Monday, August 24, 2015

Neil Tyson -- Incompetent Ass

A little more fact and a little less fiction, please

At one time I was a Neil DeGrasse Tyson fan. Our culture needs more charismatic pop figures promoting science and rational thought.

But Tyson has a propensity for just making stuff up. A true devotee of science makes it a top priority to disseminate accurate info.

I'll give a few examples.

Tyson likes to promote space exploration -- that's a good thing. He also notes our space programs have generated spin off technologies that help the economy -- also a good thing. But he exaggerates and embellishes. Here Tyson credits the space program for miniaturizing electronics:

The urge to miniaturize electronics did not exist before the space program. I mean our grandparents had radios that was furniture in the living room. Nobody at the time was saying, "Gee, I want to carry that in my pocket" Which is a non-thought

Ummm….   No.

Making electronics more compact, less massive and less expensive was an extremely obvious thought. Tyson's statement is utterly ridiculous.

Tyson would do well to read Wikipedia's history of the transistor. There were efforts to replace vacuum tubes as early as the 1920's. TR-1, the first transistor radio, hit the market in November of 1954.

NASA was formed in 1958.


The Regency TR-1 transistor radio hit the market in 1954,
4 years before NASA was formed.


NASA and military aerospace have made substantial contributions to the development of electronics. Let's crow about these real contributions. But please don't give our space program credit for the notion of miniaturizing electronics.

It damages our cause when someone like Tyson spouts complete B.S.. The tendency to exaggerate and embellish is one of the reasons space advocates suffer from a lack of credibility.

"He's an entertainer," Tyson defenders might say. "Embellishing the truth is standard practice to boost ratings. If he can recruit more supporters, who cares if he doesn't cross his t's and dot his i's?"  I didn't buy that but had to acknowledge the man has gathered a following. So I didn't grumble too loudly.

Then Tyson stepped over the line.

A malicious fabrication

9/11

Like everyone else, I was horrified by the events of September 11, 2001. I braced myself for President Bush's reaction. I thought Bush would use the tragedy to demonize Muslims. Exploiting xenophobia is an all too common political device.

But Bush's response was a pleasant surprise:
The face of terror is not the true faith of Islam.  That's not what Islam is all about.  Islam is peace.  These terrorists don't represent peace.  They represent evil and war. 
When we think of Islam we think of a faith that brings comfort to a billion people around the world. Billions of people find comfort and solace and peace. And that's made brothers and sisters out of every race -- out of every race. 
America counts millions of Muslims amongst our citizens, and Muslims make an incredibly valuable contribution to our country. Muslims are doctors, lawyers, law professors, members of the military, entrepreneurs, shopkeepers, moms and dads. And they need to be treated with respect. In our anger and emotion, our fellow Americans must treat each other with respect.
What Speech did Tyson recall hearing after 9-11? He remembers Bush loosely quoting Genesis "Our God is the God who named the Stars". Tyson says he was "attempting to distinguish we from they".

Watching the Tyson's video I'm scratching my head. Bush wasn't trying to stir up hatred against Arabs, just the opposite. And where did this stuff about star names come from? Below is Tyson's rant. Tyson starts talking about Bush at around 1:30.



Bush did give a speech where he quotes Genesis saying God named the stars. But it wasn't a post 9-11 speech slamming Arabs. It was a eulogy for the astronauts killed in the Space Shuttle Columbia disaster.


From Bush's Columbia disaster speech:
In the skies today we saw destruction and tragedy. Yet farther than we can see, there is comfort and hope. In the words of the prophet Isaiah, "Lift your eyes and look to the heavens. Who created all these? He who brings out the starry hosts one by one and calls them each by name. Because of His great power, and mighty strength, not one of them is missing. 
The same Creator who names the stars also knows the names of the seven souls we mourn today. The crew of the shuttle Columbia did not return safely to Earth; yet we can pray that all are safely home. May God bless the grieving families. 
And may -- may God continue to bless America.
Somehow Tyson conflated Bush's Columbia disaster speech with post 9-11.

Chemically enhanced perception?

How on earth did Tyson manage to conflate 9-11 with the Space Shuttle Columbia disaster? I have a theory. Carl Sagan, Tyson's hero and mentor, was thought to indulge in a little weed now and then.

Perhaps Tyson has discovered psychotropic drugs can be used as a vehicle to explore other worlds and alternate realities.



Tyson's "Apology"

In a Facebook post Tyson admits conflating the two events.

Well, he makes the admission buried in the 10th paragraph. The first six paragraphs are devoted to glowing descriptions of Tyson's favorite subject: himself. The seventh paragraph he slams those petty and small minded "lawyers" who doubt Tyson's word. How dare they question his credibility just because they catch him in the act of making stuff up?

Here's Tyson's admission:
What followed fascinated me greatly.  As others had uncovered, the President indeed utter the following sentences: 
In the words of the prophet Isaiah, "Lift your eyes and look to the heavens. Who created all these? He who brings out the starry hosts one by one and calls them each by name. Because of his great power and mighty strength, not one of them is missing."  The same creator who names the stars also knows the names of the seven souls we mourn today. 
But I was wrong about when he said it.  It appears in his speech after the Columbia Shuttle disaster, eighteen months after September 11th 2001.  My bad.  And I here publicly apologize to the President for casting his quote in the context of contrasting religions rather than as a poetic reference to the lost souls of Columbia. I have no excuse for this, other than both events-- so close to one another -- upset me greatly.  In retrospect, I’m surprised I remembered any details from either of them.
This is all Tyson needed to say. Had his apology just consisted of these few paragraphs, he might have salvaged a little credibility.

But Tyson goes on to write:
Of course very little changes in that particular talk.
Utterly and completely wrong. As usual. That talk was about President Bush's idiocy. The whole Arabic star name thing was to "confound Bush's point". Sadly for Tyson, the point being confounded comes from an imaginary Bush that lives in Tyson's crack pipe.

And still more B.S. from Tyson:

I will still mention Islamic Extremists flying planes into building in the 21sth century. I will still contrast it with the Golden Age of Islam a millennium earlier. And I will still mention the President's quote. But instead, I will be the one contrasting what actually happened in the world with what the Bible says: The Arabs named the stars, not Yahweh.
Of course the Arabs named the stars. Does that falsify the passage from Isaiah? No. How does Tyson know God didn't name the Stars? God's existence or nonexistence isn't something that can be demonstrated with experimental evidence. His confident assertion isn't a testable hypothesis. It is beyond the purview of science.

But then again, Tyson's cult of personality has never been about science.




Saturday, August 8, 2015

Lunar pogo hopper

Paul Spudis recently offered some thoughts about Drones on the Moon. He notes conventional drones would not work on an airless world.

Spudis writes:
Sub-orbital “hops” (ballistic flights from point-to-point) are possible, but come at fairly high cost—it takes nearly as much energy to fly hundreds of kilometers on the Moon in a ballistic hop as it does to go into orbit and then descend elsewhere.
This is incorrect. Here I look at suborbital hops on airless worlds. A minimum energy ellipse going from point A to B would have a focus on the midpoint of the chord connecting A & B:


The other focus would be at the moon's center, of course.

The vis viva equation tells us
v=sqrt(GM(2/r - 1/a)

In this case GM is the moon's gravitational parameter, r is the moon's radius and a is the semi major axis of the ellipse.

Let's say A is 300 km from B. That'd be  about 9.9 degrees separation. Here's a pic:


.67 km/s to hop and another .67 km/s for a soft landing. For low lunar orbit that would be 1.68 km/s to take off and another 1.68 km/s to soft land. Energy goes with square of speed. (.67/1.68)2=.16. The energies differ by more than a factor of 6! How on earth did Spudis conclude these are nearly the same?

Here is my Lunar Hopper spreadsheet. There's a tinted cell user can input distance between point A and B. This is the first document I've uploaded to Google docs, hope it works.

Spudis suggests spherical pit bots for lunar drones. These bots use micro thrusters to hop and hover. Whether the hop is 5 meters or 500 kilometers, the most efficient hop is the minimum energy ellipse described above. On the moon a ten minute hover costs about one km/s delta V. Spudis justifiably grouses about the tyranny of the rocket equation. But these pit bots rely on reaction mass to move. They don't circumvent said tyranny.

Pogo Hoppers

Various folks talk about lunar drones at Spudis' forum. Someone who goes by the name finkh mentioned pogo sticks. An interesting notion, in my opinion.

When I was a kid, my pogo stick used a spring. Solar cells might provide energy over time to compress a spring, thus avoiding the use of reaction mass. No more nasty rocket equation! On landing the spring absorbs the impact. The compression on impact might be a way to recover some energy.

I moved over a variety of terrains with my pogo stick. I could move forward, backward, left or right. It seems feasible to develop a robot with similar abilities.

But as I recall, getting from point A to B on a pogo stick was more strenuous that walking. So I'm not sure compressing a spring on impact is a great way to regain energy. Looking at existing robots like Big Dog, it looks like powerful engines are needed to power the device. Once again, the need for a better Alpha rears its ugly head. Elon Musk seems to be working on improved solar panels and energy storage. Hopefully Tesla Motor's R&D will have applications in space exploration.

How much impact can a pogo stick take? The 300 km hop pictured above hits the ground at .67 km/s or about 1500 miles per hour. No, I wouldn't want to be on that pogo stick.

This list of pogo stick records says Biff Hutchison jumped nearly 3 meters high. By my arithmetic he hit the ground at about 7.5 meters/sec or about 17 miles per hour.

Assuming 17 miles per hour is maximum jumping and landing velocity, a lunar pogo could jump about 36 meters (assuming the hop was a minimum energy ellipse from point A to B). This hop would be about 9 meters high.

A jump 36 meters long and 9 meters high isn't spectacular but such a device might have uses. And I like the image of a pogo stick on the moon.





Friday, August 7, 2015

A new tether spreadsheet

 A few notes on my old spreadsheets

Up to now, most of my spreadsheets for vertical tethers and elevators have been based on Jerome Pearson's work. The taper ratio I've used is based on equation (10) from Pearson's The orbital tower: a spacecraft launcher using the Earth's rotational energy. A screen capture from Pearson's PDF:


Pearson is looking at a very specific vertical tether here, a space elevator whose foot is at earth's surface (r0) and whose balance point is at geosynchronous orbit (rs).

But I make some substitutions to make Pearson's equations more general:

Substitute r0 with rfoot, the distance of the tether's foot from body center. 

Substitute rs with rbalance. By rbalance I mean the point on a vertical tether where centrifugal acceleration exactly balances gravity.

Substitute g0 with gfoot. By gfoot I mean gravity at tether foot. Pearson sets g0 at 9.8 meters/sec2, earth surface gravity. I set gfoot as G*(mass of central body) /  rfoot 2.

My resulting spreadsheets were cumbersome and complicated. I don't like complicated -- more opportunities for error. And indeed my early versions had many errors that gave obviously wrong results. Through careful proofreading and many bottles of aspirin I started to get numbers that matched Pearson's. But I remain uncomfortable with these sheets.

A new tether spreadsheet

Then Chris Wolfe sent me his Phobos tether spreadsheet. Chris' approach is simple and straightforward.

First he figures payload force at the tether foot: payload mass*net acceleration. In the linked spreadsheet, net acceleration is Mars gravity - centrifugal acceleration - Phobos gravity. Given the tensile strength of the tether material, this sets tether cross sectional area at the foot. Setting a safety factor of two will double this cross sectional area.

Then to the payload force he adds the force exerted by the length of tether just above the payload: density * cross sectional area * dr * net acceleration. This sets the cross sectional area of the next short length of tether. Again, the safety factor number multiplies this cell.

And so on up to the balance point.

Summing the mass of these cylinders gives a very good approximation of tether mass.

I had used a similar approach for calculating tether mass:


Tether mass is tether density times an integral giving tether volume from foot to balance point. For cross sectional area I used Pearson's equation 9 (see top of page). Being unable to solve the integral analytically, I chopped the tether into many small lengths and did a Riemann sum. In other words my numeric method for calculating mass is nearly identical to Wolfe's. Except Wolfe has a simple and straightforward method of getting the cross sectional area. 

The numbers from my spreadsheets closely match Wolfe's which also seem to match numbers from credible folks like Pearson or Aravind.

Chris' method is more versatile. A few advantages:

We can look at mass of decoupled upper tether length

If you have a huge anchor mass (like Phobos), the upper length becomes decoupled from the lower. The need to balance newtons from above with newtons from below is no longer an issue when anchor mass is 1.07e16 kg. 

If the upper length is independent of the lower, gravity at the tether foot isn't relevant. But Pearson's methods make heavy use of h, the tether material's characteristic length at the tether foot. This characteristic length has  gfoot in the denominator.

With Wolfe's method we can ditch the irrelevant h. Just as with the foot, we can start with net newtons at the tether top and then work our way down to the balance point.

We can look at moon tethers balanced from L1 or L2

Pearson's elevator model assumes two accelerations, earth's gravity and centrifugal acceleration. Wolfe's model can easily include a moon's gravity in the net acceleration. I am looking forward to tweaking Wolfe's spreadsheet to look at lunar elevators from EML1 and EML2.

More to come

Chris Wolfe's tether model enables me to scrutinize many of my favorite scenarios in more detail.

Besides this wonderful spreadsheet, Chris sent me a lot of other neat stuff. As time and energy allow, I'll use his ideas as the basis of drawings and discussions.

August 8 edit: Chris Wolfe has started a new blog Bootstrapping Space. I am predicting it will be an increasingly valuable resource as time goes by.


Thursday, July 23, 2015

Review -- Elon Musk Quest for a Fantastic Future


by Ashlee Vance.

Each chapter of this book struck a chord with me. As usual this will be a Spinrad style review where I use Vance's book as an excuse to jump on my soapbox.

Winter Is Coming

I often feel like we're trapped in a bleak George R. R. Martin story. Rate of growth may be slowing but the planet's population is still rising. Appetite for consumer goods is climbing as the third world catches up to industrialized nations. In the meantime finite resources are getting harder to come by. Hydrocarbon fossil fuels aren't going to last forever.

ERoEI should be a term on everyone's mind. But policy makers and general populace remain oblivious. What's trending at the time of this writing? Caitlyn Jenner, presidential candidate Trump is saying we need to build a big wall along our southern border to keep out Mexican rapists, Justin Beiber's naked butt on Instagram.

It's like Game of Thrones. Greed, stupidity and cruelty triumph time after time in spite of the hero's best efforts. In slow motion we're watching our derailed train head for a cliff and nobody's putting on the brakes.

A Dream of Spring

But there's a ray of hope. Unlike Martin's gritty realism, Musk seems to be a character from the golden age of Marvel comics. A Tony Stark like character who actually does triumph over insurmountable odds. Vance describes several periods in Musk's life where doom seems imminent. But through sheer tenacity he overcomes one impossible obstacle after another.

OCD

Obsessive Compulsive Disorder. Describing Musk's childhood on page 38:
… Soon he owned a Commodore VIC-20, a popular home machine that went on sale in 1980. Elon's computer arrived with … a workbook on the BASIC programming language. "It was supposed to take like six months to get through all the lessons," Elon said. "I just got super OCD on it and stayed up for three days with no sleep and did the entire thing. It seemed like the most super-compelling thing I had ever seen."
(Added emphasis mine). OCD is one of my major faults. How many times have I stayed up til 4 a.m. playing Tetris? How many hours squandered in the labyrinth mazes of Zelda? Etc.

But a crippling flaw can also be an empowering strength. Now I feel less guilty when I get lost doing a drawing or obsessed with a geometry problem.

Musk has a peculiar mental make up. Other factors came together for a perfect storm making Musk a game changing personality. His father was a well to do engineer. Musk had the opportunity and will to master several key skills during a time of dramatic change.

Electric Cars

What happens after peak oil? Nuclear might take care of our electricity needs. But what about transportation? Cars and trucks use gasoline.

There's the Prius -- a misbegotten bastard child of gas and electric with extra mass and complexity.

The fully electric cars I had seen were golf carts that needed to be recharged every 20 miles.

Then Tesla blew my opinions out of the water. An electric car with oomph as well as range. Learning of this car's existence filled me with relief and joy.

I was also delighted to hear of the improved energy storage with lithium ion batteries. This makes solar power more viable, another arena in which Musk is fighting the good fight. I still believe nuclear will be our primary source of power. But improved storage means solar will play a more prominent role.

Tesla and Solar City are traded on the stock exchange. For TSLA and SCTY he regarded going public as a Faustian deal, a necessary evil. He explains that shareholders tend to have short range goals, a profitable quarter while he has a more long range agenda. Well, I've gone on E-Trade and bought one share of Tesla and three shares of Solar City. I am one shareholder that endorses Musk's long range goals. Musk managed to avoid going public on SpaceX

Breaking Free of Cradle Earth

For decades we've been spinning our wheels in low earth orbit. Human Space Flight has been the cash cow of near monopolies that don't care about humanity's future. For our elected officials, HSF is a pork barrel program for buying votes.

New Space pundits like Rand Simberg or Henry Spencer have long been advocating a competitive space market. They rightly point out cost plus contracts encourage graft. That savings can be realized with mass production when R&D expense is amortized over many units.

But these insights weren't sufficient to overcome inertia. That is until Musk came along.

That Musk has built a new aerospace company from the ground up is an amazing accomplishment. I had placed my bets a new player would win the 100 kilometer X-prize. But a new kid on the block achieving orbit and remaining solvent? That took me by surprise.

Many of the possible economies Spencer and Simberg predicted have been realized by Musk. Economies of scale. A supply chain distributed through many congressional districts and policies set by committee guarantees waste.  Much of SpaceX parts are made in house. Central management is lean and mean with little or no duplication of effort. Musk has already brought down the cost of getting to orbit.

One of the most exciting SpaceX goals are reusable space vehicles. How much would a transcontinental trip cost if we threw away a 747 each flight? Musk correctly sees quickly and economically reusable space ships as a prerequisite for breaking free of Cradle Earth.

SpaceX is making good progress towards a reusable booster stage. Since the booster is a lot more massive than an upper stage, reusable boosters could make a huge cut in the cost of getting to space. Presently I'm giving two-to-one odds SpaceX will achieve cost savings with a reusable booster.

How about a SpaceX reusable upper stage? I'm betting against it. An upper stage's big delta V budget makes for a difficult mass fraction. If dry mass is 8% or less, it's hard to have robust structure and thermal protection. Re-entering the atmosphere at 8 km/s subjects the space ship to extreme conditions and I can't see the delicate eggshell of an upper stage surviving this abuse.

But maybe I'm wrong! I already have egg on my face for earlier bets against Musk. If I'm right, I believe Musk will find other ways to deal with upper stage re-entry. Maybe he'll look at solutions like extraterrestrial  propellent and/or momentum exchange tethers.

Musk has beat the odds numerous times in the past. I'm betting he'll continue to surprise people in the future.





Saturday, July 18, 2015

My Geoscapes books are selling!

Geoscapes

Sales of Dover Creative Haven Geoscapes recently picked up.


Last week saw sales of about 22 books per day. There was a week in March when 46 books a day were being sold. I have no idea what caused this recent upsurge. Three of my friends and relatives have told me they've seen the book on display at Barnes and Noble stores. My daughter and I walked into a grocery store/delicatessen and saw my book on display along with other Dover Creative Haven books.

I'm proud of this coloring book, it explores geometrical themes: perspective drawings, studies of polyhedra, spirals etc.  I'll post a few screen captures.


A tribute to two of my heroes: Da Vinci and Kepler. Leonardo Da Vinci would make open faced polyhedral models composed of beams along the edges. That way he could study the interior of a polyhedra. Around the edges of this page are Leonardo style Platonic dodecahedra. If you extend the edges of each pentagon to form a five pointed star, you get a Kepler solid, the small stellated dodecahedron (center). Besides revolutionizing our view of the solar system, Johannes Kepler did a lot of wonderful exploration and discoveries in solid geometry.



Study of the dodecahedron-icosohedron symmetry group. Top left: Leonardo style dodecahedron, Top right: Leonardo style icosahedron, Center: Interpenetrating Leonardo style dodecahedron and icosahedron showing the duality between these two solids.

Lower three solids are Archimedean solids that result from truncating (slicing off corners) of either the dodecahedron or icosahedron.



Bridge

I am fascinated with space filling bricks, a.k.a. honey combs. At the bottom are cubes. Cubes are a special case of a rectangular solid, the sort of bricks we're all familiar with. The structure at the top are alternating octahedra and tetrahedra, a.k.a. an octet structure. The octet faces are equilateral triangles. Height of an equilateral triangle is sqrt(3)/2 length of a side, an irrational number. So at first glance it seems like octet structures would be incompatible with cubic structures. But this gulf is bridged by a third type of space filling brick: the truncated octahedron. That's why I call the truncated octahedron the Bridge brick.



A Lego-like construction toy I invented. But instead of cubic structure, this toy would build octet structures (see image and explanation just above this one). And instead of a single male face and a single female face, every face has a hermaphrodite connector. Bridge truncated octahedral construction units might be a way to make my toy compatible with Legos.


Don't know what to say about these interpenetrating spiral structures. Except that they were fun to draw.

Hoping the people who bought my book enjoy my strolls through strange geometry gardens.

Surreal Visions

Another book I'm proud of is Surreal Visions. But it's still suffering flat sales. I'll post a few images any way:


These rhino monkeys are frolicking about a Klein Bottle. A peculiar object, somewhat like a three dimensional Möbius Strip.



The Riemann Sphere maps the points on the surface of a sphere to a plane (with the exception of the north pole!). Mathematician Chaim Goodman Strauss helped me come up with a related mapping of points from 3-space onto 3-space. Surreal Visions features several images based on this mapping.



And finally one more from Surreal Visions. This image is called Tears.

Wednesday, July 1, 2015

Review: Declaration by James Patrick Kelly

Spoiler alert: I give away events unfolding in Kelly's story. It appeared in the March 2014 edition of Asimov's Science Fiction Magazine.

"Declaration" is a thought provoking extrapolation of existing trends. In the style of Spinrad, I will use this review as an excuse to jump up on a soapbox and deliver my own opinions.

In this tale more and more people are dwelling in softtime. Softime is what today's internet might evolve into, a shared online virtual reality. Depending on sophistication of interface, the virtual reality can be fully immerseive.

A significant part of the population are severely disabled and can't interact with the world using their meat bodies. These disabled people are known as stash. They are more or less stashed in coffin like life support cubicles.

The government mandates that everyone spend an allotted time in hardtime, a.k.a. reality. Stash revolutionaries want to spend all of their existence in softtime. The story title Declaration refers to the revolutionaries' Declaration of Independence. They want to sever their connections with the real world.

But would the revolutionaries become independent of hardtime? In Kelly's story, that's not clear. Are the stashed people dependent parasites or do they provide services and do meaningful work? Robots are ubiquitous in the story but I get the impression machines haven't fully replaced humans. There still seems to be need for meat to interact with the world to maintain infrastructure and take care of business. For example the main character turns her stash brother to prevent bed sores, even though the brother has a carebot.

Primitive versions of these interfaces already exist. For example motion capture sensors control virtual puppets in movies like Shrek or Avatar, as well as virtual avatars in computer games.  Neuroscientist Miguel Nicolelis has implanted a Brain Machine Interface into the cortex of monkeys that they've used to control virtual avatars.

From inner space back to outer space

Virtual avatars aren't the only puppets controllable by motion capture or brain machine interface. Nicolelis' monkeys have also used their cerebral implants to control remote robotic arms. A paralyzed person using a Nicolelis exosuit did the opening kick in the 2014 World Soccer Cup. Surgeons use motion capture sensors to operate surgical telerobots.

Kelly's story has robots as well as a sophisticated brain machine interface. Given telerobots, exosuits, and robotic prosthetics, the boundary between hardtime and softtime blurs. There are hard as well as soft avatars.

Telerobots are becoming major game changers. They are doing work in places too hard to reach or dangerous for humans. British Petroleum uses them to build oil drilling infrastructure on the seafloor. Planetary Resources hopes to use them to mine the asteroids. Paul Spudis and Bill Stone hope to use robots to prospect and establish mining infrastructure on the moon.

Kelly is correct a severely disabled person would want to use a Brain Machine Interface every waking hour whereas a healthy person only a fraction of the time. I believe the severely disabled will be the most practiced users of telerobots. They could be the most intrepid explorers, the most able builders, the heroes of a coming age.

Fashions in Science Fiction

A Brain Machine Interface story from yesteryear was Anne McCaffrey's hopeful and uplifting The Ship That Sang. More recently we have Kelly's bleak dystopia Declaration.

Kelly's story has a lot of currently fashionable themes: overpopulation, terrorism, limited resources, alienation, inevitable decay. More often than not modern SF is gloom and doom exploring catastrophic failure modes of technology. Such storites are worthwhile, we should certainly try to anticipate and avoid possible calamities.

But we also need stories exploring technology's potential for good. I yearn for a return to tales about new frontiers and the triumph of human spirit over adversity.

We need hopeful as well as cautionary tales. Without hope there is no reason to get up in the morning.

Tuesday, June 30, 2015

Making the tether catch

In Phobos - Panama Canal of the Inner Solar System, Doug Plata had asked about tether catches:

How much time would one have to attach to the tether's end? Since it is connecting two different orbits then I'm imagining that it would be fairly brief. If one misses the connection, then what?

I liken a catch at apoapsis to catching a ball at the top of it's bounce. For a brief time, the ball hangs motionless -- and then gravity pulls it back down. The less the acceleration, the longer the ball will hover at the top of a toss.

Regions of the tether that feel a substantial net acceleration will have a greater need for fast reflexes and good timing. The regions of the tether closer to the balance point can catch at a more relaxed space. Catching at the balance point would be like docking with the I.S.S.

For an example I will use the ellipse common to the Phobos and Deimos tether:



The larger red ellipse is the path a payload would follow dropped from the foot of the Deimos tether and/or if thrown from the top of the Phobos tether. At peri and apoapsis, this path matches the speed of the tether. So the moons could exchange payloads while using virtually zero reaction mass.

Note: When I use directional words like top, foot, above, below, up or down, I'm using Mars as the center. Down means Marsward.

Making the catch at the Deimos tether foot

Both the payload and Deimos tether foot are traveling about 1.18 km/s. But it is the relative velocity that counts. After all, I am traveling 30 km/s as earth circles the sun and so is my computer monitor. Do I worry about a catastrophic collision with my computer monitor? Not since I'm moving about zero km/s with regard to my computer.

Catching at the foot of the Deimos tether:

30 minutes before the catch the payload is trailing the foot by a few kilometers and is about 55 kilometers below. It's traveling about 136 miles per hour with regard to the tether, most of that velocity is vertical.

1 minute before the catch, the relative speed is only about 5 mph.

I'll compare this to driving a car. Driving down the road at a leisurely 30 mph, I step on the brakes. I don't stomp on them, mind you. Just decelerating at my usual careful pace, it takes 6 seconds to come to a full stop. Now look at the payload 5 minutes before the catch: 22.6 mph. Compared to my Sunday driving, this payload is moving like a turtle coming out of hibernation.

From Phobos throw to Deimos catch is an ~8 hour trip. During the vehicle can make measurements of it's distance and velocity with regard to the Deimos tether foot and compare it to optimal distance and velocity.

If catching below a tether's balance point, the payload would rendezvous with the tether at the trailing edge. If the tether is in a prograde orbit, the payload would land on the western end of a ramp:


In this cartoon I have a quadpod on wheels entering on the west end of the ramp. The wheels are only partially for comic relief. Wheels would actually be helpful landing on a platform.

The quadpod is a fanciful design not really relevant to tethers. I use it because it can quickly make slight adjustments to speed along any direction. The closing velocity is almost completely vertical. There will be a time when the space ship is quite close to the tether and falling up at a high speed. So it would be good to be able to do a slight tap on the brakes or gas pedal.

Also to give a little error room to the landing on the west ramp, I imagine a folding west end of the ramp that can extend itself after the ship has matched altitudes.

Acceleration, net weight

At this part of the Deimos tether, centrifugal acceleration is -.0681 m/s2 and Mars gravity is .1017 m/s2. Net acceleration is .034 m/22. A Sumo wrestler weighing 400 pounds on earth's surface would weigh 1.4 pounds. A coin falling out of your coat pocket would take ~8 seconds to reach your foot (assuming distance from coat pocket to foot is one meter).

Making the drop to Phobos

To send a payload on it's way to Phobos, simply roll of the east edge of the ramp.

Making the catch at the Phobos tether top

Catching at the Phobos tether:




1 minute out, the tether is moving 18 mph. A faster pace than the Deimos tether catch, but still much more leisurely than me rolling my car into the driveway from a Sunday drive.

Acceleration, net weight

At this part of the Phobos tether, centrifugal acceleration is -.536 m/s2 and Mars gravity is .4027 m/s2. Net acceleration is -.133 m/22. A Sumo wrestler weighing 400 pounds on earth's surface would weigh -5.44 pounds.  A coin falling out of your coat pocket would take 4 seconds to reach your foot (assuming distance from coat pocket to foot is one meter).

From the point of view of someone on Mars, the acceleration would seem upward. Looking through a telescope, they'd see the Sumo wrestler bumping against the ceiling like a helium balloon.



Making the drop to Phobos

To send a payload on it's way to Deimos, simply roll of the west edge of the ramp.

Some general rules for vertical tethers


This is an illustration for any vertical tether in a circular orbit. It also applies to Clarke style beanstalks.

The red orbits below the circular balance point's orbit move faster than the tether except where they cross the tether. At crossing points the orbits move the same speed as the tether. I explain here how tether matching orbits are found.

For points on the tether below the balance point's  circular orbit, entrance/catching ramps are on the trailing edge of the tether (the west end for tethers in prograde orbits). To drop to lower orbits, roll off the leading edge (east end of the ramp in prograde orbits).

For points on the tether above the balance point's circular orbit, entrance/catching ramp are on the leading edge of the tether. To throw to high orbits, roll off the trailing edge.

Making catches in steep acceleration gradients

Things are less relaxed as the tether extends further from the balance point. As soon as I have time, I will look at a Phobos tether whose foot extends into Mars upper atmosphere. The net acceleration at this foot would be about 3 km/s2 or about a third of an earth g.