Monday 23 October 2017

Liquid Rhenium Solar Thermal Rocket

The maximum temperature concentrated sunlight can heat a material to is 5800K. How do we approach this limit?
We will describe existing and potential designs for solar thermal rockets. 
Solar thermal rockets
The Solar Moth
The principle of a solar thermal rocket is simple. You collect sunlight and focus it to heat a propellant headed for a nozzle. 

A rocket engine's performance is determined by its thrust, exhaust velocity and efficiency. A solar thermal rocket's thrust can be increased by sending more propellant through the nozzle. Its exhaust velocity can be increased by raising the propellant temperature. Doing either required more power, so more sunlight needs to be collected. Efficiency will depend on the design.

The main advantages of a solar thermal rocket are its potential for high power density, high efficiency and high exhaust velocity. 

Collecting and heating with sunlight does not need massive equipment - unlike solar electric spacecraft that need solar panels, extremely lightweight reflective metal films can be used. A heat exchanger above a nozzle is compact and masses much less than the electrical equipment and electromagnetic or electrostatic accelerators a solar electric craft uses. Radiators are not needed either, as the propellant carries away the heat it absorbs with it. Put together, a solar thermal rocket can achieve power densities of 1MW/kg while solar electric craft struggle to rise above 1kW/kg. 
Sunlight would follow the same path as the laser beam here.
As the sunlight is being absorbed by a propellant and expanded through a nozzle, there are only two energy conversion steps: sunlight to heat, then heat to kinetic energy. The first step can be assumed to be 99% efficient. The second step depends on nozzle design, but is generally better than 80%. 

Thermal exhaust velocity will be determined by the motion of the gas particles composing the propellant. The equation is:
  • Thermal Exhaust velocity: (3 * R * Temp. * 1000 / Molar mass ) ^ 0.5
Temperature is in Kelvins. Molar mass is the average g/mol value of the propellant at the temperature it is heated to. R is the molar gas constant, equal to 8.314 J/mol/K. 

For the very hot gasses we will be considering, we can assume complete dissociation of all molecules. H2 (2g/mol) will become atomic hydrogen (1g/mol), water (18g/mol) becomes a hydrogen-oxygen vapor (6g/mol) and so on. Low molar masses are preferred, with the best propellant being mono-atomic hydrogen unless other factors are considered. 

A nozzle can expand the hot propellant into a fast-moving stream of gas. Monoatomic gas can receive a x2.42 increase to exhaust velocity from a perfect nozzle, but this is situational and specific to each rocket engine design, so we will ignore this increase for now. 

These advantages are all the critical elements that allow for travel throughout the inner solar system without requiring vast quantities of propellant. The result is smaller spacecraft and lower travel times. 

Heat exchangers and exhaust velocity

The limiting factor for solar thermal rockets is how hot they can heat the propellant.

Directly heating the propellant is a difficult task. The lowest molar mass propellant, hydrogen, has terrible absorption. For all practical purposes, it is transparent to sunlight. Seeding the propellant with dust particles that absorb sunlight and heat the hydrogen indirectly through conduction has a major catch: the dust particles get dragged along by the hydrogen propellant flow and increase the average molar mass. 

Indirect heating involved using a heat exchanger as an intermediary between the sunlight collected and the propellant being heated. 

So far, designs have required the use of a solid mass of metal that is heated up by concentrated sunlight. The propellant is run over the metal, or through channels in the metal, to absorb the heat. Tungsten is often selected for this task, as it has a high resistance to heat, is strong even near its melting point and has a good thermal conductivity. 
Testing a Hafnium/Silicon Carbide coating.
More modern designs make the most of the latest advances in materials technology to allow for higher operating temperatures. Carbon, notably, stays solid at temperatures as high as 4000K. Tantalum hafnium carbide and a new Hafnium-Nitrogen-Carbon compound melt at temperatures of 4200 and 4400K respectively. 

However, looking at our exhaust velocity equation, the limits of modern materials technology will only provide a 21% increase over common tungsten. This is the reason why so many propulsion technologies that rely on exchanging heat between a heat source, such as a nuclear fuel or a laser beam, and a propellant using a solid interface are said to be 'materials limited' to an exhaust velocity of 9.6km/s with tungsten, or 10km/s with carbon. THC or HNC would allow for an exhaust velocity of 10.5km/s.

This is the deltaV equation, also known as the Tsiolkovsky rocket equation:  

  • DeltaV = ln (Wet mass / Dry mass) * Exhaust Velocity
Wet mass is how much spaceship masses with a full load of propellant. Dry mass is the mass without any propellant. The wet to dry mass is also referred to as the 'mass ratio' of a rocket. 

We can rewrite the rocket equation to work out the required mass ratio to achieve a certain deltaV using a rocket engine's exhaust velocity:

  • Mass ratio = e ^ (DeltaV required/Exhaust Velocity)
'e' is the exponent 2.7182... in simpler terms, the mass ratio increases exponentially as the deltaV required increases. Or, put another way, the mass ratio required decreases exponentially as the exhaust velocity rises. It is critical to have a higher exhaust velocity for rapid space travel without requiring massive rockets and towers of propellant. 

You might also have noticed that 'solid' is a keyword up to this point. Why must the heat exchanger remain solid?

Liquid Rhenium

There is a method to achieve the true maximal performance of a solar thermal rocket, which is heating up the propellant as far as it can go. This is incidentally the temperature of the surface of the sun (5800K). At this temperature, hydrogen propellant reaches an exhaust velocity of 12km/s.

A rare, silver-black metal.
Rhenium is a rare metal with a surprising number of qualities, one of which is a very high boiling point. Rhenium melts at 3459K but remains liquid up to 5903K.  

The trick to achieving higher exhaust velocities is to use a molten heat exchanger, specifically liquid rhenium at a temperature of 5800K. Rhenium is also very stable and does not react with hydrogen even at high temperatures, which is something carbon-based materials struggle to survive. It has already been considered as a heat exchanger, in solid form, by NASA.

Here is a design that can use liquid rhenium as a heat exchanger:

The diagram is for illustrative purposes only - a functional schematic would be more detailed. Here is an explanation for each component:

Solar collector: A very large, very lightweight reflective film based on solar sails that can collect sunlight and focus it through a series of lens onto the heat exchanger fluid's inner surface.

Rotating drum: The drum's inner surface contains a liquid heat exchanger. The outer surface is actively cooled. The drum is dotted with tiny channels that allow the propellant to enter the liquid from the bottom and bubble through to the top. It is made of Tantalum-Hafnium Carbide.

Fluid surface: The fluid here is liquid rhenium. Its surface is heated to 5800K by concentrated sunlight. The lower layers nearer the drum holding the fluid is cooler. The centripetal forces hold the fluid in place

Pressure chamber: The rotating gas mix gets separated here. Dense rhenium vapours fall back down, hot hydrogen escapes.

Bubble-through heating: The rotation induces artificial gravity, allowing the hydrogen to heat up and rise through the denser rhenium. As it rises, it reaches hotter layers of the fluid heat exchanger. At the surface, it has reached 5800K. Small bubbles in direct contact with the rhenium allows for optimal thermal conductivity. More detail below.

Active cooling loop: liquid hydrogen from the propellant tanks makes a first pass through the drum walls, lowering the temperature below the melting point of THC. It emerges as hot, high pressure gaseous hydrogen.

High pressure loop: The heated hydrogen is forced through the channels in the drum. It emerges into the fluid heat exchanger as a series of tiny bubbles. 

Here is a close up of the drum wall, which contains both active cooling and high pressure channels:

The configuration displayed above allows the hydrogen to enter the basin bottom at 4000K, then be heated further to 5800K before being ejected into the pressure chamber. If higher quantities of liquid hydrogen for active cooling are used, the drum and high pressure channel temperatures can be lowered to 3800, 3500, 3000K or lower. 
This pebble-bed nuclear thermal reactor has most of the components of our solar thermal rocket, except that instead using pebbles of nuclear, fuel, we use a liquid rhenium bed heated by sunlight.
If the liquid hydrogen active cooling cannot handle the full heat load, radiators will be needed to cool down the drum below its melting point of 4215K. Thankfully, these radiators will receive coolant at 4000K. Their operating temperature will be incredibly high, allowing for tiny surface areas to reject tens of megawatts of waste heat. Electricity can also be generated by exploiting the temperature difference across the radiators' entrance and exit flows, and at very high efficiency. 


The design is a Rotating Drum Fluid Heat Exchanger Solar Thermal Rocket (RD-FHE STR). It allows for hydrogen propellant to reach 5800K and achieve the maximum performance of a Solar Thermal Rocket. 

Liquid rhenium does not boil at 5800K, so it remain liquid and can be held inside the basin by simple centripetal forces.

Vapor pressure of rhenium at 5800K (0.87atm) was determined to be low enough for our purposes. A surface of rhenium exposed to vacuum at that temperature would lose 0.076g/cm^2/s, or 762g/m^2/s. It is unknown how much centripetal force affects the loss rate of rhenium. The pressure chamber would operate at several dozens of atmospheres of pressure, which is known to increase the boiling point and reduce the evaporation rate of fluids. 
The same techniques used in Open-Cycle Gas Core nuclear reactors to prevent the loss of uranium gas can be applied to reducing the loss of rhenium vapours.
At worst, the rhenium heat exchanger loses 0.76 kg of rhenium for square meter per second of operation. Looking at the designs below, the mass flow rate is measured in tons of hydrogen per second. This is a ratio of 1000:1, to be improved by various rhenium-retaining techniques.  

It should also be noted that rhenium is a very expensive material. A tungsten-rhenium mix has very similar thermal properties and is much cheaper.

Sunlight at 1AU provides 1367W/m^2. A broad-spectrum reflecting surface such as polished aluminium would capture and concentrate over 95% of this energy, so more than 1298W would be available per square meter. Solar sails materials such as 5um Mylar sheets are preferred, massing only 7g/m^2. More advanced materials technology, such as aluminium film resting on graphene foam, might mass as little as 0.1g/m^2.
The 'Solar Moth' used inflatable support structure for its mirrors. 
Based on data for the Solar Moth concept, we have estimated that a solar thermal propulsion system can attain power densities of 1MW/kg. So, each square meter of collector area will require another 1.29 grams of equipment to convert sunlight into propulsive power. 


Robot Asteroid Prospector
We will calculate the performance of two versions of the RD-FHE STR. The first version uses modern materials and technologies, such as a 7g/m^2 Mylar sheet to collect sunlight and a 167kW/kg engine power density. The second version is more advanced, using 0.1g/m^2 sunlight collectors and a 1MW/kg power density.

Modern RD-FHE

5 ton collection area => 714285m^2
927MW of sunlight focused onto the drum. 

5.56 ton propulsion system
Exhaust velocity: 12km/s
Thrust: 123.4kN (80% efficiency)
Thrust-to-weight ratio: 1.19
Overall power density: 87kW/kg

Advanced RD-FHE

5 ton collection area =>50000000m^2
64.9GW of sunlight received
64.9 ton propulsion system
Exhaust velocity: 12km/s
Thrust: 10.8MN
Thrust-to-weight ratio: 15.75
Overall power density: 928kW/kg

The principal argument against solar thermal rockets, that their TWR is too low and their acceleration would take too long to justify the increase in Isp, can be beaten by using very high temperatures and very low mass sunlight collectors. 

For example, a 50 ton propulsion system based on the modern RD-FHE STR design, would be able to push 100 ton payloads to Mars (6km/s mission deltaV) using only 97 tons of propellant. It would leave Earth orbit at a decent 0.24g of acceleration, averaging 0.32g. The departure burn would take only 20 minutes. Using the advanced version of the RD-FHE solar thermal rocket would allow for a positively impressive acceleration of 3.1g.

With 12km/s exhaust velocity, multiple missions that chemical rockets struggled to do with low-energy Hohmann transfers can be avoided. A chemical rocket such as SpaceX's BFR might achieve an Isp of 375s, which corresponds to an exhaust velocity of 3.67km/s. It would need a mass ratio of 5.13 to barely produce enough deltaV for a Mars mission. 
Earth to Destination.
If our solar thermal rocket is granted the same mass ratio, it would have a deltaV of 19.6km/s. This allows for a Mars mission to be completed in under two months (10km/s departure, 9km/s insertion). It is also enough deltaV to reach Jupiter with a single stage. 

Other benefits include a vast reduction in the propellant-producing infrastructure needed to supply orbital refuelling depots and the ability to land on Mercury. 

Alternative versions:

Blown hydrogen:

Instead of bubbling hydrogen from the bottom of the liquid rhenium basin, hydrogen is blown into the pressure chamber from the top. It is heated by simply passing over the fluid heat exchanger.

The advantage is that the rotating drum does not have to be riddled by microchannels, allowing it to be stronger and rotate faster, which would reduce rhenium losses, and also accept a higher rate of active cooling by leaving more room for liquid hydrogen channels. Another advantage is that there is less chance of hydrogen bubbles merging and exploding in showers at the surface, dragging along rhenium as they escape. 

The disadvantages is vastly reduced heat conduction rate between the rhenium and the hydrogen. This would require a long and thin pressure chamber to increase the time the hydrogen stays in contact with the rhenium, potentially making the propulsion system heavier than it needs to be and forcing sunlight to enter the chamber at very acute angles. 

ISRU propellants:

Instead of hydrogen, other gaseous propellants might be used. Nitrogen is a good choice, as it is inert and only reduces the exhaust velocity by a factor 3.7 compared to hydrogen. 

Powering a hydrogen extraction process on Mars requires huge areas of solar panels.

Nitrogen is easily sourced from Earth's atmosphere by gas scoops. Other options, such as water or carbon dioxide, are also viable and available on other planets. 

The advantage is that non-hydrogen propellants are easy to contain and are much denser than hydrogen, so their propellant tanks can be lightweight and small. They are easily sourced and only need to be scooped up and filtered, unlike hydrogen that has to undergo electrolysis.

The disadvantage is that there propellants cannot serve as expandable coolant for the rotating drum. A radiator using a closed gas loop is necessary - helium is a likely candidate. This adds mass. A lower exhaust velocity also removes the principal advantage the RD-FHE STR has over other propulsion systems.


  1. I was aware of this technology but had not seen the the numbers: they are very impressive!

    You make it sound like we could do this technology today and get torchlike performance without having to worry about nuclear reactors or magi-tech drives. Why are we not hearing more about this concept?

    What interests me a lot is the more workmanlike example of a tungsten heat exchanger, perhaps combined with a simple (non-H2) propellant. You would get a lot lower performance but still way better than a chemical rocket. Could you use water or CO2 at lower temperatures without fouling your engine?

    It also strikes me that a laser or orbiting solar concentrator could supplement your sunlight to give you a bit of a boost, especially if you are further away from the sun.

    1. Quite right! All the designs I have looked at on the internet are rather old and the biggest innovation I've seen was a design that would use a THC heat exchanger.

      This technology is available right now.

      We are not hearing more about this concept because Advanced Propulsion research is the domain of NASA and the Jet Propulsion Laboratory. They research systems that will be likely to be funded and grow into a real world project. So, safe, reliable, endurant propulsion systems are prioritized. A solar-electric ion engine that can run for a decade? Perfect! A new chemical rocket based on a hundred years of mature technologies? Even better!

      Solar thermal rockets that push the envelope with a combination of moving parts, high pressures and extreme temperatures just aren't interesting to the people who control research today.

      I should not that while I was specifically aiming for 'maximum' performance with a 5800K heat exchanger, you can use cheaper tungsten that boils at 5823K, so you can run it at 5700K. Even some carbides such as Zirconium carbide will melt at 5100K instead of sublimating like carbon. These allow for exhaust velocities only a few percent lower than with rhenium.

      Water is actually a great propellant at these temperatures. It breaks down into one oxygen and two hydrogen, so that molar mass of that gas is (16 + 1 + 1)/3: 6! We can achieve an exhaust velocity of 4.9km/s with WATER, which is better than the highest performance cryogenic LH2/LOX propellants. It is perfect for cheaply refuelled shuttles that move between orbits, as the water can just be scooped up out of the ground instead of processed, electrolysed and chilled like with LH2/LOX.

      Lasers that work in the visual or near infrared spectrum would share the collectors optimized for reflecting sunlight. They'd be a good addition if you have STRs leaving Earth for the far away planets such as Jupiter or Saturn. Instead of struggling to slow down with as little as 1% sunlight available, they can use the local lasers.

    2. So I have put a bit of thought into this and I think that there are a few issues that need to be worked through. None of them seem to be deal breakers though:

      Firstly if you are using km2 solar collectors you cannot accelerate at 0.3g as the structure will collapse. Lower acceleration over longer periods, with a smaller collector would work here though.

      The second question is how do you prevent backwards flow down the hydrogen channels as you are warming the engine up?

      Finally how do you stop your nozzle from melting when it is hit by h2 at that temperature?

      As for water, if it dissociated would superheated monatomic oxygen not react with the engine? Still, nitrogen would work nicely as you say.

      I don't want to come across as being negative here though. I just like the concept enough to put lots of thought into it!

    3. I enjoy responding to questions or criticism. It just shows that you are interested enough in the topic!

      The 'modern' RD-FHE STR with the 714285m^2 of solar collection area can configure its collectors into six disks of 389m diameter. Each disk masses 833kg and is supported by a 'stalk' or tower 194.5m tall. The stalk has to support a force of 2.45kN at 0.3g. It can be suspended from a tension structure by a single wire of common 250MPa steel about 3.53mm thick. In practice, I think the load would be distributed over a forest of carbon wires instead of a single wire at the center.

      When you are warming the engine up, I assume the high pressure channels will just be closed. Rhenium liquefies (3300K) before the drum melts (4400K), so you don't need to have active cooling or any hydrogen flow in place before your heat exchanger becomes fluid and you can start spinning it up and bubbling hydrogen through it.

      The modern example of an STR has a hydrogen flow of 898kg/s of hydrogen. This comes as a 20K liquid from the propellant tanks. If the nozzle is run at 3000K, each kg of hydrogen you use as active cooling for the nozzle can remove 60MJ. In other words, you have plenty of liquid hydrogen to use for active cooling of the rotating drum, the nozzle and more.

      Water dissociates into rabidly reactive oxygen... but the same temperature which broke up the strong water molecular bonds also prevents oxygen from forming new bonds. It will be a problem over time, especially if the nozzle is at a cooler temperature (<3000K)... so just replace it! High TWR means short burns, minutes at a time to put on kilometers per second of deltaV. That means that the nozzle is only used for short periods. Replace the nozzle and throw it overboard.

    4. On the first point, 250MPa steel is really low grade stuff. Buildings typically use 350-500MPa steel but 1000MPa is very doable if you you want pure tensile strength and are not too worried about other properties. Aerospace is not my speciality but 600-1000MPa steel would be my starting point for that kind of application. Obviously carbon fibre is much stronger and lighter than that anyway!

      Anyway, steel related geekery aside, tension is not your problem: compression is. If you pull on one point of a triangle then the 2 other points will want to move towards each other and this must be resisted. Unfortunately compression resistance is highly dependent on slenderness (i.e the ratio of the shortest side to its length). Now this can be solved by using an inflatable structure to get maximum thickness for minimum mass such as in the solar moth images at the top. Unfortunately a lightly loaded compression tube 1km long would need to be maybe 30m in diameter or it will buckle. As long as it has internal pressure the wall thickness can be arbitrarily thin as the forces are so small but any punctures would require repair and re-inflation before you can accelerate.

      If you really wanted km2 of solar collectors I would say it might be possible if you were to have 3 engines/ships and string the collectors between them to maintain tension in all members inside the triangle. Any errors in formation flying would be compensated by having a little bit of stretch in the members (say 1-2% = 10-20m) but if one engine fails the whole system fails.

    5. On the second point I would worry that moving parts heated to 4000K is a non-starter. The insane operating temperature range would result in massive thermal expansion and contraction of the materials even if it didn't fail from thermal stress. I think you could get away with it with a homogeneous drum but anything more complex than that would fail.

      I am sure it is a solvable problem but it is certainly challenging and potentially a source of unreliability.

    6. I chose structural steel specifically to demonstrate that even a relatively common material is sufficient to handle the forces involved here. With advanced materials, the structural requirements are entirely negligible.

      The design I am thinking of is a ring of lilypad-like structures handing onto a stem under tension. No compressive forces are involves anywhere. By lilypad, I mean a branching network of wires guided to attachment points from a central location, plus a series of 'guy lines' to handle the rotation and stabilization of the disks.

      They will focus onto one collector in the spaceship's central body or center of gravity.

      The high temperature working part issue is one that should be raised, but it is difficult to ascertain whether it is solvable or too much of a hassle to bother with the design at all. It is entirely an engineering problem, not a technological one. If the active cooling is performant enough, the 4000K temperature can be limited to just the inner surface of the drum in contact with the rhenium. It can be rapidly decreased until the outer surface of the drum is operating at safe or even mild temperatures of 1000K or lower. With the liquid hydrogen flow measured in tons, you have a massive heatsink able to handle all sorts of cooling needs.

  2. Seems like a great option for moving icy asteroids around, even if you have to use a boring lower temperature type.

    1. 'Boring lower temperature' can be 4400K using new materials such as THC. It still allows for 87% of the exhaust velocity of the 5800K liquid rhenium version.

  3. The performance and specs of the advanced version is far beyond I expected for a solar-powered spacecraft. Solar panel measured in square km can be made with that small weight is something I never imagine too.

    Sailing in sunlight (solar panel looks like sails, sort of) with panel of that size must be spectacular.

    You say a STR spacecraft can fly in outer solar system with lasers, can the ship do it without modifications?

    Matter Beam, after you mentioned the problems and I replied you in the discussion on G+, I find some new questions and it seems that they can’t be answered by things available on internet or source I can find.
    Can I send it to you?

    1. The very low mass of the solar collector is because it is a big piece of polished tin foil put on some graphene foam. Stronger than steel and lighter than a feather.

      If you find this spectacular then you should checkout "Breakthough Starshot"

      Depends on what kind of laser you use. If it is a infrared-visible light laser then yes, it doesn't need modifications.

      I believe matterbeam like to answer your questions.

    2. @Felix: A laser must be tuned to the range of wavelengths that the solar collector is designed for, so namely sunlight. This is very lenient requirement, as it covers everything for near-UV to infrared.

      You can always send me stuff.

      @OMG its WTF:

      Quite right.

  4. Fascinating post, I didn't thought it would be practical to use an liquid core without it being contained. Wouldn't it be possible to focus the light of the mirrors onto a transparent cooled quartz sphere filled with a high absoprptivity gas? The solar version of the nuclear light bulb. Using hydrogen exhaust velocities of 30km/s are possible. Comparable to some ion engines, but with MW/kg power levels.

    1. The high absorptivity gas cannot be hydrogen then, it would have to be seeded. Seeding the hydrogen removes its principal advantage, which is low molar mass. Also, the seeds cannot exceed their own boiling point, or else they become a rapidly expanding gas that doesn't absorb sunlight anymore.

      I don't see the quartz as helping.

    2. The high absorptivity gas isn't meant to be used as the exhaust. The gas is heated to dozens of kilokelvin, where it then starts to radiate gigawatts worth of power. Basically a nuclear thermal gas-core closed cycle, but instead of using an uranium gas it uses a solar heated high absorptivity gas. You could remove the quartz casing, which results in an isp of 5180 (hydrogen, NASA) and the loss of the high absorptivity gas.

    3. In the Closed-Cycle GNCR, hydrogen was seeded with carbon flakes so that the 'gigawatts of power' actually got absorbed by the hydrogen around the quartz bulbs. Without seeding, hydrogen would be nearly perfectly transparent.

      Another issue is that the maximum temperature of a solar-heated blackbody is 5800K. It cannot get hotter. This is why the liquid rhenium STR unlocks the 'maximum' performance possible.

    4. 5800K is the maximum temperature a solar heated black body can achieve with unfocesd sunlight, the mirrors will work as photonic heat pumps. What do you think is going happen if I focus 1TW onto an area of one square centimeter?

      How is the fact that the hydrogen was seeded an issue?

    5. Actually, a blackbody in unfocused sunlight will balance out at 1367W/m^2 received and 1367W/m^2 radiated. This is equivalent to 404K with an emissivity of 0.9.

      Focusing sunlight allows you to increase the temperature but only up to the point where the blackbody is re-emitting as much light back to the sun as it is receiving from it. The sun's surface is 5800-6000K according to sources, so no amount of concentration will increase a blackbody's temperature above that temperature.

      Hydrogen seeding is not an 'issue', its just something to be avoided if possible. When the major advantage the STR has over other near-future propulsion systems is its high Isp, you don't want to be cutting into it by lowering the molar mass of the exhaust gasses.

      One GCNR design I read about ( used 3.9% tungsten seeding by propellant density. I worked this out as 0.211kg/m^3, or 1.14 mol of tungsten. The hydrogen at 2g/mol is the remaining 96.1% and represents 2599.6 mol. The average molar mass after dissociation is reduced to (2599*2*1 + 1.14*184)/(2599*2 + 1.14): 1.04g.mol instead of the 1g/mol without seeding.

    6. Actually, a blackbody in unfocused sunlight will balance out at max at 529MW/m² received and 529MW/m² radiated. This is 5700K for an emmisivity of 0.9. 1367W/m² is only correct at earths distance, sunligh is object to the inverse square law, which means it's intensity increases as the distance decrease. 5700K is the temperature an object will achieve if it were a few centimeters away from the suns surface.

      This is correct, but temperature isn't the factor here, it is radiated power. If I had an 1km² mirror at the distance of mercury (9080W/m²) then I had a power of roughly 9GW with inefficiency losses. Foucused onto an area of 1m², at an emmisivity of 0.9 it will reach a temperature of 20500K, at that temperature it will radiate 9GW. At that point it will radiate at much light back to sun as it receives from it. Albeit at a higher average frequency.

      You said "another issue" indicating that what you said before was also an "issue".

      Good find, it is lower than I expected, I would have expected something along the lines of 1.15g/mol for an heavy metal like tungsten.

    7. As well, in the blog and unless stated otherwise, I always calculate for Earth orbit.

      For maximum temperature, here's a simple explanation I've found:

      Basically, the second law of thermodynamics prevents you from moving heat from a low temperature source to a high temperature sink without expending work. Lenses do not perform any work.

    8. The second law of thermodynamics...
      Entropy cannot decrease, entropy in a closed system can only remain constant or increase. Or so roughly. I am sorry, I have not thought that this decreases entropy globally, which is impossible.

    9. We all learn something new every day!
      Tell me, what type of blog posts do you want to see more often? Technology-focused posts? New tactical analysis of potential warfare? More worldbuilding of the sort I did in How to live on other planets? Or something more closely related to today's world instead?

    10. The thing I learned today is that I really should internalize the laws of thermodynamics properly, instead of the kinda superficial way it currently is, short: Nothing can escape the wrath of entropy, you can just put it under the carpet, but doing so produces even more entropy.

      Things more related today shouldn't really be a main element on ToughSF, it's main purpose should be to help out hard sci-fi writers with intersting and feasible concepts while also invoking interest in science. You can do them occasionally to add some fresh change into the mix.

      Technology focused blogs like this one and for example All the radiators make good reads and are often very interesting because of the unique concepts and technologies they include.

      The tactical analyses you often make are often unique and usually somewhat bizzare. But that adds to the character, in my opinion. They are usually fascinating.

      The How to live on other planets series is in my opinion on of the best series of posts on this entire blog. Wordbuilding is just very fascinating to me, especially in hard sci-fi where seeing all these concept you know of in interaction with another and how they affect live and its aspects.

      But this is just my silly opinion.

    11. No silly opinion here.

      Thanks for the input for the blog. I'm thinking of turning this all into a website (no ads) so that the earlier posts are just as accessible as the latest ones and the topics are easily navigable.

    12. "Tell me, what type of blog posts do you want to see more often?"

      On both this blog & on Rocketpunk Manifesto I tended to skim over the warfare in space posts. (I think that given the massive destructiveness of modern weapons, we get either something like the Democratic Peace idea or a world bombed back to pre-industrial conditions.) Otherwise I like most of what you are doing. I think you missed an important world in the 'How to live on other planets series' ie: the moon.

      "I'm thinking of turning this all into a website (no ads) so that the earlier posts are just as accessible as the latest ones and the topics are easily navigable."

      Good idea. I like the way this guy did that for a completely different set of topics. He set up his topics index & also a blog page that just gives links to his writings with the most recent at the top of the page.

    13. The Moon is pretty much directly linked to the Earth in any setting that allows for high-volume, high-frequency interplanetary transport. This would require me to heavily speculate on the future of Earth and how it would influence development of the Moon... something I'd like avoid in the 'How to Live on Other Planets' series.

      Interesting opinions, that Mark Humphrys guy has. My idea is a website more like this: Visually appealing, possibly with a forum section for in-depth debates.

    14. Humphrys day job is working on Artificial Intelligence. On another website he has this page:
      see especially his claim that AI is possible...but AI won't happen.

    15. His day job is working with soft AI, programs that are capable of taking
      intelligent decisions given the data fed to them. But they aren't hard AI,
      the real AI, a machine with a mind.

      These ideas of hard AI are always pure speculation, like a scientist from the 19ยบ century trying to understand nuclear fusion in the sun. So please don't take them seriously. I also work in the AI field.

      Point is, we don't know how our consciousness works, how our mind works
      detailed enough to try to create a model for it. Any idea about it has no scientific foundation, any conjecture or proof only holds based on your own assumptions, it is philosophical.

      Unless you believe we humans have a soul, hard AI is possible and will
      eventually happen. His arguments about a AI needing to develop a culture
      and society is pretty far fetched, but not a new idea. There were tries
      to apply this concept in real AI projects, take the cog project for

      Personally in my vision, a real hard AI program would be like a assistant, not much different from the ones we have today, but capable to solve the full range of problems as we are. But in practice, it wouldn't be very useful as many claim.

      The idea of an Singularity is also very far fetched just like the idea of nano gray goo, ignoring technologic capabilities and thermodynamics.

  5. An astounding idea!
    I too have some concerns about it:
    First, the Rhenium drum have to have vertical walls from both ends to prevent the molting Rhenium from spill over due to the centrifugal force. The 'upper' ends of the walls, the closer to the axis, will be in contact with the top layer of the molten which is the hottest.
    Preventing it from melting will be a challenge, sure you could provide cooling fluid in those walls too but those now have to cool down even hotter surfaces.
    Second, how do you cool down the transparent window? All other surfaces in that chamber, both fix and rotating could be cooled using backside coolant pipes but how do you run coolants inside transparent material without blocking the entering concentrated sunlight? The inner side of the window will be in contact with the hot hydrogen gas, constantly.


    1. Hi Yoel and welcome to the blog.
      If you look at the drum wall close-up, you will notice that the basin the rhenium sits in is curved towards the top and bottom.

      Cooling down hotter surfaces is easier than cooling down colder surfaces. The hydrogen you are using as a coolant and an expendable heatsink receives heat more rapidly (higher temperature gradient) and absorbs more heat per kg (heat capacity proportional to temperature).

      The transparent window can be made more than 95% transparent to sunlight, so it only absorbs a fraction of the sunlight passing through it. That fraction can be removed by active cooling - hydrogen is very transparent to sunlight and you can run it through the window to remove heat without blocking the light. This technique was used to cool the fused quartz 'lightbulbs' in a closed-cycle gas core nuclear reactor.

  6. This is quite fascinating. It also makes some other ideas far more feasible, such as Anthony Zuppero's water rockets. The idea explored in the NEOFuel site (link to the paper here:, but increasing the temperature and exhaust velocity should dramatically reduce the amount of water being boiled away as reaction mass.

    OTOH, I am always a bit disturbed by the "Rube Goldberg" light pathways needed for these systems. I am a big fan of Leik Myrabo's "Lightships" with their rather simple reflection paths (the bottom of the ship is a ring shaped parabolic mirror in most cases, focusing the laser light into an intense donut shaped focal point where air explodes into plasma in the ground launched versions). Since Hydrogen is very transparent this trick won't work, but if this sort of reflector is used in conjunction with a laser or huge solar reflectors, and injecting water or nitrogen into the focal ring should provide similar performance. If it can produce this level of performance, then we have actually eliminated the heavy rotating drum and heat exchanger (but now the challenge is to get sufficient sunlight into the parabolic mirror when your thrust line is not pointed directly at the sun or laser emitter). I will have to leave this to the much smarter people in the room.

    1. Thanks Thucydides.
      4.9km/s exhaust velocity with complete dissociation of water molecules is pretty good. For lower deltaV trips, the reduction in propellant tank mass, engine thrust requirements and solar power collector area might offset the lower exhaust velocity compared to hydrogen.

      The drum with 5800K inner surface can have an extreme power density coupled with very high thermal conduction rate into the propellant. You need a concentration factor of 49433 to achieve a temperature of 5800K, so an inner surface of 1m^2 will be illuminated by at least 49433m^2 of solar collector.

  7. Based on the discussion so far, I can envision the spaceship having a huge parabolic reflector attached by thin compression struts on the "bow", and the ship itself being a hollow cylinder with the lightpath leading to the heat exchanger mechanism in the stern. I'm picturing a sphere which can be rotated about all three axis so the exhaust nozzle can be vectored the right direction. (there is obviously going to be more to the ship than that, but this gives modellers a rough outline to work with). A somewhat different approach would be to have the ship's living/working area/fuel in a torus which lines the edge of the reflector, so there is a clear path to the heat exchanger/engine.

    In a way this is a bit like a solar sail, except the structure is rigid in compression rather than tension.

    1. I didn't want to sound too shrill earlier but I really must emphasise that 1km long compression members can never be 'Thin'. Thin-walled maybe but they must have a certain width or their effective compressive strength will tend towards zero.

      The link below explains in far too much technical detail:

      I could work out with more precision how wide the compression struts would need to be based on a more exact design but it will be in the same order of magnitude as my original estimate of 30m for a 1km long strut.

      Likewise a parachute type structure behind the ship has no drag to keep it open so will collapse into a 1 dimensional shape as soon as you accelerate.

      The only way to keep a structure that large in its (very precise) shape under acceleration would be to use more material or do it actively with thrusters or magnetic fields. Milli g accelerations may work out differently but the numbers start to move away from the usual back of envelope calculations in that case!

    2. @Thucydides:
      I tend to avoid large hollow structures. They are structurally very weak. I believe the simplest and most practical configuration is one where several concentrators are able to be focused on a single engine that is mounted on the back of a conventional cylindrical hull. This requires mounting the concentrators just like solar panels today: on swivelling mounts, that can track the sun irrespective of the spaceship's direction.

      I see the concentrators are large disks with a fixed subreflector. The subreflector can angle the focused sunlight sideways onto the target on the spaceship. It will resemble a TV dish. Because sunlight is unfocused near the main sunlight dish, we can mount struts or wires directly across and in front of the reflective surfaces. This allows us to create a tension structure with zero compressed elements: perhaps a hub pulling a web of wires in a disk, forming a pyramid, with the reflective surfaces drawn between the points on the disk, plus second set of wires that pull the disk into a parabola, and finally a third set of wires connected directly to the spaceship and attached to various points on the disk, allowing the entire assembly to be rotated. The moving wires will go from spaceship to the disk and then through the hub.

      I am struggling to find an image which shows what am am describing well, but I think visually it will resemble a cross between the millennium dome, a bicycle wheel and a lantern shade.

      @hcrof: Good point. Just note that the collector does not have to be a single massive disk. It can be divided into multiple smaller disks.

      For example, the modern STR described above has a collection area of 714285m^2. This can be a single disk of 953m in diameter... or eight smaller disks in a ring, each of only 337m in diameter. If wanted to go even smaller, I can imagine a spaceship using a stepped pyramid arrangement of small disks placed at further and further distances from the central axis. Three levels of 4, 9 and 16 concentrators, each of 177m in diameter.

    3. Matter Beam, a bicycle wheel uses wires in tension, but the rim is in compression. Having said that, a curved compression member can be more slender than a straight one as long as it is evenly loaded across its whole length. There is no rule of thumb for this but it can be determined with a spreadsheet (or geometrically if you are old-fashioned!).

      I think one big collector would be most efficient if you want to use a passive structure. You would have an inflated rim made of the same material as your collector surface and the internal pressure will prevent it from collapsing. This is because the larger circle means the edge to surface ratio is the lowest so you use the least material. Your rate of acceleration would be the largest factor determining the internal pressure of the tube - I imagine this would be a non-linear relationship as there are quite a few variables but a spreadsheet could optimise it. I would suggest compartmentalising the tube at the support points as this will mean the extra material on the bulkhead will also help resist the point loads from the support wires.

      If you want to go really big I would still suggest using small thruster drones or magnetic fields to support your rim as you will end up saving mass.

    4. Sorry, it is hard to explain. It looks like a bicycle wheel (hubs wire wire-spokes) but the rim is maintained by 3-axis tension. There's a wire loop from hub to rim to stem pulling the rim nodes outwards, then two L-shaped bends pulling in opposite directions from left and right.

    5. Here is something that may interest you:

      So, maybe have a two fer--extract some direct electricity from this clear layer (fresnel lens?) and have remaining light heat the solar thermal part.

    6. @Anonymous:
      The clear layer works by extracting energy from the solar wavelengths that we cannot see, so it blocks infrared and ultraviolet but lets the visible wavelengths through.

      However, the solar panel can only be at most 42% efficient. The solar thermal rocket is 90%+ efficient. Every watt of energy that is absorbed to produce electricity could have been better used in the engine.

      Finally, the solar collectors I describe are based on solar sails which mass a few grams per square meter. Transparent solar panels would require another layer on top which would mass ten kilograms per square meter or more. That's a ten thousand fold increase in the mass!

  8. It occurs to me that this is another piece of the puzzle in my version of a PMF setting. Rockets like this will be very useful within the area bounded by the "Solar economy", but once you get past Mars, the ever increasing size of the solar collectors start imposing a mass penalty. Alternatively, you could start around Earth with a suitable collector, but discover you no longer can generate enough power once you get to Mars unless you can deploy extra collectors or beam energy to the current unfurled collectors. (I will have to look up the figures, but I believe you only receive @ half the insolation at Mars as you do in Earth orbit).

    Still, for an inexpensive "fast packet" for moving around the inner solar system something like this seems quite doable.

    1. Well, even with the more 'traditional' 4500K solid heat exchanger STR, we can match the performance of nuclear thermal rockets. That's a massive bonus for the inner solar system.

      If an STR can achieve 1MW/kg at Earth orbit, it will still have an impressive 10kW/kg at Saturn orbit. Maybe our definition of 'inner' solar system is too restrictive...

      The worked example for the advanced STR @928kW/kg at Earth orbit would maintain a power density of 1.02kW/kg at NEPTUNE's orbit.

      Expanding the solar collectors is a good option as they are so lightweight compared to the machinery that handles their power. Deploying 10x more solar collector area at Saturn orbit would require only 45 tons more of collectors, but no more propulsion mass.

      Or, nuclear/laser hybrids could be used. The heat exchanger can accept heat from a nuclear reactor, especially if TaHC-encapsulated fuel is used. Or, the solar collectors can focus a visual-wavelength laser. It might not be too much of a stretch to assume all three heat sources can be used.

  9. Why not simply make use of a liquid core nuclear thermal rocket like LARS?
    They can provide specific impulses up to 2000 sec with a very high energy density.
    They might need radiators, but can provide a good amount of thrust and can work anywhere in the solar system, independent of the sun.

    1. The point of this blog post (and the following two 'Advanced Solar Energy in Space') was to demonstrate that nuclear energy is not the only option for high powered rockets.

    2. I see, it is interesting.
      Although the large solar collectors still bug me as the reduction of power as you go away from the sun. Which are not problems faced by NTRs.
      I also read you posts about generating electrical power with solar energy, and the numbers don't look very good compared with this thermal rocket.

      As I can see, nuclear thermal rockets still look like a more flexible approach compared with solar energy based ones.
      And again, very good discussion.

    3. Well, solar collectors only need to reflect sunlight and focus it onto a spot. They can be extremely lightweight, like solar sails (1-10 grams per square meter).

      Therefore, increasing the solar collector area to capture the same amount of sunlight is very 'cheap' in terms of extra mass required.

      The advantage of this solar thermal rocket is high exhaust velocity, power density and efficiency. However, it still cannot compare to an electric engine fed by solar panels providing an exhaust velocity two, three or ten times greater.

      Solar-electric propulsion might be slow, heavy and inefficient, but when you need a lot of deltaV out of a small rocket, they are the only option.

      Nuclear electric is the other option, of course.

    4. After reading several papers and NASA reports about research with SEP and NEP systems, I reached a conclusion. Unless you can get some really high levels of power, several MWs for probes and hundreds of MWs for manned spacecraft, with good energy density, which allow you to accelerate faster than the time required for a minimum Hohmann transfer trajectory, the extra ISP isn't really worth it. You expend more time accelerating than if you take a full Hohmann trajectory.

      It might help to economize fuel, for instance like in cargo transfers, which don’t have tight time constraints, but on missions where time is crucial, SEP and NEP systems tend to lack performance. They make mission planning difficult (good point for sci-fy), spacecraft tend to be heavy, not with fuel, but with power equipment.

      So from several concepts designed by NASA, I’m tend to be very skeptical about SEP and NEP, they tend to be very cumbersome when you compute all the numbers like vehicle mass, fuel mass, gravity losses, constant low acceleration trajectory and so on. As a rule of thumb, I tend to consider systems that can achieve acceleration of over 1 hundredth of a g, this is very hard to achieve with SEP or NEP.

      Electric propulsion systems in general aren’t really that better than thermal propulsion systems as the higher ISP might make us think. This is based on real mission concepts.

  10. Hi matterbeam, Love your blog. I am similar to you, When I have an idea, I love to calc the numbers and try to extract the best of it checking each technology or materials to accomplish that.
    With respect the solar thermal rocket, my doubts are on the solar sail reflectors.. First, they seem to big to be practical, second I guess the reflection of aluminum without passing a glass, would be something diffusive, which would reduce the efficiency.
    With respect the main propellant choice, liquid hydrogen is just fine, anything else at those scales would be really bad.
    Because in this case you can exploit the volume-surface relation which it is very usefull at large scales. Because your benefits (capacity) increase 2 times faster than your problems (tank surface mass and insulation), so you reach a point were they are negligible.
    Still, as transport method between venus, earth or mars, I would choose just solar sails (for cargo) because the diffuse reflection it is not a big problem here and to transport people, I would just use Rockets. Maybe capturing asteroids to be used as fuel depots.

    1. Thank you, AngelLestat.
      That impulse, to go do the maths and find out the science behind everything cool in science fiction, is the foundation for this blog.

      My numbers for the solar reflectors are based on reports for actual sunlight collection devices in space from the NASA Technical Reports Server (NTRS:, such as this one:
      Solid, hexagonal, aluminium mirrors are used.

      Solar sails, which only use the pressure of sunlight, are very very slow. If you are transporting cargo, then how long it takes to deliver something can be seen as a cost. If it costs less to add a large hydrogen tank and use solar thermal propulsion, than to use solar sail propulsion and wait, then solar thermal will be used!

      Capturing asteroids is another manner. The propellant mass you'd need would be incredibly huge. It makes more sense to use solar sails in that case, as even if they have very poor performance, they can work for years on end.

  11. As someone who has advocated for solar thermal rocket propulsion for a very long time I must commend you for this innovative design which as far as I know is the first to achieve in principal the highest possible performance for a STR.
    I wonder if the dissociated hydrogen atoms will recombine to a significant extent as the pressure increases in the nozzle and whether this release of heat could have a positive effect on exhaust velocity?
    Also some percentage of the hydrogen will ionize at these temperatures won't it? This could also add heat perhaps as the electrons recombine.In addition the electrical energy needed to more fully ionize the hydrogen is reduced compared to unheated hydrogen and this suggests that the addition of a downstream MPD or other electric propulsion system for additional acceleration in the coast phase of a Mars trip.
    As for electric power the use of triple junction cell able to handle high solar concentrations at efficiencies approaching 50% would seem appropriate. The cooling required can be reduced by splitting the incident light into its constituent wavelengths and arranging things so only the exact wavelengths used by the PV illuminate it.

    1. Thank you.
      Hydrogen should be fully ionized at 3300K, so I expect it to be the same at 5800-5900K.
      Recombination will not reduce exhaust velocity much, because it happens at the lower pressures and temperatures near the exit of the nozzle.
      The use of an electric 'booster' for the hydrogen is an interesting idea - I shall investigate it.

  12. Just want to add to my comment above that using a diffraction grating or prism or whatever to split the concentrated sunlight into its wavelengths raises the possibility of using the wavelengths that are not useful to the PV to heat the hydrogen in the STR. In this way most of the overall energy is used. For higher Isp the need for electrical energy would dominate but there should be an exhaust velocity that would use all the non PV wavelengths energy and all the PV electricity energy (minus efficiency loss of course) that would give a modest Isp increase. The PV itself is able to efficiently operate at nearly 100 Suns do the mass penalty per unit power is low compared to almost any other electric power generation system with the caveat that it requires cooling as efficiency drops off over 100 deg.C. This is presumably greatly reduced if only useful wavelengths strike the PV.
    Steve Mickler

    1. Steve,
      I think you will find my 'Advanced Solar Energy in Space' blog posts very interesting!

  13. I have no expertise here and have not studied this, but I looked at occasionally for at least a few months. That gave me one idea a while ago, and reading today gave me another idea, so I decided to comment here.


    Do you have any thoughts on "pulsed solar thermal" as a compromise between your proposal and a heating element that remains solid?
    (inspired by the section you can find by searching for "is pulsed" at .)
    i.e., alternating between heating part of the tungsten-or-whatever to above its melting point and letting it re-solidify, while running the propellant over it when it is at high temperature and not running propellant over it when it is at low temperature.


    Sticking with the hydrogen being heated by something that remains liquid, could one use a magnetohydrodynamic impeller to spin the rhenium, rather than a rotating drum?
    (You mentioned the impeller idea at , and the magnetohydrodynamics idea is from the section you can find be searching for "MHD-Driven" at .)

    1. Hi Eric!

      a- A pulsed device would be useful if the solar collector area or if the concentrating optics were too small to maintain a 5800K surface temperature. Remember, over 48,000 m^2 of collector is needed to heat up 1 m^2 of rhenium to 5800K. You won't get higher temperatures with this method, and your average Isp will be lower (because temperatures will drop between the beginning and end of the pulse), but it avoids the need for huge propulsion systems.

      You will probably end up cycling between 5000K and 5800K or something like that, instead of operating around rhenium's far lower 3460K melting point.

      b- Ideally, you want the drum walls and the tungsten fluid to be rotating together. This means that there will be nearly no friction between the walls and the fluid, so there is less chance for turbulence and waves to disrupt your fluids. However, this requires that the drum be mounted on rotating bearings with lubrication that can survive 4000K temperatures, or uses heavy magnetic levitation. You would use the MHD impeller only if the rotating drum design is too complicated or impractical to do.

  14. There are 1800K temperature differentials within the liquid rhenium, both axial (because of the THC 'lip' at top and bottom) and azimuthal. How sure are you that these could be maintained without infeasibly increasing solar collection and cooling requirements? It seems like a losing battle to constantly heat and cool opposite sides of a fluid to maintain a differential like that.

    1. Hello Kyle.
      It might look like a losing battle at first glance, but remember that the hot hydrogen leaving the walls is recycled back into the heating chamber. The energy absorbed from the walls is retained and used to improve overall efficiency.

      All that matters is that the heat absorption capacity of the hydrogen flowing through the walls matches the heat reaching the liquid rhenium layer; as long as those are balanced, the temperatures do not increase. All that is required is that the hydrogen pumps match the sunlight being received.