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Liquid Rhenium Solar Thermal Rocket


MatterBeam
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Hi! I've got something new for y'all!

Liquid Rhenium Solar Thermal Rocket

 
The maximum temperature concentrated sunlight can heat a material to is 5800K. How do we approach this limit?
tarokt23.jpg
We will describe existing and potential designs for solar thermal rockets. 
Solar thermal rockets
sotvlg.jpg
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. 
laserThermal04.jpg
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%. 
 
Exhaust velocity will be determined by the root mean square velocity of the gas the propellant turns into. The equation is:
 
  • Exhaust velocity: (3 * R * Temperature * 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. 
 
These advantages are all the critical elements that allow for travel throughout the inner solar system without requiring vast quantities of propellant. This means 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. A single millimeter-sized carbon dust particle in a cubic meter of hydrogen increases the molar mass from 1g/mol to 
 
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. 
ceramic_protective_coatings_09.jpg
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.
rhenium.jpg
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:
RD-FHE%2BSolar%2BThermal.jpg
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:
Bubble%2Bwall.png
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. 
pebbleBed04.jpg
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. 

Operation

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%2Bpressure.png
Vapor pressure of rhenium at 5800K (0.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. 
hfVCRLightBulbFission.jpg
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 mixhas very similar thermal properties and is much cheaper.
Aluminium.png
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.
solarMoth12.jpg
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. 

Performance
rap02.jpg
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.
a41f726b0511168326d02a.jpg
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. 
missiontable02.jpg
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. 
marsonehabitat.jpg
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.
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OK so here is the deal, lets take this by the numbers. Watts are good but ISP is mediocre, infrastructure is massive.

12km/sec is exhaust velocity, seemingly good except its much less than an ION drive and not much better than a NTR.

Ion drives run from about 3500 to a practical 10,000.

Lets say half the rocket is fuel. from this we have dV=12000*ln(Sm/fm) in this case 12000 ln2 = 8317 m/s.

Second problem, like all solar driven ION drives this drives performance drops with distance from sun.

Third problem, you see the poles, the also have to be accelerated, but those poles are not secured, as you apply thrust they move and are less efficient.

Forth, 20 minute burn time from earth, yeah . . . .right.

For a 150000 ton system and 12000 m/s ev. Lets see launch to mars in 20 minutes needing 7000 dv. That translates into  5.8333N/kg

5.83333N * 125000 average load needs a thrust around 700,000 Newtons.

So in essence solar power generates maximum 1350 Watts per meter squared. Next the Power transferance rate is

= 2 * watts *efficiency/EV so to get 700,000 N you need 700,000 x 12000 / (2 * efficiency = 1.6) = 5250000 Kilowatts

requiring 3,888,888 meters of solar collector.

 

Since most of the world plays soccer you might know that a soccer (futbol) pitch is minimally 6400 square meters. So that the area covered by the panels would be equal to

 

607,000 soccer pitches. To create these semispherical collectors you need a rigid mess and a reflective material. lets say the plastic is a thin 5 mil, about 0.00013 meter thickness. Assuming the plastic has a density of 1.2 (adding some density for metalic reflectant) the mass per meter would be about  0.153 kg per sq. meter. So that doing 595,000 kg (not 50,000 as the authors suggest).  5 mil is a good choice because of the forces involved in traveling in LEO, where there is significant heat from drag and at least some drag forces. The authors have chosen 5 um  mylar sheets. The problem is that this sheeting is about 1/5th of a mil which is several fold thinner than the cheapest painters plaster (something like 3 mil). We havent even gotten to the rigid infrastructure to hold the plastic.

On top of this 600,000 soccer pitches, thats a hell of alot of hv pressure to deal with, combine that with LEO to MEO drag and you have a wonderful application of murphy's law, Everything that can go wrong did go wrong. I could imagine this craft positioning itself getting hit by the sun slowing down  orbit decaying, drag sets in, sheets melt the space craft spinning uncontrollably as it hits earths atmosphere burning up 100,000 kgs of payload streaking through the sky.

 

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1 hour ago, PB666 said:

OK so here is the deal, lets take this by the numbers. Watts are good but ISP is mediocre, infrastructure is massive.

12km/sec is exhaust velocity, seemingly good except its much less than an ION drive and not much better than a NTR.

Ion drives run from about 3500 to a practical 10,000.

Lets say half the rocket is fuel. from this we have dV=12000*ln(Sm/fm) in this case 12000 ln2 = 8317 m/s.

Second problem, like all solar driven ION drives this drives performance drops with distance from sun.

Third problem, you see the poles, the also have to be accelerated, but those poles are not secured, as you apply thrust they move and are less efficient.

Forth, 20 minute burn time from earth, yeah . . . .right.

For a 150000 ton system and 12000 m/s ev. Lets see launch to mars in 20 minutes needing 7000 dv. That translates into  5.8333N/kg

5.83333N * 125000 average load needs a thrust around 700,000 Newtons.

So in essence solar power generates maximum 1350 Watts per meter squared. Next the Power transferance rate is

= 2 * watts *efficiency/EV so to get 700,000 N you need 700,000 x 12000 / (2 * efficiency = 1.6) = 5250000 Kilowatts

requiring 3,888,888 meters of solar collector.

 

Since most of the world plays soccer you might know that a soccer (futbol) pitch is minimally 6400 square meters. So that the area covered by the panels would be equal to

 

607,000 soccer pitches. To create these semispherical collectors you need a rigid mess and a reflective material. lets say the plastic is a thin 5 mil, about 0.00013 meter thickness. Assuming the plastic has a density of 1.2 (adding some density for metalic reflectant) the mass per meter would be about  0.153 kg per sq. meter. So that doing 595,000 kg (not 50,000 as the authors suggest).  5 mil is a good choice because of the forces involved in traveling in LEO, where there is significant heat from drag and at least some drag forces. The authors have chosen 5 um  mylar sheets. The problem is that this sheeting is about 1/5th of a mil which is several fold thinner than the cheapest painters plaster (something like 3 mil). We havent even gotten to the rigid infrastructure to hold the plastic.

On top of this 600,000 soccer pitches, thats a hell of alot of hv pressure to deal with, combine that with LEO to MEO drag and you have a wonderful application of murphy's law, Everything that can go wrong did go wrong. I could imagine this craft positioning itself getting hit by the sun slowing down  orbit decaying, drag sets in, sheets melt the space craft spinning uncontrollably as it hits earths atmosphere burning up 100,000 kgs of payload streaking through the sky.

 

Thank you for taking the time to calculate your own numbers!

I mentioned in the blog post that the mass ratio gains from increasing your exhaust velocity is exponential, so every little bit helps. One practical advantage I did not want to elaborate in the blog post is the fact that STRs do not face the nuclear controversy that NTRs do. I also mentioned that STRs can have very good power to weight ratios, especially when compared to anemic solar-electric rockets. This makes them practical for human spaceflight, as you don't want your crew spending weeks spiralling our of low orbit and being blasted full-on by Van Allen Belt radiation. STRs can accelerate quickly enough to gain a meaningful boost from the Oberth effect too!

I am not sure what you mean by the 'poles', but maybe you mean the structural support for the mirrors in the images I posted? They could be a problem, but I did state that we will be basing our designs on the lessons from solar sail development. This means lightweight distributed structures that are held in place by tension and centripetal force. At 7g/m, a Mylar sheet only has to endure a force of 0.068 Newtons even when accelerating at a full 1g. The structural requirements of handling 0.068 Newtons per square meter of area are tiny! 

The 20 minute figure was achieved by dividing the ~3.5km/s departure burn for a Mars mission by the 0.32g average acceleration of the STR being discussed in that example.

I am not sure where you got the 150000 ton figure from. 

The power calculations I used are as follows:

7g/m^2 for a modern Solar Collector dish. 1367W/m^2 of sunlight received. 1298W/m^2 is focused into the engine. Engine efficiency is 80%. Engine power density of 167kW/kg to handle the sunlight input.

With these figures, I calculated the thrust as Power * 2/Exhaust Velocity. Divide the thrust by the total or average mass of spacecraft and you get initial and average acceleration.

A 5 ton modern Solar collector dish would have an area of 714285m^2. This is a disk 953m in diameter. It collects 976MW of sunlight, and reflects 927MW into the engine. The thrust is therefore 123.4kN. 

A more advanced STR can have even better performance.

The failure scenario you described can happen with every single spaceship, just replace 'sheets melt' with 'engine failure' or other examples. 

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1 hour ago, PB666 said:

OK so here is the deal, lets take this by the numbers. Watts are good but ISP is mediocre, infrastructure is massive.

Efficiency is mediocre.  Isp does not include "dry mass".

"The maximum temperature concentrated sunlight can heat a material to is 5800K. How do we approach this limit?"

I suspect that to achieve this, the ratio of the size of the lens to the size of the target is similar to the ratio of the sky covered by the Sun.  I also suspect that hitting those levels of temperature won't make sense.  You want to take advantage of large amounts of stretched thin films which are unlikely to maintain accurate curves.  The final product is unlikely to focus well, but should be able to use easily available reaction mass (comets would be a good start).

I'm also suspicious of that Earth-Mars escape-capture plan.  I'd have to assume the bulk of the journey is matching Mars velocity (unlike standard Hohmann transfers).  Judging by the length of the "burn" to escape Earth, I'd expect the thing to sail clean past Mars and not spiral in as shown.

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2 minutes ago, wumpus said:

Efficiency is mediocre.  Isp does not include "dry mass".

"The maximum temperature concentrated sunlight can heat a material to is 5800K. How do we approach this limit?"

I suspect that to achieve this, the ratio of the size of the lens to the size of the target is similar to the ratio of the sky covered by the Sun.  I also suspect that hitting those levels of temperature won't make sense.  You want to take advantage of large amounts of stretched thin films which are unlikely to maintain accurate curves.  The final product is unlikely to focus well, but should be able to use easily available reaction mass (comets would be a good start).

I'm also suspicious of that Earth-Mars escape-capture plan.  I'd have to assume the bulk of the journey is matching Mars velocity (unlike standard Hohmann transfers).  Judging by the length of the "burn" to escape Earth, I'd expect the thing to sail clean past Mars and not spiral in as shown.

I'm not sure what you mean by your first line. 
The liquid rhenium at high temperatures is a near perfect blackbody. It is radiating at 5800K, so that's 64MW/m^2. The solar collectors are taking in 1298W/m^2, so you'd need a concentration factor of 49433.

You make a good point about the parabola. The focal length will be quite long - multiple 'corrective' reflectors and lens will be needed to direct the beam into the small opening of a Solar Thermal Rocket.

The Earth-Mars escape capture plan? Are you referring to one of the images I used? They are generally for illustrative purposes, especially when not captioned. 

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2 hours ago, wumpus said:

Efficiency is mediocre.  Isp does not include "dry mass".

"The maximum temperature concentrated sunlight can heat a material to is 5800K. How do we approach this limit?"

I suspect that to achieve this, the ratio of the size of the lens to the size of the target is similar to the ratio of the sky covered by the Sun.  I also suspect that hitting those levels of temperature won't make sense.  You want to take advantage of large amounts of stretched thin films which are unlikely to maintain accurate curves.  The final product is unlikely to focus well, but should be able to use easily available reaction mass (comets would be a good start).

I'm also suspicious of that Earth-Mars escape-capture plan.  I'd have to assume the bulk of the journey is matching Mars velocity (unlike standard Hohmann transfers).  Judging by the length of the "burn" to escape Earth, I'd expect the thing to sail clean past Mars and not spiral in as shown.

The amount of energy derived by the sun at any given distance from the sun is 2.5E25/r2 w/m2

He would not spiral past mars. The rate of acceleration is low, 6000/1200 seconds is 5N/kg  For comparison at Launch a typical rocket is producing 14 N/kg and it goes all the way to 20 N/kg at max Q.

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2 hours ago, MatterBeam said:

Thank you for taking the time to calculate your own numbers!

I mentioned in the blog post that the mass ratio gains from increasing your exhaust velocity is exponential, so every little bit helps. One practical advantage I did not want to elaborate in the blog post is the fact that STRs do not face the nuclear controversy that NTRs do. I also mentioned that STRs can have very good power to weight ratios, especially when compared to anemic solar-electric rockets. This makes them practical for human spaceflight, as you don't want your crew spending weeks spiralling our of low orbit and being blasted full-on by Van Allen Belt radiation. STRs can accelerate quickly enough to gain a meaningful boost from the Oberth effect too!

I am not sure what you mean by the 'poles', but maybe you mean the structural support for the mirrors in the images I posted? They could be a problem, but I did state that we will be basing our designs on the lessons from solar sail development. This means lightweight distributed structures that are held in place by tension and centripetal force. At 7g/m, a Mylar sheet only has to endure a force of 0.068 Newtons even when accelerating at a full 1g. The structural requirements of handling 0.068 Newtons per square meter of area are tiny! 

The 20 minute figure was achieved by dividing the ~3.5km/s departure burn for a Mars mission by the 0.32g average acceleration of the STR being discussed in that example.

I am not sure where you got the 150000 ton figure from. 

The power calculations I used are as follows:

7g/m^2 for a modern Solar Collector dish. 1367W/m^2 of sunlight received. 1298W/m^2 is focused into the engine. Engine efficiency is 80%. Engine power density of 167kW/kg to handle the sunlight input.

With these figures, I calculated the thrust as Power * 2/Exhaust Velocity. Divide the thrust by the total or average mass of spacecraft and you get initial and average acceleration.

A 5 ton modern Solar collector dish would have an area of 714285m^2. This is a disk 953m in diameter. It collects 976MW of sunlight, and reflects 927MW into the engine. The thrust is therefore 123.4kN. 

A more advanced STR can have even better performance.

The failure scenario you described can happen with every single spaceship, just replace 'sheets melt' with 'engine failure' or other examples. 

150000 ton was an error, I use kg in the calculations, no problem.

There is also thermal loss on the engine in the form or radiation, at 5800'C you are talking about fairly intense light producer (yellow green). 

The way to calculate is to take your Energry transfer (1298) and the apply the efficiency from that. The correct and accepted equations is Thrust (N) = 2 * power(watts) * efficiency(%) / Ve (m/s)

The ISP is mediocre for external power driven space craft. Although ION drives  are critically limited in thrust, their advantage is high ISP. They are a technology in wait of a decent power supply

(like a fusion power plant or matter/antimatter reactor (lol)). The technology you list is an external power plant in search of a more efficient engine. 

Finally, what type of material can form a nozzel that remains stable at 5800'?

 

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11 hours ago, PB666 said:

The amount of energy derived by the sun at any given distance from the sun is 2.5E25/r2 w/m2

He would not spiral past mars. The rate of acceleration is low, 6000/1200 seconds is 5N/kg  For comparison at Launch a typical rocket is producing 14 N/kg and it goes all the way to 20 N/kg at max Q.

What? I calculated the acceleration of the example ships at 0.32 and 3.1 gravities. Thrust per kg is just another term for thrust-to-weight ratio, that I calculated. 

11 hours ago, PB666 said:

150000 ton was an error, I use kg in the calculations, no problem.

There is also thermal loss on the engine in the form or radiation, at 5800'C you are talking about fairly intense light producer (yellow green). 

The way to calculate is to take your Energry transfer (1298) and the apply the efficiency from that. The correct and accepted equations is Thrust (N) = 2 * power(watts) * efficiency(%) / Ve (m/s)

The ISP is mediocre for external power driven space craft. Although ION drives  are critically limited in thrust, their advantage is high ISP. They are a technology in wait of a decent power supply

(like a fusion power plant or matter/antimatter reactor (lol)). The technology you list is an external power plant in search of a more efficient engine. 

Finally, what type of material can form a nozzel that remains stable at 5800'?

 

The engine is a narrow cylinder. Radiations from the internal surface mostly fall back on the internal surface. Light can only escape from the optical window on top and the nozzle opening at the bottom, which represent a small fraction of the radiating surface area. 

The 1298 is the number of watts per square meter of collector area, so the thrust calculation you made is actually in Newtons per square meter. 

The Isp at 1224 is more than enough to travel around the solar system at a rapid rate. Two months to Mars without needed massive propellant tanks, no need for a nuclear reactor or nuclear rockets, no need for a laser - just sunlight. 

There is also an evolution of the Solar Thermal Rocket possible: the Solar ThermoElectric rocket. Concentrated sunlight can be used as a heat source for a high-temperature Carnot cycle electrical generator. With a gas turbine and a 5800K heat source, we can convert 70% or more of the solar power collected into electricity. This electricity can then be used to power electric rockets. For example, the 5 ton solar collector mentioned in the blog could be feeding the 927MW of heat into a gas turbine and making 648MW of electricity out of that. It is enough to make a 3000 Isp electric engine produce 44kN.

The nozzle material would have to be a temperature resistant material such as THC that is actively cooled by liquid hydrogen. High operating temperature means massive amounts of heat from the nozzle can be absorbed by the hydrogen. At 3000K, the hydrogen that starts at 20K absorbs 60MJ/kg, and we have nearly a ton of hydrogen per second to use for active cooling of both the rotating drum and the nozzle. 

11 hours ago, 0111narwhalz said:

Would the remass be sufficiently ionized by heat to be directed with a magnetic nozzle?

A magnetic nozzle isn't necessary here.

5 hours ago, cfds said:

5800K corresponds to roughly 0.5 eV. Certainly not enough to ionize stuff like either noble gases or hydrogen.

Quite right. 

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Is nobody going to mention the cooling system for the focusing optics? Bringing up the nozzle was a good point, but that is the bigger elephant in the room, I think. I mean, at the initial reflectors, the energy density is low enough, but the final mirror focusing on the drum is going to be quite toasty in no time, if only because it is sitting right next to the 4,500K drum, never mind the operating requirements.

 

Rune. Some parts of the engine do have to remain solid, after all.

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18 minutes ago, Rune said:

Is nobody going to mention the cooling system for the focusing optics? Bringing up the nozzle was a good point, but that is the bigger elephant in the room, I think. I mean, at the initial reflectors, the energy density is low enough, but the final mirror focusing on the drum is going to be quite toasty in no time, if only because it is sitting right next to the 4,500K drum, never mind the operating requirements.

 

Rune. Some parts of the engine do have to remain solid, after all.

Fused quartz or diamond can be used in situations where the sunlight intensity becomes high and the mass per area is less critical. Active cooling with some of the liquid hydrogen will be needed.

Let's say we use fused quartz:
Uncoated_UVFS_Transmission_780.gif

Over 95% reflectivity and usable up to 1920K. At that temperature, each square meter of the reflector is losing from a black backside 740kW of heat. If the reflector is only 1.128m in diameter, it is absorbing 0.05*927: 46.35MW from the concentrated sunlight.

Sum of heat to be removed? 47.09MW

The heat capacity of liquid hydrogen at 1920K is close to 449+1920*15:  29249kJ/kg.

So, the final small reflector will need to be fed 1.6kg/s of liquid hydrogen to stay at 1920K. It doesn't necessarily have to be directly cooled by the hydrogen - a heat exchanging loop can be established where helium circulates through and around the reflector and dumps its heat into the hydrogen.

 

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Welp, it looks very cool on paper. But...

1. The farther from the Sun you go, the efficiency will drop. It will reduce the useability of such propulsion to inner system - up to Mars orbit. Problem is, we can reach Mars with chemical engines with no problems. Exotic, highly efficient drives are needed farther from Sun - where all the important stuff is: asteroid belt, gas giants and their moons, Kuiper belt.

2. Design. Pictures speak for themselves. It will be a big, relatively fragile construction with many, many elements. Masts, mirrors, focusing mirrors, corrective mirrors. And struts - a lot of struts to keep it all together. And for maximum efficiency all of this will need Sun-tracking capability. It will be engineering nightmare.

rigging-of-a-windjammer-picture-id598357

3. And you will still need radiators to prevent heating chamber from melting after thrust cuts out and gas stops flowing through it.

4. What will happen if launch window comes, and this solar powered ship will be on the wrong side of the planet - in the shadow? Any KSP player can attest that a lot of maneuvers somehow happens at night :D

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21 minutes ago, Scotius said:

Welp, it looks very cool on paper. But...

1. The farther from the Sun you go, the efficiency will drop. It will reduce the useability of such propulsion to inner system - up to Mars orbit. Problem is, we can reach Mars with chemical engines with no problems. Exotic, highly efficient drives are needed farther from Sun - where all the important stuff is: asteroid belt, gas giants and their moons, Kuiper belt.

2. Design. Pictures speak for themselves. It will be a big, relatively fragile construction with many, many elements. Masts, mirrors, focusing mirrors, corrective mirrors. And struts - a lot of struts to keep it all together. And for maximum efficiency all of this will need Sun-tracking capability. It will be engineering nightmare.

rigging-of-a-windjammer-picture-id598357

3. And you will still need radiators to prevent heating chamber from melting after thrust cuts out and gas stops flowing through it.

4. What will happen if launch window comes, and this solar powered ship will be on the wrong side of the planet - in the shadow? Any KSP player can attest that a lot of maneuvers somehow happens at night :D

As you leave the inner Solar system, your maximum temperature will remain the same but the thrust drops. If you look at the example spaceships, modern and advanced, they have an average acceleration of 0.32 and 3.1g. Around Mars, this drops to 0.14 and 1.37g. Around Jupiter, it is 0.01 and 0.11g. In other words, solar thermal rockets are able to travel to the outer solar system without too much hassle. If you increase the solar collector area without increasing the engine mass, you'll have too much power to handle around Earth but a good amount around Jupiter. For example, instead of 5 tons of solar collectors, use 15 tons. Around Jupiter, you'll retain 11% of you maximum thrust. 

The complexity of the solar thermal rocket is no worse than a solar electric rocket, if not less.

The period between shutting down the engine and cutting the active cooling is an engineering problem. I can imagine gradual transition between 'On' and 'Off', plus the ability to continue the active cooling by just throwing the hot hydrogen overboard. You'll waste a few dozen kgs of hydrogen... but you were throwing tons per second out of the nozzle a few seconds ago, so its not a big deal!

STRs will like raise their orbit to be clear of the planet's shadow. This can be accomplished by raising the altitude or launching into a slanted inclination. Also... planning. The burns can be rather short, so its not a big deal like for solar electric craft that slowly wind out of orbit. 

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How do you keep all of those little holes from plugging up with the liquid metal?

If any parts of the heating chamber solidify after being a liquid, how do you make sure that the air tunnel is the same size or even still present?

How do yo make sure that all of the air comes out of the metal instead of getting trapped in a bubble of solid metal?

If you spin your centrifuge too fast, some of the liquid metal could press it's way down into the holes, clogging them up, but too slow and some of the air could get trapped, cool down, then cause bits of metal to be thrown off when it gets re-hated and 'pops'   I do not even know if that 'too fast' is faster than the 'too slow' so you might even have both at the same time...

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14 hours ago, Terwin said:

How do you keep all of those little holes from plugging up with the liquid metal?

If any parts of the heating chamber solidify after being a liquid, how do you make sure that the air tunnel is the same size or even still present?

How do yo make sure that all of the air comes out of the metal instead of getting trapped in a bubble of solid metal?

If you spin your centrifuge too fast, some of the liquid metal could press it's way down into the holes, clogging them up, but too slow and some of the air could get trapped, cool down, then cause bits of metal to be thrown off when it gets re-hated and 'pops'   I do not even know if that 'too fast' is faster than the 'too slow' so you might even have both at the same time...

Simple pressure. 

Hydrogen at 4000K has an extremely high pressure. The holes are small just to make sure that there's a good surface area of contact between the hydrogen and the heat exchanging fluid. 

The rhenium liquefies at 3459K. It is contained in a vessel at 4000K and is constantly warmed by the 5800K upper layer - there is little chance for any part of it to turn solid again. Even if it did, the fluid is in motion. Solid deposits would be whisked around and cleared from holes by the hydrogen flow.

Hydrogen's bouyancy ensures that it escapes the rhenium, because the density difference is extreme. Due to the high temperatures, there is no chance for the hydrogen to dissolve either. 

The balance between the rhenium reversing through the holes and the hydrogen leaving is an engineering problem, which can be solved usually by just increasing the amount of hydrogen entering the drum. If the rhenium does enter the channels, it will not solidify. 

 

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I missed the part where the containment vessel was a different material, that makes keeping the entire liquid part as a liquid easier, but what happens if there are eddies in the liquid that bring 5800K material in contact with the containment vessel?  Would that not etch the containment vessel?

Is it possible that the etching could breach the containment vessel coolant lines? (the coolant is supposed to be ~4000K by the time it leaves the coolant lines, so a few eddie caused hot-spots could conceivably etch down far enough to breach those lines if the THC melts below 5800K(and if it did not, why not use that instead?)

Controlling eddies in a fluid, especially an energetic(hot) and perturbed(bubbles) fluid where you cannot use anything for baffles because the baffles would melt, is a non-trivial task, and maintaining a steady heat gradient from 4000K to 5800K in such a fluid seems improbable at best.

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2 hours ago, Terwin said:

I missed the part where the containment vessel was a different material, that makes keeping the entire liquid part as a liquid easier, but what happens if there are eddies in the liquid that bring 5800K material in contact with the containment vessel?  Would that not etch the containment vessel?

Is it possible that the etching could breach the containment vessel coolant lines? (the coolant is supposed to be ~4000K by the time it leaves the coolant lines, so a few eddie caused hot-spots could conceivably etch down far enough to breach those lines if the THC melts below 5800K(and if it did not, why not use that instead?)

Controlling eddies in a fluid, especially an energetic(hot) and perturbed(bubbles) fluid where you cannot use anything for baffles because the baffles would melt, is a non-trivial task, and maintaining a steady heat gradient from 4000K to 5800K in such a fluid seems improbable at best.

Well you need to the drum walls to be solid! 
I do not have enough information on how exactly the design will be implemented, or if something has even been tested or seriously conceptualized, so I try to avoid going into too much detail. I don't know if hydrogen at 4000K is 'too hot to handle', or if active cooling makes everything pretty easy. I can't assert that the 5800K layer of liquid rhenium directly under the spot of focused sunlight will be thin or thick relative to the depth of the fluid heat exchanger - this depends on the thermal conductivity rate of the fluid and how stable the currents are. If they are chaotic, there very well may be pockets of >4000K rhenium touching the walls of the drum and etching off sections. If it is without turbulence, then any suck pockets will rapidly mix and equalize their temperature with that of the deeper layers. 

For now, I'm considering an alternative design that relies on liquid rhenium droplets and/or gaseous lithium.

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  • 4 years later...
4 hours ago, AtomicTech said:

I really like this concept!

I'm currently researching this so I can write a mod that adds a stockalike version of this into stock KSP!

That's awesome. Contact me for any questions.

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