves less and less propellant, until you're negotiating kilograms on a multi-ton ship. Suppose we use an electrodeless plasma thruster. Let's set the Isp to a more reasonable 2000s. Per megawatt, the engine produces 102kN before efficiency losses. 

If you have a 50 ton dry mass rocket and want to go to Mars, you need a deltaV of 6km/s. That's a mass ratio of 1.36, or 18 tons of propellant. Wet mass is 68 tons. If we have access to just 10MW of power, the initial acceleration is 0.015m/s^2, with the average acceleration at 0.017m/s^2. The departure burn to Mars will require a departure burn duration of 56 hours, which is tiny compared to the 8.6 month travel time to Mars.

Let's go big. Let's dedicate an entire 50 tons to power and propulsion, averaging 10kW/kg. That gives us 500MW of propulsive power to push a 100 ton dry mass rocket. With an engine Isp bumped up to 4000s, thrust is 25.5kN. We want to cut the Earth-Mars trip down to 2 months. This is an impulse-2 trajectory that requires 52.9km/s of deltaV. The mass ratio requires is 3.85, so now our fully loaded rocket masses 385 tons. It starts accelerating at a low rate of  0.066m/s^2, but it averages 0.1m/s^2. 

This 2-months to mars rocket spends roughly 3 days accelerating away from Earth. Decent, no? This is without even using the 'advanced' designs mentioned in the blog, at 1MW to 2MW/kg. Payload should be 30 to 40 tons.

For the designs I proposed, there are no large films. There are large solar collectors, but they're just reflective dishes that only bounce sunlight. The actual solar panels are a much smaller surface embedded in the rocket, surrounded by cooling equipment and wires as thick as necessary to carry away the current. 

You must consider the engineering problems at some point. For films in space for them to be effective they must stretch over wide areas. If the efficiency is 50% (higher efficiency will eventually be self-defeating) then you know that you have 700 kw per meter. So your average home is around couple thousand kilowatts at peak usage on two bands. These are generally double or triple zero wires and thats at 120 volts. Go to the hardware store and ask to see and weight triple zero wires. The are very heavy an very stiff. The electrical supply to your house is 4160v AC take a look at the size of the conductor, this is for groups of 16 houses. So now we are looking at MW sized panels. The current flow for  a Megawatt at 120 v is 8333 Amps. What kind of wire are you going to put that on. 4160, the wire that serves electricity to your transformer is not insulated by any thing but air and distance, although there are insulators for high voltage wire (we used to use 100,000 volt electron microscope and the insulation was about an inch thick). The current flow at 4160 is  240.64. Oh and I forgot to point air is an insulator, space is not. What happens in space is that at high voltages the gas ionizes (glows at its emission spectrum) and conducts electricity through the plasma (this is how we used to carbonized EM grids); not much but enough to cause problems with electronics around your ship. The wire an its insulation create structural rigidity and add to weight.

This particular problem I have thinking about for a couple of years now. These are some of my prototype solar ships.
 

This ships panels are1 kg/square meter (much lower than the ISS's). The solar panels are 100 meters by 10 meters (1000 meters). The wattage at the base of the panel I considered as a problem.
With the newer lighter weight films the problem goes up many fold. BTW this is KSP you may note the two storage compartments, just about everything else I modeled. (Although the solar panels don't work in the current unity version).

For any system in which it is possible to create plasma it is also possible to create electromagnetic responsiveness to radiofrequencies. Because of the spin it is possible to use electromagnetic radiation to accelerate them. Although you cannot get the particle as hot as the sun, it is possible to move it in a laminar stream once it is ionized. You have to remember that thermal heat is about average collision speed. If the electromagnetism is directed at the center of the stream away from the walls it can be accelerated to well above the limit speed (that is the whole principle of VASIMR. For example if the outlet is in line with an RF generator and the heated stream is fed from a 30' angle into that line it could be accelerated even further. 

See the thread on Mercury. With thrusts in the 0.1 or 0.01 range it is still possible to use ION drive without spiraling by carefully timed kicks.
How you do this is quite simple. On the day that you are supposed to depart determine where the optimal burn (assume you have infinite acceleration). Track that point backwards say 2 or 3 days, it will be at a different angle to prograde (about 0.985 higher angle to prograde) this means the launch window needs to be offset backwards 3 minutes 55 seconds each day. Once launched begin your kicks over a span of -5 to +5 angle to prograde every orbit, keeping the periapsis at constant altitude by a small correcting burn each apoapsis. As the velocity reaches escape velocity for that orbit a single final burn needs to be done. This will place the craft on a hyperbolic trajectory where it has all the time it needs to burn.

For transit to Mars this works well because the ship will be optimal burn at an AtP180 to 90, and at 160 degrees on the prograde motion it  will be behind the sun (termination) and all the ISP in the world will not help you. Therefore doing multiple burns at higher angle to prograde days before allows better solar and after requires more battery (AtP270 has the highest power production). All the TWR in the world wont help you between AtP130 and Atp20. The problem with solar electric (see image above) there is no good way to get sun at high density in planetary exits because its always hitting at oblique angles. In the case above the angle is fixed (this is good for Interplanetary) but not so good for Oberth burns. If I rotate the angle then the first side mounted panel blocks the other two side mounted. So the best thing is to battery up and kick.

Once you get an orbit that is hyperbolic you can move to ATP20 on the Prograde outbound motion and then start using what is left of the oberth effect (once you create a hyperbolic you thrust applies oberth logic, and energy you gain in low orbit past the escape energy you must keep on system exit). If you are power burning on a round trip you definitely want that ISP, you will burn alot. First your outbound vector is going to pass ATP20 much later because it will have substantial radial component relative to the earths motion around the sun. Your burn will be earlier but once you pass ATP160 you will loose most of the rest of the Oberth effect.

 

 

 

 

 

 

 

 

[wumpus]

1 hour ago, PB666 said:

You must consider the engineering problems at some point.

[this is agreement with PB666 and mostly directed at Matterbeam.  Most of the efficiency issues appear to be optimizing irrelevant variables]

To a zeroth order, all costs can be considered in grams (to LEO).  Most of the discussion of the efficiency of solar panels boils down to one thing: how much mass do I have to lift to supply x amount of Watts or Joules (depending if usage is constant or bursty).  If you need (or can use) more sunlight, you can almost certainly reflect more light via ultralight mirrors (probably mylar reflectors) [assuming you are staying away from "as hot as the Sun" limits], but that still has issues on how heavy the heatsink for your collector needs to be.

The solar photovoltaic chart is outright strange.  Cooling in space is difficult, things in sunlight get hot, and you are suggesting increasing such heating by orders of magnitude.  Somehow I don't think max efficiency is worth dealing with the cooling cost of "the heat a thousand Suns" (I am a bit more interested if doing such on Earth is practical, although my last check implied that any lens was significantly more expensive than photovoltaic panels (mirrors may still work, and of course mass dominates in space).

[regex]

There's a lot of good potential here, especially for established space-constructed systems. You say that everything has been tested operationally in space ... including the cooling system? I know droplet systems have been proposed theoretically and fictionally.

Anyway, you've been posting some very interesting hard numbers and I find that fascinating, please keep up the good work.

Edited November 17, 2017 by regex

[YNM]

18 hours ago, MatterBeam said:

A tension-wire structure should be decent. The wires can pass in front of the parabolic disk without a problem, so you can form a 3D pyramid-like structure where the reflective films are pulled by each corner of the pyramid. Another option is inflatable rims.

You can't make bridge trusses from steel ropes you know.

You *could* make them like a "parachute" dragged behind you, but what about exhaust ?

 

My skepticism mainly arose from the scale, really. "Large, thin and strong/tough/resistent in all manner" simply doesn't quite compute.

Edited November 17, 2017 by YNM

[PB666]

36 minutes ago, YNM said:

You can't make bridge trusses from steel ropes you know.

You *could* make them like a "parachute" dragged behind you, but what about exhaust ?

 

My skepticism mainly arose from the scale, really. "Large, thin and strong/tough/resistent in all manner" simply doesn't quite compute.

The framing and wiring are big issues in my mind. If these cannot be deal with then there is going to have to be an increase in weight per unit area to provide in-panel electronics dedicated for power transmission issues. The framing issues are equally problematic. The plumbing site I was reading said that for any length of pipe there is a limit in length you cannot go beyond because any momentum (internal or external) suffices to catastrophically bend the pipe there has to be support or bracing along the length. Even in space that could become problematic.

Bigger still, MatterBeam wants to use Low ISP engines. What happens to those 100 meter long panels or panels out on a long pole when you start throwing 0.1g+ acceleration at them. The poles will bend and you will lose directional control. Every aspect of a solar-powered ship is designed for low accelerations.

Edit.

A parachute in space does not work. Imagine a space ship traveling at 32000 m/s and a solar wind traveling out at 750,000 m/s. Which way will the parachute go?

Edited November 17, 2017 by PB666

[MatterBeam]

13 hours ago, PB666 said:

You must consider the engineering problems at some point. For films in space for them to be effective they must stretch over wide areas. If the efficiency is 50% (higher efficiency will eventually be self-defeating) then you know that you have 700 kw per meter. So your average home is around couple thousand kilowatts at peak usage on two bands. These are generally double or triple zero wires and thats at 120 volts. Go to the hardware store and ask to see and weight triple zero wires. The are very heavy an very stiff. The electrical supply to your house is 4160v AC take a look at the size of the conductor, this is for groups of 16 houses. So now we are looking at MW sized panels. The current flow for  a Megawatt at 120 v is 8333 Amps. What kind of wire are you going to put that on. 4160, the wire that serves electricity to your transformer is not insulated by any thing but air and distance, although there are insulators for high voltage wire (we used to use 100,000 volt electron microscope and the insulation was about an inch thick). The current flow at 4160 is  240.64. Oh and I forgot to point air is an insulator, space is not. What happens in space is that at high voltages the gas ionizes (glows at its emission spectrum) and conducts electricity through the plasma (this is how we used to carbonized EM grids); not much but enough to cause problems with electronics around your ship. The wire an its insulation create structural rigidity and add to weight.

This particular problem I have thinking about for a couple of years now. These are some of my prototype solar ships.

This ships panels are1 kg/square meter (much lower than the ISS's). The solar panels are 100 meters by 10 meters (1000 meters). The wattage at the base of the panel I considered as a problem.
With the newer lighter weight films the problem goes up many fold. BTW this is KSP you may note the two storage compartments, just about everything else I modeled. (Although the solar panels don't work in the current unity version).

For any system in which it is possible to create plasma it is also possible to create electromagnetic responsiveness to radiofrequencies. Because of the spin it is possible to use electromagnetic radiation to accelerate them. Although you cannot get the particle as hot as the sun, it is possible to move it in a laminar stream once it is ionized. You have to remember that thermal heat is about average collision speed. If the electromagnetism is directed at the center of the stream away from the walls it can be accelerated to well above the limit speed (that is the whole principle of VASIMR. For example if the outlet is in line with an RF generator and the heated stream is fed from a 30' angle into that line it could be accelerated even further. 

See the thread on Mercury. With thrusts in the 0.1 or 0.01 range it is still possible to use ION drive without spiraling by carefully timed kicks.
How you do this is quite simple. On the day that you are supposed to depart determine where the optimal burn (assume you have infinite acceleration). Track that point backwards say 2 or 3 days, it will be at a different angle to prograde (about 0.985 higher angle to prograde) this means the launch window needs to be offset backwards 3 minutes 55 seconds each day. Once launched begin your kicks over a span of -5 to +5 angle to prograde every orbit, keeping the periapsis at constant altitude by a small correcting burn each apoapsis. As the velocity reaches escape velocity for that orbit a single final burn needs to be done. This will place the craft on a hyperbolic trajectory where it has all the time it needs to burn.

For transit to Mars this works well because the ship will be optimal burn at an AtP180 to 90, and at 160 degrees on the prograde motion it  will be behind the sun (termination) and all the ISP in the world will not help you. Therefore doing multiple burns at higher angle to prograde days before allows better solar and after requires more battery (AtP270 has the highest power production). All the TWR in the world wont help you between AtP130 and Atp20. The problem with solar electric (see image above) there is no good way to get sun at high density in planetary exits because its always hitting at oblique angles. In the case above the angle is fixed (this is good for Interplanetary) but not so good for Oberth burns. If I rotate the angle then the first side mounted panel blocks the other two side mounted. So the best thing is to battery up and kick.

Once you get an orbit that is hyperbolic you can move to ATP20 on the Prograde outbound motion and then start using what is left of the oberth effect (once you create a hyperbolic you thrust applies oberth logic, and energy you gain in low orbit past the escape energy you must keep on system exit). If you are power burning on a round trip you definitely want that ISP, you will burn alot. First your outbound vector is going to pass ATP20 much later because it will have substantial radial component relative to the earths motion around the sun. Your burn will be earlier but once you pass ATP160 you will loose most of the rest of the Oberth effect.

Higher efficiency is not self defeating. It means you reduce the waste heat production, the mass dedicated to radiators, the size of the cooling systems and the ratio of solar collector area to solar panel area. All good things.

These advanced solar electric concepts are meant for use in space. The priority is increasing the kW/kg rating. Home use is on a completely irrelevant scale with with very different concerns, such a $/kW and payback times. The wires and equipment that will be designed to handle this current will not be made to hardware store specifications, but tailored for use by the spacecraft's engines. 

The wires, electrical equipment and solar panels themselves will all be in enclosed, protected and charge-neutralized environments within the spaceships. The only thing exposed to space for both of the designs I described is the solar collectors, and all they have to do is stay relatively reflective and generally straight. Non-imaging optics can handle light coming from many directions and can therefore correct for some wobble and bending, so even those requirements are less strict than, say, on a solar sail. I seriously doubt that the wires taking the current from the solar cells to the electrical regulators/transformers/modulators ect. will be exposed to hard vacuum without protection. They will likely be protected by many layers of insulators and insulation and looped through environments filled with a safety gas. 

Your designs seems to use solar power to ionize a gas and turn it into a plasma, but you still need electrical power to accelerate it further? I'm not sure what 'angle' refers to. The details of a high powered electrical thruster are very complex and involve electromagnetic theory I am not familiar with.

The departure burn scheme you describe does not seem to be a good option.
For one, it limits the burn times to a very narrow portion of the orbit. Waiting for the next periapsis is measured in hours in low orbit, but quickly becomes days or weeks as the apoapsis is pushed past lunar distances. An orbit with an apoapsis at 400000km and a periapsis of 200km would have an orbital period of 10.8 days, and you're still only 85% done with the departure deltaV, but still well within Earth's sphere of influence. You'd do the short burn and then have to loop all the way around to do another short burn which will raise the apoapsis even more. 

A spiralling orbit allows for continuous acceleration and gradual increase in velocity. It is what NASA and Ad Astra propose for their solar-electric craft and the best way to make the most of their low acceleration.

12 hours ago, wumpus said:

[this is agreement with PB666 and mostly directed at Matterbeam.  Most of the efficiency issues appear to be optimizing irrelevant variables]

To a zeroth order, all costs can be considered in grams (to LEO).  Most of the discussion of the efficiency of solar panels boils down to one thing: how much mass do I have to lift to supply x amount of Watts or Joules (depending if usage is constant or bursty).  If you need (or can use) more sunlight, you can almost certainly reflect more light via ultralight mirrors (probably mylar reflectors) [assuming you are staying away from "as hot as the Sun" limits], but that still has issues on how heavy the heatsink for your collector needs to be.

The solar photovoltaic chart is outright strange.  Cooling in space is difficult, things in sunlight get hot, and you are suggesting increasing such heating by orders of magnitude.  Somehow I don't think max efficiency is worth dealing with the cooling cost of "the heat a thousand Suns" (I am a bit more interested if doing such on Earth is practical, although my last check implied that any lens was significantly more expensive than photovoltaic panels (mirrors may still work, and of course mass dominates in space).

I agree with your first point, hence the blog post introducing the kW/kg rating as an important figure in the introduction.
For your second point, I must insist that it is simply a matter of reaching a thermal equilibrium. If heat in matches heat out, the temperature does not rise. That's all there is to it. As for 'a thousand suns', solar cells are regularly tested in concentrated photovoltaics research to x100, x500 and x1000 solar intensities. Today's laboratories already have designs at these intensities, and they can go higher. The cells remain at room temperature (300K). The data I quote in the blog post includes link to those experimental studies. 

9 hours ago, regex said:

There's a lot of good potential here, especially for established space-constructed systems. You say that everything has been tested operationally in space ... including the cooling system? I know droplet systems have been proposed theoretically and fictionally.

Anyway, you've been posting some very interesting hard numbers and I find that fascinating, please keep up the good work.

According to wikipedia, liquid droplet radiators were tested of Shuttle missions STS-77 back in 1996 (https://en.wikipedia.org/wiki/Liquid_droplet_radiator#cite_note-Dickinson1996-6). 

[MatterBeam]

1 hour ago, YNM said:

You can't make bridge trusses from steel ropes you know.

You *could* make them like a "parachute" dragged behind you, but what about exhaust ?

My skepticism mainly arose from the scale, really. "Large, thin and strong/tough/resistent in all manner" simply doesn't quite compute.

No need for bridge trusses. I was thinking of tension structures like these:

A minimal number of 'struts' takes on the load of wires pulling the fabric (reflective surfaces) into curved shapes. 
The actual arrangement of the solar concentrators will look like the larger circles on this: 

At the 0.01g accelerations I am aiming for, the forces are relatively moderate. 

Consider a 200m wide parabolic reflector dish on a 100m 'stick' jutting from the side of the spaceship. The dish's surface area is 31400m^2. At 1g/m^2, it would weigh 31.4kg. If structural support doubles this figure, it is still only about 35kg. 
If the stick had the support the entire weight of the dish on an attachment point at its tip, it would need to handle 0.34N at the tip. 

After spending a stupid amount of time on this calculator: http://www.amesweb.info/StructuralBeamDeflection/CantileverBeamConcentratedLoad.aspx, I can say that a N moment force can be handled by a triangular diamond-like carbon stick 10cm wide and 0.1cm thick that masses 15kg. It will bend by 17 degrees under maximum acceleration. Total mass per m^2 with structure would be 1.59g/m^2.

If we add a 'guy wire' to the tip of the stick, we can support most of the bending forces (0.28N) by a tension wire such as Zylon only 0.25mm thick. The 'stick' can now be considerably lighter, about 5.3kg and allowing for a deflection of 13.6 degrees. Total mass per m^2 to 1.27g/m^2.

44 minutes ago, PB666 said:

The framing and wiring are big issues in my mind. If these cannot be deal with then there is going to have to be an increase in weight per unit area to provide in-panel electronics dedicated for power transmission issues. The framing issues are equally problematic. The plumbing site I was reading said that for any length of pipe there is a limit in length you cannot go beyond because any momentum (internal or external) suffices to catastrophically bend the pipe there has to be support or bracing along the length. Even in space that could become problematic.

Bigger still, MatterBeam wants to use Low ISP engines. What happens to those 100 meter long panels or panels out on a long pole when you start throwing 0.1g+ acceleration at them. The poles will bend and you will lose directional control. Every aspect of a solar-powered ship is designed for low accelerations.

Edit.

A parachute in space does not work. Imagine a space ship traveling at 32000 m/s and a solar wind traveling out at 750,000 m/s. Which way will the parachute go?

Did the calculations above. They would increase the mass per area by 30 to 50% for the solar collectors.

Parachute was only a description of the shape. Nothing to do with drag or wing. 

[Elthy]

I dont know how much of an issue it is, but wont extremly thin reflectors or solarpanels get eroded by micrometeorites?

[MatterBeam]

4 minutes ago, Elthy said:

I dont know how much of an issue it is, but wont extremly thin reflectors or solarpanels get eroded by micrometeorites?

It is an issue! But not a big one. The micrometeorites will make very small holes. The area of the hole, divided by the total area of the reflective surfaces, would be insignificantly small. Decades of hits would be required to make an impact on the amount of light you can focus onto the solar cells. 

[YNM]

@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.

Edited November 18, 2017 by YNM

[PB666]

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).

 

 

Edited November 18, 2017 by PB666

[YNM]

30 minutes 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.

Would still weigh 300 tonnes though.

[PB666]

Not sure where you got the number from. The balls do not have to be a km, they could be on a tether as to reduce the internal volume.

[YNM]

@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.

Edited November 18, 2017 by YNM