Wednesday 15 November 2017

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 bromine coated in black paint, spaced by 0.5mm and released at a velocity of 1m/s across a 1m wide gap would cool down from 300K to 283K before being captured as solid mercury balls. The radiators would remove 10.4W of heat for every 1m^2 of droplets. The power density of the radiator is 4.6kW/kg.

The component masses for 1m^2 are 0.85kg of solar panels, 7kg of collectors and 169kg of radiators. It produces 519kW.

The system power density becomes 2.9kW/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 2.5kW/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 353K 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.

An 90% efficient heat pump will be needed to increase the radiator's temperature and improve the overall power density. Based on the Brayton turbopumps used in the Space Shuttle's SSME's, we can expect 150kW/kg from these heat pumps. 
Turbo expander-coolers are in use today.
Increasing the waste heat's temperature from 353K to 700K will require 1.1W of electricity be consumed for every 1W of heat moved. The heat pump will consume 5.7MW and mass 38kg.

We will use a hybrid wire/droplet radiator.

The wires can have alternating hydrophobic and hydrophilic surfaces.
Small droplets of sodium 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. Each 1m^2 of radiator area is composed of 1000 parallel wires holding droplets of 0.1mm diameter each, moving along at 10m/s. The utility of this design is that the droplets can be held very close together (0.1mm). 
The passage through the vacuum cools the droplets from 700K to 624K. The high heat capacity of water means that more than 4027W of heat can be removed by 1m^2 of water and wires. That surface allows for a power density of 64.6kW/kg.

The component masses are 0.25kg of solar panels, 10kg of concentrators, a 38kg heat pump and 80kg of radiators. System power density can approach 16.3kW/kg

Even more advanced designs that use thinner reflectors, faster wire/droplet radiators and lower temperature (higher efficiency) solar cells can probably reach 20kW/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. 88kg 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 88kg for the droplets. 

System power density is 6.1kW/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 heat pump and sodium wire arrangement of radiators from the advanced version of the concentrated sunlight generator to handle this. 

It would require a 2.2MW heat pump massing 14.7kg, and 30.96kg of radiators.

Component masses are 0.1kg for the solar cells, 2.57kg for the heat exchanger, 0.2kg for the solar collectors, 14.7kg for the heat pump and 30.96kg for the radiators. System power density should be close to 119kW/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.


  1. Hello, 100MW/kg power densities for InGaP cells don't sound right to me, neither do 10MW/kg power densities.
    Gas/steam turbines in combination with solar concentrators could allow for relatively high power densities, maybe even higher than that of nuclear reactors as elements like shielding are not required. Operating likewise to concentrated solar power

    1. The indium-gallium-arsenide-phosphide cells I quoted in the modern example for thermophotovoltaics are actually producing those results right now. 1.15MW/m^2 goes in, 701kW/m^2 of electricity comes out. This is very impressive.

      50nm thick n-p junctions means they are not going to be very heavy either. Even if it is composed 100% of indium, which has a density of 7300kg/m^3, the solar cells would have an area mass of 0.36 grams dedicated to the semiconducting layer. The silver plate which reflects non-absorbed light back into the heat exchanger should not be much more than 10um thick, since just 1 micron is really needed to maintain a reasonable reflectivity. 10um of silver is 105g/m^2. Worst case scenario, the panels have a mass of 106g/m^2, which fits the results achieved by thin film solar panels today.

      I agree, I had to speculate about the area mass the other unmentioned components. Equipment that transfers heat from the solar cells to the droplet radiators. Layers which conduct electricity away from the solar cells. Structures that simply hold everything together. These will certainly increase the mass of components and reduce the system power density. And yet, I am confident that the numbers I ended up with are 'close enough' for use in an SF setting.

      I will write about gas turbines and other non-photovoltaic options in Part II.

    2. Interesting, though energy densities high enough to ionize the entire solar cell sound somewhat absurd to me, and waste heat is more than capable of completely vaporizing the cell. As soon cooling fails the cell will just turn into hot gas.
      I'll stay tuned for part II.

    3. Quite true. If there's a disruption in the flow of conductive fluid behind the solar cells, they'd just vaporize. Thankfully, the thinness of the cells works in their favour.

      I calculate that for a 50nm thick plate of GaP, resting on 10nm of silver, operating at 300K while an infinite amount of coolant circulates behind it at 64K, over 958kW/m^2 can be removed simply by thermal conduction. Using ridges, microchannels and other techniques to increase the surface area for cooling helps a lot in this case.

  2. I like the concept, and I think that it could work really well, but I would worry about having a collector 6.3mm wide. The tiniest misalignment of your concentrators means zero power so the system is quite sensitive to things going wrong. For example, the concentrators might distort under acceleration or even from temperature changes, moving the focal point a few mm - away from the collector.

    As a result I thing realistic power densities are going to be well below the theoretical maximum, but still pretty high compared with other options.

    1. For the smaller end-cap absorbing plates for the advanced heat exchangers, I envision something like this:

      It is based on a zero-length lens that directly focuses light onto the heat exchanger. It will be fixed over the end-cap. The lens is a much bigger target than the end-caps, and might even be resistant to small deviations in the angle of the light it receives.

      I agree, realistic power densities are going to be lower. The theoretical maximum is actually quite far in fact, especially if we manage to overcome the limits of thermal conductivity between the solar cells and the cooling system through the use of nanofluids, micro-channels and other techniques. This would allow for even greater radiation intensity (>10MW/m^2).

      If we look at the advanced thermophotovoltaic example, the most massive component is the heat exchanger. If it is replaced by an electromagnetically confined plasma heated by intense sunlight, the mass per square meter dedicated to heat exchangers becomes negligible. If we manage to produce sub-millimeter sized droplets of water, shoot them out across a liquid droplet radiator at 50m/s then flash them with an UV laser to suck them back in electrostatically, the radiator mass also drastically drops.

      A few calculations tell me this 'extreme' thermophotovoltaic system would have a power density on the order of 13MW/kg. A 25km^2 solar collector with a thermophotovoltaic generator producing 26GW would mass only 2 tons.

  3. How do you imagine the overall layout of a spacecraft like this? I'm having some trouble figuring out how all the major components (solar cells, concentrators, radiators... and of course the spacecraft proper with the engines, payload and propellant) would go together.

    I've been wanting to model some sort of advanced solar electric craft for a while so I may have ulterior motives for this question. :P

    1. I wrote this description on the spacebattles forum:
      The thermophotovoltaics spacecraft will look like a cylinder hoisted by a parachute. The 'parachute' is the massive surface area of the solar collectors. They are parabolic, so they curve outwards in a concave fashion. The sunlight is focused onto an optical array that looks like a bug-eye of crystals. These crystals divide the sunlight into many small beams of concentrated light. Each beam lands on the exposed end-cap of a tungsten rod. Each rod is contained inside a cylindrical 'thermal well' that traps the rod's radiations. They will be clustered together. From these clusters will run thick pipes of coolant. The coolant will likely be a nanofluid with very high thermal conductivity. It is pumped to the liquid droplet radiators through a long insulated boom that runs into the spacecraft's shadow. The radiators will be mostly invisible, but if they catch the light, it will look like a shower of tiny, bright raindrops running quickly from a pipe to a trough that collects them. That shouldn't happen though, as the radiators are supposed to operate in the spacecraft's shadow. I hope this is enough of a description.

      Alternative designs will maybe use a set of parabolic dishes, that look like massive antennas on swivelling arms, to divide the surface area of the solar collectors into several circles instead of one big 'parachute'. Smaller collectors means that their structural support is shorter. Shorter 'arms' means their is less of a lever torque applied under acceleration. This means the arms can be thinner and lighter, which is important!

      I think the latter description is more relevant for a spacecraft that needs to track the sun as it orbits a planet. Think of the dishes as a massively oversized version of these ( shaped like these dishes (

      Light from these dishes will go through a reflector that kind of resembles a laser turret, so that the light they collect can be redirected onto the spacecraft. The actual photovoltaic 'thermal well' is an insulated cylinder with coolant pipes running from it, leading to a set of droplet radiators. The droplets must be black and generally cold, so they should not be visible.

      I hope this helps.

  4. Here's a brief article on some thermal/photovoltaic research work; the prototype is only running about 7% but it does demonstrate some of this technology.

    1. That's pretty interesting, even if it is a bit behind the curve. I cited a study in the blog for thermophotovoltaics achieving 61% efficiency with 3000K emitters in actual laboratory tests.

      One factor to consider is that flat absorbing surfaces like those described in nearly every photovoltaic work immediately wastes 50% of the sunlight they receive. If they emit heat equally from both sides, then the side facing away from the solar cell is wasting 50% of the energy the heat exchanger receives. In reality, it is even worse as the absorbing side is usually a near-perfect blackbody (emissivity 0.9+) while the emitting side has to be selective of its wavelengths, so had a lower emissivity. This tilts the balance towards even more of the sunlight's energy being wasted.

  5. Though this update is not about piracy that I am expecting since the guest blogging at laser sub, I am still stay tuned for Part 2.

    The parabolic design helps me to solve some problems in the stories that I am still planning.

    1. I'm sorry about that. It is still in the plans!

    2. Take your time. :D

      "An alternative would be electromagnetically contained plasma, such as cesium ions."

      Are Cesium ions being used as an alternative coolant or to replace rhenium in exchanger? It sounds a little bit unclear for me.

    3. The Cesium ions have the lowest ionization energy. I think that concentrated sunlight would heat them to the point where they ionize and become an electromagnetically-controllable plasma, and then continue to absorb sunlight and re-emit it as a heat exchanger. This plasma does not require physical support structures, will have no problem reaching 6000K and will have 100% emissivity.

    4. Cesium is even more expensive than rhenium.

      The price for rhenium and cesium about US$3000/kg and over US$12000/kg respectively.
      If there is no unique advantage, I suppose only the high-end system may use cesium in their system.

    5. Ah, expense. It is extremely hard to assign prices to these sorts of things from the generalist standpoint I am coming from, especially as I want to keep all of this relevant to all authors of all hard-sf settings.

      For example, from a strictly scientific standpoint, I'd use the solar system abundance of elements to determine that cesium should be over 1000 times cheaper than rhenium. But, it is not the case to day, which goes to show that science-based estimations are not very useful when it comes to prices.

    6. I forget the price can be decided by the abundance.
      Maybe asteroid mining can lower its price.

      When I am searching the information about cesium, I find that cesium conpound are much cheaper than high purity (99.9%) cesium. Can cesium plasma heat exchanger use lower purity cesium or even compounds instead?

    7. If you are going to vaporize the cesium, it becomes very easy to separate the cesium from the impurities.

  6. Hey Matter Beam, could you do an article about how to conduct a troop landing on a planet when under heavy fire from hypersonic projectiles?

  7. a planet with an atmosphere I mean

    1. Assuming the hypersonic projectiles are aimed at the troops... you'll need to make a very rapid transit from space to the safety of ground cover. This means both extreme G-loads on the troops, powerful rockets to dodge during landing, and either a massive ablative heat shield, or very powerful magnets to deflect the re-entry plasma.

      The real issue however is why you would troops on an enemy planet while it still has the capacity to fire back at you. The phases of ground attack usually are:
      -Space warfare
      -Orbital bombardment

      Space warfare is what we usually cover on this blog. If you win space warfare, your ships can come and go without risk to re-supply and maneuver without constraints.

      Orbital bombardment is where you start destroying anti-orbital defenses using lasers, missiles, torpedoes and kinetic strikes. If you've read the Anti-Orbit Laser Submarine post, you'll know that it isn't always a done deal.

      Third step is where the actually go on to win the war. You negotiate a surrender with whoever is left in command on the surface. If they don't comply, wreck a few more cities and start talks again. How this goes usually depends on politics, something I can't really comment on. Once they surrender, you land a few representatives, secure control of the planet and start occupying/colonizing/exploiting/developing/rebuilding on the surface. There might be a bit of resistance.

      Of all these steps, ground troops would only be needed at the very end. Only after the spaceships are destroyed, the guns are silenced and the white flag goes up and do troops actually land, and their job is just to remind the locals who is in charge and to protect your representatives from resistance attacks.

    2. I don't think orbital drop under anti-orbital fire is a good idea except some desperate situations, though, as a casual Halo fan, the "feet-first-into-hell" Helljumpers are very cool.

      If you really want to drop ODST or equivalent somewhere on an enemy planet, blindspots of anti-aircraft or anti-orbital fire should be the first choice. Feet first into hell doesn't mean die first in vain.

      Ground troops needed at very end only...they may be needed in some earlier stage already. I think after the offensive force destroyed part of the anti-orbital network, they would start to land at there, setting up a bridgehead and ground forces may start pouring on the surface. Ground troops can help the space fleet to take out facilities, soften the resistance of enemy.

      We have air force (and space corps in future) to bomb the hell out of the enemies, yet only the ground troops can mop-up enemy forces that still holed up somewhere on planet.

    3. Conventional doctrine would have it go the other way around. Artillery softens targets and missiles destroy defenses so that troops can secure the remains, not the other way around.

    4. But you still need the ground troops do much of the combat.

      Air force and space corps can bomb or shoot enemies on the ground, you can't win with bombing/orbital bombardement and placing troop simply to remind who's the new boss only.

      That kind of bombing-only(?) doctrine sounds like the ICBM only doctrine (I don't know the exact term in English, if there is really one, but I remember back in the Cold War, ICBM proponents went so far that wars were going to be won by ICBM alone or something similar).

      If this works, war is much easier to fight, yet it doesn't.
      All parties are still needed to deploy the ground troops, doing all the dirty things, taking and defending the hard-earned land with other branches.

    5. It's a tricky affair, I agree. It will never be a clear-cut attack followed by a surrender, but historically, we have fallen for that kind of thinking time and time again. See the 2003 US attack on Iraq. The 'war' was won within two weeks, with the country brought to its knees after two days of air strikes. And yet, US troops only left the country in 2011...

    6. If a win means making Iraq a relatively stable and free country, then US never won the war.
      But maybe there are still many politicians think that wars are nothing but dropping bombs, firing missiles and news network lives (OK, light-speed lag makes lives not live anymore), making the same mistakes on another planet or moon.

    7. It's human nature. It is the way we are wired. We are social creatures, compassionate and we are subconsciously forced to put ourselves in the shoes of other people, even if it is just a photo. This is why campaigns for donations always feature a suffering child or a distressed family on the front page.

      Throughout history, we have suppressed this natural reaction by demonizing the enemy, by seeing the armor and not the man in the armor. Today, we have technological tools that relay the outside world through screens and symbols. A target crosshair does not trigger our empathic response.

      When it comes to politicians... well, they are ten layers removed from the horrors of war, but I don't want to comment too much on current affairs!

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    1. I get the impression this is a bot. How did it sign in I wonder?

    2. Some guy is paid peanuts to write these messages on blogs. I don't mind as long as it isn't offensive.

  9. Meh...I guess landing troops onto a planet's surface from space is kinda stupid.

    But when I was first thinking about this, I was playing with the idea that the planet's surface defenders had mobile electromagnetic cannons that were as prolific as self-propelled AA guns. And these electromagnetic cannons had a muzzle velocity that could propel a projectile that could reach the Low-Earth orbit around the Earth. The projectile could also have a detachable ram accelerator rocket attachment that could boost it further to the higher Earth orbits. So essentially these cannons would be a threat to any ships in orbit (sure, the ships in orbits will be able to drop anything down to Earth's surface for free, while the guns on the ground will have to expend enormous energy to have their projectiles escape Earth's gravity. So the attackers in orbit will have a definite advantage...but these guns (and maybe even your anti-orbital laser submarines (SUCH A GR8 IDEA :3 ]) will still be able to reach out at targets out at orbit, and could cause those ships to abandon their orbits [But I have some questions about this, and I will get back to this]

    So anyways, these guns were hard to target, because they were mobile, and they employed a sort of fire, and move to 'attempt' to escape counter battery. Secondly, they were hard to target, because each guns were spaced far away from each other to avoid all them being wiped out from counter-battery. Third, and lastly, they were hard to destroy, because some of the guns will fire, however the others will hold their fire (they will start firing once the enemy ships in orbit believes all the guns on the planet's surface are eliminated, and decide to drop personnel onto the sneaky attack)

    So, it was, because of this hypothetical idea of a threat that I started thinking about landing troops on the ground in a practical way (wwwweeeell, at least as best as I could) to eliminate the surface gun threat. Some of the ideas that I conceived about it were this:

    1. At first I thought that stealthily reentering the atmosphere by utilizing a airship that employs both lighter than air gases (helium), and hot air (to provide thrust to slowly lower you to the surface). I thought this was a good idea, because some website suggested that an airship (with just lighter than air gases, such as helium/hydrogen) could brake earlier in the planet's atmosphere. And because of this ability, the surface temperature of the airship craft is less than 100 degrees celsius (but this isn't the same temperature as the air around the craft. And also, frankly I am a little bit iffy, and skeptical about this figure, because the space shuttle travels extremely fast during reentry, and therefore it has a surface temperature of around 1500 degrees celsius I think. And the air around it was 5500 degrees celsius). And this temperature would decrease as the craft's altitude decreased, and slowed down. Here's the website, so that you can validate the reliability of the source if you want to,

    Anyways, in my mind hydrogen steamer ships could unload the airships into orbit. And these stealth airship would then covertly enter the atmosphere of the planet due to their significantly lower heat signature, and slip past the gun defenses. Once the airships land on the surface, their mission priority is to do anything in their power to mess up the anti-orbital gun defenses in any way possible...

  10. -The troops that landed on the surface could do this by sabotaging the road networks that the anti-orbital (ATO) guns use, so as to significantly hinder their mobility

    -They could also collect information on the precise location of the ATO guns, so that they can destroy the guns themselves, or relay the info to the ships in orbit themselves for them to take care of the guns.

    -The troops that covertly landed could also set up an small airbase (they could also accept landings from space shuttles maybe) that could employ extremely mobile, and dispensible drones that could hunt down the ATO guns

    -The aforementioned methods that these covert troops employ will be done to vanguard/protect the MUCH LARGER, MAIN TROOP LANDINGS that ride in conventional aerobraking (blunt body aerobraking, no balloons/airship) vehicles that are EXTREMELY VULNERABLE, because of their immense heat signature. Due to the small size (they could maybe have a small amount of tanks/heavy armoured cars too) of the troops covertly inserted to the planet's surface via airships, they will have to rely on the MAIN TROOP LANDINGS to guarantee a complete occupation, and clean up of the planet. But until then, they will have to employ guerilla warfare to knock out those ATO guns

    2. I thought that troops could safely (relatively) land on the planet's surface through conventional aerobraking vehicles if they employ both their high speeds, and decoys. But I slowly realized that this may not be a gr8 idea, because of the decoys (tiny carbon pikes that produce immense temperatures by travelling fast. They are released by the aerobraking troop transport) I thought of, would only simulate the temperature of the vehicle that it's trying to protect. This is, because infrared sensors can measure the speed, and even the mass of the aerobraking objects (both the main vehicle, and decoy) from the plasma plume that it produces. So meaning that it can discern the main vehicle from the decoys. For the immense speed of the main vehicle for as a means of protection, this is flawed, because it's high speed is causing it to be easily tracked from the immense thermal signature that it produces. Even if its altitude decreases, and slows down, the vehicle is still leaving a significant thermal signature

    3. Do you remember about the covert troops deploying a small air base, and deploying small, dispensible drones that deploy from them in the above-mentioned text that I wrote? Well, these drones will be mounted with a laser in the infrared frequency that will blind the optics, and infrared sensors attached/networked to the ATO guns, so as to prevent them from accurately firing upon the MAIN TROOP LANDING

    ...IDK just something that I thought of

  11. But before I go any further, is it practical for a tungsten projectile to have a speed of 10000-15000m/s while inside an atmosphere. Like would it melt? And to what distance will it be able to go? I read that meteors travel at MUCH faster speeds, and manage to impact the surface of the Earth, but then again the factors concerning meteors are a bit different/unique

    1. A 10cm wide sharp projectile travelling at 10km/s through the lower atmosphere will experience a drag of 47.1kN. If the projectile is 3m long and made of tungsten, it will mass 461kg.
      This means it slows down by 102m/s every second. This means it is losing 2.4MJ of energy every second, which is enough to melt off 3.7 kg of tungsten.

    2. Huh...that's not so bad I guess. 40km range for tank battles would only melt off a bit of tungsten. And I guess melting would be a good thing, because maybe it can act like a sort of self-destruct mechanism the farther it goes.

      As for making it fly out of a planet with an atmosphere, I guess this would be doable as it will be travelling rly fast, and encountering less denser atmosphere the farther if goes up

      Cool :)

      Just out of curiosity, would this tungsten projectile at sea-level atmosphere have a shock layer forming in front of it, similar to how a shuttle has a detached shock layer formed in front of it to prevent heat transfer through convection between the hull, and the surrounding air? And would this shock layer even protect the tungsten projectile from heat, or does the denser, sea-level atmosphere prevent that? :/

  12. IDK, what to do guys think about what I said? :(

    1. The only way for the anti-orbital guns (on the ground or air) to survive this double threat is if it can survive a beating from orbital lasers, but remains fast enough to dodge kinetic strikes that take tens of seconds to minutes to reach the ground. You basically want a bunker to move like a jet aircraft. Doable in some settings (read about the Bolo tank). Other options include trying to be invisible from orbit (vehicles matching the temperature, colours and radar return of the surrounding environment), being able to deflect the laser with something like an atmospheric plasma lens so that you don't need the armor which will slow you down, or actively shooting down incoming kinetic strikes with our own interceptors.

      Note that you cannot avoid 'heavy armor' schemes because if you have an effective lightweight armor material, then the spacecraft in orbit can use that same material. Unless that's the point, and you want to eliminate lasers from the picture and make everyone use kinetics and missiles. It would allow for a much more conventional surface vs orbit scenario, where ground vehicles use big guns to shoot projectiles straight up (2km/s to reach 200km altitude) while spaceships dodge and drop long rods capped by ablative heat-shields.

      2) Those airships would have to be incredibly massive even for small payloads. Even if the upper atmosphere is too thin to make them heat up much... the air is still ramming into a surface at near orbital velocity (7km/s+). It will heat up and create a red-hot haze of plasma in front of the airship. It will be bright and easily spotted.

      3) Roads are large, visible and don't move. You can hit them from orbit easily.

      4) If the Anti-orbit guns fire, they are necessarily shooting projectiles fast enough to leave a bright streak of fire through the sky pointing right at the launch point. The gun platforms cannot reasonably both remain hidden and leave the area fast enough to matter. Assume that if you're firing, the enemy can see you.

      5) Think of the planet Earth. Imagine you've an extraterrestrial invader and you want to land troops somewhere. Where would you land them? Straight on top of New York city? Maybe a bit further away, so they're not immediately spotted by people on the ground and have tanks rolling on their position? How about the middle of Canada's North. They might remain hidden for weeks over there... but the question becomes: what's the point of well hidden troops if they've hundreds of km away from any target of interest? It's a difficult question. Also, because the re-entry was brightly visible to everyone, the troops better move away from their landing site quickly. Tanks rolling around at 50km/h aren't going to cut it when the nearest military base sends jets at Mach 2 to inspect the site.

    2. Anti-orbital class artillery (or lasers?) is going to be very large and heavy.
      Can we solve these problems by putting anti-orbital weapons on some LCAC-like crafts? That may make the weapons move relatively faster.
      Or simply let the ABL (plane-based/airship-based), laser-armed warship and AOLS handle orbital drop troops?

      I think landing outside the anti-orbital network range should be enough. Space fleets eliminate some key defence, clearing a landing zone. Then they can drop ground troop at there.
      This forces the defensive side to deploy troops to stop them, weakening their defending ability.

      Ground troops may become some kind of "auxiliary unit", but they should be far from "show of force after occupation".

    3. Lasers have an advantage in that the generator does not have to be next to the focusing optics. The spacecraft in low orbit might just be mirror drones focusing and aiming a beam generated by a spaceship in a much higher orbit.

      The same can be true of ground lasers. A beam generating station and send a beam to a very high altitude aircraft, which bounces it back down to 'laser fighter jet's closer to the ground. The latter can be fast and maneuverable without having to carry power and laser generating equipment on-board. It might be difficult to escape a ground-powered laser network when a laser craft at an altitude of 40km can point a laser at any target on the ground in a 825km radius.

  13. 6) Decoys can be the same mass as the re-entry pods, if you fill them with something you don't care about losing, like water or ammunition. Also, there are ways to manipulate re-entry plasma with magnetic fields to obscure the mass and shape of the re-entering object.

    7) A lot of what the troops can deploy on the ground can be dropped from orbit more easily. If you can blind the ATO guns with microwaves that drones can carry, then you can also blind the ATO guns from orbit with bigger microwave devices on spaceships.

    8) Yes! Meteorites lose most of their mass by the time they reach the ground. Tungsten is a strong, heat-resistant material, so it will only lose a fraction of its mass to re-entry heating by the time it reaches the ground. However, it will slow down significantly, down to 3km/s or most after pushing through the very thick lower atmosphere. Maths can be done to determine the rate of ablation and the final velocity.

  14. Since the hydrogen steamers, my faith that there is only one way to do things has been shaken somewhat. When I saw Byran Coffey mentioning the faint possibilities of troop landings, I was shocked. He was the most resolute opponent of them in 2010.
    I’m just going to suggest a compromise. I’m kinda tired of the either/or polarization, so here is something that hopefully will leave everyone happy.
    Scenario 1: Attackers scream in and suppress laser subs and short range anti-orbital missiles. The defender does not have so many under-seabed factories that they can’t be suppressed by concentration of nuclear depths charges. Result: Attacker victory and orbital occupation.
    Scenario 2: Defenders have so many well-defended deep-under-seabed factories, that the attackers cannot marshal enough nuclear depth charges to destroy more than a few via concentrated fire. While they do nonetheless dominate the surface and airspace due to lasers, the attacker cannot just sit and wait for defender to rebuild/gain overwhelming advantage in defences. Landing representatives to take surrenders/annihilating cities is all very well, but when the machinery below is still churning, you may want to deal with it.
    Result: Surface is used for materials to make ‘ground’ units and nuclear weapons to go under the sea and ground to eliminate defences to make way for orbit-to-surface nuclear ordinance and demand of surrender. A lot of logistics assumptions, but when you completely control the surface, you can probably keep the factories intact from saboteurs.
    Whichever scenario you choose depends on your world-building and (as usual) your tech assumptions. If you want space warfare only you can have it, and if you want both Endor and Hoth, you can have them. In the interests of not going completely insane, I’m going to take the above points (both scenarios) as my final position on this.

    1. There's no pressure to crystallize your views one way or another, Geoffrey! Even I regularly change my opinions on things after doing my own research. One example is when I dismissed solar energy as viable for colonies around Jupiter or Saturn. And yet, look at the power densities achievable as mentioned in this post. They'll be competitive even when reduced to 10% or 1% sunlight.

      For scenario 1: If you manage to 'scream in' and overwhelm all defenses, and land troops to capture valuable cities and command centers... you can create a situation where there is nothing left to defend by underwater forces. A complete and massive takeover, where even shooting the spaceships out of sky won't remove the threat of your troops already on the ground, might lead to immediate surrender. Not every state is suicidal, like North Korea or WWII Japan. If there's no war left to be fought, might as well settle for better terms.

      My opinion is that the diversity of the possible outcomes, even when the technology is fixed, in addition to the number of details and nuances you can add to a situation such as ground attack, will only enrich science fiction in both literature and more general worldbuilding.

      That's the point of my blog after all!

    2. Those who like to use solar power even at outer planets may be hiders, small off-the-grid communities or someone who hate to pay electric bill for whatever reason, it is unlikely to be used at large scale.

      I remember the moon-wide Iapetus solar plant at your G+, but if Outers can build something that big, they have to find some justification. Things may be even more difficult if they already have thousand-km-long wind wheels for power and supported by fusion fuels harvested by the wheels as by-product.

      Perhaps moon-wide solar plants provide power to moon-based laser launching stations (almost) exclusively, that is the only justification I can figure out at this moment.

    3. Sorry- you did respond to Felix After me didn't you? Just to make sure I don't respond to Felix and confuse things.

      "Not every state is suicidal, like North Korea or WWII Japan. If there's no war left to be fought, might as well settle for better terms."

      Absolutely. Some of it depends on how down to the wire things are. I freely admit alot of my worldbuilding already had large underground civilian infrastructure before I even thought about military operations. The nuances I have already are rather mindboggling. The last bastion of a civilisation might be absolutely desperate to defend itself, an outlying outpost might be more sanguine about things. Even American democracy has Curtis le May (2 Americans left, 1 Russian, etc).

      I imagine an attacker's attempt to intimidate the defender into surrendering would involve crippling rather than destroying the economy first. Even with lasers and nukes, an entire planet would be difficult to reduce to slag quickly- especially after the invader has had numbers and munitions reduced by the initial defences. Making life miserable for surface civilians, whilst keeping them mostly alive and retaining mining and heavy industry just in case, seems like the best option. Thus- destruction of transport infrastructure, certain food production centres and anything within rigidly defined areas.

      Ugh. This is morbidly interesting. A separation of the civilain and military spheres, with the civilians vulnerable and the military protected.

      Thanks for your reply. That has lifted quite a weight off my mind.

    4. It has been the case with most of history, and only recently, with modern weapons such as bombers and missiles, has the 'rear line' become just as exposed as the 'front line'. In space-to-ground combat and with precision lasers, the distinction between civilian and military can be brought into sharp definition.

      Of course, there's always asymmetrical warfare to make a mess of things, but handling that is the domain of politics and plot!

    5. High atmosphere nukes to generate EMPs seem like solid "warning shot" tactics. They'll disrupt infrastructure and civilian equipment without massive loss of life (depending on local need for life support), creating political pressure for low cost and low casualties.

  15. Hey Matter Beam, this may be off topic, and this may be a stupid question...but is it possible that a projectile fired from a cannon (that is placed on the surface of the Earth) with a muzzle velocity of escape velocity (11.186 km/s), or maybe higher (20000 m/s) be able to hit a target (without burrowing through the Earth) on the surface of the Earth that is placed 10-40 km away from the cannon? Because at first, I thought that, due to the escape velocity of the gun, it would go into orbit instead of hitting a target on the ground. And I also thought this, because my dum ass brain believed that this was true. Due to the fact that I read some sci fi works where very tall machines were used in order to get around this problem, because they were sooo tall that they could extend their firing range without the problem of having the EXTREMELY FAST projectile to leave orbit. But I looked at the projectile motion equation, and it told me that 'apparently' it CAN (I didn't know Earth's gravity curved the projectile that much, when it's travelling that FAST) if you put in the cannon's elevation angle at (0.00001...something of that sort). But I am still confused if this is true, or not, because the projectile motion equation doesn't take into account the curvature of the I am literally stumped. Mind helping out?

    1. The only stupid question is one that is intentionally designed to be stupid!

      If you are firing projectiles at higher than escape velocity, then it will travel along a trajectory that does not 'bend' enough to close a circle around the planet.

      It will curve, yes, due to the force of gravity, but the magnitude of the curve is necessarily lower than the curve of the ground.

      Let's do a calculation. We will ignore drag for now.

      The force of gravity accelerates a projectile towards the ground at a rate of 9.81m/s^2. For every 'T' seconds of flight, the projectile gains a downwards velocity of 9.81 * T and it will fall by a distance of 0.5 * 9.81 * T^2 meters.

      At a distance of 10km, the ground curves away by 7.84 meters. If you want to hit a target on the ground 10km away that is at the same height as your cannon, you need make sure your projectile falls by 7.84 meters by the time it reaches the target.

      So we have 7.84 = 0.5 * 9.81 * T^2.
      We need to work out T. T = (7.84/(0.5*9.81))^0.5 = 1.264 seconds

      Divide 10km by 1.264 seconds and you get 7.9km/s. That's the orbital velocity!

      Use this calculator to find out how far away the target is below the horizon:

      Then, use the equation I wrote as I did to work out how far the projectile drops at the velocity it is going, and compare the numbers. If your projectile does not drop enough, it flies over the target.

      The elevation angle allows you to add some initial upwards velocity so that it takes longer for the projectile to start falling down.

      Nonetheless, be mindful that it becomes extremely impractical to fire projectiles at higher velocities through the thick lower atmosphere. Even a tungsten rod will melt into nothing if it is shot through the lower atmosphere at higher-than-orbital-velocity for more than a few seconds of flight. It might just be simpler to use a rocket or missile.

    2. Thanks Matter Beam, you da mann :D

  16. I didn't see any mention of optical rectennas. Although no working examples have been made to date (AFAIK), the theoretical ability to generate electrical energy directly from solar photons at high efficiencies would make this a huge game changer if the technology can be realized.

    I also have this proposal for converting solar energy directly into microwave or laser beams:

    If I understand the presentation correctly these would be more in the line of base stations beaming energy to distant spacecraft, but if the receiver is "tuned" to the frequency that is being emitted, then high levels of conversion efficiency should be achievable and high levels of performance can be had by leaving a lot of the mass back at the base stations in the form of solar energy converters.

    1. I did actually consider an optical rectenna. It would be very efficient at converting light into a single frequency that a solar cell can absorb and use at very high efficiency. The overall efficiency of the system could reach 0.8*0.8: 64% efficiency or better.

      There are complications however, which is why I left it out.

      The first is that the rectenna is great at converting one wavelength into another, but its ability to convert a range of wavelengths all at once is not something I have read as feasible. Another factor is that the Sun emits wavelengths ranging from the centimeters to the nanometers. Visible light represents only 41% of the Sun's energy.

      An optical rectenna trying to use the Sun as a source of light would be capped at 41% efficiency, making the set-up no more efficient (0.4*0.8*0.8: 25.6%) than an well optimized solar panel.

      If you used multiple layers of rectennas, tailored for microwave, then infrared, then visible wavelengths, you might be able to capture up to twice that amount... but I don't see how it could be done. Is a three-in-one rectenna even possible?


      Not 3-in-1, but there is a proposal for hybrid design, TPV rectenna


      Though the essay is different for me to understand, I find something called multiband rectenna.
      Is that a kind of primitive 3-in-1 optical rectenna?


      Sorry for the wrong link, this is the multiband rectenna essay

    5. Thank you. This has prompted me to do some extra research (read the comments below).

  17. 41% might be sufficient if the mass of a rectenna is less than a PV array with equal output. From what I've read of them, rectenna could dispense with a lot of the ancillary equipment and power conditioning that PV arrays use, but I might be reading this all wrong.

    The best solution might be to have a generator/emitter array somewhere sunny, like orbiting Mercury, and beam the energy at carefully selected wavelengths matching the highest efficiency solar cells (or rectenna or whatever handwavium system you have) to minimize conversion losses. Then you can really hustle along when you're riding the beam, but even if there is a service interruption, you should be able to get hotel power out of the array from being in the sunlight as a minimum. As a practical matter, you might simply tap the beam whenever you need a change in deltaV, so much of the time you are coasting anyway. Only a fast packet or a warship would need continuous power (and I'd expect the warship at least would have an on board system ready to fire up when it left the beam. The externally powered stage is a booster, but can be dropped off the moment the ship needs to clear the decks for action).

    1. 41% is the maximum visual spectrum power than can be collected from sunlight. The rectenna's overall efficiency would strictly be lower.
      The current figures are promising in terms of kg/m^2 and kW/kg, very similar in fact to photovoltaic cells, but as I mentioned, I do not know of techniques to increase the range of wavelengths that rectennas can accept.

      If terms of how they are best used, laser-transmitted power is the number one option. Lightweight rectennas means that you can use large collector surface areas to either drastically reduce the size of the beaming station's focusing optics, or massively increase its effective range.

      However, I've done some extra research and come up with this study:

      It's from 2002, and nanometer-scale electronics have improved since then, so the 400nm-1600nm coupling of the diodes should be easier now, covering over 80% of sunlight's energy. They also tested the diodes at 3.25kW/m^2. I've read 0.25kg/m^2 figures for rectennas from other sources, so we can easily accept 13kW/kg using solar power.

  18. I'm sorry guys, I've had to rework the radiator masses as the calculator I relied upon has been updated, which led to a downgrading of the kW/kg ratings of the designs.

  19. How to solve the second problem though? Even with very high power densities, how do you effectively use the electricity to get high thrust out of an electric engine? Electrothermal systems work fine for high thrust since you can set propellant flow to whatever you like, but they can't perform much better than the high-temp solar thermal systems you already proposed. Electrostatic systems are extremely difficult to push past very low propellant flow. Electromagnetic systems maybe? Mass drivers seem to be a solid bet, given that thrust at a given isp is essentially unlimited except by cooling requirements and the practical length of the system. As a bonus, every ship is armed to the teeth.

    1. I suppose electromagnetically triggered fusion (z-pinch, etc) or microfission isn't out of the question, though fusion is typically beyond the tech level considered here and microfission requires exotic fissile materials.

    2. This post was simply to demonstrate that electric engines are not necessarily restricted in use by the low power density of their power generating equipment. If you can create a high power density electric propulsion system, then you can use an equally high power density generator without having to switch over to problematic nuclear technology.

      Overall, I think that electric engines will have to be on the lower spectrum of power densities as a simple drawback of their design. Electromagnetic acceleration in electrodeless designs is the most promising, as strong magnets can massively increase the acceleration gradient in their acceleration chambers in the near future. VASIMR is such a design, with 1kW/kg reported as not only possible, but to be exceeded at larger scales.

      Ultra-high Isp is pretty pointless within the confines of the solar system. After a certain point, you are doubling, tripling the travel times while saving single-digit percentages of your ship's mass by reducing the propellant requirements. It is not worth it!

  20. For some values of "solar", a light sail such as the ones proposed by K Eric Drexler as far back as 1975(!) using metal foils only a few molecules thick would have dramatically better performance than any powered system. I should have kept the link or at least the calculations page, but I do recall reading that a Derexler type solar sail capable of accelerating at 1mm/sec^2 can reach Pluto a bit over 3 years from a standing start from Earth.

    Of course such a sail powered beast would simply flash past Pluto, unless you were willing to "lithobrake", so there are limitations to this as well (the other being your initial build up takes a tremendous amount of time, after two years you are just clearing Jupiter's orbit in the above example). Still it may be worth comparing high performance Solar Sails to other systems to get a good reality check. Solar sailing may be useful to ship unmanned cargos at low cost. or to boost payloads on their way (for example the solar sail is sent on a highly elliptical orbit around the sun, and releases the spaceship or cargo at the opportune moment during the orbit to allow it to continue on its way without having to have used any on board power or propellant/remass to do so. For electric engines, this might be a good hybrid system, the sail gets you going and you spend most of your energy and reaction mass slowing down and entering the target planet's orbit, rather than having to spend any energy or reaction mass accelerating in the first place. The opposite may be true on the return leg, you make an RV with a passing sail and then use it to slow you down to reach Earth's hill sphere.

    1. I have shied away from doing calculations for solar sails, as the diminishing solar intensity and local gravity makes for equations that involve a lot of integrals.

      One point I'd have to make is that materials a few molecules thick are generally very transparent: a light doesn't get absorbed or even reflected. Another point is that 'sunlight' is actually a very large spectrum of radiations. Many of which won't be efficiently reflected, such as the shorter wavelengths, and a lot are readily absorb and contribute to the heating of the sail.

      Working on your hybrid sail, I can foresee a triple-mode light sail. It is a combination solar thermal, solar reflective and solar electric propulsion.

      The solar thermal uses a reflective dish, such as thin aluminium. Tiny wires draw the dish into a parabolic shape, so that sunlight is focused onto a point close to the spacecraft's main body. In low solar orbit, sunlight intensity can be extreme, especially after being focused by the reflective dish. It can be enough to vaporize a plastic propellant and create a lot of thrust, like a laser ablative rocket. We add the thrust that comes from reflecting sunlight photons for a quick boost out of low solar orbit.

      During interplanetary travel, the solar sail continues accelerating by reflecting photons.

      For braking, the reflective sails are drawn again into a dish. The faint sunlight is now focused on a patch of solar cells. The electricity is used to power a solar electric rocket for a gradual braking burn. This is much more convenient than one-way trips.

      Further developments might include a set of magnetic coils to use the solar winds as well. The initial solar thermal rocket will produce a hot plasma, which can be directed by a magnetic nozzle. During interplanetary operations, the mag-loop will be powered by the solar cells. For some planets such as Jupiter, braking against the magnetosphere provides non-negligible acceleration.

    2. That is far more elegant than what I was proposing (more of a solar sail "tug" to get you going). The essential issue is using a sail to overcome the tyranny of the rocket equation, especially by reducing or eliminating the need for fuel or reaction mass during one leg of the voyage.

      Drexler's calculations should shed some light (heh) on the subject, but his proposal was essentially to cut the mass of the sail down to the practical minimum. the extreme thinness of the sail increased performance dramatically over a "conventional" sail backed by a plastic layer, and if the sail is transparent over some wavelengths, it might be an advantage in terms of temperature control.

      Drexler's sail is actually much "simpler" (for some values of simple) compared to proposals by people like Robert L Forward, who cheerfully wrote about making the sail a mesh with holes 1/4 the wavelength of the light in order to lighten the sail (the engineering and production of such a sail would be mind boggling).

      Still, I would like to suggest an article on solar sails for the mathematically challenged readers, like myself.

    3. I have doubts that extremely thin metal sheets will survive any sort of movement in space. The forces involved might be small, but they are to be divided by the thickness of the solar sail. The force per area (tension) can become extreme!

      A 1/4 wavelength lightsail is not a bad idea. It cuts your mass per area by a factor 4, and we already have manufacturing techniques that can print out nanometer-sized grids far smaller than the wavelengths of visible light.

      I posted some useful maths on light sails in my 'Interstellar Trade Part II'. Most relevant is:
      Photon Thrust: Laser Power * 6.67 * 10^-9 * (1+Reflectivity)

      For sunlight at 1AU and a very good reflector, that's 1366*6.67*10^-9*1.95: 17.8 microNewtons.

      Most reflectors won't be bouncing back 95% of sunlight. They'll handle 98% of the visual spectrum, and get decent performance in the infrared, but let microwaves right through and simply absorb ultraviolet and above. If they can handle 70% of the sun's energy, they are doing great.

      You divide that thrust by the mass per square meter. At 1g/m^2, you get an acceleration of 1.8 milligees. Using larger solar sails allows you to tangentially approach the mass per square meter of your solar sail.

      In terms of hybrid sail performance, I have worked out some impressive numbers if the solar sail's material can be used as propellant for an electric thruster during the braking burn...

    4. How impressive exactly?
      If the sail can be used as propellant, what kind of material should be used?

    5. You get to benefit from your 'mass ratio' twice.

      Let's imagine a solar sail of 1g/m^2, carrying a payload for a total dry mass of 1000kg. If 50% of your payload is solar sails (mass ratio 2), you'll have a dry mass of 1000kg, of which 500kg is solar sails, which works out to an area of 500000m^2. That area will produce a thrust of 8.9 Newtons and an acceleration of 0.9 microgees. If you increase the 'mass ratio' to 10, you'll have 900kg of solar sails providing 1633microgees of thrust.

      Now, when you consume your solar sails, that ratio between solar sail and payload becomes ratio between propellant and payload.

      I can imagine a solar sail made up of aluminum wires 100nm wide, criss-crossed into 400nm grids that can reflect all wavelengths of 400nm and longer. An electric rocket can unspool these wires like a cat pulling on a string from a wool jumper. The wire is vaporized into a plasma and accelerated to high velocity (100km/s+). A high exhaust velocity in combination with a high mass ratio can give you a deltaV of ln(100)*100: 460km/s or more!

      Mind you, this is braking deltaV. You slow down from this velocity to a stop at your destination. You actually gained that velocity for free, from the sun. So this hybrid solar sail can have the performance of a pure electric rocket with the square of the mass ratio.

      For example, if I have a mass ratio 100 hybrid sail and 100km/s electric rocket, I can accelerate to 460km/s for free, then slow down at the destination. If I only used the electric rocket, I'd need a total deltaV of 460+460km/s, for a mass ratio of 100*100: 10000. Massive gains!

      The best thing about all this is that your mass ratio 100 solar sail has a surface area of 900kg of reflectors, which can collect 12.3MW of solar power all the way out to Saturn. As the solar sail wires are 'eaten', mass drops and the acceleration remains mostly constant.

      I'll write more on 'Hybrid Wire Sails' in the future.

    6. For pioneers of the solar age, it might actually be better to keep the sail at your destination. While your acceleration and deceleration is all done by the sail itself, once you have reached your destination you have a very large solar mirror, and as per your calculations you now have the ability to collect 12.3 MW of solar energy in the orbit of Saturn, a pretty useful resource for "ice busters" looking to homestead around one of Saturn's moons.

      This is even better, since the energy can be used directly (focusing the energy on a hot spot to process materials) or to generate electrical energy (using photovoltaics or some sort of heat engine at the focus). In fact, if I were running the pioneer settlement, one of the key decisions would be to salvage every solar sail coming our way from manned or unmanned ships and cargo pods. Access to cheap and plentiful energy via platoons of mirrors will give the settlement a running start.

    7. That's a good point. Colonies starting up are limited first and foremost by the equipment available, then by how much power they can generate. Solar sails solve both problems if they can serve a double purpose once they arrive.

      Although, if you are an asteroid colony with access to a lot of water in the outer solar system, ice lens are a possibility. If you can't create clear ice, a simply curved reflective is reflective enough to focus sunlight. I can imagine a shaped crater focusing sunlight onto a heat engine running off a steam loop as a dirt-cheap generator.

  21. HIYA MATTER BEAM!!! Do you mind if I asked what your next article will be on?

    1. Hello there.

      The next article will be Solar Power Part 2, and after that, Space Piracy is Possible.

    2. *ears prick up* Was any of that piracy article useful? (the one I sent you aeons ago)

    3. All the way back in March 2016.
      Yes, I've picked up a few points.
      The real issue these days is finding the time to write out all these topics I have listed on my to-do list!

    4. I know that feeling very well....

      Glad to know it was of some use! If you need any historical research done, I work in a university library filled with maritime history, so feel free to let me know.

    5. While we may disagree over things like stealth in space, and I have some pretty good physics and orbital mechanics reasons to think "Space Piracy" may only be possible by stealing things off the loading dock, I look forward to the post simply because you find ways to make very implausible things seem plausible.

      The debate in the comments section should be fantastic as well.....

  22. Thanks for the reveal Matter Beam. I will just leave you to your sekrit documents :3

  23. Slightly OT, unless you consider using space based solar energy generation to drive the laser beams for nano craft concept spacecraft to be "electric propulsion". There are a great many links to the concept and various issues being liked at' perhaps younger readers will actually see nano craft concept sails being projected towards Alpha Centauri at 20% of the speed of light on the first interstellar mission.

    1. It is hard to fit interplanetary and interstellar propulsion schemes in the same page without passing over a lot of either cases' details. I promise to look into this at a more appropriate time in a future post.

  24. A bit of a diversion, but an interesting comparison to solar electric, solar thermal or other forms of propulsion:

    1. You always come to me with interesting topics, so it's all good!

      The paper suggests that 1.38g/m^2 is the limit for a heliostationary solar sail. That's a tough requirement if we want the sails to hold any significant payload, such as a space station.

  25. "Despite these limitations, nuclear reactors producing over 10kW/kg have been designed."

    What's your source on that? NASA's Kilopower reactor, which uses 20% enriched U-235 and Stirling engines for power generation has a downright pitiful power to weight ratio of 7 W/kg. The best nuclear submarine reactor, which have ample water for cooling, do not exceed 50 W/kg. 10000 W/kg seems way out there to me.

    1. Hi!
      10kW/kg has been surpassed by a large margin in NERVA, DUMBO, Rover and SNRE nuclear reactor test programs:

      Some designs attain more than 150kW/kg.

      But, admittedly, that is the reactor core alone. Adding a closed-cycle heat exchanger, turbine, alternator and radiators knocks down the power density by quite a bit, and would yield a more relevant figure, but would prevent apples to apples comparisons with solar energy components on an individual basis.

      If we include gas-core nuclear rockets, we can expect MW/kg power density, and with nuclear pulse propulsion (Orion and derivatives), we can go even further.

  26. Solar radiations range in frequencies from infrared through the visible to ultraviolet frequencies. We receive light through the visible radiations and heat through the infrared radiations.

  27. These electricity levels are crazy (for the advanced systems). What kind of propulsion system would best make use of all that power?

    1. Any electric propulsion system would benefit from more power! For practical reasons, you'd want designs that scale up well, like MPD thrusters or arcjets.

  28. what will be the benefit of solar energy in space? kindly explain me in details.

  29. Nice post. Thanks for the reveal Matter Beam. GenH2


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