Micro-Space >> Ultralight Manned Spaceflight

[rpspeck]

We have been pretty busy for the last two years doing SBIR proposals.  They are interesting and at least address the needs of customers who want something for use in space and actually have the money to pay for it!  If you try it, keep in mind that the customer usually has something specific in mind – which may not be all that obvious in the solicitation.  Try to figure it out, since “Innovative” suggests a wider range of possibilities than most customers are ready to consider.  Also keep in mind that these are small projects, from the funding standpoint, and won't carry a radically new idea very far toward a usable product. (Skip new SSTO launcher proposals!)  In fact, these customers have a LOT of experience with “New Ideas” which went nowhere!

For years the SBIR customers (particularly in the DOD) have been trying to  encourage companies who are organized to actually develop and produce products, and discourage “SBIR Mills” which produce only concept paperwork, which sits in a file, or a “prototype” with no potential for production.

A history of producing customized products for DOD, Researchers and Industry shows that focus and often gives you “Modules” you can reuse as you address the new need.  A proposal has a lot better chance if it shows real insight and preliminary “Phase Zero” (self funded) effort to rough in some of the ideas.  Although the process is slow, encouraging “debrief” notes can produce a “Win” the next year since the outlined need will often not be satisfactorily filled for several years.

We are doing preliminary work (unfunded until the contracts are signed) on our NASA “Lunar Navigator” with encouraging results. The wide field optical systems we have evaluated look pretty good, and will reduce the number of camera modules we need to monitor the entire sky with the required  resolution.  This effort has also led to the recognition of both enhanced operating modes and terrestrial applications for the same basic system in “GPS Compromised and GPS Denied” environments.

Another of our proposed technology efforts has received promising reviews from DARPA.  This involves application of our operational, magnetic propulsion and sensing system for use to assemble and maintain formations of small satellites.  In addition to our self funded efforts to upgrade our magnetic demonstration systems, we are now programming a microprocessor to do the signal analysis  required for 6DOF magnetic position sensing and handle the orbital dynamics of planning, and generating, the forces needed to optimize the position of member satellites in the formation.  It looks like these computing systems will mass only 2 to 5 grams – allowing their use in the smallest satellites. 

We have plenty of operational hardware to implement representative sensing and propulsive fields, but a full demonstration will require operation in a tiny orbital satellite cluster. We have roughed in plans for conversion of our lab hardware to a demonstrator that could be run in a “Zero Gee” aircraft flight, but even those flights will require moderate funding. 

[rpspeck]

The Way Forward

Those who are passionate about spaceflight and deep space exploration – including the possibility of personally participating – should keep in mind that nothing related to NASA is relevant to those interests. I once thought NASA's thinking, about how they would use their money, was really important: then I realized that NASA has no money!  NASA only has orders from Congress with the promise that money will be sent as those orders are obeyed. (There can and has been some fudging involving not quite doing what they are being paid to do, but that is all in the accounting “noise” .)  What we see is the “NASA-Congressional Complex” at work.  Congress-critters are not interested in your passions – they are interested in theirs.  This NASA+Complex has done some really neat stuff, and will continue to do so.  Options are being hashed out – once again – which could change that picture modestly.  But the “NASA Congressional Complex” is firmly committed to low risk activities which will create a lot of Jobs along with good publicity.  Affordable exploration in space doesn't fit into that picture!

NASA's public domain information does, however, show us how to do what we want to do.  Their “Paths not Taken”, including low cost space hardware options, also underscore and affirm the “Affordable Expedition” plans I continue to discuss. The fantasy of “What we could do...”, combining NASA+Complex money with our ideas and priorities, will forever remain a fantasy!  We will get into space, but look more like “Linus Rawlings” (mountain man in “How the West Was Won”), or – eventually – a wagon train on the Oregon Trail, than any of the technology in “Avatar”!

Since you can't walk to the Moon, the result will look more like the early days of aviation than the Old West.  Early aviation depended on Advertising/Publicity (associated with Air shows and Races), Communications (associated with the Air Mail contracts), Science/Technology (associated with aerial reconnaissance for both civil and military use) and Adventure (epitomized by Barnstormer Rides). There was a great deal of synergism between these components.  Details change with time (particularly when a whole century goes by), but basics don't change much.

The picture for entrepreneurial spaceflight will closely resemble the one outlined for aviation history, and have the same four components.  The “Adventure” component is the focus for “Virgin Galactic”, although (with typical synergism) the potential for these flights to increase productivity in space related Science/Technology is being recognized.  Advertising/Publicity was the key in both of the Lunar Lander competitions.  But Synergism will kick in big time when the fourth components starts feeding $$ Cash $$ into this community.  And that will come with ComSat maintenance and repair!

More than $5 Billion is “sent into space” each year with high value Communications Satellites and similar equipment. Assets totaling some $100 Billion are working in space to serve humans on Earth.  The ability to repair and maintain failed and dying satellites will, in some cases, bring immediate returns.  But more important is the “virtuous spiral” which will result from the Possibility of repair!  If things can be fixed, a risky new technology – which promises to quadruple ComSat capability – becomes a viable corporate option. Significantly better cost/performance ratios always open up new markets, and that boosts production rates to bring down costs further. Synergism again. If a compact Astronaut/Technician can reach an ailing ComSat, and fix it with only $16 Million costs (something marginally possible today), someone is going to make a hansom profit! 

This is not a one shot proposition.  Once demonstrated as a possibility, funding and capabilities will grow steadily.  But it is far more economical to access GEO ComSats from the Moon than from Earth.  So if the traveler can keep His/Her Wife/Husband happy at Moon Base One, that will support the existence of this outpost. 

The existence of profitable “GEO On Site Service” will of course fuel vastly greater ambitions for space Adventure,  Advertising/Publicity and Science/Technology, and hammer the costs for Deep Space activities down in every category. 

It is not too early to begin assembling the equipment required to get a compact Astronaut/Technician from LEO (delivered by a Falcon 1) to GEO and back.  Since this idea is no mystery, it may already be too late, for a startup with no preliminary experience, to capture this market!   

[rpspeck]

Satellite Formations

The potential performance of satellite formations is not widely discussed because practical methods  for  assembling and maintaining these clusters have never been demonstrated.  But clusters of small satellites promise to exceed the performance of massive satellites at far lower costs! 

For both Solar Power generation and RF Antenna performance, the area covered is the primary consideration.  A 100 kg bundle of 1 kg satellites (totaling 1/10 the LEO payload of the Falcon 1), with simple foldout solar panels on each, could actually generate over 10,000 Watts of Solar power when dispersed in orbit.  When cooperating as an Active Electronically Scanned Array (AESA), one form of Phased Array Antenna for Radio Frequency (RF) communication, this cluster could equal a 6 meter diameter antenna: One far too big to fly in the Space Shuttle!

With the cumulative power available, and the narrow focus of this power on Earth's surface (possibly a 30 meter diameter spot)  awesome signal strength is possible!  Practical applications would use the AESA system's ability to split the power, and send independent signals simultaneously focused on up to 100 customer's receivers.  One Hundred Megabaud communication becomes possible for each subscriber, in even the most remote places on this planet, with modest ground equipment.

Other satellite formations will produce extreme resolution, overhead Synthetic Aperture Radar imagery, and even higher resolution interferometric data to locate objects on the surface.  These estimates will not of course be  reached in the first test versions, but they can be reached and exceeded.  On top of this, individual satellites in the formation can be replaced, by maneuvering a failed unit out and an new one into its place.  The entire formation can also be expanded by adding hundreds of new satellite members to support additional customers and enhance the overall performance.

I won't try to cram more about the vast possibilities into this message.  But what is frustrating is that I have been trying to find funding (to show that our technology can make all this work) for over ten years without success. As noted, we at last have tentative (but far from firm) interest from DARPA.

[mlorrey]

Satellite Formations
....snip

I won't try to cram more about the vast possibilities into this message.  But what is frustrating is that I have been trying to find funding (to show that our technology can make all this work) for over ten years without success. As noted, we at last have tentative (but far from firm) interest from DARPA.

An interesting thing you can do with these picosats is that since drag is considerably more influential, you should be able to use your solar panels as steering fins to help maintain formation.

[Downix]

Any discussions of the N-Prize on here?  I've been pondering giving it a go.

[rpspeck]

The Way Forward - 2

Granting the real possibility of delivering a Solo, Deep Space Vehicle to LEO with a “Falcon-1” launch vehicle,  the “Way Forward” is much simpler than might be assumed. The payload of the “Falcon-1e”, at 1000kg, is sufficient to carry a typical astronaut, with his/her life support equipment and a lightweight reentry system, not only to GEO altitude, but also around the Moon and back to Earth!  The third stage propulsion can be produced using motors and propellant tanks Micro-Space already has in stock. Other entrepreneurs have also demonstrated adequate motors for “Trans Lunar Injection”, some using the storable fuels preferred.  But the extra orbital angular momentum required to Rendezvous with a satellite in GEO makes getting there harder than a loop around the Moon.  The return is also complicated, but Delta V for that leg can be reduced by passing around the Moon on the way back.  Since, as with most everything in space, stage masses scale nearly linearly with Payload Mass, selecting a “compact astronaut” makes a GEO service mission feasible with the Falcon-1e.

Micro-Space and others have already demonstrated the lightweight life support equipment required.  A number of adventurers have demonstrated comparable duration activities with similarly minimal “accommodations” and comparable risks, even without a multi million dollar $$$ bonus waiting  at the end! The main technological barrier to launching tomorrow is the lack of a proven reentry system.  Aerobraking into earth orbit, and rendezvous with a space station, is a possibility and can further reduce the vehicle mass flying above LEO, but that process has more risk and today would require coordination with space station owners who have shown no interest in cooperating! 

Adequate reentry shield materials are easy to come by (the Chinese once used Oak wood  successfully) but lab testing will be an unavoidable need.  Entrepreneurs who have tried to  use “National Labs” for tests have found that effort frustrating, very expensive and often unproductive.  Entrepreneurial sources for appropriate testing are going to be necessary. Fortunately, such tests for reentry materials are not all that difficult to arrange – as I will detail next week – and could be offered by any entrepreneur who has produced a smooth running liquid fuel rocket motor of 200 to 500 pounds thrust, and has a good place to run static firing of that motor.   

[rpspeck]

NASA Contract Real!

It is nice to see even a small dream realized!  Our Funded NASA SBIR project: Automatic Solar and Celestial Navigation on the Moon and Mars‏ , is now covered by its official paperwork!

This effort taps decades of work we have done with high precision optical measurements and image analysis, and our work towards space applications of these technologies. Our professional products in this area use what we call an “Imaging Microphotometer” to emphasize the quality we obtain from each of the sensor Pixels.  We have, however, managed to approximate this performance with more common, high resolution image sensors, including fraction of a gram mass sensor units.

The NASA work of course has direct application for both manned and unmanned exploration of the Moon, including our Google Lunar X PRIZE (GLXP) efforts.  These sensors can verify the relocation required  by the GLXP contest rules.  Even more important, they will provide a very high resolution location for any and all interesting features found by one of our Lunar Rover/Prospector systems.  (We have prototyped enhancements to the proposed NASA system which can push surface position accuracy to less than a meter!) 

Some of our early comments noted that our “Stand Up” lander configuration can easily incorporate an automated core drilling system. Using just 3% of the landed mass as propellant, our unit can “Hop” and re-land with 500 meter displacement. (1% propellant allows 55 meter displacement.) Thus dozens of  test holes can be analyzed in an interesting lunar field.

Related technology has already been evaluated for “Planetary/Star Cameras” to compute desired interplanetary and trans-lunar “mid course corrections” and guide Lunar and Planetary capture plus orbital insertion.   A variant of that technology would be used for altitude determination before our prototyped LIDAR system began providing good Lunar Altitude information during descent. 

We don't yet have a “Ticket to Orbit” (even for the 100 kg mass in LEO we expect to use to win the Google Prize), but we have many of the pieces necessary to go the rest of the way!

[imcub]

Congratulations!!! NASA funding is a great way to pay for your research if you can get it. 

I will continue following your progress in the coming years.

[rpspeck]

Lowest Mass Lunar Systems

It has been interesting to connect my closeup observation of “Jet Pack” fliers with my thoughts about Lunar Landings.  (The “Rocket Man” was taking off just the other side of the fence from us at the “X PRIZE Cup event, 2006.)  The roughly 22 seconds of flight available with a “Jet Pack” stretches to about 180 seconds on the Moon (at 1/6 G thrust, and assuming a 35%  increase in ISP working into a vacuum.)  What these skilled fliers do exceeded my expectations for what is humanly possible, in a difficult control environment!  (Flying these is NOT EASY and involves a lot of cautious training!)

On the Moon, the control actions are effectively in slow motion, and much less demanding.  The total energy and momentum involved do not, however, diminish and even greater caution is necessary. Good altitude and velocity measurements are highly desirable, since at the greater altitudes attainable, operation is less “instinctive”.   Using ½ the fuel for lift off, vertical velocity can approach 150 meters per second, and reach 6,750 meters ( 22,000 feet) altitude or reach 13.5 km horizontal distance with optimally angled flight!  (Both numbers are reduced by “gravity loss” with practical thrust values.)  These calculations assume that ½ of the usable fuel is saved for landing (plus all of the normal 10% reserve for safety) since the 150 meter per second landing velocity represents a 1100 meter (3,300 foot) free fall on Earth, without the assistance of air drag! 

But this is only the performance using the same “Jet Pack”!  A practical limitation on Earth, is the mass of the unit strapped onto a flier's back.  The standard system masses 50 to 60 pounds with full fuel.  This reduces to 10 pounds weight on the Moon, added to the flier's 30 pound lunar weight.  Keeping in mind that the flier's legs are not able to absorb much more momentum or energy on the Moon, with care, a user can handle much greater total backpack mass.  A modest increase in fuel ISP can also be arranged, since 90% Hydrogen Peroxide monopropellant  is far from the best obtainable storable propellant.  Doubling the Delta V available quadruples the obtainable altitude and distance, giving 54 km distance for a single hop.  The back pack could still “weigh” only 15 pounds (90 pounds mass).  Gone are thoughts of Lunar Explorers slowly plodding over the surface to return from from an excursion!

I have just begun visualizing how this could change lunar operations, so I won't pursue those thoughts now.  But consider that lightweight systems with a fueled mass equal to the suited astronaut's (about 100 kg (220 pounds) added to his suited 100 kg (220 pounds)), could allow him to achieve orbit, and rendezvous personally with a lunar orbit habitat.  The weight on his legs, preparing to take off, would still be only 33 kg (73 pounds)! 

Keeping in mind the astronaut's need to manage two and a half times his normal mass (and the greater resulting inertia with every motion), it is obvious that a he could also land with that mass on his back.  Again, noting the “Rocket Man's” ability to conduct precision landings on Earth with three times that weight on his legs (landing just after takeoff, with nearly full fuel still in his backpack) – and without the “slow motion” - factor of 2.45 increase in time available for each flight adjustment at 1/6 G -  it is obvious that this would be a very practical way to get astronauts down onto the Moon with their full orbital return equipment strapped on.

[wjbarnett]

Don't forget to add more mass for EMU/lifesupport!

[A_M_Swallow]

{snip}

Keeping in mind the astronaut's need to manage two and a half times his normal mass (and the greater resulting inertia with every motion), it is obvious that a he could also land with that mass on his back.  Again, noting the “Rocket Man's” ability to conduct precision landings on Earth with three times that weight on his legs (landing just after takeoff, with nearly full fuel still in his backpack) – and without the “slow motion” - factor of 2.45 increase in time available for each flight adjustment at 1/6 G -  it is obvious that this would be a very practical way to get astronauts down onto the Moon with their full orbital return equipment strapped on.

Various cargo only landers have been proposed that can lower Moon base buildings.  At least one version of the Jupiter launch vehicles could place the Orion capsule in low lunar orbit.  Does manned jet pack descent amount to back to the Moon in this decade?

[rpspeck]

Absolutely, YES!  The only question is what the expedition cost will be.  That primarily depends on what the cost of the single Falcon-9 launch to LEO, necessary for a 1 or 2 person lunar landing, will actually be. The rest of the project costs will be less than this key cost. It is inconceivable that the cost of an ultralight expedition will exceed the $100 Million cost of an  “America's Cup” racing sailboat, or four years funding for an average “Indy Car” racing team.  (Ultralight EMU/lifesupport mass - based on our operational prototypes - is included in these estimates.)

[A_M_Swallow]

We can estimate the Falcon 9 launch price from SpaceX's costs.
900 people * $200,000 per person per year / 4 launches per year = $45 million.
The company may find ways of doubling that.

Falcon 9 to LEO?!?  How were you planning on getting from LEO to lunar orbit?  Space suits are designed to operate for hours not days.

[kkattula]

We can estimate the Falcon 9 launch price from SpaceX's costs.
900 people * $200,000 per person per year / 4 launches per year = $45 million.
The company may find ways of doubling that.

Falcon 9 to LEO?!?  How were you planning on getting from LEO to lunar orbit?  Space suits are designed to operate for hours not days.

Or you could just get the price from their website:

Mission Type                 Price 
LEO (s/c<80% capacity) $44M 
LEO (s/c>80% capacity) $49.5M 
GTO (s/c<3,000 kg)**    $44M 
GTO                            $49.5M 

[kkattula]

Finance as a TV show:

"Survivor Moon"

20 people train & compete for the chance to go to the Moon. Top 1 or 2 actually get to go, and that's covered via a second reality TV show:

"American Astronaut"

Follow the real, life & death drama of the new moon mission. 24 hour status monitoring with regular web cam diaries etc. 1 hour daily TV highlight show.

[A_M_Swallow]

Or you could just get the price from their website:

Mission Type                 Price 
LEO (s/c<80% capacity) $44M 
LEO (s/c>80% capacity) $49.5M 
GTO (s/c<3,000 kg)**    $44M 
GTO                            $49.5M 

Those prices are for unmanned missions and are not what NASA is paying for cargo to the ISS.

[rpspeck]

Rockets Gain Traction

(Of course, Rockets don't need “Physical Traction” and that allows them to work in Real Space.  But they certainly need Financial Traction in “Cypher-Space”( = $Mx10^6 -- $Nx10^9)!)

The announcement that Tulsa, Oklahoma will conduct an Air Show April 24, 2010, highlighted with demonstration flights by the “Rocket Racing League” is very good news!  It shows that rocket operations are finally gathering some of the attention they deserve!  Those who have attended Northrup Grumman, Lunar Lander Competitions know that Rockets are fun to watch. Monstrous flames, accompanied by roaring noise, have always been fun to watch (from a safe distance!).  These features of rocket flights have been augmented in recent Rocket Racing developments.  Gone is the nearly transparent flame produced by alcohol fuels.  Now long bright flames will be standard – reminiscent of the enormous flame behind a Saturn-V Moon Rocket on takeoff!  Except that John Carmack, of Armadillo Aerospace – who makes the Racers new Propulsion System – has developed a way to “seed” the combustion and produce bright Red and Green rocket flames to distinguish specific race competitors.

Oklahoma has had a large aerospace industry for a very long time, and would like to increase it.  This state has multiple advantages over California – many of them spelled $$$.  Oklahoma has already spent quite a bit promoting entrepreneurial space and rocket efforts.  These include turning the old “Burns Flat” military airfield into a Spaceport.  It was originally a military airbase, then – with its  13,503 foot long runway – it was a primary base for SAC (Strategic Air Command).  Now, it is a licensed Spaceport!    I imagine that Oklahoma is negotiating to bring the Rocket Racing League headquarters to their state , and is willing to cut better deals than Las Cruces, NM, which insisted on being paid the promised rent.

In any case, these long awaited Rocker Racer flights will be showing up, at last!

[rpspeck]

RE-ENTRY-1   

I repeatedly discuss entrepreneurial Human Space Expeditions.  Obviously, a proven Earth return and Re-entry system will be required for these efforts.  I have made the point that entrepreneurial  rocket motor developments are not far from what is needed for these flights (if expedition mass and cost are minimized as they are for extreme terrestrial adventures).  Adequate control systems have been flown.  Communications and navigation is no longer a difficult problem.  Similarly we have demonstrated that  SCUBA + Mountaineering hardware can be adapted and upgraded for human Life Support in space.  A variety of problems NASA publicizes are simply not significant compared to the risks serious explorers are regularly facing.  The regulatory, launch license issue, has also been addressed, and will not be a barrier.  The return and re-entry systems remain the biggest obstacle, but are not out of reach if an appropriate approach is taken.

An “appropriate” approach provides what is necessary – reasonably available and affordable – and does not waste time dreaming about concepts which are not ready to use.  Pioneers on the Oregon and California Trails did not wait for “Reusable” transportation.  Neither wagons nor their animal propulsion systems returned to make regular, multiple trips!  Leave dreams of reusable spacecraft to another generation and keep in mind the ENORMOUS cost of completing a railroad to the Pacific so that Reusable Transportation to those territories was available.  Focus instead on an older idea: when transportation is expensive, pack light and go anyway!

I will continue to discuss the achievable costs and opportunities which will open “Entrepreneurial Spaceflight” using lightweight versions of conventional rocket propulsion.  But for the moment I want to focus on “Conventional” re-entry.  That involves, of course, the ablative heat shield used in the Mercury, Gemini and Apollo.  This technology has virtually never failed.  Of course it is possible for design or manufacturing of a future unit to be so poor that fatal failure results.  And there lies a significant problem and entrepreneurial opportunity. 

I will review details of re-entry design later, and provide insights to help others understand the available literature. But as an overview: Hypersonic re-entry with a traditional (blunt) heat shield brings the relative gas flow to a standstill at some central point, the “Stagnation Point”.  This produces a “Detached Shock” some distance ahead of the heat shield as the supersonic gas flow is forced to accommodate the obstruction by slowing down or stopping.  Such shock waves, and the accompanying deceleration of the relative gas flow, always increases the gas density, pressure and temperature in that region.  Behind the Detached Shock, the hot, compressed gas follows the laws of classic, subsonic aerodynamics!  This includes the formation of a boundary layer, separating the solid surface from the relatively uniform bulk gas in the flow field around the heat shield. 

At some distance from the Stagnation Point, the gas flowing over the heat shield usually accelerates again to supersonic flow, with modestly decreased density, pressure and temperature.  But experimental data proves that the greatest thermal load on the heat shield occurs at or near the Stagnation Point, so for our purposes this may be the only point we need to understand.

In these discussions, it makes no difference if the gas is rapidly moving past a fixed object, or if an object is moving rapidly through a gas initially at rest: the local physics is identical.  In either case a large force is exerted on the solid object, and a correspondingly large amount of energy (that force times the flow velocity) is deposited in the gas flow behind as heat.  The heated gas flows “gradually” inward when it is past the body, but a moderate taper can keep the after body separated from this hot gas.

A much smaller amount of heat is conducted through the boundary layer to the walls of the re-entry vehicle!  (Often less than 1% of the total heat generated by re-entry.)  Typically, the boundary layer will average half the flowfield velocity and temperature, and only the heat transferred out of that small portion of the gas flow will reach the heat shield.  (In other words: the Boundary Layer itself is the most important Heat Shield!)  The boundary Layer does not have a sharp boundary on the outside, nor a uniform velocity or temperature inside. Rather, it has a velocity gradient running from zero at the re-entry body wall to a speed approaching that of the adjacent gas flow at its outside.  Its velocity profile tends to retain its shape as its thickness changes. 

The aerodynamic boundary layer grows on the surface of a sharp edged plate, parallel to the gas flow for minimum drag, with the square root of the distance from its leading edge (where the gas flow first encounters the surface).  This is required by the nature of classical viscosity and basic momentum equations.  (The surface drag force acting on the body is balanced by the momentum loss of decelerated gas as the boundary layer grows into the slipstream.) The same equations require that the boundary layer Have Uniform Thickness over the spherical leading portion of a body obstructing the gas flow (and producing a stopped flow, Stagnation Point). (In this case, the flow stream lines are squeezed closer to the body as the gas flow accelerates away from the Stagnation Point. Some of these stream lines cross into the fixed thickness boundary layer and that gas slows down.  This produces the momentum loss required to balance the surface drag, as in the flat plane case.) 

Both flow situations are characterized by defining Reynold's Number (Re) = (Rho*V*L/Mu), where Mu is the standard viscosity, Rho is the gas density, V is the gas flow velocity and L is a characteristic dimension.  Re is a dimensionless parameter when quantities in appropriated units are inserted in the calculation.  The boundary layer has a typical thickness of L/Sqrt(Re), although a multiple of this is used to identify the distance at which the local flow practically equals its velocity outside the boundary layer.  In many situations, including practical re-entry  vehicles, Re = Reynold's Number runs from 10,000 to 1,000,000 or more, so the boundary layer often is < 1% of the scale parameter (L).  (A similar situation exists inside pipes and rocket motors, where L is the inside diameter.  The rocket nozzle is the smallest diameter section, and has an increased velocity and Reynold's Number, so the boundary layer is thinnest there.  This layer also limits the heat transfer to the throat material, but its thinned dimension allows the greatest heat transfer in that throat region.)
               
Over a spherical “nose”, L is the radius of curvature of that spherical surface. Thus making that radius larger increases the boundary layer thickness and decreases the heat flow through that layer!  The limit of “large radius” is flat, but that face is not stable in subsonic or hypersonic gas flow.  The curved surface produces stable re-entry aerodynamics if the center of gravity of the capsule is more or less enclosed within that curved surface.   Aerodynamic stability, like the boundary layer properties discussed, may be dominated by subsonic gas flow in the region behind the hypersonic shock and can be modeled by something as simple as a dropped Styrofoam bowel or plate.

 Note that while the critical portion of re-entry involves a modest range of velocities (entry speed to about ½ that speed), a very large range of gas densities is involved.  Thus Reynolds Number (Re) has a large range during the process.  As the gas density increases, Re increases linearly (normal viscosity Mu does not change much with gas pressure and density, but DOES change with gas temperature.)  As the density increases (deeper in the atmosphere) Re increases exponentially, and the boundary layer (proportional to L/Sqrt(Re)) becomes thinner, allowing greater heat transfer.  Eventually, the large form drag of the blunt capsule reduces the velocity enough so that the reduced stagnation gas temperature drops the heat transfer below its peak value. Eventually, the reduced velocity also reduces Re, allowing the boundary layer to grow somewhat. 

If the heat shield radius (L) is increased, Re increases proportionally, but L/Sqrt(Re) still increases producing a thicker boundary layer with less heat transfer. 

Note that a low mass reentry vehicle of conventional (Mercury Capsule) size, will decelerate higher in the atmosphere, where the air density is lower.  This will produce a Lower Reynolds number when the heat transfer is greatest, a thicker boundary layer and less heat transfer.  However, the Heat Transfer is a Larger Portion of the total kinetic energy of reentry, so the heating problem is somewhat worse.  If reentry mass is decreased by a factor of 6.25, the heat transferred is reduced to 40% of that for the heavier unit, but this still represents 2.5 times the relative proportion.  So heat shield mass will become a modestly larger percentage of the reentry mass. 

To Be Continued...

[Patchouli]

We can estimate the Falcon 9 launch price from SpaceX's costs.
900 people * $200,000 per person per year / 4 launches per year = $45 million.
The company may find ways of doubling that.

Falcon 9 to LEO?!?  How were you planning on getting from LEO to lunar orbit?  Space suits are designed to operate for hours not days.

My guess would be to resurrect the old Gemini capsule for that task.
http://en.wikipedia.org/wiki/Project_Gemini
F9 may be able put one of those into TLI with a third stage.
Another nice aspect someone else is already interested in resecting the basic design.
http://www.aio50.org/

[rpspeck]

Micro-Space Press Release: Denver, Colorado,   May 27, 2010  
 
Micro-Space is currently manifested to fly TWO tiny CubeSats "Ride Sharing" launch with EduSat, Sich-2 and other spacecraft, to be flown on a Dnepr into Sun Synchronous (near Polar) Orbit, Oct. 29, 2010. Payload Integration for this satellite group is being handled by Morehead State University, involving Dr. Ben Malphrus (Space Science Center director) and professor Bob Twiggs. Micro-Space will also be delivering two similar spacecraft to Morehead State University, and the University of Colorado at Colorado Springs. Additional research systems will be added by the two universities.

The complete, four satellite "PQ-Gemini ++" mission group, in addition to validating general satellite systems, will be capable of demonstrating Micro-Space interferometric techniques to characterize orbital differences using only precision range data between ultralight spacecraft in preparation for autonomous rendezvous. Additional systems will allow the relative positions, distance and rotational alignment of the four satellites to be continuously monitored. This information is necessary for the final, docking procedures. Other developmental steps will follow, leading to ultralight Sample Return Missions on the Moon and Mars.

The tiny size of these satellites, 5 cm cubes massing 120 grams, is totally in tune with the Micro-Space strategy of radically downsizing space systems to minimize launch cost and make mission financing feasible. Even with today's high transportation cost to orbit, exploration is affordable when spacecraft are downsized from the mass of a Volkswagen to that of a lunch box. The cost effectiveness grows further when the systems are reduced to the mass of a modern cell phone! Grams or even milligrams of material from a selected spot on a planet or moon can be analyzed with great precision using modern techniques.

Micro-Space is discussing with several organizations both return sample analysis and Lunar Prospecting.  The latter will be aimed at locating concentrations of extractable Lunar Gems and Minerals. High grade Titanium, rare earth metals and Helium Three (a potential Fusion Reactor Fuel) are all known to exist on the Moon. Low cost flight of concentrated ores to the Earth is feasible using Solar Powered, electromagnetic "Rail guns", and other technologies.

Propellant to complete rendezvous and docking is not allowed in this satellite cluster launch. Arrangements are being negotiated for launch next year of small Micro-Space spacecraft with propulsion systems to demonstrate the complete rendezvous and docking process as will be used with “Planetary Ascent Vehicles” carrying prospecting samples. Negotiations with this launch supplier also cover subsequent launch of our “Lunar Lander” and Lunar Transfer spacecraft, as well as the Planetary Ascent and Return vehicles.

Our corporate sponsors include “Legacy Stone Products, Inc.”, of Denver, Colorado, which has purchased an option for “The First Moon Rocks returned by Micro-Space to Earth for Architectural Use.” A small slice of this unique material can highlight the “Old World” look of classic stone with its “Space Age” reality!