New Mars Forums

kbd512 mentioned that his knowledge of thermodynamics is not strong.  Mine also is not strong: Thermodynamics is a notoriously difficult subject and most of what I know is what to ignore when analyzing a thermodynamic engine.  Luckily, that is the relevant portion for most practical applications.  I don't know how much kbd specifically knows or doesn't know, but in this post I would like to cover the basics of thermodynamic engines for anyone who cares to learn.

My background is in mechanical engineering and my knowledge of the subject comes from a single class, which in my opinion was poorly taught by a professor who was an expert in his field but didn't care for teaching.  Thermodynamics is in some ways the bastard child of physics and chemistry, relevant to both but firmly part of neither.

Anyway, I'm going to start by defining the relevant variables:

T: Temperature, a familiar measurement which should be measured on an absolute scale (i.e. Kelvin or Rankine)
S: Entropy, measured in J/mol-K or J/kg-K.  I'll be honest: I don't know what entropy is and I'm not sure anyone does.  It has something to do with "disorder" in a system.  Hotter things have more entropy than colder ones, all else equal; gases have more of it than liquids, which have more of it than solids.  Entropy after a process will always be the same or higher than before it.
H: Enthalpy or heat, measured in J, J/kg, or J/mol.  This is a measurement of heat added to or subtracted from the system to get it to a certain state, which usually means some amount of fluid.
Q: This is a measurement of heat being added to or subtracted from a system.
U: Internal Energy, measured in J, J/kg, or J/mol.  This is a measurement of the energy stored in atomic vibration and physical or chemical bonds.
W: Work, measured in J, J/kg, or J/mol.  This is a measure of the useful (usually mechanical) output of a thermodynamic process.
X (technically the greek letter chi): Quality.  This refers to the portion of a fluid, by mass, that is vapor.  For example, you might have a X of 0.7, meaning that 70% of your fluid is gas and 30% is a liquid.  Turbines will not work with a quality factor below roughly 0.9.  Pistons are somewhat more robust but you will have difficulty clearing the piston on a downstroke if there's too much liquid in it.

The first law of thermodynamics is:

dU=dQ-dW

"d" as used here refers to an infinitesimal change.  You can replace the "d" with a "∆" (change in) without changing your understanding of the First Law.  This equation means that the change in the internal energy of a system (the energy stored in molecular vibrations and chemical bonds) is equal to the amount of heat added to the system minus the amount of work done by the system. 

In a thermodynamic engine like a piston, a rocket engine, or a turbine we are converting heat energy into useful work by exploiting a temperature differential.  Below, I have included a Temperature-Entropy diagram for a typical one-stage steam turbine.

Entropy is on the horizontal axis and Temperature on the vertical axis.  To the left of the red curve water is entirely in the liquid state.  To the right of the red curve water is entirely in the gaseous state, as steam.  Under the curve water is partially vaporized, with a quality between 0 and 1.  Here's what's going on in that graph:

• Between points 1 and 2, water near its boiling temperature is compressed (i.e. there is an input of work)

• Between points 2 and 4, the water is heated to its boiling point at said pressure (at point 3) and then further heated until all of the water has vaporized, and then further heated beyond that temperature (i.e. there is an input of heat energy)

• Between points 4 and 5, work is extracted from the fluid using a turbine.  In the idealized model this is adiabatic (Q=0) and isentropic (∆S=0).  A process that is isentropic is also reversible because no energy has been lost.  Real-world turbines can achieve roughly 85% of the work output of the isentropic value.

• Between points 5 and 1 the fluid is cooled back to its original state.

The value that we as users are interested in is the efficiency.  Here's how you calculate it:

Efficiency is the net work produced by the engine divided by the heat input to the engine.

The net work is the work output (between points 4 and 5) minus the work input (between points 1 and 2).

In the abstract, work done by a compressor is:

dW=d(PV)

In general, this is difficult to solve analytically because you need to determine how pressure affects temperature and vice versa when temperature is not constant (PV=nRT is not useful here).  However, water is much easier because the volume doesn't change with pressure.  Therefore, we have:

W=V∆P

To calculate the work output, we use the difference in H between points 4 and 5.  For water, we can look this up in Steam Tables and look at the difference in H between points 4 and 5.

Calculating the heat input is quite simple: It's equal to the difference in H between point 4 and point 2.

If working with Carbon Dioxide, the process is quite similar.  I just discovered that the back of my old Thermo textbook has steam tables for CO2, meaning I can give more accurate numbers for efficiency and work output.  I will do this in a following post.

As I said in the other thread, I believe that your post started out in a good place but went rapidly downhill once you started getting into the details of how your proposed society would work.  Before I get to responding to what you said, I want to talk about how I think about the ideals of government.  It's hard to design a good society from scratch, after all, and I don't think it's entirely fair to criticise without proposing an alternative.

In my opinion, a good society is one which maximizes freedom, democracy, justice, and prosperity.  These ideas are all related, but can also be in conflict and require choices to be made for one over the other.  Here's how I look at each of those terms:

Freedom: Freedom is the ability to do the things you want to do.  Freedom has both positive and negative aspects, meaning that you are both not prevented from doing those things and that you are able to do them.  The important aspects of freedom are different for different people.  What this means is that freedoms in the abstract are different from the freedoms that actually matter to people in a specific place and time.  Both are important but I would say the latter is more important.

Democracy: As Abe Lincoln described it, democracy is government of the people, by the people, for the people.
Democracy means that the people affected by something get to make the important decisions about it.  Democratic governance is what happens when a group of people make decisions about matters as a group. In some sense, freedom is for an individual, and democracy is a corresponding attribute of a group.

Justice: Justice can mean a lot of things to a lot of different people, but fundamentally I think it means living in a society where ideas triumph over power dynamics.  Justice is the foundation for things like peaceful conflict resolution, fairness, and the rule of law.

Prosperity: Freedom, democracy, and justice exist in the real world, where human beings need food to eat, air to breathe, and homes to live in, and where the fruits of a well-functioning economy can enrich the lives of their beneficiaries.   Freedom, democracy, justice, and prosperity can exist alone but each is more meaningful in context and balance with the other three.

Anyway, I'll start with the good: I absolutely agree with the idea that the main levels of government should be local and global.  Most functions of government like education, infrastructure, safety, health, and community planning make sense as things that should be handled locally.  Then, there are some things like long-term planning, common defense, rights enforcement, etc. that should be handled at the highest possible level.  There's not much need for something in between, although towns and cities may want to form common councils or leagues for specific purposes.

Preventing war is a valiant goal, and designing a good political system to resolve tensions can go a long way to help it out.  But looking forward to hundreds of years of the future there's no way to guarantee a war can't happen.

On the topic of libertarian government: It's important, of course, to distinguish between the local and planetary government, which you have done.  And I think in the abstract "you can do whatever you want as long as you're not harming anyone" is a reasonable-sounding rule.  The thing is that every action every person takes affects other people for better and for worse.  You suggested, for example, that people should be able to buy and sell codeine without regulation or prescription.  I don't feel the need to say that it should necessarily be handled at a planetary level, but I would say absolutely that highly addictive substances like opioids (of which codeine is one) should have limited circulation.  If a town did want to make drugs legal and available, well--that would be a good example of freedom, democracy, justice, and prosperity coming into conflict.

Speaking more generally, again, I like the idea that each town can follow its own path and I think we would all agree that there would need to be limits.  I think the problem comes from the idea that, whatever limits are set, there won't be constant transgressions.  Most cases will be gray areas, and this becomes a trickier and trickier problem the more different the different towns are.

On the topic of taxation: All individuals and businesses exist in a society and benefit in various ways from the existence of that society.  Having a society costs money.  Therefore, members of a society pay taxes into a common treasury to support the institutions that make their way of life possible.  Charging citizens and businesses for use of public resources such as living quarters may or may not be good policy, but I take no issue with it.  Fundamentally, though, all wealth is created from common property (the land) and common labor.  The choices people make about how to use those resources affects other people, both in the positive sense (if you build a settlement somewhere, there is a settlement in that place) and the negative sense (if you build a settlement somewhere, I cannot build a mine on that same spot).

I think the place where I disagree most strenuously is your description of how it is to be paid for.  The claim that the colony will become profitable by overcharging immigrants for transportation seems questionable.  If a settlement isn't profitable on its own terms, wages likely won't be very high, and a family or individual won't drop everything to go.  Such things may have worked before the telegraph and the internet; they won't work now.

Broadly speaking, the society you've described seems to be one where the Corporation spends a lot of time bilking its employees and uses its power to profit off the acts of government.  Such a thing may come to pass but it's nothing to aspire to and indeed is a great reason to be skeptical of private space colonization as something that's worthwhile.

From the Martian government and importance of communication thread:

kbd512,

No reason whatsoever from a technical standpoint.  The only reason is that, in my judgment, there are better ways to convert the heat from the Pu-238 into usable energy. 

From my perspective the biggest benefit to the system I described is that it can operate with an extremely low-grade energy source.  If I recall correctly, RTG sources generally operate at temperatures of several hundred degrees centigrade, meaning they're way overmatched for a system that can operate happily with a hot-side temperature of 0 C.

The other thing is that, from my perspective, the best thing about RTG is that it will produce power at a predictable, consistent rate with no fuel consumption for decades.  On the other hand this system consumes liquid CO2 as a sort of "propellant" so I think the benefits of the two systems are mismatched.

Based on the power production of an RTG unit (usually in the range of 1 kWt, if I recall correctly?) I think you'd want to look more towards a piston or turbine system operating at higher temperature, probably with Nitrogen, Helium, or Argon as a working fluid.  I know there's been some advances in microturbines lately but a piston system is simpler, if a little less efficient.

So: It would work but it's not the best use of the system imo.

Hey louis,

Interesting article!  If I recall correctly there was a thread about that a while back but I don't think I got involved in that one.

While dry ice definitely has potential as an energy store, I don't think that particular device is the best way to extract energy from it.  The key fact about the leidenfrost effect that it's based on is that it slows down heat transfer, after all, which is the opposite of what you'd want.  More of a curiosity than a useful technology in my opinion.

Having said that, it's been pointed out various times on this forum that low nighttime temperatures on Mars mean that it's relatively easy to freeze CO2 out from the atmosphere.  For reference, solid CO2 has a density of 1.56 g/cc and liquid CO2 has a density of 1.1 g/cc.

Because it liquefies at a relatively low pressure and high temperature, CO2 happens to be a poor choice of gas for compressed gas applications without an external heating source.  Virtually any other gas is better.  On Mars, Nitrogen is probably the appropriate choice.

Having said that, I'm interested in the possibility of using liquid CO2 with a source of heat from the ambient environment as an energy store.  To start, here's some numbers:

The heat of vaporization of liquid CO2 is 15.326 kJ/mol.  The specific heat capacity of CO2 at constant volume is 47 J/mol-K. The triple point is at -56.6 C (216.6 K) and 510 kPa.

Let's say you store your CO2 as a liquid near the triple point, -57 C.  The pressure will be 5 atmospheres, 500 kPa and once released you further heat the gas to -20 C. Let's say that through a turbine or piston you reduce the pressure and allow the gas to cool to a temperature of 198 K, when it will begin to freeze.  The outlet pressure will be 1.9 atm, at which point you can reheat the gas to -20 C and re-expand (reducing the pressure once again by 62%) if you so choose.  The benefit is a more efficient use of LCO2.  The cost is that you'll get a worse efficiency, because you need to heat your CO2 by a larger amount.

The heat input required for the first stage once the CO2 has boiled is roughly 1300 J/mol (30 kJ/kg), and you will generate up to about 675 J/mol (15 kJ/kg), depending on your efficiency.  The reason your efficiency is so good on such a small temperature differential (the theoretical efficiency here is 52%; carnot efficiency between -20 C and -75 C is just 22%) is that it's possible to obtain the energy of vaporization from the environment which, while cold, is not that cold, usually.  You might use methanol in a heat exchanger to transfer the heat from the ground to the generator.

As far as the question of where that heat is supposed to come from, I believe there's actually a pretty simple answer: From freezing water which, as we all know, freezes at 0 C and releases 334 kJ/kg in that transition.

This is not a good fuel source for a vehicle, but actually seems quite promising for stationary applications.  A good nighttime energy source for a colony if you can freeze the CO2 during the day, perhaps?

Edit: I wrote this post over several days and I see that there's been substantially more discussion in the meantime

Okay, I've got a couple more for you.  This is a building owned by Spokane County in the city of Spokane, WA just north of the river.  It really looked to me like the kind of structure you might see on early Mars:

Here's what I like about this building as something you could see on Mars:

For reference, I described how I think buildings should be built in this post.

• Brick outer layer: Would provide some radiation protection and thermal insulation, plus bricks are modular and relatively simple to manufacture (Sidenote, probably will be strengthened with basalt fibers)

• The four corners are capped cylinders with narrow windows: This is a great shape for pressure retention and thermal insulation

• Roof is well-shaped for 5-10 m of sandbags/regolith to contain pressure and protect from radiation, perhaps with a greenhouse on top (I would say every building should have a greenhouse on top with a lower level people can walk around in, it's important for people to have ready access to outdoor-feeling space)

• Strongly fortified side-walls are well-designed for the potential to contain pressure in the lateral direction (If you look at the post I referenced above, most of the lateral pressure retention should be done with steel cables which lightens the shear/bending loads on rectangular walls)

• Building is square in cross-section, which is good for pressure retention as described, for efficient use of a structure, and for thermal/radiation protection

• Windows are tinted, which can provide a good view while still offering some protection

Given all the windows this building might find use as some kind of arcade or public space, or could just be a regular workspace/living space.  I would love if they followed Arkady's suggestion and used the brick faces of the buildings for murals.

How many PhDs in engineering does it take to operate a projector?

I'm not sure, but it's more than I've ever seen in a room together at once.

Higher education can be a valuable addition to a person's skillset, but it often comes alongside with overspecialization and an unwillingness to speculate on topics outside one's particular, narrow area of expertise.  That's fine if you're seeking to become preeminent in your field but in the context of the wide spectrum of tasks and jobs settlement entails is a big problem.

GW-

Do you have an estimate of how switching from a turbopump to a positive displacement pump would affect the mass of the engine?

Hey Tahanson,

This seems super interesting and just the sort of thing we might look to when the time comes to build the actual tower.  Because we'd be operating at a much larger scale we might choose to go for some sort of winch/hook assembly that operates on each level with a temporary seal over the top of the cup while lifting

This is a worthwhile goal, but the way you've suggested going about it seems to be in most respects the polar opposite of how I would try to do it.  It seems to me that the sacrifice you're trying to make (much lower engine mass in exchange for much lower Isp) won't really pay off.

To get rough numbers, I used the equation here.  It's not perfect, but does give a good approximation of the exhaust velocity for most fuels.  According to this page, kerolox at a mixture ratio of 2.3 has a flame temperature around 3550 K, a mean exhaust molecular weight of 21.7, and a gamma (Ratio of specific heats) of 1.22.

Assuming that the nozzle is perfectly expanded to vacuum, this gives a vacuum exhaust velocity of 3,883 m/s.  Real high performance kerosene engines can get as high as 3600, and 3500 is reasonable for a well designed engine.  I will therefore introduce a "fudge factor" of 0.82 within the square root to account for the finite efficiency of the engine.

The stoichiometric mixture ratio for kerolox is 3.4.  At 2.3 my expectation would be that the exhaust would be a mixture of CO2, CO, and H2O.  It happens to be the case that at a ratio of 2.3 the exhaust will be entirely CO with no CO2 admixed at all.  At mixture ratios below 2.3 the exhaust will contain either Carbon or Hydrogen.  In order to move on, I wrote down the following chemical equation:

CH2 + nO2 → aCO2 + bH2O + cCO + dC + eH2

The equation is valid for values of n between roughly 0.1 (hot enough to dissociate the kerosene into its constituents) and 1.5 (stoichiometric combustion, above which excess molecular oxygen will exist in the exhaust).  Here are the results for three selected values of n:

R, in this case, is the mixture ratio in terms of mass that we use when discussing rocket fuels.

Below n=1.0, combustion will not reach a level near what could be considered "complete" and there will either be uncombusted carbon or hydrogen in the exhaust.  In terms of enthalpy, it is favored to produce water and carbon; in terms of entropy it is favored to produce hydrogen and carbon monoxide.  I'm not sure where the equilibrium lies and it's entirely believable that rocket exhaust is not at equilibrium.  I will therefore consider three possible cases: In the first case, H2O predominates with a small amount of CO and H2.  In the second case, H2O and CO are produced in roughly equal proportion.  In the third case, CO predominates with a small amount of H2O and C.  The numbers I will use are as follows:

To calculate the combustion temperature, I will assume that the unreacted elements absorb heat in accordance with their heat capacities and proportion.  I will deal with solids by ignoring them (except for the heat they absorb) and reducing exhaust velocity in proportion to their mass.  In other words, I will assume that if the exhaust is 75% gases moving at 4000 m/s and 25% Carbon the effective exhaust velocity will be 3000 m/s.  I will assume the ratio of specific heats remains constant.

Using the equation above with the modifications I have described, here are my results:

Naturally these results are approximate, but they suggest that the actual exhaust velocity is not strongly sensitive to the location of the chemical equilibrium, and furthermore that the vacuum exhaust velocity should probably be in the range of 2500 m/s.  It's also worth noting that at low mixture ratios there's potential to produce really substantial amounts of Carbon in the exhaust.  It' hard for me to believe that an engine will continue to work well for long periods of time when 20% of the exhaust produced is a solid.

You also said this:

This is not correct.  Reducing the combustion temperature does not reduce the chamber pressure.  The combustion temperature is a function of what is being combusted.  The chamber pressure is a function of the inlet pressure generated by the propellant feed system.  It is possible to lower the chamber pressure in conjunction with other changes, but you will suffer further reduced Isp for doing so if you are operating in the atmosphere.

You certainly could see some mass savings from reduced temperature as you can have a smaller cooling system, perhaps even a passive one, but I don't think they're very substantial.  I don't see why your tankage or structural mass should change at all, for example.

Here's some numbers: Let's say you have a two-stage rocket where each stage has a delta-V of 4700 m/s.  With ideal kerolox at 3500 m/s Vex your dry mass fraction will be 26%.  With the mixture ratio you have suggested (Vex=2500 m/s) the dry mass fraction is just 15%. 

I would choose to go at it the opposite way by allowing for a moderately higher engine mass while keeping performance close to constant.  The biggest change the pumps from turbopumps to something more traditional such as a reciprocating pump.  I suppose you could also build a combustion-based pump where the detonation of a small amount of fuel serves to pressurize a much larger amount of fuel and push it into the combustion chamber.  Turbopumps have a higher efficiency and lower mass but they are also more complicated and last less time (alternatively, you could build a turbopump and run it to failure and see what breaks, make that part stronger and do it again)

I would say Mars is the biggest prize and the Moon is low-hanging fruit (Literally, if you're a geocentrist!).  Both are valid targets for exploration and settlement, and I would support a program targeted at either.

What I can't endorse is an unfocused program that includes spurious missions to secondary targets.  The moon is not on the way to Mars in any consequential way.  The relevant technologies and procedures can be tested on Earth, in LEO, or perhaps in a free-return mission if necessary.

I have basically no power over the direction of any space program, so my "endorsement" really doesn't matter.  I don't have a ton of hope right now for anyone's space program.  Here's what would give me hope that settlement was really happening:

1. A reason for going that makes sense.  Examples include:

   • Profit

   • Opening a new frontier

   • Establishing an off-Earth tax haven for billionaires and corporations

   • Research

   • Military Supremacy or Geopolitical Preeminence

2. A single, clear destination (vs. "Moon and Mars", "All of the Above", "Moon on the way to Mars", "Let's just build this rocket and use it for everything", "Hey what if we try to capture a NEO and put it in Lunar Orbit that's cool isn't it", etc.)

3. A mission design that makes sense as a way of fulfilling the program's purpose

   • A program designed to turn a profit for a company is probably going to go to the Moon for the shorter timescales and should have a reasonable expectation that their efforts will eventually make them money

   • A military program will probably be composed overwhelmingly of robots with a few human minders, possibly stationed temporarily

   • A program whose aim is research will probably be lightly and temporarily staffed and focus on regions that are of scientific (rather than economic) interest.  For example, a lunar farside radio telescope; An IR observatory in a permanently shadowed crater; [Something about geology and planetology--hard for me to say exactly which sites are of the most interest]

   • No side missions to secondary destinations

4. The organization should have the financial, technical, logistical, etc. resources to accomplish the task they are undertaking or the ability to acquire them; the organization's broader purpose should align with the purpose of the mission (Universities won't fund a program aimed at military supremacy or profit; Private companies won't fund pure research, etc.)

If the image is on your computer you need to upload it to the internet first, then follow the procedure I mentioned.  I normally use imgur.com to do that.