Thursday, February 16, 2012

Puppets, Telerobots and James Cameron

Please support my efforts. I just finished a conic sections and orbital mechanics coloring book. I need help with printing costs. Through this Kickstarter you can pre-order a signed coloring book. I look at conic sections, Kepler's laws, Hohmann transfer orbits, the Oberth effect, space tethers, Tsiolkovsky's rocket equation and lots of other space stuff. The coloring book is $5 plus $5 shipping and handling ($10 shipping and handling if you're outside the U.S.).

Kickstarter for this coloring book ends 4:30 a.m. April 13, 2020.

Cameron’s movie Avatar looks at telepresence and remote interaction. The biological telerobots portrayed are well beyond our present state of the art. However telepresence and telerobots made of metal, silicon and plastic aren't science fiction, they are being used today.

Avatar also portrays more plausible puppets made of metal, silicon and plastic. The mercenaries will don exosuits for heavy work or hand to hand combat. An exosuit user will slip inside a motion capture suit within the exosuit. The user’s movements are mimiced by the exosuit’s movements. If a robot puppet can be operated by a motion capture suit from within, it could also be operated by remote motion capture. The notion of exosuits is related to the notion of telerobots.

Cameron’s movie The Abyss featured Remotely Operated Vehicles (ROVs). James Cameron and his brother Mike developed ROVs for underwater exploration and filming. Their ROV dubbed “Snoop Dog” was used to explore the Titanic in preparation for making of the movie. Later ROVs named “Jake” and “Elwood” were used for further exploration of the Titanic as well as the sunken battle ship Bismarck. Cameron and Vince Pace developed 3-D cameras to film the sunken ships. 3-D cameras bring us a little closer to the goal of a fully immersive telepresence.

The Cameron brothers aren’t the only players developing telerobots and telepresence.

Existing markets are pushing advances in the state of art. As easy to reach resource bodies are exhausted, industry is looking to ore bodies in wastelands and under the ocean. Any hard to reach and/or dangerous workplace could benefit from telerobots. Rio Tinto Mining company is developing teleoperated devices (see page 10 of this pdf). British Petroleum uses submersible ROVs with their underwater oil platforms. There are also military applications. It is becoming more common to use drones for reconnaissance or telerobots to disarm bombs.

The movie industry uses motion capture suits. Actor Mike Meyers operates the virtual puppet Shrek with motion capture. The blue beings in Avatar are virtual puppets operated in a similar fashion. Motion capture is starting to move into the video game market, Wii and Kinect being early platforms.

Given various market forces, it’s inevitable telerobots will climb in ability as they drop in price.

Improved telerobots could be a huge game changer in efforts to settle and exploit space.

Remotely operated rovers Spirit and Opportunity were a spectacular success in gathering science on Mars. Cameron had offered to put his 3-D camera on the Mars Science Laboratory rover, but there wasn’t enough time to redesign the rover before the November, 2011 launch window.

For several reasons, a lunar telerobot could be far more able than a Martian telerobot. Light lag to a Mars rover ranges from ten to fifty minutes. Lunar light lag is about three seconds. Another factor is bandwidth. An able telerobot needs to send lots of sensory data as well as receive complex instructions. Signal strength falls with inverse square of distance and a weak signal is more easily lost to noise. So the moon’s proximity makes high bandwidth less difficult. The Lunar Reconnaissance Orbiter achieved 100 megabytes per second.

James Cameron sits on the board of the Google Lunar X Prize. This competition will award 20 million dollars to the first team that lands a rover on the moon. The rover must travel 100 meters while sending video images back to earth. It is my hope that Cameron will eventually work with these teams to land lunar rovers with his 3-D cameras on board.

Telepresence may become an early form of space tourism. A tourist could move about the lunar surface, picking up rocks and interacting with the lunar environment in other ways. All while his flesh and blood body moves about in a motion capture suit safe and comfortable on earth’s surface.

The Cameron brothers took great satisfaction in capturing light passing though the Titanic’s lead windows. Windows that hadn’t felt light since 1912. I like to imagine the Cameron/Pace 3D cameras filming the terrain of a crater floor at a lunar pole. An environment that hasn’t felt sunlight for billions of years. Inky black pits that fall to 40 degrees above absolute zero, even colder than Pluto. These craters are bound to contain some of the most bizarre and surreal landscapes in the solar system.

Besides strangeness and mystery, the lunar cold traps are thought to have abundant water and CHON (Carbon, Hydrogen, Oxygen and Nitrogen). Lunar water ice is exciting. Ice can be used for drinking water, radiation shielding, and water can be split into hydrogen and oxygen for rocket propellant. The nitrogen and oxygen compouds could provide air to breathe. Besides giving us vicarious experience of alien landscapes, we might use lunar telerobots to prepare an enduring human home on the moon.

The Futurist: The Life and Films of James Cameron
Big Dog. A robot with balance, a technology that could mitigate the slow reaction time from a 3 second light lag.
Google Cars. A robot with collision avoidance, another technology that could mitigate a 3 second reaction time.
Shackleton Energy Company. A TED video by Bill Stone. Stone hopes to mine lunar propellant with the aid of robots. The video features Stone's semi-autonomous robot, DepthX, a device for exploring subterranean caves.
Spudis and Lavoie's Lunar architecture. Dr. Paul Spudis and Tony Lavoie also propose to utilize lunar propellant with the aid of telerobots.

Murphy's Mangled Math

In his blog Stranded Resources Tom Murphy argues that space resources will likely remain beyond our reach. He concludes humanity should learn to live within its means and conserve our resources. This sound advice is the theme for most of his Do The Math blogs.

But the math on which he builds his argument is wrong.

To calculate delta V from earth to Mars he adds 3 quantities:

Earth escape velocity (~11 km/s),

Earth to Mars velocity (~6 km/s)

Mars escape velocity (~5 km/s)

Which totals ~22 km/s.

But you don’t simply add these three quantities. Break the Earth to Mars velocity into two parts. These parts form legs of two right triangles. The other legs being Earth escape velocity and Mars escape velocity. Add each hypotenuse for the actual delta V.

So the total delta V is around 17 km/s, not 22 km/s.

But wait. Murphy did generously round his 22 km/s to 20 km/s.

And there is also a ~2 km/s gravity loss incurred during vertical ascent. Add this 2 km/s to 17 km/s and you get 19 km/s. Murphy isn't shy about mentioning gravity loss. But he doesn't include it in his calculations, giving the impression that he's being quite generous to the addled space cadets. Including gravity loss takes the actual delta V to about 19 km/s. This isn't too far off from Murphy's 20 km/s.

But Murphy neglects the use of aerobraking.

For the Mars orbiter missions, a small burn is done to park the probe in a capture orbit rather than a low circular orbit. This can be done with as little as .7 km/s. The lowest point in these capture orbits pass through Mars upper atmosphere. Each time the probe passes through Mars' upper atmosphere a little velocity is shed by atmospheric friction. Using aerobraking, a capture orbit can be reduced to a low circular orbit using virtually zero propellant.

For the Mars landers, aerobraking sheds around 6 km/s.

Including gravity loss and using aerobraking the delta V budget for Earth surface to Mars surface is more like 14 km/s, about the same for delivering a comsat to geosynchronous orbit. So even Murphy's apparently generous 20 km/s is 6 km/s too much.

Given that the exponent of Tsiolkovsky's rocket equation scales with delta V, 6 km/s is a serious error.

Tsiolkovy's equation:

(start mass) / (final mass) = e(delta V/exhaust velocity)

Where e is Euler's number, about 2.72.

The dramatic power of exponential growth is illustrated by The Legend of Paal Pasam. An east Indian king enjoyed challenging his guests to a game of chess along with a friendly wager. Unknown to the king, one of his guests was Krishna. Krishna offered this wager: 1 grain of rice on the first square, 2 on the second, 4 on the third, doubling the grains each square of the chess board. The king agreed. Only after losing to Krishna did the king realize the enormity of his bet. Krishna revealed his true identity and told the king he could pay his debt over time. To this day the king’s estate gives rice to Krishna’s followers during their pilgrimages through that land.

Exhaust velocity of hydrogen and oxygen is about 4.4 km/s. 3 / 4.4 = ~ln(2). Each 3 km/s added to the delta V budget is a square on the above chess board. That is, each 3 km/s doubles the starting mass.

Murphy's 6 km/s error quadruples the starting mass.

Refuel In Space?

If you can get propellant along the way, it changes the picture:

At each square with a propellant depot, you get to start over at 1 grain of rice.

Murphy takes a look at refueling in space. A good propellant source would be close to earth in terms of delta V. So what does Murphy suggest? Jupiter or Titan! If he is looking for the most absurd propellant sources to debunk, he would do better to look at sources from Alpha Centauri. Or better yet, the Andromeda galaxy.

What are potential propellant sources that are close in terms of delta V? Earth’s moon is one.

At the lunar poles are craters floors which never see sunlight. Temperatures in these basins are as low as 40 degrees Kelvin, colder than Pluto. After a comet impact, volatile gases that don’t escape spread over the lunar surface. Gases reaching the cold traps will freeze and stay there. India’s Chandrayaan-1 lunar orbiter found evidence of thick, relatively pure ice sheets in many of these cold traps. It is estimated the anomalous north pole craters have at least 600 millions tonnes of ice.

These lunar volatiles are potential propellant only 2.5 km/s from Earth Moon Lagrange 1 (EML1) and Earth Moon Lagrange 2 (EML2). Using 3 body mechanics, there are paths that enjoy delta V savings over Hohmann orbits. And EML1 and EML2 are hubs for this Interplanetary Transport Network.

Lunar volatiles can also provide water for radiation shielding, water to drink, as well as nitrogen and oxygen to breath. All 2.5 km/s from EML1. This is a huge mass that doesn’t have to be lifted from the bottom of earth’s gravity well.

Are there other potential propellant sources?

The low density of Mars’ moons Phobos and Deimos could indicate volatile ices. The low density could also be caused by voids within the moons, so the jury’s still out. If these do have ice, they are potential propellant sources quite close in terms of delta V. It is about 3 km/s from EML1 to Deimos. Possibly a little less if aerobraking is used.

Murphy looks at delta V from one low planet orbit to another. This is common, Atomic Rockets does the same, for example. But there are a multitude of possible parking orbits. Parking in a low circular orbit takes the maximum delta V. A high apogee capture orbit can take much less. Given the possibility of departing from propellant sources high on the slopes of a gravity well and shedding velocity using aerobraking, he would do better to look at delta V between elliptical capture orbits.

Grab That Asteroid!

Murphy suggests 5 km/s to capture an asteroid in earth orbit. There are near earth asteroids that could be captured with much less. The comet Oterma suggests a possible capture method using 3 body mechanics. Oterma will sometimes fall through the Sun-Jupiter L1 (SJL1) neck into Jupiter’s realm. It spends some time in Jupiter’s realm and then exits through the Sun Jupiter L2 (SJL2) neck. Then later it will fall back into the SJL2 gate, dwell in Jupiter’s realm, then exit trhough the SJL1 gate. This is described in the online textbook Dynamical Systems, The Three-Body Problem and Space Mission Design, a 17 Mb pdf.

An asteroid slowly drifting by the Sun-Earth L1 (SEL1) or Sun-Earth L2 (SEL2) could be parked in these regions with a minute nudge. From SEL1 or 2, a tiny amount of delta V suffices for delivery to EML1 or 2. For some asteroids .3 km/s can suffice for capture.

Only a small number of asteroids are amenable to capture this way though. A much larger number of Near Earth Asteroids pass within 1 km/s of EML1.

Murphy’s hypothetical asteroid is a cubic kilometer. The Tunguska object is thought to have been about 50 meters in diameter. Murphy’s asteroid is about 10,000 times larger than a meteorite big enough to wipe out a major city. So his absurd asteroid is a nonstarter due to safety considerations as well as the difficulty of moving such an enormous mass.

If we find a 20 meter asteroid of value, this could more safely be parked in earth’s orbit. This is small enough to burn up in earth’s upper atmosphere.

If we find a large ore body, it makes no sense to park the entire asteroid in earth orbit. Rather import the resources in small enough loads that it’s safe and doable. This also avoids flooding the market and thus devaluing the commodity.

Given a 20 meter object and 1 km/s delta V, the energy required differs by a factor of about two and half million from Murphy’s scenario -- somewhat less difficult.

Murphy ignores a number of things: 1) The Oberth Effect. 2) Aerobraking. 3) Moving between capture orbits rather than low circular orbits. 4) Nearby propellant sources. 5) Exploiting 3 body mechanics for delta V savings. 6) Small asteroids close to EML1 or EML2 in terms of delta V.

Tom Murphy does use weasle words like "simplified, approximate terms" or "crudely speaking". But his errors are truly enormous, too big to be salvaged by these disclaimers.

So I have to give Stranded Resources a grade of F.

Which is a shame. Murphy is correct to urge less consumption. But he doesn't have to resort to wrong arguments to support his view. That only subtracts from his credibility.