Construction on Mars, Part Two: Design, Details, and Evaluation

This is the second post in a series on Construction in Space.  You can read the first part, General Principles and Design Assessment Criteria, here.

In this post, I will present a possible architecture for Martian habitats which I believe has many strengths as a solution to this design challenge.  The design I will present is modular, adaptable, and could be used on most planetary bodies in the solar system.  For the purposes of this post I will discuss the case of a standalone habitat on Mars with an internal pressure of 50 kPa.

DomesPhoto

Is it glass domes?  This is a cool picture but no, it’s not glass domes.

I would like to begin this post by restating the First Rule of Space Construction:

The fundamental structural load on any pressurized structure in space is the outwards force of the internal pressure.

The dominant structural load is the internal pressure of the structure, so the structure is designed first and foremost around containing that pressure.  Unlike typical structural loads experienced on Earth, this pressure force is omnidirectional, so I will consider all three directions.

The two lateral directions are effectively identical.  The vertical direction can be treated identically as well (like the example of a propane tank) or you can take advantage of some property of the surface or of gravity to use a different containment method in the vertical direction.

This realization leads to the first of two key aspects of my design: Pressure containment in the vertical direction can be achieved by using a mass of material on top of the structure, weighed down by gravity, which counteracts the vertical force of the internal pressure.

Combined VertHorForce

Schematic diagram showing vertical and horizontal force containment, in which gravity, ground support, and cable tension counteract the internal air pressure.

The second key aspect is how pressure is contained in the lateral directions.  In most pressure vessels, internal pressure is contained by tensile stress in the outer wall.  This creates a need for an outer wall which is strong, curved, and uniform.  It also creates a multitude of failure points: Damage to any portion of the wall can cause complete structural failure of the entire enclosure. While all pressure vessels necessarily have curved walls, my design improves on this as follows.

Pressure is contained on a wall-by-wall, level-by-level basis.  The load-bearing exterior of each wall is a curved, semicircular piece of material which is attached to a corresponding piece of material on the opposite wall by way of a number of steel cables strung between them.  This pressure containment jacket is shown schematically in the diagram above.

cable-stayed-bridge

A Cable-Stayed Bridge uses a similar combination of tension and compression elements

This results in two main benefits, and numerous side benefits: The first is massive redundancy.  The failure of a single cable, if it occurs, won’t cause structural failure.  Neighboring cables will take up the slack, and the cable can be replaced.  The second is that the footprint of each habitat can be square or rectangular with flat floors.  This massively cuts down on wasted space and improves the usefulness of the enclosed volume.

Other benefits include the relative ease of inspection and regular maintenance (shirtsleeve environment, direct visual and tactile inspection possible), the fact that a single point of failure does not make the entire habitat useless, and the cost savings derived from mass production.

Second-Order Design Concerns

The First Rule of Space Construction states that the first-order concern for any pressurized habitat is how you contain the pressure.  Having addressed this first-order concern, I will now address various second-order concerns.  These are still important, but you can only have one first priority.

An important aspect of the structure that I haven’t yet discussed is the compressive structure.  The compressive structure is a necessary part of the habitat and serves a number of different vital functions: It supports the lateral pressure trusses and walls, supports internal fittings (walls, floors, furniture, etc.), and also supports the counterweight overload.

The counterweight necessarily needs to weigh more than the theoretical equivalence value because you need that extra force to hold it in place in the structure and to make sure that there is good contact on a continuous basis between it and the rest of the structure.  I believe that a counterweight overload of about 5% is sufficient for this function.  The most important limiting factor is that the internal pressure never exceed the actual weight of the counterweight.

Tetrapylon

The Tetrapylon in Palmyra stood for about 2,000 years until it was destroyed by ISIS.

At this point I would like to describe an important design choice.  The compressive structure can be designed to be able to withstand the full weight of the counterweight, even without the upwards pressure of the internal atmosphere (vacuum stable) or it could be designed only to support the loads it will experience with the habitat fully pressurized (pressure stabilized).

A vacuum stable design is safer, because in the event of an unplanned depressurization the structure will not collapse.  By contrast, a pressure-stabilized design can use much less material because it doesn’t need to be nearly as strong, but requires a more complex construction process (partial construction of the counterweight, followed by incremental pressurization, followed by incremental construction of the counterweight, etc.).

While it is easy to imagine large gas reserves that boost the pressure by matching the gas outflow in the event of a depressurization, I believe it is safer and easier to build a vacuum-stable design.  I will spec for this in future posts and discussions on this topic.

radmars

Radiation map of Mars

Something else I want to talk about is radiation.  I may address my full thoughts on radiation generally in a later post, but in short I think it is a real concern worth discussing, although not one so serious that it can stand in the way of a robust settlement effort.

As you can see in the above map, Mars’s atmosphere provides meaningful shielding from radiation: Low altitudes experience about half as much as the tops of the tallest volcanoes.  This shielding effect will be strongest in the horizontal direction and weakest in the vertical direction.

This structure provides an excellent complement to that.  It provides tons of shielding in the vertical direction which should cut radiation from that direction down nearly to zero.  The residual horizontal-direction radiation will be weaker than the vertical component, but additional external walls can be built to shield the habitat if desired.

IMG_20191207_134536.jpg

Low-rise, mid-rise, and high-rise buildings in Manhattan’s East Village.

Every rendering in this blog post shows the habitat as a multi-story building like a mid-rise apartment tower, rather than as a single-story building that spreads over a large area like a warehouse.  I believe that given the broader constraints of this design that is what makes the most sense.

On Earth, it is cheaper to build a one-story building than a two-story building, and we typically build out before we build up.  Land values on Mars will be low, and it’ll be a long time before any settlement reaches a size where, in the United States, we start building up.

The reason it makes sense to build up with every structure is related to the first rule of space construction: The additional compressive forces related to building up do not dominate habitat design in space in the same way they do on Earth.  For a “regular” pressure vessel (propane tank style), the most efficient (but not necessarily the cheapest) shape is a sphere, which maximizes the ratio of internal volume to surface area and thus minimizes material usage.

Because pressure containment in the vertical direction is achieved by a counterweight whose mass need not increase with increasing height, the optimum dimensions are for the structure to be somewhat taller than wide.  I will address the reasons for this in a more rigorous way in a math-heavy appendix.

caulk

On Earth, we use caulk for waterproofing and weatherproofing; On Mars it may also be used to seal small leaks.

I want to bring up two more things before I close.

The first is that the design as described does not address how corners would deal with pressure containment.  It would not work for the outer jackets to meet at a point.  There are a number of ways to deal with this.  The best way depends on the specific function of the structure and I see no particular reason to go into detail at this time except to mention that one thing you can do is take advantage of the gap as a place to build in your windows or airlocks.

The second is leak prevention.  This design is optimized for pressure retention, but pressure retention and leak prevention are not the same thing.  This design features more joining points than others, and thus is somewhat more leak-prone.  It will be desirable to cut down on leaks by introducing a sealant layer; this also ensures that pressure is applied to the outer walls in the correct places and the correct ways.

I will finish out this post by scoring my design against the six criteria I introduced in the previous post.

1. The structure sustains a pressurized atmosphere

In this post, I have repeatedly referred back to the First Rule of Space Construction.  Pressure retention is a fundamental aspect of this design, and it is accomplished elegantly.

2. The structure provides protection from radiation

This structure will inherently create a large reduction in the amount of radiation experienced by its inhabitants and can be upgraded to provide nearly complete protection, to whatever level of radiation exists naturally in Martian materials.

3. The structure is failure resistant

The most important safeguard in this design is that tensile stress is local and not global.  This enables redundancy: In a “regular” pressure vessel, multi-axial stresses are distributed across the entire structure, which means that the structure is only as strong as its weakest point.  By contrast, this structure depends almost entirely on uni-axial stresses shared across independent members, and cuts out material pressure containment entirely in the vertical direction in favor of gravitational containment.

4. The structure is failure tolerant

The most important aspect of failure tolerance in this structure is the redundancy of the cables which hold in the pressure.  Failure in any one cable will not cause structural failure, but rather a reallocation of stress to other cables.  But it goes deeper than that.  While the larger number of joints increases the likelihood of leaks, a sudden increase in the leak rate helps to serve as an indication that components are becoming deformed and need to be repaired.  All of the main structural components are internal and can be inspected visually.  Even in the case of a total depressurization the structure will not collapse: It is both pressure-stable and vacuum-stable.

5. The structure can be constructed in an affordable way

One of the most important strengths of this design is that it’s made primarily from simple, mass-produced components assembled in simple ways as well as bulk materials such as regolith, sand, or concrete. I believe that, compared to other habitat designs, this design will have both a lower cost of components and lower cost of construction. I will discuss specific construction methods in a later post in this series.

6. The structure is useful as such

The most important difference between this design and other designs is that internal space has uncurved floors and ceilings and square or rectangular footprints, which substantially increases the usefulness of its internal volume. It has all the otherwise desirable aspects of a building, including adaptability, habitable internal volume, ability to regulate internal temperatures, and size can be modified depending on need.

The next post in this series will look at the materials to be used in structures of this kind and what kind of dimensions and measurements this will result in.

Construction on Mars, Part One: General Principles and Design Assessment Criteria

I’m going to try to start publishing weekly posts on here where I work through interesting problems in engineering design for outer space. This is the first post in a series on construction in space. In this post I will describe the design requirements and assessment criteria.

render

One artist’s render of what a Martian settlement might look like while under construction

Housing is recognized on Earth to be a basic human need. This is true despite Earth’s breathable air and generally mild temperatures. Nowhere in the known universe is as habitable as Earth, so indoor space is fundamental. In this series, I’m going to look into architectures and designs for the settlement phase, specifically on Mars, when hundreds of people or more are living on-planet and most things are built locally, rather than imported from Earth.

My philosophy for outer space is that best practices on Earth are universally applicable, except for where they aren’t. So what are best practices on Earth?

Buildings on Earth are compressive structures, whose most significant structural demand is to support the weight of the building itself and the things inside it against gravity. A rule of thumb is that a single-story single-family home has a mass of 1000 kg/m2, with an additional 375 kg/m2 for each additional floor. The original World Trade Centers weighed 450,000,000 kg each, with a footprint of 4000 m2 on each side and 110 floors, suggests a mass of around 1000 kg/m2 per floor.

structural-loads

Schematic diagram of the load forces on a structure

Buildings on Earth are, in general, built by digging a hole for the foundation and basement, then building and enclosing the structure. Typically structures are made from wood, steel, concrete, stone, or brick (depending on size, purpose, aesthetic preference, and relative costs), with non-structural walls whose functions are simple enclosure and thermal insulation.

In this sense, terran construction practices are irrelevant. The external pressure on Mars is very close to zero, and the internal pressure needs to be breathable: 50 kPa or higher, probably. By comparison, 1000 kg/m2 per floor corresponds to 10 kPa per floor under Earth gravity: The upwards and outwards internal pressure force of a building in space corresponds to 5 floors worth of downwards weight for a terran skyscraper, and 11 floors at the weight of a typical single-family house.

On Mars, gravity is 38% as high as Earth. This means that the structure can be proportionally less massive, and weighs proportionally less per kilogram.  This suggests that internal pressure will be equivalent to the weight of 35 stories of heavy-duty construction and 90 stories of light-duty construction.

hycon

The Hudson Yards development under construction on W. 34th St in Manhattan

This is what I will call the First Rule of Space Construction:

The fundamental structural load on any pressurized structure in space is the outwards force of the internal pressure.

Another major consideration not present on Earth is radiation. Opinions vary about whether this is a major or minor consideration, but it is desirable to have as much shielding mass as practicable to minimize exposure.

In addition to these two specific considerations, I want to bring up three general engineering principles that are almost universally applicable:

1) Failure Resistance

When you’re designing something, it needs to work. It needs to work when conditions are perfect, and it also needs to work when conditions are not perfect. It needs to work over the years of its lifetime (for buildings, often measured in decades, although perhaps in early settlement it will be shorter). And in the case of a building, it needs to do so without routine deconstruction, which would be both dangerous and disruptive.

2) Failure Tolerance

No matter how strong and redundant your design, all things fail eventually, sometimes unexpectedly. For something so critically life-sustaining as a building, the failure mode matters. The worst possibility is explosive decompression with no warning: Everyone inside the building will die. In the absolute worst case there may even be cascading damages to neighboring structures, like when one single balloon popping causes a whole bunch of them to burst.

It would be more ideal for failure to be of the sort that is visible but not catastrophic: One strut fails and neighboring members take up the load; the failure is reported or observed in the course of regular inspections, then repaired. Alternatively, rather than fracture, the structure develops a leak which is audible, pluggable, and fixable.

3) Design for Manufacture

One example of a pressure vessel is the propane tank people buy to fuel their barbecue grill. You might imagine building a structure that is essentially a giant propane tank: A single, large, curved piece of metal, perhaps welded together at the seams, perhaps partly or completely buried.

The logistics of building such a structure suggest substantial problems. Welding is expensive, for starters, and having a structure that is entirely welded is going to be expensive, perhaps unnecessarily so. Plus, manufacturing facilities for metal forming will need to be indoors to allow people to work. There is a limit to how big an airlock can feasibly be built, and no structure could be built which is larger than the structure it was built inside.

This is where the best practices from Earth do seem to be universal: Design for Manufacture would mean that the construction process is one of assembly, in which mass-produced components, each as similar to the other as possible are assembled into a single structure.

proptank

Might a Martian habitat look something like this?

Finally, the example of a propane tank, which is curved because curved structures are necessary to contain pressure, illustrates another important design criterion. As all of us who have inhabited buildings know, straight walls are a better use of space than curved ones, and the ideal shape for a building is a rectangle, or at least a shape made from straight lines and right angles.

What I’m getting at is that the structure needs to be functional, and useful as a building. It needs to integrate as well as possible with the built environment of the settlement.

So here are the six criteria, developed in this post, for thinking about and evaluating construction plans for Mars:

  1. The structure can sustain a pressurized atmosphere
  2. The structure provides protection from radiation
  3. The structure is failure resistant
  4. The structure is failure tolerant
  5. The structure can be constructed in an affordable way
  6. The structure is useful as such

I will present a concept which meets all six criteria in part two of this series.

This is the first post in a series.  The next post is Construction on Mars, Part Two: Design, Details, and Evaluation.

Electric Propulsion, VASIMR, and 39 Days to Mars

I’m writing today about a very dubious claim made by the Ad Astra Rocket Corporation about their electric propulsion system VASIMR.  VASIMR is a type of electric propulsion, and is probably one of the better kinds under development at this time.

If you don’t know much about electric propulsion or VASIMR, Wikipedia is an excellent reference for both and I recommend it highly before reading on.

The claim that I find so objectionable is that VASIMR enables transportation to Mars within 39 days.  Electric propulsion is great for what it’s good for – missions with long travel times where mass is at a premium and power is not.  It is not good for manned missions for exactly these reasons.

Dr. Robert Zubrin, true to form, has responded with a bombastic but very much correct rebuttal to this claim.  I would like to expand upon his intuition here using some numbers to demonstrate why this claim is so fundamentally and probably intentionally deceptive.

What follows is my methodology.  If you don’t care, by all means skip down to the results and the graphics below the second divider line.


In order to do so, I’m going to assume a couple things:

  1. The change in gravitational potential energy of the Earth and Sun are small in comparison to the kinetic energy of the spacecraft.  This is justifiable: The minimum distance between Earth and Mars is about 75 million km.  Traversing this distance in 39 days implies a mean velocity of 22 km/s, so 44 km/s to accelerate and decelerate, although the actual peak velocity and therefore total delta-V budget will be much higher.  For comparison, the delta-V from Low Earth Orbit to Low Mars Orbit on a minimum energy trajectory is about 6 km/s.  Therefore I will treat this as a straight kinematics problem.
  2. The spacecraft accelerates, turns around, and decelerates with no time in between.  This minimizes the power requirements but not the delta-V requirements.  While this is not strictly the optimum result (depending in large part on what you’re optimizing for) it’s justified by the fact that electric propulsion systems, VASIMR included, have very low thrust and thus accelerating to acceptable velocities in shorter time spans is even less reasonable.  Furthermore, because of the high exhaust velocity the relative cost of higher exhaust velocities is low.
  3. The transit speeds will be too high to make aerobraking at Mars or Earth a reasonable proposal.  In some senses, the possibility of aerobraking cancels out the change in gravitational potential energy which I am neglecting.
  4. The engines will produce a constant force at all times, but because the mass will vary with time the acceleration will change.

I will cite the sources for my numbers if possible or justify them if not.

Newton’s Second Law states that:

afm

Where F is Force, a is acceleration, and m is mass.  Of these, only Mass is a function of time:

mot

So we have:

aot

Where m0 is the initial mass, r is the rate of change of mass (always negative) and t is the time since the engine began firing.  Keeping in mind that acceleration is a function of time, I integrated and got the following (Checked with Wolfram Alpha):

dV

Where ΔV is the change in velocity from time 0 to time 1, but not the ΔV of the mission taken as a whole.  Basically, we need to solve for when the ship needs to change from speeding up to slowing down by calculating the ΔV from 0 s to t1 and t1 to 39 days, setting them equal to each other, and solving for t1.  The result is as follows:

t1

Finally, we need to solve for the amount of force that’s required to do this maneuver.  This is a function of total distance.  But rather than integrate again and try to solve a nasty and possibly un-solvable algebraic formula (we’re not savages, after all!), I wrote a Matlab code to do the integration for me and allowed me to guess various levels of force until I found one that was right.  I realize there are better ways to do this and don’t care very much because this one worked fine.

In order to give real mass breakdowns, payload fractions, etc., I also have to give some numbers to the thrust-to-weight ratio of engines, power sources, and fuel tanks.  Therefore, I will use the following numbers for the mass of system components:

  1. 830 W/kg for the VASIMR engine, as given in this paper.  Please note that this is actually an estimate for an engine that hasn’t been built, meaning it is very much open to manipulation, since the author of the paper is also the owner of Ad Astra Rocket Corp.  The paper also suggests a pathetic electric-to-kinetic efficiency of 4% for presently existing engines.  I will use Mr. Chang Diaz’s projections that future engines can reach 50% efficiency.  This means that the kinetic energy of the exhaust will be 415 W/kg of engine.
  2. I will assume that a solar power system with a specific power of 300 W/kg will be used.  This is higher than currently existing designs, which as of 2004 were getting less than 100 W/kg.  This is also higher than nuclear systems.  Even the SAFE-400 (Go to Wiki) is a very modern nuclear design and doesn’t include any systems to convert thermal energy to electrical energy, its specific power is under 200 W/kg.
  3. I will assume that tankage requirements constitute 5% of the mass of whatever is in the tank.  This is actually really optimistic because VASIMR uses a very light Hydrogen fuel.  For example, the Space Shuttle External Tank massed 29,930 kg, and contained 721,045 kg of fuel.  However, most of this weight is Liquid Oxygen, which is much more dense than Liquid Hydrogen.  Pure Liquid Hydrogen is about 5 times less dense (70 kg/m^3 as compared to 360 kg/m^3) than the Hydrogen/Oxygen mixture used in the shuttle; If the tank contained the same volume of only liquid Hydrogen, the tank’s mass would be more than 20% of the mass of the stuff in the tank.  So this is a really generous assumption.

Here are the two MATLAB scripts used for this calculation, linked to on Pastebin.  It’s important that the two scripts retain their names, so save VASIMR.m as VASIMR.m and rocket.m as rocket.m.  Capitalization matters!

VASIMR.m

rocket.m

They need to be saved into the same folder in order to work.  If you don’t have MATLAB on your computer and don’t want to pay for it, FreeMat should be able to run these programs just as well and doesn’t cost anything.  The way the script works is that once you’ve chosen your parameters (I believe I’ve mentioned all the important ones in this post, but please note that the script uses exhaust velocity, which is a factor of 9.8 times higher than Isp) you do guess-and-check by changing the force value until it outputs a “Distance” (This is the ratio of the distance travelled to the minimum distance from Earth to Mars) equal to 1.  As I said, there are better ways to do this and I didn’t feel like doing any of them because this works well enough.


Here are my results:

Results for Various Isp values.

Results for Various Isp values.

I chose to give a large number of significant digits for the initial acceleration, because it’s very sensitive to slight changes in this value.  All numbers are used in their typical way.  Normal mass ratios for Marsbound vehicles using chemical fuel are around 3, and anything above about 10 is very high; Above 20 is probably impossible.

The most important number in this chart is the Necessary Reduction Factor (NRF).  It describes the ratio of necessary solid mass to the amount of allowable solid mass.  For example, if you choose an exhaust velocity such that your rocket has a mass ratio of 4, and its initial mass is 80 tonnes, you can have up to 20 tonnes of solid mass.  But let’s say your tanks mass 3 tonnes, your engines mass 17 tonnes, and your power source masses 20 tonnes.  That would mean you would need 40 tonnes of solid mass to complete your mission, and you would have a NRF of 40/20=2.  Basically, it describes how much you need to shrink down your components to make the mission feasible.  For NRFs below 1, you have some amount of payload carrying capability too.

As you can see, there is no value of the exhaust velocity for which the NRF of this system is below 1, or even anywhere close.  By picking an Isp value between 5,000 s and 10,000 s, it’s possible to get a value slightly below 12, but not one below 11.

For Dr. Chang Diaz’s claims to be true, VASIMR and all related technologies would have to be at least twelve times lighter than they actually are.

But its even worse than that: The engines that Ad Astra Rocket Corporation has actually tested have Isps of about 2,000 seconds.  For rockets with exhaust speeds that low, the mass ratios get so high that it’s nearly impossible to get a value for how much mass is actually left.

Basically, Ad Astra Rocket Corporation is about as close to being able to do this as Ford is to building a car that gets 200 miles to the gallon at 1,500 mph.

The image below shows just how much this technology blows past the mass limits available to it.

Engine Mass and Total System Mass relative to maximum allowable mass

Engine Mass and Total System Mass relative to maximum allowable mass

The maximum allowable mass is normalized to 1, with the mass of the engines and total system masses expressed relative to this.  As you can see, they’re much, much higher.

For anyone who’s interested, here’s a plot of the Position-Time and Velocity-Time profiles for a typical scenario (I used Isp=5,000 s):

Position-Time and Velocity-Time graphs for typical transit

Position-Time and Velocity-Time graphs for typical transit

If you took high school physics, these graphs should be familiar to you.  Notice that the velocity graph’s peak corresponds to the turnaround point, which happens towards the end of the transit because the acceleration increases at the mass decreases.

So, there you have it: Claims debunked.  Spread the word.