Construction on Mars, Part 2, Appendix: Height

I had said in an earlier post that I would try to post once a week. That was wildly optimistic and life intervened. Instead of posting once a week, I will try to post on an ongoing basis.

One thing I mentioned in the previous post was that that the height of structures designed according to the design I described really would tend to be larger than their breadth. I will show the math behind that in this post.

In order to do so, I will start off with a very simplistic model for the cost of the structure:

Eq1

Where C is the total cost of construction, CW is the cost of the counterweight structure, CS is the cost of the compressive structure, CJ is the cost of the outer pressure jacket, CT is the cost of the tension cables, and CA is the additional cost of other things. I will assume that the structure has a square base with side length x and height z. By assuming simple linear behavior, we can expand each of these terms as follows:

expansions

The constants W, S, J’, J, T, and A are constants of proportionality describing the cost per unit of counterweight, compressive structure, pressure jacket, tension cables, and additional costs respectively. All assume a constant internal pressure driven by physiological needs.

Given a constant internal pressure, the thickness of counterweight is constant, and the amount of counterweight increases with area, x2.

The compressive structure needs to support the full weight of the counterweight, and thus its cross-section is therefore proportional to its total weight, itself proportional to area. Per the first rule of space construction, this force strictly dominates the weight of the compressive structure. The compressive structure also needs to be as tall as the structure, and thus costs an amount proportional to its height, thus total cost is proportional to internal volume, x2z.

The pressure jacket refers to the curved metal structures and framing support members that contain pressure on the outer wall. Cost can be described as being proportional to the external area of the vertical walls of the structure, perimeter times height, 4xz. By introducing a constant J 4 times larger than the initial constant J’, we can simplify the expression to xz.

The tension cables have to bear a load in proportion to the total external area, which means their cross section is proportional to xz, and have length proportional to the width of the building x, so that the cost is proportional to x2z.

The additional cost term is a placeholder and is assumed to be proportional to the internal volume of the structure.

Plugging in the expansion of each term and dividing by the volume, x2z, we can determine the cost per volume of the structure as follows:

cdivv

Naturally we want this C/v value to be as low as possible. We can determine by intuition that the optimum lies somewhere in the middle, rather than at an extreme, and therefore we can determine the answer through differentiation. The optimum is the place where the price per volume remains the same as you modify the aspect ratio of the structure while holding the internal volume constant.

pd

Each of these will, when evaluated and solved, provide the same correct answer:

finaleqfull

Where W is the cost per square meter of the counterweight and J is the cost per four square meters of tensile jacket, and J’ is the cost per single square meter of tensile jacket.

It’s worth mentioning “cost” is, both in general and in this specific case, a pretty complicated thing to talk about. Construction costs can vary widely for similar projects, even within the same country, depending on all sorts of technical and social factors.

As an example, thinking in the abstract: What is the cost of one unit of iron ore, energy, capital (in the form of machines), and labor on Earth? And how will circumstances on Mars change the relative costs of those inputs (and other important inputs) as compared to Earth?

Even comparing between countries on Earth can be complicated. This report on the relative sizes of the economies of the United States and the Soviet Union in the latter half of the Cold War shows how complicated the comparisons can get, even in two developed countries of similar size, at the same time, with similar resource availability.

All this is to say that it would be inappropriate to try to quantify the optimal ratio of height to width. Instead, I will simply make general observations and look at Earth’s costs for reference.

I will speak at greater length on the construction of each element in a later post. Schematically, the tensile jacket is made from stacked layers of steel half-pipe, attached to a frame with sealant to contain internal air. Assuming a typical strength of plain carbon steel of 300 MPa, a safety factor of 5, and each layer being 3 m tall, this will require just 50 kg of steel per square meter or 200 kg per four square meters (more material of some kind will likely be required to reduce the potential for puncture).

The counterweight is made from some bulk material (concrete, or sand, or gravel) contained within a large frame. A 50 kPa internal pressure with a 5% counterweight overload requires 14 tonnes of material per square meter of counterweight.

It does not require much imagination or analysis to believe that 200 kg of formed steel and structure costs less than 14 tonnes of concrete and structure. It is this basic truth, that W > J, that drives the buildings towards more height and less breadth.

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.

Andrew Cuomo is Full of Shit

Happy late Festivus! I’m mad as hell at Gov. Andrew Cuomo and you’re gonna hear about it, because you should be at least as pissed off as I am.
 
Earlier today the governor of the great State of New York announced that the L train shutdown (which had been expected to last 15 months) would not be happening. To explain why this seemingly good news is so infuriating, I will start with a timeline of events. It’s long so you can scroll past if you like for conclusions at the bottom.
cuomo
 
MARCH 25TH, 2009: Facing a $1.2 billion budget shortfall in the depths of the Great Recession, the MTA enacts draconian “Doomsday Cuts” to subway and bus service. 2 subway routes and 52 bus routes are eliminated, 2 more routes are shortened, nearly 1000 MTA employees are laid off, and fares rise by 13%.
 
NOVEMBER 2, 2010: Running on a platform of responsible government, transparency, and efficient public services (if you can believe that), Andrew Cuomo wins 63% of the vote and is elected to be governor of the greatest of these United States. He holds supreme executive authority over its 20 million citizens, including the MTA. He takes office early in 2011.
 
OCTOBER 29TH, 2012: Hurricane Sandy makes landfall in the United States, killing 157 people and causing $68 billion in damage, second at the time only to Katrina. There is damage from flooding, wind, and fire across the 5 boroughs and beyond. The city that never sleeps grinds to a halt. 2 million New Yorkers have no power, 20,000 flights are cancelled, no Amtraks run, there is no water in some places, and gas stations have no gas. Every tunnel under the East River (whether for Subway, car, or LIRR) floods with corrosive East River saltwater along with the Holland Tunnel and the Hudson River train tunnels. The subway and PATH don’t run at all for two days. LIRR, NJ Transit, and Metro North are down for a week.
 
NOVEMBER, 2012: Cuomo receives national attention, praise, and a bump in approval ratings for his bipartisan efforts (alongside NJ Governor Chris Christie and President Barack Obama). He basks in the attention.
 
JANUARY 29TH, 2013: Congress passes the Disaster Relief Appropriations Act of 2013, authorizing $60 billion in emergency recovery spending.
 
MARCH 3, 2013: Subway fares increase by 11%.
 
JULY THRU DECEMBER 2013: The IND Crosstown Line (G train) closes intermittently for repairs.
 
AUGUST 2ND, 2013: The Montague St. (R train between Manhattan and Brooklyn) tunnel closes entirely to train traffic for repairs. The tunnel remains closed for over 13 months and reopens on September 15th, 2014.
 
JULY 25TH, 2014: The IND Crosstown Line closes entirely to train traffic for five weeks and reopens on September 2nd, 2014.
 
SEPTEMBER 9TH, 2014: Andrew Cuomo receives 63% of the vote in the Democratic Primary for Governor, with Zephyr Teachout (the most incredible lady in New York State Politics) surprising everyone by garnering 33% against him.
 
NOVEMBER 4TH, 2014: Andrew Cuomo wins reelection with 54% of the vote and will remain governor of New York (and remains in charge of the MTA)
 
MARCH 22, 2015: Subway fares increase 10%
 
JANUARY 2016: The MTA notifies the public that due to damage caused by Hurricane Sandy, it is necessary to do extensive repairs on the tunnel which will require an 18-month shutdown.
JANUARY 1, 2017: Andrew Cuomo, who has run the MTA since 2011, takes credit for the opening of the opening of a Second Avenue Subway on the Upper East Side.
 
APRIL 3, 2017: The MTA announces that the shutdown has been shortened to 15 months.
 
2017: Increasingly bad subway and bus service prompts an outcry from New Yorkers. Andrew Cuomo, who has run the MTA since 2011, blames the mayor.
 
JUNE 29TH, 2017: Governor Andrew Cuomo, who has run the MTA since 2011, declares a state of emergency on the Subway over poor service.
 
DECEMBER 2017: After over almost two years of study and public comment, the MTA releases full plans for a 15-month L Shutdown and mitigation/transportation options. Andrew Cuomo, who has run the MTA since 2011, does nothing.
 
2018: The MTA continues working on plans for the shutdown. Andrew Cuomo, who has run the MTA since 2011, does nothing. The shutdown is scheduled to begin in April of 2019.
 
NOVEMBER 2018: After a stiff primary challenge by Cynthia Nixon in a campaign focused on the Subways, Andrew Cuomo wins reelection to his third term with 60% of the vote.
 
DECEMBER 14TH, 2018: Six years after Sandy damaged the tunnel and nearly three years after planning began, Andrew Cuomo, who has run the MTA since 2011, takes an interest for the first time and decides to temporarily halt L service to visit the tunnel with some of his friends.
 
JANUARY 3RD, 2019: Three weeks after visiting the tunnel, Cuomo announces that the MTA’s 3 years of planning are null because the shutdown will not happen and is actually unnecessary. The tunnel apparently is not (?) structurally unsound and instead of massive repairs they’re just going to install new cable racks.
 
In sum: Andrew Cuomo has been running the show the whole time, through fare increases, disasters, and steadily worsening service. I don’t know if the L shutdown is necessary or not. I don’t know if Cuomo’s plan will fix the problem or if it’s just a band-aid that will put the problems off until later when he’s not the governor.
 
I do know this: 400,000 people take the L train every fucking day and damage to this critical tunnel is a Huge Fucking Deal. Either we were lied to before, when we were told the shutdown was a necessary sacrifice, or today, when we were told it wasn’t.
 
In either case, Andrew Cuomo has been running this whole thing for a long time and whatever happens is his fault. Where was he when the MTA was planning this? Why did he wait so long to take an interest?
 
Based on my read of his plan–if you can call a powerpoint presentation a plan–this dipshit is putting off hard decisions for short-term political gain so he can look like a hero, and if he gets away with it we will pay down the line.
 
This is not a plan, and this whole process is an insult to the people of New York. This guy asked a couple of his buddies who have never managed a transit project to come up with something that sounds good so he could declare victory. This is not the seriousness that his high office deserves. This is not the seriousness that the people of New York deserve.
 
Either the MTA, which Cuomo runs, is grossly, criminally dishonest, or Cuomo himself is. Or both.
 
I look forward to more coverage of whatever bullshit Cuomo is proposing but this has been a disgrace and an insult to the people he has pledged to serve.

Self-Replicating Machines are the Next Big Thing

What About Progress?

Where” many people ask “is my flying car?

Progress is the idea that, in both the short and long term, things get better.  For much of human history, progress meant better tools for farming and hunting which allowed more people to live free from hunger.  It meant the development of strong nation-states that freed people from the horrors of civil war.  It meant medicine, urbanism, industrialization, ships, trains, cars, planes, computers, and smartphones.  It meant that people can live longer and better lives while working less and seeing more of the world.

Flying-Prius-630x420

I’m sure this is exactly what you had in mind

There is a growing feeling in the most advanced countries that progress has slowed or even stopped.  Life expectancy and income for some is lower than it was for their parents.  The growing threat of climate change makes others question the foundations of industrial civilization itself.

There is another way.

Human labor is the magic ingredient that provides us with everything we have, and progress ultimately depends on increasing people’s standards of living without necessarily increasing the amount of human labor they provide.  This improvement is frequently in terms of material goods: More living space, an air-conditioner, better food, or more clothes.  It can be a service: Healthcare, art, or a taxi ride.  It can be structural: Democracy, disease prevention, or nondiscrimination laws.

Self-replicating machines can only provide the first of these.  But they can do so in such an effective way that they will massively increase the standard of living of all people.  In doing so they will make it possible for us to fulfill even our most outlandish dreams.

work-in-progress

We’re much better off now.

Globally, economic growth is about 2%-3%.  At this rate, the world economy will double in size every 25-35 years.  Reducing this doubling time is the most basic way in which self-replicating machines (SRMs) will help humanity:  With short reproduction times and efficient, labor-free operation, our ability to provide for ourselves will increase much faster than it ever could traditionally.

What Can Self-Replicating Machines Do?

Although it’s cool, a machine that can build a copy of itself is of no intrinsic value.  SRMs in the abstract are as economically useful as plants, animals, or bacteria in the wild: Interesting, but not of any material benefit to people.

In order to build a copy of itself, any SRM will have a wide variety of capabilities.  It will obtain resources from the surrounding environment; it will convert these resources into usable materials; it will form these materials into usable parts; and it will assemble these parts into a self-replicating machine.  It will need to generate electrical and thermal energy, dispose of waste materials, and create structures to house its machinery.  Each SRM will be massively complex and will contain a large number of different components.

In short: If you can build a machine that can build a copy of itself, you can also build nearly anything else.  An SRM will be able to shape materials in a variety of different ways to produce a large number of different components.  It will be a Universal Constructor.

A Universal Constructor is a machine that can build anything.  An SRM, on the face of it, is not this.  There will be a limit to the capabilities of the machine.  Perhaps there will be a minimum feature size it can attain.  Perhaps it will be unable to find and extract certain elements from its environment.  Perhaps there are certain kinds of assembly that it is unable to do.

advanced_automation_for_space_missions_figure_5-19

Artist’s Rendition of an SRM on the Moon

The important point to recognize is that while it is possible to build a machine to do these things, an SRM will not be designed to do so.  What it could do is build a machine that could do these things, or build a machine that could build a machine that can do them, et cetera.  An SRM will necessarily be flexible enough in its abilities that such progress is possible.  All we need to do is tell it how.  This is not so different from the development of human technology:  In the beginning, we could only create things on a relatively human scale.  Now we can create things as small as a few atoms or as large as a cross-continental highway.

The difference is that, with no inputs of human labor and potentially operating on common or otherwise unused land, SRM can do so at a cost approaching zero.

Where Will This Take Us?

There are accomplishments that we can dream of, but which we don’t do because of their prohibitive cost and scale.

It’s possible to dig a tunnel from New York to London on which trains will travel at supersonic speeds.

It’s possible to build every person on Earth a house and allow them to live in it for free.

It’s possible to solve world hunger with robotic farms that create and deliver all the food humanity needs.

It’s possible to have factories in space that create all of the goods that people could want and land them right in front of you as-needed, and also in doing so to create new habitable worlds on which people live.

Self-Replication and Universal Construction are incredibly powerful technologies, especially when combined.  Given time, the only limit to our capabilities will be our imagination and our ability to describe what we want done.

vrS6aas

The future of Mars?

Will This Be the End of the World?

No.

SRM is most frequently discussed as part of a “Gray Goo” scenario, where self-replicating nanomachines replicate out of control and turn the whole world into replicators.  Real, near-term SRM will not be like this for the very simple reason that it won’t be made of nanomachines.  Like any large, complex system it’ll be relatively easy to stop an SRM if you want to by damaging its components.  A good design would also include simple but effective safety features such as an on/off switch.

Perhaps SRM will be designed with one small but necessary component requiring human installation.  Perhaps they will be designed to need a small amount of some rare element or compound that they can’t obtain from their environment.

No matter how well they are designed, SRM will have replication times measured in months and years, not milliseconds.  They simply won’t move fast enough to be a serious threat.

How Do We Get There?

There are Five Fundamental Stages through which matter must be transformed in order to create SRM:

  1. Resources: Matter in its state of nature, before incorporation into a machine
  2. Ores: Resources which have been extracted from nature and are ready to be transformed into useful materials
  3. Ingots: Purified materials which can be formed into different parts
  4. Parts: Single components of a machine made from ingots via some process
  5. Systems: Fully functional machines or parts of machines

The Four Fundamental Processes are the classes of technologies that allow matter to move forward through these Stages:

  1. Extraction
  2. Smelting (By analogy to Iron, meaning the processes required to create a simple substance from ore)
  3. Forming
  4. Assembly

Depending on the material being worked with and the properties of the final product, each of these four processes will be done in a number of different ways using different technologies.

I do not mean to oversimplify: What I have described above is a framework for a very challenging endeavor.  However challenging it may be, it is one of the most worthwhile things that we could strive to do.

I propose that the best way to attack this project is to begin at the middle and work outwards.  The middle is ingots of the most useful industrial material the world has ever known: Mild Carbon Steel.

Starting from this ingot, we move both backwards and forwards: How do we smelt this ingot out of the relevant ores?  By which technologies do we turn this steel into useful materials?

Carbon Steel contains just two elements: Iron and Carbon.  Iron ore is normally smelted into Iron using Coal.  However, Hydrogen works just as well, has a larger number of applications, and can be extracted from water by electrolysis.  Carbon could be obtained from charred biomass.  By mixing the two in appropriate quantities at high temperatures, you have Steel.

solartower

One way for an SRM to generate power is a Solar Power Tower, which uses arrays of mirrors to focus sunlight on a small area.

There are a number of ways in which Steel can be formed into useful parts, but two particularly useful technologies will likely be Investment Casting and Profile Cutting.  Investment Casting can take advantage of 3D Printing technology to create a complicated shape in 3 dimensions, form a mold around it, and then turn the 3D Printed part into a cast Steel part.  Profile cutting can create a wide variety of 2D shapes in Steel Plates of various thickness.

Each process will require its own mix of parts and materials.  From this it will be possible to add to the lists of Resources, Ores, Ingots, Parts, and Systems as well as to the lists of Extraction, Smelting, Forming, and Assembly processes that will be used in SRM.

Design Philosophy

There are a few ways of thinking that are vital to making SRM technology real and successful.  To my mind, some of the more important ones are as follows:

  1. Sustainability: SRM enables us to realize our ambitions on a global scale but also requires us to think of our actions globally.  Therefore it’s vital to design these machines to have no emissions of Greenhouse Gases or other pollutants.
  2. Minimum Viable Products: Perfect is the enemy of Good Enough.  The first products of any development effort will be closer to proofs-of-concept than to SRM.  Even as we approach SRM, there will be some human labor required to enable self-replication.  This will ideally take the form of cartridges of hard-to-find but important materials (Fluorine or Copper being great examples) loaded onto the machines at the beginning of the self-reproduction cycle.  Long-term it will be desirable to find substitutes for these materials such as using Aluminium in wires instead of Copper and finding ways to make Aluminium without fluorine.
  3. Modularity: SRM is similar in a lot of ways to a living organism.  Like living organisms, different configurations of SRM are better suited to different environments.  Therefore it is important to make it easy to modify the Self-Replicating system to adapt it to different environments.
  4. Commonality of Parts: It’s easier to make 100 of 1 thing than 1 each of 100 things.  The fewer different techniques are required to create a SRM, the faster its replication time will be.
11-img-13

We could live like this if we wanted to.

What Now?

I have laid out the bare-bones outlines of the future we can live in.  What we need to do is to make it happen.  We need to design the subsystems, develop the technologies, and implement them for our own purposes.  We can do this by direct design and by spreading awareness of the revolutionary potential of SRM.

I would encourage anyone who is interested to comment or to contact me.  Talk to people you know about the possibilities of SRM to raise their interest.  SRM is just a dream until we make it happen.

Replace the Electoral College

People are making a lot of noise this year about the Presidential Primaries being undemocratic and unfair.  However, I would like to focus on an equally undemocratic and unfair process that renders the general election votes of most Americans virtually meaningless:  The Electoral College.  The Electoral College is one of the most undemocratic, unrepresentative, and archaic institutions in the politics of the United States and should be eliminated in favor of a national popular vote.

The electoral college is the system by which the United States indirectly elects its President and Vice President every four years.  It was written into the Constitution in 1787 as a way to filter the voice of the masses by allowing them to pick “Electors” who would actually decide who became President.  The system has on several occasions (1800, 1824, 1860, 1876, 2000) caused Constitutional Crises that alternate voting systems might have avoided.  Every four years, the system takes away the ability of most Americans to have a significant effect in determining the outcome of the General Election.

It is this last point that I would like to home in on.  Election turnout in the United States is low compared to other countries, in part because many people feel like their votes don’t matter.  For most people, this is probably true.  The problem here is similar to gerrymandering:  While the general election results are typically fairly close (Obama beat Romney nationally by 3.9 percentage points), individual states are typically not (On average, whichever candidate won a given state won by 19.5 percentage points).  This has the effect that, unless you live in a state that tends to be balanced politically, your vote has little effect on the final election results.

This shouldn’t be news to anyone.  The states I just described are called “Swing States”.  These are the states that decide the election, time after time.  Although every person’s vote “counts” equally as one vote, a vote in these states matters more in determining who actually becomes the president.

This is calculable after-the-fact, too, in the following way:

  1. Find the margin of victory for the winner in a given state
  2. Take the inverse of this number.  This gives you the importance of each vote in determining the winner of this state.
  3. Multiply that by the number of electoral college votes this state has.  This is the importance of your vote, expressed in electoral college votes.
  4. Divide this number by half of the margin of victory for the winner of the electoral college.  This is the importance of the decision by each voter to vote in that state, expressed as a fraction of a win.

I have done this for each state in 2012 and mapped the result:

vote importance map

The states varied in importance from Washington, DC (Where a person’s decision to vote is 194 billionths of a general election victory) to Florida (Where a person’s decision to vote is 6,195 billionths of a general election victory, 32 times more important).  The numbers vary from year to year:  In 2000, a vote in Florida would have been worth much, much more than a vote in any other state.  In 2008, a relatively easy win for Obama, less so.

What if we did it differently?  If the Electoral College were abolished in favor of a national popular vote, everyone’s vote would count equally.  Voters in California and Utah would be equally important to a candidate’s hopes as voters in Ohio and Florida.  Instead of candidates competing for the votes of people who are similar to (but not the same as) you, they would actually be addressing your concerns in your neighborhood.

We Can Fix This

Although the electoral college is in the Constitution, State laws describe how electors must vote.  Most states require their electors to vote for whoever won the popular vote in their state.  However, a state could require its electors to vote for whoever won the national popular vote.  If 270 electoral college votes worth of states (a majority) were to do so, the president would effectively be chosen by the national popular vote.

There is just such a movement.  It is called the National Popular Vote Interstate Compact.  It has already been signed by 10 states and DC comprising 165 electoral college votes.  As few as four more states could be required to enact this into law: Texas, Florida, Illinois, and Pennsylvania combined have 107 electoral college votes, just enough to put the Compact over the top.

It’s not too late to make this law for 2016.  If you live in a state that has not yet adopted the Compact, please call your representatives in State government and ask them to improve American Democracy!

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.