I find it amusing that so many of the opponents of Obama’s proposed space plan are so happy with this, when it doesn’t actually resolve most of the things they said were wrong with his policy. To whit:

1. There are no details, plans, or near-term destinations.  Just an unfocused non-plan to build an HLV without really having a plan on how it will be used or when.  So unfocused spending and lack of a plan or near-term destination wasn’t the issue?
2. Even the Moon isn’t outright dismissed, it’s pretty clear the plan is a modified version of flexible path.  Ie this isn’t going to give people that moonbase they craved so soon.  So actually going back to the Moon anytime in the forseeable future wasn’t the issue?
3. Without the shuttle extended, and with commercial crew being delayed (let’s get real folks, moving most of the funding to the out years is a cheap way of defunding a project without actually having to have the huevos to do it honestly), it is now guaranteed that the ISS is going to be accessible only via Russia for most of the rest of this decade.  There will be no way of launching those critical spares that were the reason Jeff Bingham was always giving for a shuttle extension.  So apparently the gap isn’t an issue?
4. The KSC portion of the Shuttle team is going to get decimated next year still, this time with no commercial crew projects ramping up to help soften the blow.  So apparently workforce retention wasn’t really an issue?

As far as I can tell, the only issues people really cared about were not having to compete for a real job if you were a USA/MSFC/JSC shuttle guy, and making sure we get a big HLV as soon as possible, even though we won’t have anything to do with it once we get it.

The good news is that the “dot-product” of NASA’s direction and sanity is a fair deal of money, and it grew quite a bit compared to last year.  At least some elements of useful things survived.  Instead of being 99% orthogonal to the actual development of space, it’s now only 95% orthogonal.  It’s just so frustrating and disgusting when we actually had a chance for something so much better.

Here’s to hoping that now that JSC and MSFC got their rattle back, the creative and useful parts of NASA can be moved to locales better-matched to small development programs.  Even the pittance they’re being given compared to feeding the HLV albatross can go a long way if managed by the right group.

May 25th, 2010, Mojave, CA, USA: XCOR Aerospace and Masten Space Systems, two of the leaders in the New Space sector, have announced a strategic business and technology relationship to pursue jointly the anticipated NASA sponsored unmanned lander projects. These automated lander programs are expected to serve as robotic test beds on Earth, on the lunar surface, Mars, near Earth objects and other interplanetary locales, helping NASA push the boundaries of technology and opening the solar system for future human exploration.

Masten’s award winning automated vertical take off, vertical landing (VTVL) flight vehicles combined with XCOR’s strong experience in liquid oxygen (LOX) / methane powered propulsion systems and nonflammable cryogenically compatible composite tanks, brings to NASA a powerful and competitive combination of innovative talent with a proven record of producing exceptional results quickly and affordably.

Last October, Masten won the $1 million first prize for Level II of NASA’s Lunar Lander Challenge, beating out a host of New Space rivals, and demonstrating they are the leading VTVL development group in the country. In 2007 XCOR Aerospace’s LOX/methane engine, developed for NASA, was named by Time Magazine as one of the “Inventions of the Year”, recognizing XCOR’s successive advancement in the state of the art of both pump and pressure fed reusable, throttle-able rocket propulsion systems. XCOR and Masten have also demonstrated the ability to rapidly take from concept to live fire, new propulsion and control system designs using innovative rapid prototyping techniques that surpass client requirements in much shorter periods of time than traditional aerospace methods.

Dave Masten, founder and President of Masten Space Systems commented “Masten Space and XCOR are next door neighbors here in Mojave. We’ve worked together on many tactical problems over the years and our corporate cultures mesh well. Working together on something like this simply made too much sense. We can’t wait to start working with Jeff, Dan, and the XCOR team to help NASA build affordable and responsive landing platforms.”

“Our company work ethic and styles are very compatible, and with XCOR propulsion and Masten VTVL technology, we can solve problems of national interest, and I am excited about the possibilities,” said Jeff Greason, CEO and Founder of XCOR.
Andrew Nelson, Chief Operating Officer of XCOR added, “It’s a no brainer, Dave’s team is the absolute best New Space company when it comes to VTVL and autopilot unmanned operations – they demonstrated that in October by winning NASA’s lander challenge. And we feel our LOX/methane engines are unsurpassed in the trade space today by anyone. We should bring this tandem set of best in class capabilities to NASA, it just makes sense for them and for us.”

XCOR and Masten will be jointly marketing their skill sets and services to the NASA community as prime contractors, and as joint teaming partners for larger systems integrators and prime contractors servicing the NASA community.

# # # # #

Masten Space Systems is a Mojave, CA based aerospace company developing fully reusable vertical takeoff, vertical landing (VTVL) launch vehicles, rocket-related products, and engineering services. The company’s 6000 square foot production facility and 200,000 square foot testing facility is located on the Mojave Air and Space Port. The company designs and builds aerospace solutions that focus on durability, long operational lifetimes, and minimal per-flight maintenance. For more information on the company see http://masten-space.com

XCOR Aerospace is a California corporation located in Mojave, California. The company is in the business of developing and producing safe, reliable and reusable rocket powered vehicles, propulsion systems, advanced non-flammable composites and other enabling technologies for responsive private space flight, scientific missions, upper atmospheric research, and small satellite launch to low earth orbit. The Lynx is a piloted, two seat, fully reusable, liquid rocket powered vehicle that takes off and lands horizontally. The Lynx production models (designated Lynx Mark II) are designed to be robust, multi-commercial mission vehicles capable of flying to 100+ km in altitude up to four times per day. XCOR’s web address is: www.xcor.com.

Contact:
Michael Mealling
Masten Space Systems
Phone: +1-888-488-8455 x102
Email: mmealling@masten-space.com

Mike Massee
XCOR Aerospace
Phone +1-661-824-4714 x127
Email: press@xcor.com

I can’t speak for the company, but personally I’m really glad we were able to find a way to make this partnership work. I’ve got nothing but respect for the XCOR team, and have been trying to find a way to work with them for years. As Jeff said at Space Access, it’s deals like this that show that the industry is starting to grow up.

Traditional Aerobraking and Aerocapture
One of the challenges of orbital mechanics is that it takes just as much energy to descend into a gravity well as it does to ascend out of it. One technique that has been used for lowering the propellant cost of descent into the gravity well of a planet with an atmosphere is aerobraking. Aerobraking is the process of taking a spacecraft in an ellpitical orbit around a planet with an atmosphere, and using atmospheric drag at the lowest altitude portion of its trajectory to slowly decrease the altitude of the high end of the elliptical orbit. This process has been used now on about a half-dozen planetary missions, in some cases reducing the propulsion requirements by 1km/s or more, over the course of a couple hundred passes. Aerobraking has been traditionally been done by satellites that aren’t explicitly shaped like a reentry vehicle–in fact most of the drag for typical aerobraking vehicles is produced by using the spacecraft’s solar panels as massive drag brakes!

Artist's Impression of MRO Aerobraking (credit JPL and Wikipedia)

A more aggressive maneuver called aerocapture takes a spacecraft in a hyperbolic (interplanetary) orbit and in a single pass decelerates that vehicle into an elliptical orbit around a planetary body.  Typically the term refers to maneuvers where the ending orbit has an apoasis near the altitude of a circular orbit, though it could also be used to describe a maneuver that uses a single pass through the atmosphere to replace the “capture braking burn” that would normally be used. Aerocapture is a lot more challenging, since the deceleration has to take place a lot lower in the atmosphere in order to provide the required deceleration in such a short distance. This implies much higher forces and heat-fluxes, which require some sort of aeroshield/TPS system.

Here are a few of the main challenges of aerobraking and aerocapture:

1. Dynamic Pressure Loads: Dynamic pressure is the pressure felt on the vehicle by the impingement of the atmospheric molecules.  The equation for dynamic pressure is q = 1/2 * rho * V^2, where lower case q is the dynamic pressure, rho is the instantaneous atmospheric density, and V is the instantaneous relative velocity.  For MRO, the dynamic pressure limits were set at 0.35 Pascals, which correlates to moving at about .76m/s at sea level (ie a slow walking pace).  To give you an idea of how this compares with orbital reentrythe peak dynamic pressure of say a Soyuz in its emergency ballistic reentry mode, is over 40,000 Pa of dynamic pressure, and even a low-G lifting reentry is still in the 10kPa+ range.  Direct entry into the Venusian atmosphere from a hyperbolic interplanetary orbit gets you into the 1MPa range!  Another fun comparison is that the max-Q Xombie or Xoie have seen in flight was around 250Pa.Most of the very low allowable dynamic pressure load for past aerobraking efforts has been driven by the fact that most aerobraking craft to-date have used large flimsy solar panels as their main drag structure.
2. Peak Heat Flux:  The shockwave caused by slamming into gas particles at hypersonic velocities compresses and heats the gas particles to substantial temperatures.    Heat from this shock wave is convected and radiated into the aerobraking spacecraft.  The equation for heat flux is Q = 1/2 * rho * Ch * V^3.  Capital Q is the heat flux (in W/m^2), rho and V are the same as before, and Ch is the heat transfer coefficient.  The heat transfer coefficient, I think, represents what portion of that heating goes into the vehicle itself instead of being carried off by the now quite ruffled atmospheric gas molecules who didn’t see you coming.  Yes it is confusing that dynamic pressure is lower-case q, and heat flux is capital Q.Once again, to give you some scale, the worst case pass for Odyssey had an estimated heat flux of about 500 W/m^2,  which is about 40% of the heat you get in LEO from the solar radiation. For that Soyuz reentry case mentioned earlier, the total heat generated at max-q is in the 240 MW/m^2 range–several times higher than the heat flux at the throat of the SSME or RD-180.  The Venusian direct entry example according to one source would actually be in the 4000MW/m^2 range! Fortunately, I think that for atmospheric reentry the Ch term is relatively low–most of that heat gets carried away by the atmosphere.As with dynamic pressure loads, the reason why peak heating rates are kept so low for most aerobraking missions is that you’re using the large solar panels as most of the drag surface, and they can only take so much heating before their temperatures rise to levels that could permanently degrade their performance.
3. Atmospheric Density Variations: If atmospheric density was nice, constant, and well-known, aerobraking could proceed a lot faster and in a lot fewer passes.  The problem is that at the altitudes where aerobraking takes place (100+km), the density can vary significantly over length scales as small as 20km.  This can be driven by many processes including variations in the solar wind and solar radiation due to sun cycles, weather effects like dust storms for Mars aerobraking, and other effects.  Going off of some data from the Odyssey mission, variations as big as 2-3x were seen in density from pass to pass.   A second-order effect of density variations is that both the drag coefficient and the heat transfer coefficient will vary with atmospheric conditions by noticeable amounts.  Unfortunately,  in many cases you don’t know the density along a given trajectory in advance, so you have to plan for not the average density, but the worst case pass density.   Which means that most of the time you’re getting less deceleration and heating than you could actually withstand, but some of the times you might actually find yourself pushing your limits more than you would like.   This drives you to taking more passes than you’d really like to take in an ideal situation.  These variations get more and more pronounced at higher aerobraking altitudes, where atmospheric density is measured in kilograms per cubic kilometer.Once again, this is an area where using large, sensitive solar panels as your drag devices really hurts. Because you can’t stand high dynamic pressures or heat fluxes, you have to do your passes higher up in the atmosphere. But due to variability in density at those higher altitudes, you end up getting driven even further up to deal with worst case variations. That said, even aerocapture trajectories are high enough altitude that atmospheric variations can be important challenges to deal with.
4. Aerobraking Duration: For most previous Mars and Venus aerobraking missions, velocity changes in the 1-1.2km/s range have taken between 70-150 days, over several hundred passes.  While this is fine for unmanned missions, it’s harder to do for manned missions, where radiation concerns make you want to minimize your time spent in-transit.  The large number of cycles is also a difficulty for missions aerobraking at earth, where each pass will take you through the Van Allen belts.  Lastly, for reusable in-space transports, the total turn-time is an important economic parameter–the more missions you can fly in the same period of time, the fewer vehicles you need to support a given mass throughput.

A couple more quick observations before we jump into using MHD forces to enhance aerobraking:

• For typical aerobraking, the parameter you can control easiest is the periapsis altitude, and thus indirectly the average density.  In other words, if you want to double the drag on a pass, you lower your periapsis to an altitude that has about double the average density.  This also means that to a first order approximation (ie ignoring the relation between density and the heat transfer coefficient) heat flux for traditional aerobraking is going to scale fairly linearly with drag.
• Ballistic coefficient ends up being really important for aerobraking as well–this is the whole reason why the solar panels are used unstowed for aerobraking.  Higher ballistic coefficients mean that you have to dip lower into the atmosphere (and thus get a higher heat flux) to get the same amount of deceleration per pass.
• In spite of the disadvantages of using solar panels as your drag brakes, there are some real advantages to being able to use a aerobraking scheme that doesn’t require your vehicle to be explicitly crammed into a typically reentry-vehicle shape behind a massive heat shield.  It would be nice for instance to be able to get tanker vehicles or orbital tugs back from lunar trajectories or martian trajectories without them having to carry a big aerobraking shield like you see in all the old literature.

Anyhow, that was a quick introduction to aerobraking by a complete non-expert.

Some Backstory on Why I’m Interested in Aerobraking
I started looking into this a few months ago as an alternative to propulsive retrobraking for Centaur-derived cislunar tanker vehicles.  While a Centaur stage actually can do a lunar round trip fully propulsively, with at least some payload delivered to the Moon, the “gearing ratio” (initial mass in LEO compared to payload delivered to LUNO or the Lunar Surface) was pretty pathetic.  Just to use some ballpark numbers, without digging up my more precise calculations, I’m getting around 8000lbs payload to LUNO if you drop it off in orbit and the Centaur only returns to earth, dropping to only 2500lb if the Centaur has to haul the payload all the way there and all the way back propulsively.  However, if you could do 3km/s worth of aerobraking (assuming about 1200m/s worth of burns between the Trans-Earth Injection burn and any periapsis raising maneuvers, including the final circularization), all of the sudden you’re talking about almost 20,000lb of payload on the dropoff mission, and about 13000lb on the round-trip maneuver.  Depending on how massive and expensive the aerobraking system weighs, it makes a massive difference in the performance of a reusable cis-lunar architecture.  For a long time though, I had sort of dismissed aerobraking, because any aeroshield big enough to allow single-pass aerobraking (or few enough passes to be interesting) also ended up looking like it would either be very heavy, or very bulky, or require lots of orbital assembly or some sort of new deployable technology.  Not that any of those other than being too heavy was a total show-stopper, but it definitely made it less attractive for a near-term commercial operation.

Another line of thought I had been wondering about recently was manned cislunar transportation, especially in light of the Augustine Committee report.  One of the big suggestions they made that rubbed a lot of HLV-advocates wrong was the idea of launching the crew on commercial LEO taxi vehicles, and flying Orion up to LEO unmanned.  A lot of people said this was just silly–if you’re launching Orion may as well launch it manned, even though this would require adding launch escape and emergency detection capabilities to the HLV.  I started thinking down the lines of what Orion could look like if it was designed from the start not to carry astronauts until they got to space.  The LAS would go away, as would all the structural requirements for taking those sorts of loads, being able to rapidly drop the service module, etc.  The whole thing could fit inside a fairing, thus simplifying aerodynamics and loads on the front end of Orion.  Heck, it could even be attached to the rest of the stack in whatever orientation made the most sense for mission ops–it wouldn’t be constrained by needing to be on the top in an orientation where the capsule could “get out of Dodge” in a hurry if something “went south” with the HLV.  The more I thought about it, the more I realized that Orion could end up looking like a drastically different vehicle if it was optimized for in-space use and reentry instead of needing to also handle manned ascent to orbit as well.  Then I made an interesting leap of logic.  What if Orion was only meant to be used in space?  I originally sort of dismissed this, since most single-pass aerobraking schemes I knew of would require the thing to be designed like a reentry capsule anyway.

Jumping back to the Centaur-based tug idea, I toyed around with the idea of doing a blog series, seeing if I could make an aerobraking simulator to figure out if a Centaur could without any sort of fancy aerobraking shield actually do a multi-pass aerobraking mission that would get it back to LEO within a reasonable amount of time (say three weeks or less).  However, I stumbled on the papers about magnetic aerobraking right about this point in my thought process, which may possibly provide a solution to both of these problems.

While I don’t have anywhere near the analytical chops to know for sure how far you can push this technology, if it could enable single-pass or at least small number of pass aerobraking without requiring a huge traditional aerobraking shield, interesting things might become possible. Magnetic aerobraking could potentially revolutionize cislunar transportation, enabling low-cost reusable manned and unmanned deliveries based on modified versions of existing LOX/LH2 upper stages, and could allow fully-reusable in-space only manned vehicles that weren’t just an overglorified 1960s-style reentry capsules.  But more on that later.

For now let’s get back to how we can use magneto-hydrodynamic interactions to enhance traditional aerobraking, and see if we can figure out if this idea has merit at all.

Magnetic Aerobraking
Going back to our previous two discussions, one of the key takeaways was that the enhanced braking and thermal protection provided by strong magnetic fields was strongest at high altitudes where atmospheric density was lowest. At high altitudes, the ambient atmospheric density is low, but Joule heating caused by the interactions between ions in the shock layer and the superconducting magnet keeps the electrical conductivity of the plasma in the shock layer high. Also, for aerobraking or aerocapture short of reentry, by definition you are both always at a speed and altitude high enough that you don’t have to worry about the shock layer losing sufficient conductivity for MHD effects to dominate aerodynamic drag effects. The magnetic interaction parameter (Qmhd) introduced in my first post in this series can easily be in the 250-1000+ range at high altitudes compared to down in the 5-50 range you might see during atmospheric reentry. For example, the paper I cited in my first article (Otsu et al) showed that for a vehicle coming back from a GTO-like orbit, you could cut the return time by 70% with a 0.1T magnet, which is about 5x weaker than the magnet assumed for most of the reentry magnetic TPS studies.   While magnetic effects may be helpful for reentry, they truly come into their own for aerobraking and aerocapture.

A few other thoughts:

• While the total drag for a magnetic aerobraking concept can actually be several times the drag of a similar non-magnetic vehicle, the gas-dynamic portion of the total drag actually decreases substantially in the case of magnetic aerobraking.  This is due to a much lower velocity behind the shock layer in the magnetic case.  Figure 9 from the Fujino et al paper I used in the last post (”Numerical Analysis of Reentry Trajectory Coupled with Magnetohydrodynamics Flow Control”, JS&R Vol 45 No 5, pg 911-920) illustrates this beautifully:
• For a vehicle using magnetic braking, most of the total drag force is actually reacted electromagnetically through the magnet itself, not through the surface of the vehicle.  The dynamic pressure that the vehicle surface itself sees is greatly reduced compared to what you would expect at that altitude and entry velocity.
• While in the above case, the dynamic pressure reduction was about 4x at ~75km, this effect is likely to be even more pronounced at the altitudes used for aerobraking (90-120km) where the electromagnetic interaction parameter is substantially higher (40-160x higher) than it is in the case shown above for atmospheric reentry.
• The heat flux seen by the aerobraking vehicle will also be greatly reduced compared to a non-magnetic aerobraking system at a similar altitude and velocity.  This is due to the much thicker shock layer standoff distance and the lower velocity of the particles behind the shock layer.  The Fujino et al paper estimated that the heat flux would roughly be cut in half at 75km with a 0.5T magnet (due to a boundary layer between the bow shock that is twice as thick at that magnetic interaction parameter).
• For higher parameters in the 100-1000 range that you would likely see for aerobraking, this effect should be even more pronounced.  The trend in shocklayer thickness vs. Qmhd shown in Fig 3 of Fujino et al  was linear over the Qmhd range of 0-6.  If it continued out linearly up into the Qmhd 100-1000 range, the shock layer standoff distance would be in the range of 100-125x thicker than without MHD effects, implying a drastically reduced heat flux at aerobraking altitudes.  Unfortunately without having them run the actual analysis, it would be hard to know precisely how well this would work.
• All these factors mean that the same vehicle could use a lower periapsis with a magnetic braking system than without.  The dynamic pressure and heat flux that the vehicle sees at a given periapsis altitude is going to be at least 2-4x and possibly more than an order of magnitude less than it would be without the magnetic field.  Even in the most conservative case (ie assuming that the effect at 100km and aerobraking speeds is no better than at 75km in spite of having a Q 40-160x higher) this would allow you to go to an altitude with at least double the density while keeping the heat flux and dynamic pressure loads within tolerances.  With an effective total drag 4x higher at a given altitude combined with being able to go to a lower periapsis, you get bare minimum a 8x reduction in total aerobraking time compared to the non-magnetic case.
• For the aggressive, “I don’t know if I’m extrapolating way too far” case, you could get even larger reductions in aerobraking time.  Going back to my linear extrapolation on shock layer standoff vs. Qmhd (and thus heat flux vs Qmhd), at Qmhd=250 this would put the shock layer standoff at about 25-30x thicker than the non-MHD case.  The example in Otsu et al gave a Qmhd of 250 using a 0.1T magnet and a 100km periapsis.  Since Qmhd is proportional to B^2 and inversely proportional to rho.  If you increased the magnetic field from 0.1 to 0.5T (similar to what was being suggested for the reentry studies done by Fujino et al and some of the others), you could maintain a Qmhd of 250 even if you increased the local density by a factor of 25.  At Qmhd of 250, the effective drag coefficient is about 3x higher than the non magnetic version.  That would give up to a 75x reduction in aerobraking time compared to the non-magnetic case.
• One other advantage of magnetic aerobraking is that you can drastically vary your effective drag coefficient electrically.  Also, the heating and dynamic pressure are far more driven by the magnetic field strength than by the atmospheric density for the MHD aerobraking case.  These mean that you can afford to take deeper passes without having to worry as much about variability.  If the density is higher than expected, and you have some head-room on your magnet, you can increase the MHD field strength a bit to keep the shock layer back and the dynamic pressure down.  This also could cut trip times in half just by allowing you to base your planning off of the average atmospheric density instead of having to take the mean + 3 standard deviations as your predicted atmospheric density.

I’m rapidly coming up to the point where I’m pretty sure I no longer know what I’m talking about.  At least from here, it looks like there’s a good chance that MHD aerobraking could allow for aerocapture (at least into a high eccentricity elliptical orbit), and very rapid aerobraking down to a circular orbit compared to the non-magnetic case. I think you can extrapolate the conclusions of these papers in these ways, but without having the people with the analysis tools actually verify these claims, I’d still take them with the appropriate sized grain of salt.   Also, my intuition on how a MHD aerobraking vehicle would compensate for density variations is not very good.  That alone could be a paper or a thesis.

So, whether this ends up being a mild curiosity that ends up only being useful in niche applications, or a game-change remains to be seen, but the potential for this being a game-change is real.

In my last post in this series, I’ll go more into some of the implications of what this could do if it works, and some thoughts on how to actually flight-demonstrate MHD aerobraking.

[Edit: It turns out I had misspelled Fujino's name in the original post. Fixed that and added the title of the paper in case people want to get a copy--it's free if you have a JS&R subscription, $15 if you're an AIAA member without a JS&R subscription, and something like $30 if you're not an AIAA member--highly recommended if you're interested in this topic]

The expression uses the Gaussian error function, erf(x), which is not typically available in a spreadsheet or scientific calculator. erf(x) also cannot be calculated in closed-form–typically the expressions used to calculate it are iterative. Since the tapered tether mass ratio is such a useful design tool to have, I derived a recursive algorithm that computes the ratio in a simple loop, given only the velocity ratio of the tether (tip velocity/characteristic velocity).

Here is the recursion:

and here is psuedocode for the recursion:

subroutine getRatio(double VR, int k) {
double VR2 = VR*VR;
double sum = 0.0;
for (int i = k; i >= 1; i--) {
sum = (VR2/(double)i)*(1.0/(double)(2*i+1) - sum);
}
return 2.0*exp(VR2)*VR2*(1.0 - sum);
}

With about 8 recursions, the results are extremely accurate. The recursion is unstable when the velocity ratio is greater than about 3, but no one should be building tethers with velocity ratios greater than 3! and you can just use Moravec’s expression with erf(x) = 1.0, which is a pretty safe assumption for x > 2.0 or so.

The first idea of concept of a tether dates back to the imagination of Konstantin Tsiolkovsky, the Russian schoolteacher who first developed our modern concepts of rocketry and first derived the rocket equation. In the late 1800s, Tsiolkovsky visited Paris and saw the Eiffel Tower. He was so impressed by the sight that he imagined a tower reaching up far into space. He calculated the height at which such a tower would have to be before the centrifugal force from the Earth’s rotation balanced the pull of gravity (inadvertently calculating the altitude of geosynchronous orbit).

Tsiolkovsky, of course, could not conceive of any material that could withstand the compressive forces of such a structure, but sixty years later, a Russian engineer named Yuri Artsutanov picked up the thread of Tsiolkovsky’s work and first worked out the engineering principles of what is now called a “space elevator”, a long tether hanging all the way from geosynchronous orbit to the surface of the Earth. The space elevator required materials with specific tensile strength far in excess of any known material, and still does. Further conceptual engineering work on the space elevator concept was done in the early 1970’s by American engineer Jerome Pearson.

The space elevator was a hanging tether, and payloads were required to traverse its length in order to achieve orbit. The beginnings of rotating momentum-exchange tethers date to the late 1970s, when Hans Moravec, a robotics researcher at Stanford University (now at Carnegie-Mellon) was intrigued by a suggestion of his friend John McCarthy of a satellite that “rolled like a wheel” around the Earth. Moravec began a scientific investigation of the concept, which he first called a “non-synchronous orbital skyhook” and later a “Rotovator”. Like the space elevator, it reached all the way to the surface of the Earth, but unlike the elevator, it rotated about its axis a number of times per orbit. A payload would be picked up by the tip at the surface of the Earth and then thrown half a rotation later into an interplanetary trajectory. The Rotovator was a good deal shorter than the space elevator (~4200 km vs. 40, 000 – 100,000 km) but was not much better in terms of materials required. Moravec published a paper on the subject in the Journal of Astronautical Sciences where he speculated on advanced forms of matter that might have the strength needed to build the Rotovator.

About a year after the JAS paper was published, Dupont’s development of Kevlar excited Moravec to the possibilities of Rotovators built with conventional materials. He wrote a short paper called on the subject which was never published. The paper showed that Kevlar skyhooks were not feasible around the Earth but could be reasonably built around the Moon and Mars. In an appendix to this unpublished paper, Moravec speculated on the possibility of skyhooks built in interplanetary space that would assist spacecraft traveling between the Earth and Mars. To the great benefit of future tether researchers, his equations for the cross-section of a tether, in the absence of a gravitational field, could be integrated in closed-form. Thus, the Moravec “tether equation” was first derived.



Moravec was able to derive analytical expressions for the area of the tether as a function of its distance from the rotational center. He then numerically integrated the area expression along the length of the tether to calculate volume and mass. As an aside, in an appendix, he considered the case of a tether spinning in free space. When the tension on the tether was only due to centrifugal forces, the area expression could be analytically integrated to a closed-form solution. Thus the Moravec mass ratio was derived.

The equation could be simplified by realizing that fundamentally, the mass ratio is a function only of the velocity ratio, which itself is the ratio of the tip velocity of the tether and the characteristic velocity of the tether material.


Further insight into the value of the equation was gained by comparing it to the rocket equation and noting the similarities and differences.

Moravec wrote a few articles on the subject for space-themed publications, but basically returned to his robotics work. Nevertheless, Moravec’s equation still serves as a foundation to all momentum-exchange tether work to this day.

The rendezvous required for a rotating tether and its payload is far more dramatic. The whole point of the operation is to have the tether and the payload in different orbits, so that the rendezvous can lead to an exchange in angular momentum and orbital energy between the two, resulting in a payload boosted to a higher energy orbit (or dropped to a lower energy one).

Thus, you can’t match orbits like you do in conventional rendezvous. The best that you can do is to instantaneously match position and velocity (but not acceleration). So you need an approach to rendezvous that is pretty tolerant of error.

So we threw out the book when it came to trying to think of how to do rendezvous, and came up with something totally different and designed to meet the specific needs of the mission. And I was pretty proud of the result, and still am. Because, you see, this is a bit of an anniversary for tether rendezvous technology. It was five years ago (February 2005) that we successfully demonstrated that the rendezvous technology we had postulated could work, at least at the lab scale.

We took advantage of the fact that the tether was under rotation and experiencing centrifugal acceleration, and that the payload was in free-fall. We simulated this (quite accurately) by hanging the tether’s “catch mechanism” from the ceiling of a racquetball court at Tennessee Tech, and then we “shot” our simulated payload up to the catch mechanism, with its boom positioned to be captured by the catch mechanism when it penetrated the aperture of the catch mechanism. Then the catch mechanism would release and close around the boom, quite quickly, allowing the simulated payload to be caught.

It all worked out a lot better than I thought it would–take a look at our results:

First Catch Mechanism Test

Second Catch Mechanism Test

More Testing with Animation

And here was the press release that came out months later announcing the accomplishment. Our video footage of successful testing got on NASA TV…once.

NASA Engineers, Tennessee College Students Successfully Demonstrate Catch Mechanism for Future Space Tether

Oh, and one small caveat before I jump in–while I think there’s some real potential here, electromagnetics is a topic that I’m truly awful at. I’ve never had another class, including a PhD level turbulent fluid dynamics class that made me feel like such a brow-dragging neanderthal as my Physics 122 class on Electromagnetism. This may be yet another niche technology that while somewhat interesting, ends up not being all that useful. But it looks at least possible that this may become a game changing technology in many space transportation fields. Without further ado, let’s go over some of the basics.

Some Background on MHD Aerobraking and Thermal Protection
The basic concept behind MHD Thermal Protection is that during hypersonic flight, above about Mach 12, the shockwave formed in front of a blunt-bodied vehicle reaches a high enough temperature to form a weakly ionized plasma that is conductive enough to be manipulated by strong magnetic fields. A powerful magnet near the leading part of the vehicle interacts with charged particles in the plasma via the Lorentz force. This force bends the trajectory of charged particles, creates large hall currents, which if I’m understanding correctly repel the magnetic field. These charged particles also impact with the uncharged gas particles nearby (the plasma is only “weakly ionized”) transmitting these forces to them as well. Here’s an interesting diagram I’ll reference from one of the papers I’ll talk about more later (”Trajectory Analysis of Electromagnetic Aerobraking Flight Based on Rarefied Flow Analysis” by Otsu, Katsurayama, and Abe–well worth the $28):

Figure 1 (from Otsu et al): Schematic View of the Flow Around a Vehicle With Applied Magnetic Field and Induced Current

If the magnet is strong enough, this leads to two interesting effects–first, the distance from the vehicle to the bow shock increases (I think the plasma density between the bow shock and the vehicle also decreases, but I’m less sure about that). This can significantly reduce the heat transferred into the vehicle for a given velocity and altitude. The other big effect is that the Lorentz forces create forces that can produce drag or lift. At high altitudes these Lorentz forces can greatly augment the aerodynamic drag forces, effectively making it as though the vehicle had a much lower ballistic coefficient. It should be noted that this force is electrically controllable. In fact, depending on the sophistication of the magnetic apparatus and its location within and orientation with respect to the vehicle, it can possibly also produce lift as well as control torques without the need for aero control surfaces.

Both of these help from a reentry thermal standpoint, because by the time you hit the denser air, where the heating is the highest, you’re going a lot slower than you would’ve been otherwise, and a lot of that earlier braking is done at much lower heating loads than would have been the case without the electromagnetic effects.

Several of the papers I’ve read introduce an interaction parameter term, Q, that relates the relative strength of the Lorentz forces to drag forces. The relationship takes the form:

Equation 1 (from Otsu et al)

Sigma is the conductivity of the weakly ionized plasma, B is the magnetic field strength, L is a reference length (I think related to the magnet configuration), rho is atmospheric density, and V is velocity. As you can see, for a given magnet, the drag forces start dominating as the conductivity drops and as the atmospheric density increases. Atmospheric density increases dramatically as you descend from orbit, so for a reentry application, you get most of your benefit from the first little bit of descent.

We’ll go more into some of these ramifications starting in my next installment.

I’ve been a bit busy to weigh in on this for a while, but being a propulsion engineer myself, I can see *several* potentially interesting technologies that could be invested in.  To me, I don’t think the reason they’re suggesting investing in HLV technologies instead of building an HLV right now has anything to do with whether or not we can build one with existing technology.  My guesses at the reasoning are more along the lines of:

1-If they build an HLV right now and keep Orion going, they would either need to greatly increase the budget, stretch timelines out so far that it would drive the costs way up, or sacrifice the other parts of the plan that are what they’re actually interested in (tech demonstrators, ISS utilization, commercial crew maturation).
2-If they punt on actually building an HLV until after this first five-year chunk, then they’re no longer conflicting with the most immediate tech demonstrators or the commercial crew development efforts, which would allow them to build such vehicles without requiring a big increase in NASA’s budget.
3-By punting for a while, they both may have better technology options to start with, allowing for a cheaper, lower manpower HLV, but there will also be a much better baseline to start with for a new Orion vehicle.  By that point there will likely be at least two commercial capsule providers out there, and possibly some new tricks up their sleeve, which may make Orion a much smoother, better vehicle overall.
4-By punting on the actual HLV development until after the technology demonstrations, it may be clearer what capabilities you really need for the HLV.  Going ahead with one right now either has to assume that the tech demonstration will work (risky) or assume it won’t work (risky via overconservatism).  Waiting until you know more about if depots and high-Isp in-space propulsion systems are reasonable allows you to pick an HLV better matched to the new technology.

Going back to the technologies, if you understand that this isn’t a question of “we can’t do it with the technology we have today”, but more of a “we don’t want to do an HLV for other reasons, but what stuff could we do to make an HLV more affordable when we do have the budget to move on it”, then it becomes a lot clearer.  To me, the goal of any of the booster engine R&D should be to take technologies that have potential for drastically better cost/performance ratios, and mature them to the point that they could be rolled into an HLV effort when it is time to move.  TAN is one option, since if done right you could get enough thrust that a shuttle derived HLV wouldn’t need SRBs anymore to takeoff, and commercial EELV-class vehicles could either reduce their engine size, or increase their propellant load drastically for the same weight booster engine.  It might also allow you to get good performance with a lower pressure booster engine.  Other options include stuff like pistonless pumps, or some of the other pump concepts I’ve seen that while they may not have quite the performance of staged combustion, have most of the performance at a tiny fraction of the complexity/cost.  Flow separation control is another cool trick that can allow you to get more performance out of lower chamber pressure engines.  Imagine being able to build an engine that had better T/W ratio than an existing staged combustion engine, had no turbomachinery, and similar or better mission averaged Isp, but cost about a tenth as much?  That would be a game-changing set of technologies in my book.

There may be some other work relating to getting domestic high-thrust LOX/hydrocarbon engines ready.  There’s also the high thrust expander cycles you mentioned, which would be beneficial to EELVs as well as HLVs.  Depending on the engine size, it might even be interesting to further develop the Mid-Air Recovery idea that LM was investigating for their Atlas V engines.  Being able to recover the engines from an HLV launch and reuse them a few times without having to deal with salt-water corrosion issues is a great way to reduce some of the big marginal costs of a flight.  For upper stages, putting some money into ACES/Raptor related technologies might not be a bad investment either–find something that can give you some commonality between your HLVs and other stages flying (or make it so your HLV is just a family member of an upgraded EELV-class launcher family).  Or doing at least a little funding on reentry technologies could also be interesting (to allow for easier reuse of currently expendable booster stages, low the hurdle for true-RLVs, and also possibly make Orion-like vehicles easier to build and more capable down the road).  Some concepts like transpiration cooling and electromagnetic TPS/aerobraking are both really interesting.

Anyway, I’m an ideas guy and a propulsion engineer, so I may have a different view of this than most, but I for one think this is a reasonable approach.  To me, cutting back drastically on the amount of people who are needed to launch an HLV, while also using new technologies that allow you to get better system-level performance out of lower-cost, lower-complexity hardware is potentially game changing in my book.

As far as implementing this idea, the technology isn’t the hard part. Technologically, this is something that could’ve been done in the 70s. Modern technology and modern launch services make it a whole lot easier and more feasible, but the technology isn’t the key obstacle. Money is and always has been the biggest obstacle. But I think I have an idea, and it’s just crazy enough that I want to share it.

Any business plan whose first step is “first we convince a billionaire to give us lots of money” usually deserves to be laughed off the stage. But this isn’t a business plan competition entry, or some pitch before VCs that I’m demanding to be taken seriously, so I’m going to suggest just that. Even with a wealthy philantrocapitalist, I think you’d still want a concept that both gives you a reasonable chance of making the money back if things go well as well as minimizing your losses if it doesn’t work out.

Anyhow, this is a bit of a long-shot, and definitely not fully-baked, but here’s what I have so far. The business case revolves around a few core concepts:

• A privately developed simple lander and an ITAR approved method for launching it on both US and domestic launchers.
• Using barter with various space agencies with domestic medium-lift vehicles to provide both the startup launches and the sustaining launches
• Making revenue off of selling remaining space to corporations, research institutions, and smaller countries that are interested in lunar experiments, but lack indigenous launch capabilities
• Possibly offsetting initial lander development by selling rover delivery services to NASA or other large space agencies.

Some of these sound a bit crazy, so why don’t I explain them in turn.

Private Landers
The key technology piece in the project is obviously the lander. As discussed before, I’m thinking of something in the 10-20klb IMLEO range, with a payload in the 4-6klb range. The propellant combination for the lander doesn’t hugely matter. It could use storables like Martijn likes, it could use space storables like LOX/Methane or LOX/Propane. Heck, it could even use LOX/LH2. While the state of the VTVL industry isn’t quite mature enough where you could just order one of these custom and have it delivered to your launch pad 6 months ARO, a lander in these capability ranges isn’t a huge stretch for the commercial space industry, especially if they can partner wisely with some of the more traditional space companies or work with NASA via Space Acts. DC-X was actually a much bigger, probably more complicated system, and was done by a traditional aerospace company for around $100M in current dollars. A bare-bones lander, developed leveraging the emerging capabilities in the entrepreneurial community could probably be fielded for less than that. Possibly in the $50M range. You don’t need to push too hard on mass fractions or engine performance (you need to push a bit, but it isn’t as weight critical as some of the Apollo LM systems), and the technology is a lot more mature than it was in the 60s.

An important part of this process is not just developing the lander, but also working from the start with ITAR to make sure a process is in place that will allow you to launch on as many international launch vehicles as is feasible. This may not be fun, but is probably doable with appropriate precautions.

International Horse-Trading
Most space agencies prefer to spend money within their own borders, and interact with other agencies on a barter basis as much as possible. While this can sometimes lead to suboptimal solutions, it might just work in this situation. On the launch side, the barter would go something like this–the private entity would provide a lander, all lander ops, and physical launch integration work, and the space agency (NASA, ESA, RSA, JAXA, ISRO, or CNSA) would provide the lifter and upper stage for the mission. The launching country would get a certain share of the lander’s cargo space for their own experiments, a certain portion would be reserved for consumables and spare parts, and the remainder would be owned by the private entity to resell to other countries without launch capabilities (say a 40/40/20 split). In addition to transportation of the space hardware, the launching country would also get a share of the astronaut’s time on the surface. So basically you’re providing them with transportation and manned experimentation on the lunar surface in exchange for them providing a launch done by their own people. If one of the countries is willing to take some additional risks, they could even “buy” one of the two initial astronaut slots, in exchange say for a commitment to a certain higher share of the logistics launches per year. In exchange they’d get both the prestige of having one of the initial lunar crew, as well as a higher share in the available time. Over time, as the risk decreases, the initial crew could also be expanded (once again on barter terms that would have the agency in question shouldering a larger share of the required launches).

It should be mentioned how crazy of a bargain this really is for them in comparison to the typical lunar mission approach. Look at Constellation. It will be a lot more capable, but ultimately, somewhere around $10B/yr (and about $150B up-front), you get 4-person years/yr (2x 4-man crew rotations) and about 75klb of cargo (2x 17mT landings) on the moon once you have a base setup. Calling it a 60/40 split on costs (for manned vs cargo flights), that comes out to $1.5B per person-year, and about $53k/lb on the lunar surface–ignoring development costs. With a program like this, say you gave a country 1/4 of a man-year per launch, and about 1800lb, at a cost to them of call it a $200M launcher plus extra upper stage for the transfer. Splitting that $200M the same way (60/40), that gives you $480M per person year, and about $45k/lb on the surface. You don’t save a huge amount per pound of cargo on the surface, but your cost per person hour is about 1/4 as much (which is once again not too surprising–you’re not rotating crews, and not having to carry enough propellant to get them home–which takes about 4x as much mass per mission compared to a one-way manned landing). And you don’t have to spend tens of billions up-front, and you can buy your lunar program “by-the-slice”. Paying for an extra launch every year (and some lunar systems costs) is well within the budget capabilities of many of these agencies. While they might not be willing to take the risk of flying their own astronauts, or of “owning” the program, they are a lot more likely to be interested in a program like this, where someone else is shouldering the key risks, and they’re just getting a cheap deal. Even if they have their own lunar ambitions down the road, using a service like this would allow them to drastically reduce their technological risk moving forward, and might allow them to get a lot more benefit out of their investment when they eventually get that capability themselves.

“Sovereign Customers”
One of the key markets Bigelow is looking at for his inflatable space habitats is providing smaller countries with a way to participate in space for much cheaper than trying to do everything in-house themselves. By lowering the cost to participate, it makes it a lot more feasible for smaller countries, and even some corporations or research institutions to participate. This may be a country like South Korea wanting to send a rover that can get maintained by the astronauts over time. It may be a country wanting to do its own sample return mission–with the ability to have a human on the ground helping to presort/preprocess samples to maximize the bang for the buck. It could be a company like Catepillar that wants to get involved in lunar surface systems for future exploration programs sending a bunch of bearing concepts to test exposed to the lunar environment. It could be some small startup that has a crazy idea for lunar dust mitigation that it wants to try selling to future government programs, but needs testing and debugging first. There are many possibilities. The key here is that since the launch is already paid for, the private entity running all this can price the payloads however makes the most sense. You do need to cover lander costs, ground-ops costs, and the time of the scientists, but it might be possible to offer these slots at a price that is lower than they could buy commercially to try and stimulate demand, or if there is enough demand already you could price it high enough to make a decent profit. If there’s enough demand, you might even be able to justify paying for an additional “purely commercial” flight or two per year. You would want to save up some of the money to cover contingencies–like if something breaks down and you have to fly an emergency resupply flight on short notice, or if you decide for one reason or another to throw-in-the-towel after a few years, you can send enough propellant to get the settlers home. But depending on the interest level, this could easily be a business that has revenues in the low hundreds of millions per year.

Minimizing the Initial Risk
One additional market for the lander, and one that could allow the initial investment to be recovered a lot faster, would be to see if you could sell it to one of the space agencies for landing a rover or some other scientific package. The key here is that the lander is getting developed, on the philantrocapitalist’s own dime regardless of if he can presell any lander slots. This makes it easier to sell it as a commercially available service instead of a government funded development program. Using a light Atlas vehicle for instance (maybe with one or two strapons) you could probably short-load the vehicle enough to put a couple hundred pounds of useable payload onto the lunar surface. For a bundled price of say $200-250M for the launcher and lander, it would still be a steal transportation-wise for your customer, but could possibly pay off the initial costs of the project in one shot, even before the initial landings. The good news is that while its great if you can presell the landers for other applications, it isn’t the end of the world if you can’t.

One other way of minimizing the downside may be to see if you can prearrange the initial several launches. If you can line up enough international partners, it may be possible to get the initial setup done without having to actually buy any of the launches yourself. You’d still have to pay for the landers, but this way your total capital at risk for the startup is only the cost of 3-4 landers.

Anyhow, comments? thoughts? attempts to send nice young men in their clean white jackets to cart a certain space blogger away?

So we might want to try to figure out what kind of size of tether it would take to do these nifty tricks. The first place to start is to ask how big the tether needs to be–is it huge or tiny relative to our payload? To answer that question we need to know two things: what the velocity of the spinning tether is at its tip, and what it’s made out of.

There is a simple relationship between the mass of an untapered tether and the payload it is meant to catch and throw. Actually, it’s a ratio, much like a mass ratio in the rocket equation:

MR = 2(VR)^2/(1 – (VR)^2)

MR is the mass ratio, or the mass of the tether divided by the mass at the tip.
VR is the velocity ratio, which is the tip velocity divided by the characteristic velocity of the material.
The characteristic velocity of the material is the square root of two times the tenacity divided by the product of the safety factor and the material density.

VR = Vtip/Vc

Vc = sqrt(2*tenacity/(safety-factor*density))

An example might make this more clear:

Let’s say we wanted to throw a payload from LEO to a geosynchronous transfer orbit (GTO). That’s about a 2400 m/s delta-V beyond LEO, applied impulsively at LEO altitude. Assuming that the tether is in an orbit intermediate between GTO and LEO, and assuming that the tether will give half of the delta-V at catch and the other half at throw, let’s run the numbers:

Let’s assume we’re using a material with a characteristic velocity of 1600 m/s. To get the 2400 m/s of DV we need a tip velocity of 1200 m/s. This gives us a velocity ratio of (1200 m/s)/(1600 m/s) = 0.75. Plugging VR=0.75 into the equation gives 2*(0.75)*(0.75)/(1 – (0.75)*(0.75)) = 1.125/0.4375 ~2.57.

So the untapered tether will have a mass 2.57 times that of its payload, in this scenario. This very simple analysis also assumes that the tether is connected to a counterweight that is, for all intents and purposes, infinite, so as to save us the step of computing the mass of the tether on the other side of the center-of-mass. So assuming we had a payload of, say, 1000 kg, the mass of the tether would be 2570 kg.

The equation I’ve just described shows that the characteristic velocity of a material has a physical meaning. If you look at the denominator of the equation, you can see that when the velocity ratio goes to one, the denominator goes to zero and the mass ratio goes to infinity. So the characteristic velocity is the maximum tip velocity of an untapered tether (of any length) with a safety factor of 1, at which speed it will break under its own tension.

In my next post, this simplified approach to tether modeling will get more complicated by describing TAPERED tethers whose velocity ratio can be greater than one. But the mathematics will be more complicated.