Saturday, January 26, 2013

Aboveground Mars Houses

The design approach depicted herein is for permanent inhabited structures on Mars. This is not first mission stuff, it is for the follow-on voyages that plant permanent bases. There are at least a couple of necessary supporting technologies required to make this structure possible, technologies not currently in hand.

One is a concrete substitute made from local materials on Mars (“icecrete” or “pycrete” will not serve, since interior temperatures will necessarily be above freezing). The other is a window transparency material of overall characteristics similar to glass, but made locally on Mars. Neither currently exists.

Suspend disbelief for this discussion, and assume that the concrete and glass replacements have been perfected. What might serve as an aboveground habitation space, given the near-vacuum, the cold, and the radiation environment that we face on Mars? There just won’t be a cave to live in everywhere that you might want to go.

The structure must be pressurized, so that at least some surfaces must be round in order to be structurally efficient. It needs an upper surface that can serve as a radiation shield against both the steady drizzle of high-energy cosmic rays, and the erratic brief and intense blasts of lower-energy solar flare radiation.

Because this is a planetary surface, but with little atmosphere and no magnetic field, essentially half the interplanetary radiation fluxes are good design values. This is simply because half the sky from which the danger comes is blocked by the planet beneath your feet. For cosmic rays, the interplanetary flux varies with the solar cycle from about 24 to about 60 REM per year, so that would be 12 to 30 REM per year, as exposed on the surface outside.

The problem with cosmic rays is secondary particle showers from your shielding. It either needs to be thin, or else very thick. 20 cm of water will cut these exposures roughly in half (that’s down to about 6 to 15 REM per year on the surface of Mars). The applicable exposure limits for astronauts are currently 50 REM per year, and a career limit that varies between 100 and 400 REM accumulated, depending upon age and gender. The higher-level short-term limit (25 REM in 30 days) is not an issue here. No limits are available for children yet.

Clearly, the thin shield approach is inadequate for more-or-less permanent adult residents, because the career limits get reached in as little as 6 years, discounting completely the travel exposures incurred reaching Mars. However, such a shield would be quite adequate for solar flare exposures, and anything thicker is even better.

The other shielding approach is many meters of regolith, which essentially eliminates the exposures from both sources. It does have to be many meters thick, so that secondary showers also get absorbed in the shield. This is heavy, and could also do double-duty resisting vertically-oriented pressure blow-out forces. You could even bury ice-as-a-permafrost-layer in this structure, getting a lot of extra shielding benefit from the hydrogen in the water.

That last point (thick regolith layer as shield) leads directly to the notion of vertically-oriented cylindrical structures resisting internal pressure by tension in the hoop direction, and by ballast weight in the longitudinal (vertical) direction. The roof should have some overhang, so that these will essentially look like man-made mushrooms. See the figure at the end of this article.

The more-or-less flat roof “plate” must be capable of supporting the full deadweight regolith loading in the depressurized state. Pressurization can unload those stresses somewhat. This structure is supported by a central column, and by the surrounding pressure wall ring, which in turn is very likely to be a series of columns between which flat transparency panels are mounted. Such columns must be radially and circumferentially-restrained at both top and bottom, to provide the hoop stress resistance.

All of the column structures must resist heavy compression, and those in the ring must also resist bending, assuming the flat-facet approximation to a cylindrical shape applies, for ease of transparency panel construction. I also assume these panels are brittle like glass, so that the ring wall columns must be very stiff, stiffer by far than the transparencies. The transparencies themselves need to be fairly narrow to minimize panel bending due to pressurization, although they can be tall. There will be lots of columns in the ring wall.

The central column can be simple masonry, of local rock and the concrete substitute, with minimal reinforcement. It can be hollow, so as to provide closed architectural spaces in its interior. Such a structure is not a pressure vessel, so it cannot be used as a shelter in the event of a depressurization accident. I would recommend inflatables well-distributed within the building for that purpose, each with supplies and pressure suits stored within.

The ring wall columns must be shaped to achieve great bending stiffness indeed, and they must be capable of supporting great compressive load. Structural steel shapes seem ideally suited for this purpose, although it might be possible to achieve the same ends with a pre-stressed beam shape,  made of the concrete substitute. These would be an analog to the concrete highway bridge beams, stood on end, and loaded from the inside out.

This building is going to require large concrete-substitute foundations, in order to provide stability without movement upon pressurization. This is little different from construction practices here on Earth. One difference is the gas seal through the Martian regolith underneath the ring wall foundations. It might be prudent to lay down a buried layer of artificial “ice permafrost” well under the foundations, rising up to the bottoms of the ring wall foundations to effect a contact ice seal. This may or may not be necessary, depending upon how fast gases can percolate through Martian regolith. That requirement remains to be determined. But we can do this if required.

The roof can be a flat slab with an integral “waffle” grid of stiffening beams, much like a slab foundation on Earth. I would put the slab below and the beams above, to simplify the interface with the ring wall and the central column. The beams can extend tapered onto the overhang. Pockets in the roof slab,  and on the foundations, provide ring wall column restraint by simple socketing.

There are two cylinder-end blow-out-load sealing problems to worry about: at the ring wall foundations, and at the wall-roof joint. If the roof, the foundation, and the ring wall can be built to the same effective stiffness, and the roof (with its regolith shield cover) is heavy enough, then sealing becomes nothing but interior caulking, something we have centuries of experience with, in ship-building.

I suggest double or even triple glazing in the transparency panels. These could be set separately into stepped pockets pre-manufactured into the columns, foundation, and roof panel, and then caulked there to “lock-in” while depressurized. They would be positively-pressed into place while pressurized. I would suggest graduated-step lower pressures in the spaces between layers, thus requiring that a means to control and monitor inter-panel pressures be built into every window bay. Double or triple glazing in this fashion provides both accident protection and good thermal insulation.

Inside the building, you have a large space with a dirt floor. Parts of this can be paved and used as desired, and parts of it can be farmed or gardened, as desired. With the roof, there is no direct exposure to the harsh UV component of Martian sunlight. Yet there is plenty of daytime illumination coming through the transparencies in the ring wall.

This is terrain-reflected sunlight, and it will be lower in UV content. The transparency material will also likely reduce the UV a little, as well. Some UV is required for plants to grow, so you do not want to completely eliminate it. You can adjust and augment the terrain-bounced sunlight with suitable reflective surfaces positioned and angled outside the building. Illumination and UV content can thus be easily tailored to each construction location.

Inside these buildings, you can easily run an Earth-normal atmosphere. Using local ice as a water source, Earth-type agriculture and living conditions become entirely practical inside these buildings. That eliminates the risks,  for pregnancy and birth, of exposure to a low-pressure oxygen atmosphere. It also reduces fire dangers considerably!

Smaller structures can be habitations and parkland recreation spaces, even small gardens. Larger ones can be agricultural food-growing spaces, which can include both plants and animals brought directly from Earth, and not modified in any way for an alien environment. We can just do what we already know how to do, as regards farming, and in our shirtsleeves, too!

The rooftops are perfect places to mount solar-thermal and solar-electric energy-gathering equipment. I suggest the water reclamation equipment be located outside these buildings in simple sheds in the near-vacuum conditions. That way, vacuum-flash distillation becomes trivially easy, and can be an integral part of the overall reclamation process. Recovered solids can be airlocked-in for use as fertilizers. (That total water reclamation process is another technology that is not yet in-hand.)

We do have some agricultural methods and food sources associated with both fresh- and salt-water aquaculture. That does not require buildings like this, and is not ultimately limited in size by the square-cube scaling effect, the way these mushroom buildings are. This is a self-pressurizing ice-covered pond approach, described in the article “Aquaculture Habitat Lake for Mars”, dated 3-18-12.

If you want to build the classic pressurized dome of science fiction, there are some structural considerations described in the article “Pressurizable Domed Habitat Structures”, dated 6-9-12. This approach does not address radiation shielding or thermal insulation, so I like the mushroom-building approach better. However, it might be useful for some purposes, not specified here.  We do not yet have the materials from which such a dome might be constructed.

Some structures might well be built from “icecrete” or “pycrete”, just not those exposed to above-freezing temperatures, or exposed to sublimation. For a discussion, see ““Icecrete”, a Substitute for Concrete as a Building Material on Other (Colder) Worlds”, dated 3-11-12.

Clearly, a supple spacesuit is necessary to carry out major construction activities on Mars. In my opinion, we will never “get there” with the standard “gas balloon” suits we have been using since the late 1950’s. I believe the answer lies with the mechanical counterpressure approach, pioneered by Dr. Paul Webb, who developed it from the “partial pressure suit” designs of the late 1940’s.

This design approach has been ignored for decades, and is currently held back by inappropriate design compression requirements, although funded small-scale by NASA at some academic institutions. See “Fundamental Design Criteria for Alternative Space Suit Approaches”, dated 1-21-11, for a discussion of design criteria that are actually appropriate, and which could be met successfully with technologies available ever since the late 1960’s.

I got the radiation data from NASA itself, and posted it in “Space Travel Radiation Risks”, dated 5-2-12.

I see lots of proposals for establishing bases on Mars that will require multiple vehicles landed at the same site. That will indeed be required to establish any realistic permanent bases. Multiple vehicles landed together raises not only the issues of precision-guided landings, but also the issues of collision risks, and of close-proximity rocket-blast damage effects. Those last two are among the several practical issues included in the discussions contained in “Mars Landing Options”, dated 12-31-12.

I do not think we are yet technologically ready to attempt long-term settlements on Mars. But we soon could be! Perhaps very soon. And, it is time now to think realistically about how we might go about building these settlements. That is the purpose of this article: to bring good ideas to that debate.

Update 1-28-13:  I forgot,  we'll need a good caulk/adhesive that can be applied in vacuum,  and works with concrete and glass.  We're also going to need heavy machinery (functional on Mars) that fulfills the roles of backhoes,  bulldozers,  and construction site cranes.  I don't see much problem obtaining this stuff,  but none of it is yet actually in-hand.  Like the concrete and glass substitutes,  we cannot build habitations like this,  until all those things are in-hand.  (Rebar we can ship from Earth until somebody builds a steel mill equivalent on Mars.) 

Monday, January 21, 2013

BOE Entry Analysis of Apollo Returning From the Moon

I used my Back-of-the-Envelope (BOE) Entry Analysis to model an Apollo command module capsule returning from the moon. Historically, this was a very shallow entry angle below local horizontal, and essentially at Earth escape speed. I used the very best estimates I could find for the Apollo capsule ballistic coefficient (313.5 kg/sq.m) and heat shield radius of curvature (4.59 m). Historically, we also know that Apollo returning from the moon peaked at about 11 gees deceleration during entry.

The BOE model is described in reference 1, and again in the more detailed user’s guide (reference 2). The original Earth entry workbook in the spreadsheet model was set up as a generic example. I modified this to reflect Apollo data, and tweaked the entry angle from the original 1 degree, up to 2 degrees, at which point peak gees matched the historical value. (At 1 degree, peak gees was closer to 5.5, and the heating numbers were a little smaller.)

All the other spreadsheet results are then presented here, for others to compare with actual Apollo entry results, at their leisure. I think that at least the dynamics look pretty close, especially considering just how over-simplified this model really is. As I have always said, the heating model leaves a lot to be desired.

Figures 1-4 present the trajectory profiles of relevant data, annotated to show the Mach 3 point at which model applicability ends. Figure 5 is an excerpted spreadsheet image of the inputs. Figure 6 is a set of excerpts from the entry analysis portion of the spreadsheet showing the relevant calculated values. All figures are below, at the end of this article.


1.“Back-of-the-Envelope Entry Model”, 7-14-12, posted at “”
2.“BOE Entry Model User’s Guide”, 1-21-13, posted at “”

Figure 1—BOE-Predicted Apollo Deceleration

Figure 2 – BOE-Predicted Apollo Velocity Profile

Figure 3 – BOE-Predicted Apollo Range versus Altitude Profiles

Figure 4 – BOE-Predicted Apollo Heating

Figure 5 – Spreadsheet Inputs for Apollo Entry

Figure 6 – Spreadsheet Results (Excerpts) for Apollo Entry

BOE Entry Model User's Guide

Update 12-30-17:  

Be aware that this model is an oversimplified 2-D representation of an inherently 3-D process.  It is more applicable to warhead entry at steep entry angles,  where gravity bending of the ballistic trajectory is an insignificant factor.  Yet,  it seems to generate more-or-less in-the-ballpark estimates for planetary entry,  if you bend the range around the circumference of the planet.  That presumes a bit of off-angle capsule lift offsets the gravity bending that would otherwise steepen the trajectory.

Also be aware that I had to correct the estimates for peak gees and peak heating,  as the closed form estimates seem to have been recorded incorrectly in the old literature.  I used instead instantaneous or integrated values directly from the calculations.  These are by far more reliable. 

This is a user’s guide to my entry spreadsheet model that is comprehensive enough for the reader to literally create his own spreadsheet from scratch. It presumes the reader has Microsoft “Excel” on his computer. I believe without proof that the Microsoft “Works” spreadsheet could be used to execute the calculations, but I have doubts about its graphing capabilities. “Excel” has the graphing capabilities that I used quite effectively.

When I first set this up, I created workbook pages in Excel for generic entry data regarding Earth, Mars, and Titan. The same analysis was programmed into one (Earth), and then copied to the other two (Mars and Titan), and then customized for each set of input data. I have since used the Mars spreadsheet the most, and I also added a bit to that analysis (in terms of speed of sound for local Mach number). That Mars entry model is the baseline spreadsheet layout presented here. I have never updated the other two.

Some of these spreadsheet cells have color shading. The yellow refers to user input data. The green is where I highlighted “end-of-hypersonics” at about Mach 3, and the brown is the closed-form estimates from the original 1956-vintage analysis that I found to be unreliable, and labeled “DO NOT USE”. The simplified model was described in reference 1, and its convective heat transfer estimates I edited in an earlier article here on “exrocketman” (reference 2). Actually, the closed form solutions for peak gees and peak heating rate are not bad. It is the closed-form total heat absorbed estimate that is really very wrong. But, I just do not trust any of those closed-form estimates. Numerical integration I trust.

The entry model uses an exponential scale height approximation to the density versus altitude relationship, and uses altitude as the ultimate independent variable, just as it did in 1956. It assumes constant ballistic coefficient, and constant local flight path angle, and is therefore set up in two-dimensional Cartesian rectangular coordinate format for simplicity. Calculations begin at “atmospheric interface” conditions, and work downward from there. I used the data given in reference 1 for those interface altitudes. (This is also a model that I do remember seeing in engineering graduate school, although my notes from then are long gone.)

In particular, as a custom user-input (also highlighted yellow) I inserted some extra rows to provide a finer digitization of the altitude, so that I could get explicitly-calculated data closer to Mach 3. The user is always free to do things like that. Just be sure to drag your calculations down across the inserted rows, because sometimes formulas do not increment in the spreadsheet in the way you intended.

User Inputs

Figure 1 (at end of this article) is a bitmap image of the Mars entry model spreadsheet copied into Windows “Paintbrush”, and edited there to restore the overall cell headings. It will be a little hard to read the detailed data in that overall view, but that is not the point. The point is: where are the basic user inputs? They are in the block of cells from columns A to O, and rows 1 to 5. Variable names, units of measure, and values are in separate cells, with the actual input values highlighted yellow. The user just needs to plug in the appropriate numbers for his case.

These basic inputs comprise the (constant) vehicle ballistic coefficient beta in cell C2, and its “nose radius” rn in cell C3. That radius is actually just the radius of curvature of the heat shield surface facing the oncoming flow. The value refers specifically to radius of curvature at the stagnation point, if the curvature varies.

The density versus scale height model is an exponential curve fit approximation involving scale height and an effective density at “zero” altitude that is a curve fit constant, not the actual surface density. There is a range of altitudes, between which this curve fit approximation is valid. Those four items are input as follows: density “zero” in cell F2, scale height in cell F3, lower altitude limit of applicability in cell F4, and upper altitude limit of applicability in cell F5.

Those last two inputs are for simple visual comparison with the altitudes where “things are happening” in your analysis. They are not used in the calculations at all. If the computed deceleration pulse falls outside those limits, then you need to revise your density scale height model so that it falls inside. The density “zero” rho0 and scale height densH need to be selected so that calculated density matches rather closely the actual atmosphere density versus altitude (as in reference 1) between the two limits.

The entry conditions are described by interface altitude, vehicle velocity at that interface, and the flight path angle at interface (as degrees of depression below local horizontal). The over-simplified analysis will hold that flight path angle as constant, but experiences with non-lifting warhead entry show this to be a pretty good approximation, surprisingly enough. Those input data go in as follows: interface altitude zatm in cell I2, interface velocity Vatm in cell I3, and interface path angle theta in cell I4.

For the convection model, the stagnation-point convective heating rate k-factor (krate) in the old correlation goes in cell L2. A separate k-factor (ktot) for the closed-form total absorbed heat went into cell L3, but that is not to be used, because it is inaccurate, and has been shaded brown “DO NOT USE” as shown. The heating rate k-value krate used here is the correct metric-units version of the factor discussed in reference 2, not the somewhat-incorrect value used in reference 1. There is no correct value to use for the total-absorbed k-factor ktot.

I have shown the escape velocity at interface altitude Vesc in cell N4, although that is not required to be a user input, and is not used in the analysis. I included it merely for easy visual comparison of entry conditions with escape conditions. The analysis can be used for entry interface velocities above interface escape speed. Circular orbit speed at interface is escape divided by the square root of 2.

The C-factor value in cell O2 is not a user input, but it is a constant used in the analysis. It is computed from the listed user inputs as follows:
Cfactor = Rho0*1000*densH/(2*beta*sin(theta/57.296)) where densH is the scale height value and rho0 is the “zero” value in the correlation, beta is the vehicle ballistic coefficient, and theta is the depression angle of the trajectory in degrees.

The actual formula contained in the cell O2 is:
where the 57.296 converts degrees to radians

Entry Analysis

Column A from rows 7 to 40 describe the altitudes in the analysis, with an alphanumeric heading in cell A7. Going down the column, each altitude is the previous altitude minus 5, units being km. The first altitude is the entry altitude, which it copies from the user input in cell I2. That cell formula is simply
with all the drag-down calculations below it looking like that in cell A9:

Velocity at any given altitude is computed from the corresponding altitude by means of the old modeling equation, and it is listed in column B from row 8 down to row 40, the alphanumeric heading being in cell B7. That formula is
V = Vatm*exp[-Cfactor*exp(-z/densH)]
where z is the altitude in km
and with the corresponding spreadsheet formula in cell B8 being:
note the $ signs that lock in the constants against incrementing with the pull-down of the calculation.

The next column (C) contains horizontal range data computed as R=-(z-zatm)/tan(theta), for which the corresponding formula in cell C9 is typical:

Slant range is on column D, and is computed using the sine instead of the tangent. The corresponding formula in cell D9 is typical:

Computed time starts from zero at entry interface in cell E8. From there the increment of time is the difference in slant range from current to previous, divided by the average of the current and previous velocities. This increment is added to the previous time to estimate current time. The formula in cell E9 is typical:

Deceleration gees is really just the velocity difference current minus previous, divided by both the time difference current minus previous, and the standard acceleration of gravity. There is a meter-km conversion in it, and the negative result is made positive to minimize confusion. The formula in cell f9 is typical, and it starts from zero in cell f8:

Column G is just a repeat of column B, just to get the velocity data in the spreadsheet table located to the right of the slant range data in column C. That enables cross-plotting of the data using slant range as the independent variable. Intuitively, that slant range is your position in the sky between the entry interface and the “end-of-hypersonics” at around Mach 3. Horizontal range “wraps” around the curved surface of the planet or moon, and altitude becomes the radial extension beyond the surface radius.

Column H contains the calculated density coming from the scale height correlation equation given above. It is calculated from the corresponding altitude very simply, and the formula in cell H8 is quite typical:

Column I contains the computed stagnation point convective heating rate, below the alphanumeric heading in cell I7. It is computed from the empirical (and dimensionally-inconsistent) correlation equation:
Q = krate*[(rho/rn)^0.5]*[(V converted to m/s)^3.0]
where rho is the density in column H

The formula in cell I8 is typical:

Column J is the numerically-integrated total absorbed heat up to the corresponding time t in column E. The increment in heat is the time difference current minus previous, multiplied by the average of the current and previous heating rates. This increment is added to the previous total heat, starting from zero in row 8. A typical cell formula is that in cell J9:

The speed-of-sound and Mach number computations in columns K and L of the Mars spreadsheet were never added to the Earth or Titan spreadsheets, as can be seen in Figures 2 and 3 below. I added these specifically to incorporate a linear variation approximation of Martian speed of sound applicable between 10 and 60 km altitudes. It’s not all that far off, all the way down to the surface. This was based on the typical Mars atmosphere model reported in reference 1. That speed of sound correlation was c, m/s = -0.740*(z,km)+236.4, and the corresponding Mach number in column L was nothing more than just V/c, with due regard for the km/s-m/s conversion.

I did not fill the entirety of columns K and L with this, as can be seen in Figure 1. I started arbitrarily at 80 km in row 19, and carried it all the way down to the surface. Any reader can do exactly the same thing, you just need to curve-fit speed-of-sound data versus altitude to suit your needs. The corresponding typical cell formulas are those of K19 and L19, as follows:
=-0.74*A19+236.4 speed of sound in K19
=1000*B19/K19 Mach number in L19

Processing Output Graphs

I usually set up my sheet to start at interface altitude, decrementing by 5 km to the surface or maybe one increment below. This works just fine for both Earth and Mars. For Titan, I used 25 km decrements, because the atmosphere is so deep. There are not enough rows available at any such decrement to “capture” the Mach 3 point, so I have to insert extra rows at finer decrement to “capture” it closely enough. Be sure and re-drag your calculations down across the inserted rows, in order to be sure all the cell formula incrementing gets done correctly – I have seen this fail otherwise.

I recommend cross-plotting your output data right there in the spreadsheet. I use four “standard” formats: (1) deceleration gees (column F) versus slant range (column D), which shows exactly where in the trajectory that pulse is, (2) velocity (column G) versus slant range (column D), which shows the sudden and dramatic decrease in speed through the deceleration pulse, (3) range (column C) and slant range (column D) versus altitude (column A), to illustrate the constant-angle nature of this trajectory, and (4) heating rate (column I) and heat absorbed (column J) vs slant range (column D) for comparison to gees (the heating rate pulse occurs a little earlier in the trajectory than the deceleration pulse).

I usually copy these plots to Microsoft “Paintbrush”, where I can easily add labels and notations and extra artwork, as desired. In particular, I like to mark the Mach 3 points on the plots. The analysis happily calculates data past that point, but the entire entry model is no longer applicable beyond it, because the flow field is no longer hypersonic. But the major effect is a shift from aerodynamic force dominance to gravity force dominance. From this point, gravity drags the trajectory ever more sharply and quickly downward (the two-dimensional straight line assumption is bad).

The Revisited Mars Lander Model

An example is the Mars entry spreadsheet, as it is currently set up for entry from low circular orbit. The detailed inputs are blown up for legibility in Figure 4, and correspond to the image in Figure 1. The revisited vehicle design has a larger ballistic coefficient than any of the probes, being “representative” of a much larger manned lander (400 kg/sq.m), with a fairly blunt heat shield (12.4 m radius of curvature at the stagnation point). The four annotated graphs were presented in reference 3. Entry interface is time zero at 135 km altitude, 3469 m/s, and 1.63 degrees depression angle.

The Mach 3 end-of-hypersonics point is 4140 km downrange and 17.2 km altitude. This is at 4141 km slant range: remember the estimated path is still locally depressed only 1.63 degrees, even though the range actually stretches quite a way around the curved planetary surface. Velocity is 675 m/s, and 1.17 KJ/ of heat has been accumulated by convection at the stagnation point. All of this is about 1426 sec (not quite 24 minutes) after entry interface.

Peak deceleration gees (near 0.72) occurred at about 1187 sec, 25 km up, and about 1772 m/s velocity. Peak stagnation point convective heating rate (about 2.6 W/ occurred at about 1034 sec after interface, and 35 km up. Velocity was about 2800 m/s. One can even compute the delta-vee afforded by hypersonic drag, as the entry interface velocity minus the end-of-hypersonics velocity: some 2794 m/s, which is about 80% of the total interface velocity.

The Earth Entry Model

This is a generic model that somewhat resembles some of our 1960’s-vintage unmanned space payloads, but at conditions similar to those of Apollo coming back from the moon. These are 200 kg/sq.m objects with a 1-meter nose radius, entering at escape speed (11.058 km/s) and 1 degree below horizontal. (Apollo was over 300 kg/sq.m, with a much blunter heat shield.) Interface altitude (time zero) is 140 km. The original annotated results plots for this case were given in reference 2.

The model predicts end-of-hypersonics about 684 sec (just over 11 minutes) after interface, at an altitude of 45 km (just over 147,000 feet), 5443 km downrange, and 837 m/s. About 35.2 KJ/ convective heating has been accumulated at the stagnation point. From there the trajectory would bend sharply downward, with stabilizing drogue chutes deployed at no more than about Mach 2.5 (near 690 m/s).

Peak deceleration gees would be near 5.4 at 470 sec, about 50 km up, and near 5770 m/s. Peak convective stagnation point heating would be near 182 W/, about 395 sec after interface, and 65 km up, and at about 9385 m/s velocity. Aero deceleration delta-vee is some 10.221 km/s, for about 92% of the entry velocity.

The Apollo capsule had a “heavier” ballistic coefficient, and a blunter heat shield. It would be an interesting study to run Apollo at these entry conditions and compare to the actual entry trajectory returning from the moon. Amazingly enough, even this model “looks pretty close”.

The Titan Entry Model

This is a generic model of a large probe entering Titan’s atmosphere at something “typical” of interplanetary transfer speed, and at 1 degree depression below horizontal. Interface was at 800 km and 3 km/s. The ballistic coefficient is 200 kg/sq.m, with a 1-meter nose radius. The original annotated results plots for this case were given in reference 2.

End-of hypersonics at local Mach 3 is estimated to be 11,472 sec (a bit over 3 hours) after interface, at about 300 km altitude, and wrapped around the moon about twice at nearly 29,000 km range. Speed is 730 m/s. The numbers show a very low peak deceleration of around 0.06 gees, peaking right before the end of hypersonics. 6.4 KJ/ was accumulated, with a very low peak of 1.4 W/ at about 400 km and 2509 m/s.

I rather doubt this entry model is very realistic, because of the way it wraps around the moon. The entry depression angle is too low.


1. “Atmospheric Environments for Entry, Descent, and Landing (EDL)”, C. G. Justus (NASA Marshall) and R. D. Braun (Georgia Tech), June, 2007
2. “Back-of-the-Envelope Entry Model”, 7-14-12, posted at “”
3. “Manned Chemical Lander Revisit”, 8-28-12, posted at “”

Figures are below (click on one to see them bigger,  "esc" gets you back):

Figure 1 – Spreadsheet Image for Mars Lander Design Revisited (per ref. 3)

Figure 2 – Spreadsheet Image for Earth Entry (original generic model per ref. 2)

Figure 3 – Spreadsheet Image for Titan Entry (original generic model per ref. 2)

Figure 4 – Image of Spreadsheet Inputs for Mars Lander Revisited Case (per ref. 3)

Saturday, January 5, 2013

Using Nuclear Rockets Safely for Manned Space Travel

Update 4-8-2024:  Should any readers want to learn how to do what I do (estimating performance of launch rockets or other space vehicles),   be aware that I have created a series of short courses in how to go about these analyses,  complete with effective tools for actually carrying it out.  These course materials are available for free from a drop box that can be accessed from the Mars Society’s “New Mars” forums,  located at,  in the “Acheron labs” section,  “interplanetary transportation” topic,  and conversation thread titled “orbital mechanics class traditional”.  You may have scroll down past all the “sticky notes”. 

The first posting in that thread has a list of the classes available,  and these go far beyond just the two-body elementary orbital mechanics of ellipses.  There are the empirical corrections for losses to be covered,  approaches to use for estimating entry descent and landing on bodies with atmospheres,  and spreadsheet-based tools for estimating the performance of rocket engines and rocket vehicles.  The same thread has links to all the materials in the drop box. 

The New Mars forums would also welcome your participation.  Send an email to to find out how to join up.

A lot of the same information from those short courses is available scattered among the postings here.  There is a sort of “technical catalog” article that I try to main current.  It is titled “Lists of Some Articles by Topic Area”,  posted 21 October 2021.  There are categories for ramjet and closely-related,  aerothermodynamics and heat transfer,  rocket ballistics and rocket vehicle performance articles (of specific interest here),  asteroid defense articles,  space suits and atmospheres articles,  radiation hazard articles,  pulsejet articles,  articles about ethanol and ethanol blends in vehicles,  automotive care articles,  articles related to cactus eradication,  and articles related to towed decoys.  All of these are things that I really did. 

To access quickly any article on this site,  use the blog archive tool on the left.  All you need is the posting date and the title.  Click on the year,  then click on the month,  then click on the title if need be (such as if multiple articles were posted that month).  Visit the catalog article and just jot down those you want to go see.

Within any article,  you can see the figures enlarged,  by the expedient of just clicking on a figure.  You can scroll through all the figures at greatest resolution in an article that way,  although the figure numbers and titles are lacking.  There is an “X-out” top right that takes you right back to the article itself. 


I am not a specialist in this topic (nuclear rocketry), but I am an older, well-experienced aerospace/mechanical engineer, and I am well-read about these things. I have no hard numbers here, but these concepts really do look feasible and fruitful for manned Mars missions (and more).

Using solid-core nuclear rockets as propulsion in anything resembling a safe manner is not a trivial issue, to be sure. I do think the applications of orbit-to-orbit transport, and planetary landing, end up addressing this risk entirely differently.

For the orbit-to-orbit transport, most interestingly a Mars mission, issues of artificial gravity should interact very constructively with the need to provide radiation shielding from your reactor. There is a need to stage-off emptied propellant tanks after every “burn”, but if the design comprises a set of docked modules, it is easy to reconfigure into the same length “slender baton” shape at each stage-off. Spin the “baton” end-over-end for gravity: 56 m radius at 4 rpm is 1 full gee at a tolerable spin rate. (This is true even for chemically-powered designs.) See Figure 1.

Figure 1 – Reconfigurable Docked Module Design Provides Both Shielding and Artificial Gravity

This reconfigurable “slender baton” shape not only maintains radius for artificial gravity at low rpm, it also maintains the much longer distance that is so very necessary for getting shielding benefits out of your remaining propellant tanks. Somewhere around 40 meters of propellant tank fluids and structures should be quite effective at shielding the crew from nuclear radiation, during or between “burns”.

The lander is a vastly different proposition. Compact as it has to be for landing stability, shielding “steady state” by distance with tanks and fluids is impossible. The alternative is tons of lead or concrete, etc, also very undesirable. But since the descent and ascent “burns” are brief (minutes only), there is no need to shield “steady state”. Using what little tankage-and-structures shielding benefit that there is, the crew need only endure brief intense exposures, integrating to a very modest accumulated dose, actually. But this does require that the crew evacuate to a surface shelter remote from the lander during the surface stay. And you keep your distance from these landers in orbit, too, except when in use. See Figure 2. However, the numbers show such landers could fly both descent and ascent on a single fueling, and in a very practical design with significant cargo capability, at Mars.

Figure 2 – Nuclear Mars Lander Safety Depends Upon Short Exposure Times

The intensity of the exposures might be mitigated slightly by a shift to thorium reactors instead of uranium. This gets the worst-offender plutonium-239 out of the picture. But, fission leaks neutrons, no matter what, so it remains a very serious risk. I like the thorium approach better than uranium, in part because of the slightly-reduced danger from shut-down cores, but mostly because it is a more plentiful fuel. But, I recognize that we have to start with what we know: uranium.

Dangers of radiation from a contained core after engine shutdown (the worst risk of all) could be mitigated greatly by the open-cycle gas core concept, which is essentially an “empty steel can” between “burns” (see Figure 3). The light-bulb concepts feature a retained core, and suffer the same risks as solid core after engine shutdown. Only induced radioactivity in the engine shell is still a problem, and that is far less intense, and it decays far quicker. That’s why I’m such a fan of developing the open-cycle gas core technology as soon as possible, although we still have to start with what we know, that being a highly-enriched uranium solid core. No one has ever actually yet built and tested an open-cycle gas core engine, however.

Figure 3 – Radiation Danger Sources With Nuclear Rockets

I am also a very big fan of revising the nuclear rocket engine to use water instead of liquid hydrogen as the propellant fluid. I think the better heat-absorbing characteristics of the water may allow higher reactor power levels, thus offsetting in part the loss of specific impulse due to the higher molecular weight. This has never been implemented and tested. The water provides a better radiation shield, and logistically is far easier to handle and store in space. Further, it seems to be very widely available as native ice, at many interesting destinations in the solar system, including Mars.

There are several related articles on this site where I have posted design concepts and estimated performance numbers for “typical” designs, for both the orbit-to-orbit transport, and the landers. The best and most realistic of these articles are listed below, by date, title, and a content summary:

9-6-11 Mars Mission Second Thoughts Illustrated - looks at a revision of the original modular design in my original Mars Society convention paper, one with solid core nuclear/min energy transfer propulsion, instead of gas core/fast trip. Otherwise, the mission scenario and hardware designs are the same as that paper. This is revisited,  and the discussion extended,  in 4-23-12 Update to Mars Mission Design.

7-25-11 Going to Mars (or anywhere else nearby) the posting version – is the posted-here version of my original Mars mission paper at the Mars Society convention in Dallas, Texas, August 2011. The transit vehicle baseline propulsion in that paper was gas core nuclear/fast trip. The reusable solid core nuclear single stage lander performance is outlined very well in that paper. This lander design is very over-conservative, as no credit was given to aerodynamic drag during descent: the descent delta-vee was assumed to be the same as the ascent delta-vee.

7-19-12 Rough-Out Mars Mission with Artificial Gravity – this is the first analysis I ran that deliberately explores the integration of spin-generated artificial gravity into a slow-boat mission by using reconfigurable docked modules to build the orbital transport vehicle. This one assumes the same 60-ton reusable nuclear landers as the original paper, plus solid core nuclear/slowboat propulsion. The landers go with the transport in this analysis. In the original paper, they went separately. But the lander propellant supply still goes separately to Mars in this article. This design uses the 56 m radius figure at 4 rpm to provide 1 full gee of artificial gravity.

6-30-12 Atmosphere Models for Earth, Mars, and Titan – this provides realistic and traceable data for the “typical” Mars entry environment for lander design purposes. (Typical atmospheres for Earth and Titan are also defined.)  I got these data from a posted NASA paper,  cited within. 

7-14-12 “Back of the Envelope” Entry Model – this provides a traceable and realistic means of quickly estimating how much velocity reduction can be achieved on descent to Mars (or any other location with an atmosphere), given a ballistic coefficient, a velocity at entry interface, and a descent angle at entry.  I corrected the heat transfer model from a 1956-vintage warhead re-entry calculation that was discussed in the same posted NASA paper.  The dynamics were fine. 

8-10-12 Big Mars Lander Entry Sensitivity Study – sensitivity study of end-of-entry altitude to ballistic coefficient,   primarilyfor grazing entry from low Mars orbit.  The inherent grazing entry angle from low Mars orbit is important,  and this shows up in the sensitivity study.  Run with the corrected 1956-vintage model.

8-12-12 Direct-Entry Addition to Mars Entry Sensitivity Study – grazing entry for a typical interplanetary direct transfer speed. As expected,  higher entry speeds do put end-of-hypersonics at a much lower altitude.  Run with the corrected 1956-vintage model.

8-28-12 Manned Chemical Lander Revisit - A two-stage non-reusable chemical Mars lander design and performance estimate, using the entry results and direct rocket braking for the descent propellant requirement. Ascent is “standard” rocket equation with experiential “jigger factors” for gravity and drag losses. This is a multi-engine approach, using slight cant for supersonic retro plume stability. This article uses a more realistic ballistic coefficient than the design presented in an earlier article.  Run with the corrected 1956-vintage model.

Some closely-related discussions are given in two very recent articles:

12-31-12 Mars Landing Options – this one discusses the choices to be made (and their effects on mission design) of in-situ return propellant manufacture versus bringing the ascent propellant with you, and of landing one vehicle at any given site versus landing several close enough together to interact effectively.  Too close is also a bad outcome.

12-31-12 On Long-Term Sustainable Interplanetary Travel – this one discusses the merits of choosing a solid-core nuclear propulsion design revised to use water instead of hydrogen as the propellant fluid. Future developments that might prove beneficial are also explored.