Wednesday, 27 December 2017

Advanced Solar Energy in Space: Part II

In this post, we continue looking at high power density options for solar energy.

Brayton cycle
We commonly see the Brayton cycle used to convert heat into work in jet engines and the steam turbines of power plants. There are three main components: a compressor, a heat exchanger and a turbine. Gas is compressed to a high pressure by the compressor, then is heated by the heat exchanger. The turbine expands this gas to convert its energy into the mechanical rotation of the turbine's shaft. The latter is used to compress more gas, with the energy remaining able to be put to work. In a power plant, the remaining energy is used to spin an alternator to generate an electric current. Together, this forms a Brayton-cycle turbo-generator. 

A closed cycle gas turbine adds an additional step: the exhaust gases released by the turbine are recycled back into the compressor. The gas is heated externally and is typically inert, as it is not being burnt up like in an open-cycle gas turbine. This makes it it ideal for space applications. 

Let us have a look at the pressure and temperature conditions at each step of the closed Brayton cycle to understand where the turbine's power is coming from. We assume typical component efficiencies of 80% for the compressor and 90% for the turbine.

We will set Temp1 and Press1 as the temperature and pressure of the gas at the compressor's inlet. Temp 2, Press2 at the compressor's outlet, Temp3, Press3 at the turbine's inlet, Temp4, Press4 at the turbine's outlet. We will use example figures for these to make it easier to understand, in Kelvin and bars respectively. We will assume a monoatomic gas, such as helium, with a constant volume heat capacity of 3.12kJ/kg/K

The work cycle of a turbine. The lines are not straight due to inefficiencies.
The gas starts at Temp1: 300K and Press1: 1bar. This is a warm gas at sea level pressure. It contains very little energy: 936kJ/kg.

The compressor raises the pressure to Press2: 10 bars. The gas's temperature increases by a factor determined by the following equation for isentropic expansion:

  • Inlet Temperature/Outlet Temperature= Pressure Ratio ^ (1 - 1/y)
The compressor increases the pressure tenfold, to the pressure ratio is 10. 'y' is the adiabatic gas constant. For simple mono-atomic gases, it is equal to 1.6.
We work out that the compressor increases the temperature by a factor 2.37. Temp2 is therefore 711K and the gas contains 2218kJ/kg. Due to the compressor's efficiency of 80%, this step consumes (2218-936)/0.8: 1602kJ/kg.
The gas then arrives at the heat exchanger. It is designed to heat up the gas at constant pressure. The gas exits the heat exchanger at Temp3: 1300K and Press3: 10bar, reaching 4056kJ/kg.The heat exchanger grants an energy increase of (4056-2218): 1838kJ/kg.

The turbine is the most critical component. Here, the gas is expanded back to a pressure of 1bar, so Press4: 1 bar. Isentropic expansion causes a temperature drop. Using the same equation as above, we know that a tenfold pressure decrease will reduce the temperature by a factor 2.37. Therefore, the gas exits the turbine at Temp4: 1300/2.37 = 548K. It falls to 1710kJ/kg. Because the turbine is 90% efficient, it extracts only (4056-1710)*0.9: 2111kJ/kg.

This is exhaust at Temp4 and Press4 must then be cooled down back to initial conditions, of Temp1 and Press1, using a radiator.

The find out the net energy extracted by the turbine, it is easiest to calculate the difference between the energy consumed by the compressor and the energy extracted by the turbine. This amounts to 2111-1602: 509kJ/kg.

Compare this to the energy granted by the heat exchanger to find the overall efficiency.

509/1838: 0.2777 or 27.8%

Technically, gas pressure also contains energy, but in a closed cycle, what is spent in the compressor to increase the pressure is regained in the turbine when it expands the gas.

To extract more power and increase overall efficiency, we can immediately understand that we need a higher temperature gradient. As we have seen in Part 1 of Advanced Solar Energy in Space, it is possible to design a heat exchanger that reaches thousands of Kelvin under concentrated sunlight. We will use this as the heat source for our space-based turbogenerator, as has been considered before by NASA.

However, we must make sure that the turbine blades are able to survive the Temp3 conditions. While there are many materials that do not melt even at very high temperature, there are few that remain strong enough to rotate at thousands of RPM without deforming under those same conditions. 

Strength/Temperature curve for a Nickel superalloy.
Shown above is the yield strength of a Ni-Cr-W-Al-Ti-Fe-Si-C-B (Nickel, Chromium, Tungsten, Aluminium, Titanium, Iron, Silicon, Carbon, Boron) superalloy. It is designed to survive for 100000 hours under conditions of high stress (1000 bars) and high temperature (1023K). Looking at the graph, we notice that it retains most of its strength up to about 750oC, making it ideal for the conditions it was designed for. However, if we used it in the turbine we used as an example above, operating at 1300K (1027oC), it would have a strength reduced by over 80% compared to what it was designed for!
Blades must survive both centrifugal forces and thermal stresses.
The choice of materials is therefore critical in designing a turbogenerator. 

Silicon Carbide is a good material choice, used in jet turbines at up to 1700K temperatures. Nickel-based superalloys are another option, retaining their strength at up to 70% of their melting temperature, but they are much denser.

Tungsten-based alloys would obtain the best strength at 2273K+ temperatures. It is very dense though, which would increase turbine mass.
If we want even higher temperatures, we need to use active cooling of the turbine blades and ceramic materials (such as hafnium carbide). This allows us to reach 2500K or better operating temperatures. 

There are also other considerations. 

Only the first turbine stage really handles high temperatures.
We aim for a high specific power. This means reducing the mass of the equipment required to handle a certain level of heat input while maximizing efficiency by using a high temperature gradient. High pressure ratios are therefore also necessary, as they allow a large pressure (and temperature) drop in the turbine. 

We also want a higher rather than lower turbine exhaust temperature. This is because all waste heat must be radiated using radiators, and their performance rises by the power ^4 with increasing operating temperature. For example, if the turbine releases gases at 600K instead of 400K, it allows for radiators that are over five times smaller and lighter. 

Modern Brayton cycle example

We will be using existing technology for this example.

Solar receiver.
As in previous 'modern' examples, we will be using a concentrated solar power set-up, where large parabolic surfaces of a thin, reflective material, such as Mylar, is used to focus sunlight onto a solid heat exchanger.

A 10000x solar concentration means that 10000m^2 of reflectors will focus sunlight onto 1m^2 of heat exchanger. 

Possible configuration of solar concentrators.
Mylar is 98% reflective. If the reflectors have a mass of 7 grams per square meter, as solar sails have demonstrated, then this means that 70kg of reflectors will deliver 1367*0.98*10000: 13.4MW of solar power at an average power density of 191.4kW/kg

The heat exchanger we will be using is made of tungsten, and we will heat it to a temperature of 2500K. It has a very high heat tolerance and high emissivity. It also has the strength to survive a high pressure flow using thin channel walls, which reduces the overall mass of the heat exchanger. 90% efficiency is expected, with 12MW of heat absorbed and the remainder re-radiated.

We will be considering a square grid of microchannels. The grid walls are thin tungsten maintained at 2500K. To maintain a constant pressure while heating the gases, the grid must be contained inside nozzles inspired by turbojet burners. 

1mm thick heat exchanger fins spaced by 1mm allows for a very large effective surface area in a small, lightweight volume. The fins will mass 19.3kg/m^2. The average distance between the gas and the fins is 0.5mm.

The gas that will flow through the turbine will be a 50/50 mixture of Xenon and Helium. The Xenon makes the gas denser, which reduces the turbine rotation velocity, so the strength requirements of the turbine blades is lower and therefore makes for a lighter turbine. Helium has a high thermal conductivity, which allows for smaller heat exchanger. Both are inert, so there is no fear of oxidation of the turbine materials. It has a molar mass of 67g/mol, a heat capacity of 2596J/kg/K and a thermal conductivity of 0.29W/mK (Xenon does not contribute much), based on figures from here.
Using the this distance, the temperature gradient and the thermal conductivity of the gas mix, we can calculate the heat transfer rate.
  • Heat transfer rate: Thermal conductivity * Temp. Gradient/Fluid thickness
Heat transfer rate is in W/m^2. Thermal conductivity is in W/mK, temperature gradient in Kelvin and fluid thickness in meters. To calculate this figure, we first need to find the initial and final temperature of the gas mix as it travels through the heat exchanger.

The initial temperature here will be the temperature of the gas after leaving the compressor. The final temperature will be the maximum temperature the turbine materials can handle. 

As will be calculated below, the initial temperature will be 484K and the final temperature will be 1600K. This means that the heat transfer rate is an average of 1170kW/m^2 (484K) and 522kW/m^2 (1600K), or 846kW/m^2.

Using the heat capacity of the helium-xenon mix, we can determine that 5.18kg/s mass flow rate is required to absorb the 12MW of heat. The surface area to do is 12000/846: 14.18m^2, which will mass 271kg.

The heat exchanger's power density is therefore 12000/271: 44kW/kg

Let us now design the compressor.

We will be using an axial multi-stage transonic compressor. They are suitable for our purposes as they are very efficient and will operate in a single, carefully controlled environment.

Based on this paper.

Each stage of the compressor increases the pressure of the gas mix by a certain ratio. For efficient subsonic designs, this can be at most 2.1. The effect is compounded by the number of stages. 

Based on the equation for isentropic expansion, we can assert that a higher pressure ratio allows for higher efficiency, as the temperature gradient in the turbine will be greater. We therefore aim for a pressure ratio of 30.

To achieve this pressure ratio, the compressor must contain (30^(1/2.1)): 5 stages. If the initial pressure is 1 bar, the final pressure is 30 bars. Normally, if the initial temperature is 300K, the gases exiting the compressor would be heated by a factor 30^(1-1/1.66): 3.866 to 1160K.

There is little margin between 1160K and the maximum operating temperature of modern turbine materials. The gas would not absorb much energy, so a large mass flow rate is required, which would lead to a larger compressor that consumes even more energy.

The solution is one employed by actual high pressure ratio engine: to split the compressor into low pressure and high pressure sections, and to cool the gases in between.

We will therefore split the 5 compressor into two parts, with an intercooler. The first part is three low pressure stages (1 bar to 9 bar) that raise the temperature from 300K to 718K. It is followed by an intercooler that reduces the gas temperature from 718K back down to 300K. The second part is two high pressure stages (9 bar to 30 bar) that raise the temperature from 300K to 484K. 

There is a significant difference between 484K and 1160K!

Using the energy contained in the gases, we can calculate the work done by the compressor. The low pressure compressor raises the gas temperature from 300K (779kJ/kg) to 718K (1864kJ/kg). Since the mass flow rate is 2.89kg/s, this translates to a power consumption of 3.14MW. The intercooler then has to get rid of 3.14MW of heat. The high pressure compressor raises the gas temperature from 300K to 484K (1256kJ/kg), which requires an input of 0.48MW. 

We can expect an 80% efficiency from the compressors, so the total power consumption of the compressors is 4.53MW.

Next is the turbine stage.

Based on Silicon Carbide composites developed by NASA's Glenn Research Center, we can expect a turbine to operate at 1600K without requiring any active cooling. 

Turbines expand the gases they receive in multiple stages. Pressure compounding turbines lower the gas pressure without changing the gas velocity much. 
Pressure compounding impulse turbine.
We will use a turbine pressure ratio of 5.5. Only two stages are required to expand the gas from 30 bars back down to 1 bar. 

The temperature drop that accompanies that pressure change is by a factor 30^(1-1/1.66): 3.866, from 1600K to 413K.

The turbine reduces the thermal energy in the gas from 4153kJ/kg (1600K) to 1085kJ/kg (418K). It therefore should extract 8.87MW from the 2.89kg/s gas flow. However, we should only expect about 90% efficiency, for an actual figure of 7.98MW. 

The exhaust gases must then be cooled down from 418K to 300K, at a rate of 0.88MW. 

If we add up the power generated and consumed, we obtain a net figure of 3.45MW.

To move onto calculating an estimate of the turbine's mass, we must first estimate its dimensions. The helium-xenon gas mixture will exit the heat exchanger at Mach 1 (choked flow). The speed of sound in this mixture is 578m/s. The mass flow rate translates into a volume flow rate of 0.194m^3/s. An inlet area of 0.000336m^2 is needed to allow this flow to pass, which is a disk 0.021m wide.

However, looking at actual turbine designs, the exposed blades on the first turbine stage only represent a fraction of the total radius. The blade-to-hub ratio can be as low as 10%. This means that the first stage of the turbine is 10% blade (where gas flow) and 90% hub, so the total width is increased ten-fold and the total area a hundred-fold. The smallest turbine stage is therefore 0.21m wide for 0.336m^2. 

The final stage expands by a ratio equal to the pressure ratio, like any nozzle. Therefore, the second stage must have a surface area 5.5 times larger, or 1.85m^2. This requires a width of 1.54m. 

The average width of our turbine is 0.87m.

The LHTEC CTS800 is representative of modern high-performance turboshaft engines, using composite materials and being optimized for light weight. It has a similar number of stages as our design, and is 1.5 times as long as it is wide. Its density is roughly 200kg/m^3. Using these numbers, we can expect our turbine to be 159kg. The 'modern' turbine alone has a power density of 21.7kW/kg.

The turbine's shaft is connected to an electrical generator that converts mechanical energy into electricity. 7kW/kg has already been tested using current technology, at an efficiency of over 95%. The operating temperature is as high as 370K.

308mmx150mm, 24.4kg, handles 170kW.
Using that generator to handle 3.45MW of mechanical power would require a mass of 493kg. It would produce 3.28MW of electricity and 173kW of waste heat.

After the turbine and the generator comes the waste heat management systems. There are three sources of waste heat: the compressor intercooler (3.14MW@718K), the turbine exhaust (880kW@418K) and the generator (173kW@370K).

A design with multiple radiators at different temperatures.
We will use three sets of radiators:
-a graphite fin radiator for the intercooler, at 718K.
-a magnesium fin radiator painted black for the turbine, at 418K.
-a magnesium fin radiator painted black for the generator, at 370K.

The high thermal conductivity of graphite and magnesium allow us to do away with any coolant loops within the radiator, which makes then very thin and with a low mass per area. Instead, coolant loops exchange heat with the fins at the attachment point at the base of the fins.

Black paint, such as a micrometer thick vapor-deposited layer of graphite flakes, is necessary to increase the emissivity of magnesium closer to 0.98.   

1mm thick graphite fins work out to 2.3kg/m^2. At 718K, the radiators remove 29535W per square meter (double-sided). Handling 3.14MW of waste heat requires 106m^2 of radiators with a mass of 245kg.

1mm thick magnesiums fins have 1.7kg/m^2. At 418K, the radiators remove 3392W per square meter. 880kW of waste heat requires 259m^2 of radiators with a mass of 441kg.

The same magnesium fins at 370K remove 2083W per square meter. 173kW of waste heat requires 83m^2 of radiators with a mass of 141kg.

If we put together all these components, we obtain an output of 3.28MW of electrical power produced by 70kg of solar collectors, 271kg of heat exchanger, 159kg of turbines, 493kg of generator and 827kg of radiators for a total of  1820kg. The system power density ends up as 1.8kW/kg, although realistically it will be lower.

Advanced Brayton cycle example

We will now consider a turbogenerator made using more advanced materials and techniques. 

Let's start with the same solar collector surface area of 10000m^2. However, the reflective surfaces will mass only 1 gram per square meter, for a mass of 10kg.

The critical difference between the 'advanced' and 'modern' designs is the use of carbon materials currently only being tested in laboratory environments. One such material is graphene. It has an exceptional thermal conductivity. By using a thin layer of graphene on vitreous carbon, it can also gain the strength of diamond while surviving very high temperatures.

Compressed vitreous carbon weave.
This allows us to design a heat exchanger that supports higher temperatures and higher pressures with even smaller walls. We will operate the heat exchanger at 3500K. Efficiency will depend on the ratio between sunlight intensity absorbed and heat re-radiated, which will set for 95% efficiency. As before 12MW of heat is absorbed.
The plate fins will be as thin as 10 micrometers. This reduces the mass per area to 15 grams per m^2.

We will aim for a gas to reach a temperature of 3000K while leaving the heat exchanger. At such high temperatures, typical helium mixes reach extreme velocities, which would force the turbine to spin at unsustainable rates. One method of reducing the gas velocity is to increase its molar mass. 

Therefore, Mercury is ideal. It has a very high molar mass of 200g/mol, so it will be (200/67)^0.5: 1.73 times slower at the same temperature as the 67g/mol Helium-Xenon mix from the previous design, so the turbine fans can be three times lighter. Mercury boils at just 630K, so it is unlikely that it will condense at the turbine exit. 

However, the metal has a relatively poor thermal conductivity in the gaseous state, at roughly 0.02W/mK, based on this table. To compensate for this, we will use a very narrow spacing between the heat exchanger's channel walls, at 10 micrometers. The average distance between the gas and the walls falls to 5 micrometers.

The heat transfer rate in this micrometer-scale heat exchanger ranges from 2MW/m^2 at 3000K to 7.03MW/m^2 at 1742K. On average, it equals 4.56MW/m^2. The heat exchanger for 12MW of power will mass 0.039kg

We will now work on the compressor.

Carbon fibre is ideal for compressors. It is very strong yet lightweight, meaning that fan blades and disks can reach very high RPMs. Centrifugal compressors become competitive even in large diameters. Their downside is that they become rather inefficient when used in multiple stages. The trick is to reach a very high pressure ratio within a single stage: this requires the use of supersonic centrifugal compressors.

Gas flow simulation in a centrifugal compressor.
Current test bed compressors achieve a pressure ratio of 12 with an efficiency of 90%. Improvements are likely, but we will use these numbers.

The Mercury is kept at 650K to prevent condensation. It enters the compressor at a pressure of 1 bar. At the exit, it reaches a pressure of 12 bar. As Mercury is monoatomic, the temperature increases by a factor 12^(1-1/1.66): 2.68, up to 1742K.

Supersonic impeller.
Mercury vapour has a heat capacity of 872J/kg/K. It enters containing 378kJ/kg (650K), and exits with 1053.7kJ/kg (1119K). The work done is 675kJ/kg.

To transport 12MW of heat, a mass flow rate of 12000000/((3000-1742)*872): 10.9kg/s. The compressor therefore inputs 7.35MW of work. At 95% efficiency, it consumes 7.75MW.

The turbine must expand this flow.

A radial turbine of equal pressure ratio is ideal, although thanks to high molecular weight gases, much higher is achievable. 
Single stage centrifugal compressor with radial turbine.
A pressure ratio of 12 allows for a temperature drop by a factor 2.68. The mercury gas is expanded from a temperature of 3000K to 1119K. It initially has 2616kJ/kg (3000K), and exits with 975kJ/kg (1208K), so the turbine extracts 1640kJ/kg.

At a mass flow rate of 10.9kg/s and 95% efficiency, this works out as a turbine output of 18.8MW.

The net power generated by the turbine is 18.8-7.75: 11.05MW

The combination of centrifugal compressor and radial turbine is commonly found in automobile turbochargers. 

At the inlet, this turbine accepts 10.9kg/s of mercury at 650K. This corresponds to a volume flow rate of 2.94m^3/s. We expect this design to mass roughly 2kg, based on approximations relative to turbochargers that accept similar volume flow rates and factoring in the specific strength of the carbon materials compared to steel and nickel alloys more commonly used.

As the turbine shaft spins, it drives an electric generator. Superconducting magnets offer very high magnetic field strengths and zero-resistance current flows.

While achieving superconductivity is difficult with current magnets due to the extremely low temperatures that must be achieved (2-4K), there is research currently being done on high temperature superconductors based on copper oxide ceramics (BSCCO and YBCO). Mercury-Barium-Calcium cuprate HBSCCO can operate at temperatures as high as 133K. 
Many high temperature superconducting (HTS) electric generators are currently under development.
American Superconductor Corporation and Northrop Grumman 36.5MW HTS motor.
NASA research into electric aircraft that can compete in terms of output and specific power with conventional turbines provides estimates for the power densities achievable with superconducting generators: 80kW/kg or more, at 99.98% efficiency, for use on the N3-X hybrid-wing airliner.

Using carbon materials for the rotors, and statene for wiring, could easily increase this power density to 100kW/kg. With these materials, handling 11.05MW of power requires a generator mass of 110.5kg and would produce 2.22kW of waste heat at 100K. 

The total amount of waste heat to be radiated out of the system is 6.5MW from the exhaust gases at 1208K, and 1.11kW from the generator at 100K.

The exhaust gas heat can be handled by a wire radiator. 

Carbon fibres.
Thanks to carbon materials such as carbon fibre, we can design the radiating wires to have a high thermal conductivity, high emissivity and high strength despite being very thin.

1 micrometer wires will be used with 1750kg/m^3 density and 0.98 emissivity. They are exposed to space at 1208K. Each meter length of carbon wire has a mass of 1.375 nanograms and a surface area of 3.14*10^-6 m^2. 

One million such wires can be aligned in parallel in a 1m^2 space. Interreflection reduces radiative efficiency to 70.4%. This means each square meter of microwire radiator has a mass of 1.375 grams and an effective area of 2.21m^2. At 1208K, it radiates 118.33kW/m^2. So, the power density of the microwire radiator is 190.2MW/kg.

The radiators for the turbine exhaust will mass 0.0347kg.

If those same wires were used to cool the cryogenic generators at 100K (5.6W/m^2), we would need a mass of 0.248kg.

We can now add up the mass of all these components to work out an estimate of the system power density. The advanced turbine design produces 11.05MW of power for a mass of 122.82kg, thereby achieving a power density of 89.9kW/kg.

Next, we will look at the Rankine cycle, as well as some rather exotic power generating schemes.


  1. If your "exotic" power generating schemes include MHD generators, then there is a rather amazing situation where your high temperature advanced turbine is the "bottoming cycle" engine utilizing the waste heat and exhaust of the MHD system.

    The main issue with turbo machinery in space is the rotating masses become gyroscopes or reaction wheels, and would tend to cause issues with spacecraft orientation unless they are built and paired in counterrotating sets. True pendants will object that we would need six turbines, paired and placed orientated in the X, Y and Z axis of the spacecraft, but the amount of effort (and high temperature plumbing) needed seems excessive for the benefit, unless you need extreme accuracy in pointing and station keeping.

    1. You're on-point, as always. An MHD would fit in between the heat exchanger and the turbine stage.

      I'm not sure that the rotating stages of a turboshaft engine would have a significant gyroscopic influence over a spacecraft. Even in the 'modern' example, the entire turbine is just 8.7% of the power system mass, itself likely to be 10% of the spacecraft's entire dry mass and 30% or less of the total mass.... it is also a very predictable effect which can be perfectly countered with confidence. A problem it is, yes, but a solvable one.

      Also, come join us on the discord channel:

  2. Hi MB,

    Just wanted to let you know I've included this blog in the acknowledgements page of my upcoming sci-fi novel. Thanks a lot for your help.

    1. Thank you very much. I'm always here to help you further.

  3. Off topic, but there was a lecture at this year's Tennessee Valley Interstellar Workshop about a magnetic sail design with a ridiculously high thrust to mass ratio, so much so that it can bring a large payload up to solar wind velocity in a few days. Seems to me like a big game changer that is relatively unknown in the space community, which is why I wanted to bring it up here.

    Here is the lecture:

    And here is the NIAC report:

    1. Hello Crazy Eddie.
      I believe this is the Plasma Magnet (or more commonly known as mag-sail) that Centauri Dreams reported on.
      I do believe, if the numbers on power requirements for the magnetic fields of 10-30km diameters can be verified, that this will be a game-changer.

      We could reach 400-700km/s on outbound journeys.
      Braking would require a small boost to slow down, then a magnetohydrodynamic loop that generates electricity from the ions travelling through the magnetic field at high relative velocity. As the craft slows down, the relative velocity increases even further and even more power is generated. The power is used for a high Isp engine.

      There are other potential uses. I'll add this mag-sail development to my list of topic planned for ToughSF.

      Thanks for linking the original report.

    2. I didn't see the Centauri Dreams article, but yes it is the same concept.

      I'm not sure about that breaking idea. If you were generating power from a stream of ions, then you would be slowing them down relative to the spacecraft, not speeding them up, which is what you would need to do to slow down. If this is to generate power for an ion engine, then the engine would be fighting against the particle drag that is powering it, which would be a losing battle. I think you might be confusing this with another magnetic sail concept for interstellar breaking.

      As far as I know, the only way to slow down within the solar system is to use a stationary particle beam or plasma beam like Robert Winglee's Magbeam concept to push on the sail, or to go slower and use ion drag within the magnetosphere or ionosphere of the destination planet.

    3. So long as your braking ion engine has a lower exhaust velocity than the solar winds, it will create a thrust that overpowers the drag force that comes from using the solar winds as a power source.

      For example, to produce 1MW out of 400km/s solar winds, you'd expect a drag force of 5 Newtons.

      If that 1MW if used in an ion engine with an exhaust velocity of 100km/s, you'd produce a thrust force of 20N.

      The net effect is 15 newtons.

    4. Crazy Eddie beat me to it, this extension of the Magsail or M2P2 idea looks like a true game changer. With the sort of electrical energy that can be generated either on board through solar panels, or nuclear reactors, or beamed to spacecraft, you could power impressive plasma magnet array and have swift "frigates" capable of high deltaV manoeuvre throughout the Solar System.

    5. For 400km/s of delta-v with an exhaust velocity of 100km/s you need a mass ratio of 54.6, but with exhaust velocity of 200km/s and 95% system efficiency (ion engines do 96%) you get a net thrust of 4.6N and a slightly more practical mass ratio of 4.95

      It would take at very least a few years to slow down which is on the order of how long it takes to get to the solar gravitational lens point or other targets usually classed as interstellar precursor missions. It would probably work for catching up to 2017 U1 Oumuamua, for example.

      This technology is really too powerful to use at its maximum performance within the solar system without a network of mass beam installations at all destinations farther than earth from the sun, but according to some rough calculations that I did, a sailcraft capable of .5m/s^2 in the solar wind could get to Jupiter in 60 days and Saturn in 300, only using the planetary magnetosphere for breaking. Also, I think it might be possible to use Jupiter's rotating plasma torus to get a boost to a transfer orbit back to earth, but I haven't run the numbers on that. If it does work, it would make Jupiter a very attractive destination especially since the spacecraft would have a magnetic radiation shield by default.

    6. Speaking of mass beams, you can build a kinetic impactor interplanetary 'rail-road'. You can launch a series of mag-sail accelerated drones carrying a 1kg or smaller payload. These payloads reach a very high velocity, let's say 400km/s.

      You spaceship's engine consists of a bag of water and a large electromagnetic loop.

      You shape the water into a disk and let it freeze. This 'ice puck' is set to gently drift into the center of the electromagnetic loop just as mag-sail payload arrives. The collision between the ice and the kinetic impactor releases incredible amounts of energy (on the order of 80GJ).

      This energy is enough to completely ionize both the payload and the ice's atoms. The resultant plasma expands spherically. If the collision happens behind the ring in the direction of travel, up to half of the impact's energy gets transmitted to the magnetic field, propelling the spaceship forwards. The reverse is possible for braking.

      This creates an incredibly powerful propulsion system, with the only downside being that you need to accuracy to hit each impact with an ice puck spot-on.

      A decently efficient mag-loop spaceship riding this 'rail-road' can reach extreme velocities with very little on-board propellant.

      The mag-sail drones don't even need to perish with the impacts. They can drop their payload and make the very long trip back to Earth by using gravity assists to turn their trajectory from straight out of the solar system into something a bit more elliptical, and then deflecting the solar wind to cancel their horizontal velocity until they fall back towards the Sun.

      Jupiter's magnetic field spins with the planet. At Io's orbit, it is whipping past at 60km/s relative to the moon, so this is the velocity you can expect from the ions around Jupiter.

    7. Hey matter beam.

      This might be a crazy idea but have you heard about ferrofluid mirrors. They can be held in magnatic fealds.

      If we can hold this magnetic mirror in the plasma megnito spear then we might be able to focus km squares of sun light on our heat exchanger.

      What do u think about that system and how much power to weight ratio can we get.

    8. Well, the focusing mirrors are a small part of the advanced solar energy designs mentioned so far. For example, the 'modern Brayton' example has only 3.8% of its mass dedicated to the solar collectors.

      If you reduce this to practically nothing, you've only gained a 3.8% better power to weight ratio...

    9. The magnetic mirror are not just for reducing mass you are having huge solar collection area. We are focusing Gws of sun light on our heat exchanger.

      The structural requirement to hold kmsq of solar collectors quickly adds up also such huge solar collector is impractical on a space ship.

      Mag solar mirrors can be put on massive ships in around kiloton range the normal solar panels are only practical on small satalite size ships.

  4. So, one more part before piracy...
    Still waiting for it and the exotic schemes, also the power densities of superconducting generators in this post is much higher than you once mentioned in G+.

    Finally, I can make the generators for fusion ships much lighter reasonably.

    1. Next is definitely Space Piracy.

    2. I'm most excited about space piracy, especially as it is a central plot point of my novel in progress.

      Tangentially, I really appreciate this blog for the engineering applications of various ideas. I have a physics degree, but there's a world of difference between general relativity/field theory ( my focus) and materials science.

    3. Thanks, I'm working on that right now.

  5. Hi Matter Beam, after taking the time to write about space piracy, do you mind making an article explaining phase change materials for me (and the other people here), and how they work exactly (because, I am kinda rly confused how exactly they are able to store soooo much heat)? From what I have read about them, they can apparently store 10-14 times more heat per weight than sensible heat storage (thermal storage systems that rely on storing Joules/kg k, raising temperature of material, and what not), because they utilize latent heat storage

    Soooo...would you kindly plz? :3

    1. I'm not exactly sure about your question, as I understand that a 'phase change' material is simply any material that is heated up past its melting or boiling point.

      If you're considering a heat sink, you can start for example with a solid block of sodium. Sodium has a good heat capacity as a solid, at 1234J/kg/K. If you heat it up from room temperature (293K) up to sodium's melting point (370K), you can store 95kJ/kg. However, if you continue heating it, the sodium starts to melt. The temperature does not rise - all additional energy is spend breaking the bonds that hold its shape as a solid. The 'phase change' allows you to store an additional 113kJ/kg.

      With the phase change, you are able to store 119% more energy than by just heating up the sodium. There are more extreme examples, of course, for which phase changes are even more interesting.

    2. I just thought it was a topic worth writing about :)

    3. Heat sinks in general would be an interesting topic

    4. Agreed. I'll add it to the list.

  6. Hey Matter Beam, I got a question for you regarding Phase Change Materials. Is Beryllium the perfect PCM material (If not, which PCM material is the best?)? So, Beryllium has a latent heat of vaporization (Latent heat of vaporization means the energy required to change from a liquid to gas phase right?) 297 kJ/mol. And there are 110.96091934228582 moles of Beryllium in a kg. So this means it's able to store 32955393.044633 joules of thermal energy per kg...but is it possible for Beryllium to stay as a liquid rather than a gas by absorbing 295 kJ/mol rather than the latent heat of vaporization of 297 kJ?

    And one more thing, I have read from PBS Nova that when the phase change material is undergoing a phase change, the PCM material's temperature doesn't change. <<“To cool one pound of water from 33˚ F to 32˚ F takes 1 BTU of energy,” says Mark MacCracken CEO of CALMAC Manufacturing Corporation, whose company sells ice-based air conditioning systems. “Taking that same one pound from 32˚ F water to 32˚ F ice takes 144 BTUs as it changes from a liquid to solid. By freezing instead of simply cooling the water, you are storing 144 times as much energy.”>> (Quote source: Is this true? And if it's true, then why does it do that? :/

    1. To determine the 'best' heatsink material, you have to consider the temperature range you are working with, what pressures you can handle, environmental factors and heat capacity on top of the heat of fusion/vaporization. For example, sodium looks like a great material, but it is very reactive and any leaks can cause it to burn/explode in contact with air. On the other hand, steam is non-reactive but at high temperatures becomes very corrosive.

      Beryllium has a high heat capacity but is also very reactive, so you have to watch out for that.

      When a liquid is brought close to the boiling point, you will have a mixture of phases. Some of it bubbles off and condenses immediately back into liquid. In closed containers, the partial vaporization increases the pressure and you might reach a 'critical point' where the liquid is above its boiling point, but the pressure is too high for it to vaporize into a gas. Its overall pretty complex.

      The statement from PBS Nova is correct. Boiling water stays at 373K exactly until the last drop turns into vapour.

      This page has a nice, simple explanation of how phase changes occur:


  7. A) Holey shet, so water can ACTUALLY store 144 times more thermal energy during a phase change?!?!?!? That's wwwwwwwwwaaaaaaayyyy more than the statement of PCM materials being able to store 10-14 times more heat. No wonder NASA is interested in using PCM materials for their next generation of future heat sink/thermal management systems :D

    B) Ok, so if a material is brought close to the boiling point, it will experience a mixture of phases...but that means that the material will absorb ALMOST (but slightly lower) as much energy as its latent heat of vaporization right? (SRRY if this is a stupid question, I just wanted to make sure that I got it right without any confusion)

    C) So, you already mentioned that Beryllium is very reactive during its phase is there any way to get around that problem, or what? And on top of that, are there any other problems that Beryllium will present during heat absorption?

    1. The PCM materials other than water are usually considered for storing heat because their phase change happens at a specific desirable temperature point. For water, it is 373K (100C), which is not the best temperature for many applications.

      The temperature graph during a phase transition is a flat line. 'Close' to the boiling point is 99C for water. At that point, you only store energy from the heat capacity. A centigrade above that, and a thin film of vapour forms over the surface of the water. Any extra energy goes straight into vaporizing the water. There is no intermediate value of energy stored, although I'm not quite sure what you're asking.

      Beryllium is reactive, toxic, expensive and rare. That is simply not a good combination of properties in any situation, even if you engineer a hermetically sealed, teflon-coated system to manage it.

  8. Also, I forgot to mention one more when a material is really close to its latent heat of vaporization, will it still have a density close to being a liquid?

    1. Latent heat of vaporization is a unit of energy, not a temperature.
      When boiling, you'll have water, and steam, that is all.

  9. Just one point, regarding mercury as a working fluid: I think there is some confusion here between centigrade and Kelvin. You say that mercury reaching a low temperature of 450K means it won't condense; I disagree. The boiling point of mercury at standard pressure is roughly 357 deg C, which is probably where these numbers are coming from, but that is 630K.

    In addition, at the working pressure of this generator the figure will probably be slightly higher than that.

    1. Thank you for the correction. I'll update the article with this in mind.

  10. "And on top of that, are there any other problems that Beryllium will present during heat absorption?"

    It is extremely toxic. Machining Beryllium was considered challenging because of the toxic dust, so having bubbles of this splashing around to Beryllium vapour leaking into the pressurized compartments will be a major emergency.

    If I consider the use of heat sinks, I generally think of taking tanks of water and freezing them, and letting the heat be poured into the ice. If you have the mass budget, a strong tank which can hold the water as it turns into high pressure steam gives you even more heat carrying capacity (you could also use a flexible membrane, essentially creating a steam balloon). The final step is to release the steam into space to rapidly dump the excess heat if you cannot extend your radiators to deal with it otherwise.

  11. Moving closer to the topic at hand, Atomic Rockets has released an new update of the design of a low pressure nuclear thermal rocket. While not directly on topic, a nuclear reactor makes a handy heat source when you are not generating thrust, so could be considered as the heat energy source for a bi-modal nuclear system, where the coolant is circulated and used to run a heat engine to generate electricity:

    And the low pressure engine is lightweight, cheap and quite rugged and reliable. Many spacegoing "Unimog" utility vehicles could be designed around this sort of engine.


    1. It is quite interesting, yes. It has prompted me to reconsider the exhaust velocity discrepancies between what I was calculating based on the Root Mean Square Gas Velocity model and what was being reported by various real-world designs.

      This led me to the equation which takes into consideration the gas's gamma and the effect of pressure and expansion on the gas velocity.

      For monoatomic gases, such as dissociated hydrogen, a 29.5% increase in exhaust velocity is possible over what I was previously reporting. For example, the 'maximum temperature solar thermal rocket' can actually achieve 15.7km/s.

      Also, it has got me thinking of dual-heat-source thermoelectric generators. One nuclear, one solar, both converted into electricity with a Thermophotovoltaic system...

      I'm not sure what the Unimog analogy means.

    2. A Unimog is a utility truck built by Mercedes Benz which is pretty common in Europe in both military, commercial and even farm use. Unimog chassis are used in a wide variety of different roles, so it would seem that there is probably a market for some sort of utility spacecraft which can be mass produced and adapted for a multiplicity of roles.

      A cheap, rugged nuclear engine like the one described, or a cheap, rugged solar thermal rocket would be the basis for such a ship, and adding modules or adjusting the length of the spinal truss would be the two major options the builder or subsequent owners need to do.

    3. I remain wary of putting several kilograms of fissile materials in 'cheap, rugged' designs oriented towards private use.

      With regards to modularity: I think the propulsion system 'module' that comprises the engines, generators, waste heat management systems and navigation computers form the 'heart' of a spaceship. Propellant and payloads stretch the ship to the mission, but the engines generally stick around.

    4. Cheap & Unimog are two words very rarely used in the same sentence!

  12. Considering a spacecraft powered by "anything" moving at interplanetary velocity is a giant kinetic energy weapon, the extra risks associated with fissile materials is quite small in the grand scheme of things. A solar sail towing a cargo pod crashing into a moon or space station at 10 km/sec is already going to deliver kilotons of energy. The risk of using the missiles in a nuclear weapon have to be balanced by the fact they cannot be delivered unless you have the energy to provide interplanetary deltaV, which means the carrier is already going to be a potential threat, and if you are using missiles for the weapon, then you need something else for the power plant. That alone might raise flags, when your fleet is converting to solar or other energy sources for no obvious reasons.

    You are correct about modularity, and I may have not worded this correctly. The basic idea of common "body" (chassis and engine) that can be adapted for a wide range of uses has been tried in a lot of places, and the theoretical advantages of being able to do so will draw the attention of planners engineers and investors for a long time to come, even in space.

    1. The thing is, spacecraft are large and visible. They can reach high velocities, but in practical terms, they crawl at a snail's pace between destinations. Even the short distance between LLO and LEO takes days to cross.

      In other words, all spacecraft will be an existential threat to space stations and exposed surface colonies, but they are also threats that you see coming and have a lot of time to prepare for.

      My qualms with fissile materials in civilian hands is that they can be stolen to covertly manufacture nuclear bombs. These bombs can be small, smuggled into cities normally protected against external threats, and deal massive damage. They flip the table on the balance of power, which is not a good thing.

    2. Have the chemothermonuclear bomb pan out, or some other type of practical pure-fusion design. This way, nuclear arms control will focus to tritium (or antimatter or any other vital component of the design) and no-one will bother with uranium and huge centrifuge farms running for who knows how many months. As such, while uranium won't be trivial to use due to its toxicity and radioactivity, controls will be less drastic for commercial or private use.

      The story will have to explain why there is not more nuclear proliferation, though, or otherwise deal with it.

    3. I have thought a bit along those lines, in terms of ORION pulse drives or CASABA Howitzer type weapons. In general terms, the best way for this to work is to harvest the anti-protons suspended in the magnetospheres of planets with magnetospheres as the trigger mechanism, so the problem is self limiting to a certain extent: there are only going to be so many anti protons to harvest.

      And the harvesting rigs are going to be fairly visible, and in predictable orbits (i.e. where the anti-protons are), so there is that to consider as well.

    4. @Eth:
      That is the opposite of what anyone wants!
      Just because staged chemical-implosion fusion devices become practical, does not mean that gun-type fission warheads become any less simple to make or deadly in the wrong hands! Controls on fissile materials will forever be 'drastic' for private/commercial use, if they are authorised for use in that way at all.

      @Thucydides: What are you trying to make work? I'm not clear on that.

    5. Essentially trying to work out world building implications of the availability of antimatter in a planetary magnetosphere. With current observations and thinking about how antimatter can be harvested, I suspect it is still a non issue, you are not going to get industrial quantities of antimatter. Now noodling around with just what the best leverage is for the limited amounts of anti matter you can harvest.

    6. @MatterBeam The main difficulty with making nukes is enriching uranium. If reactors run on low-enriched civilian uranium, controlling those should be more or less manageable, particularly if there is a much easier uranium-free design available.

      Then again, is there a particular reason why those couldn't run on thorium? That would neatly solve the military uranium problem.

  13. "If you are using fissiles for the weapon". Autocorrect can be very sneaky.

  14. Somewhat OT yet again, but Atomic Rockets looks at a magnetic mirror design for a spaceship. Since the exhaust product is a beam of charged particles, it could be considered a form of high powered electrical system (you could certainly use the exhaust beam to energize a very powerful weapons suite, for example), although at 79m long and @ 8m diameter, it is hardly "compact"

    1. That looks interesting, yes. The engine can certainly be made smaller using stronger magnets.

      Reactors that use a stream of high velocity ions from a fusion reaction to produce power are known as Direct Conversion Fusion reactors, of which you can find much research being done.

  15. When is da Blackbeard in Spess update gonna come out? :D

  16. Thanks for the elaborate explanation.

  17. Thanks for this in-depth review. I was looking for information about this but didn’t get any information what exactly
    I am looking for. Fortunately, I come across to your website and it helps to make my decision.
    It’s really made my day.
    Thank you again for this great article.