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An elderly gentleman wanted consultation from a psychotherapist, suffering from severe depression. His wife had died two years ago and he still could not accept that she had passed.

“What can I say to this man to alleviate his burden?” The Doc thought.

After a short moment, he decided not to tell him anything, but to ask him a question. “What if it had been you that died, and your wife would of had to live without you?” The man answered; “Oh, she would of been heartbroken! The love we had was like that in fairy tale. I’m sure she would of felt the same as I.”

The Doc replied; “Then you see, she has been spared the need to suffer that which you are going through, and it is you who has spared her the suffering. Now what is expected of you sir, is to continue living so you can mourn and celebrate her existence. As long as a memory of her resides within you, she will never disappear”.

The man said no words, but stood up, shook the Doc’s hand, and walked out of the building.

A Murakami short story I recently read…

100% PERFECT GIRL by Haruki Murakami.

One beautiful April morning, on a narrow side street in Tokyo’s fashionable Harujuku neighborhood, I walked past the 100% perfect girl.

Tell you the truth, she’s not that good-looking. She doesn’t stand out in any way. Her clothes are nothing special. The back of her hair is still bent out of shape from sleep. She isn’t young, either – must be near thirty, not even close to a “girl,” properly speaking. But still, I know from fifty yards away: She’s the 100% perfect girl for me. The moment I see her, there’s a rumbling in my chest, and my mouth is as dry as a desert.

Maybe you have your own particular favorite type of girl – one with slim ankles, say, or big eyes, or graceful fingers, or you’re drawn for no good reason to girls who take their time with every meal. I have my own preferences, of course. Sometimes in a restaurant I’ll catch myself staring at the girl at the next table to mine because I like the shape of her nose.

But no one can insist that his 100% perfect girl correspond to some preconceived type. Much as I like noses, I can’t recall the shape of hers – or even if she had one. All I can remember for sure is that she was no great beauty. It’s weird.

“Yesterday on the street I passed the 100% girl,” I tell someone.

“Yeah?” he says. “Good-looking?”

“Not really.”

“Your favorite type, then?”

“I don’t know. I can’t seem to remember anything about her – the shape of her eyes or the size of her breasts.”

“Strange.”

“Yeah. Strange.”

“So anyhow,” he says, already bored, “what did you do? Talk to her? Follow her?”

“Nah. Just passed her on the street.”

She’s walking east to west, and I west to east. It’s a really nice April morning.

Wish I could talk to her. Half an hour would be plenty: just ask her about herself, tell her about myself, and – what I’d really like to do – explain to her the complexities of fate that have led to our passing each other on a side street in Harajuku on a beautiful April morning in 1981. This was something sure to be crammed full of warm secrets, like an antique clock build when peace filled the world.

After talking, we’d have lunch somewhere, maybe see a Woody Allen movie, stop by a hotel bar for cocktails. With any kind of luck, we might end up in bed.

Potentiality knocks on the door of my heart.

Now the distance between us has narrowed to fifteen yards.

How can I approach her? What should I say?

“Good morning, miss. Do you think you could spare half an hour for a little conversation?”

Ridiculous. I’d sound like an insurance salesman.

“Pardon me, but would you happen to know if there is an all-night cleaners in the neighborhood?”

No, this is just as ridiculous. I’m not carrying any laundry, for one thing. Who’s going to buy a line like that?

Maybe the simple truth would do. “Good morning. You are the 100% perfect girl for me.”

No, she wouldn’t believe it. Or even if she did, she might not want to talk to me. Sorry, she could say, I might be the 100% perfect girl for you, but you’re not the 100% boy for me. It could happen. And if I found myself in that situation, I’d probably go to pieces. I’d never recover from the shock. I’m thirty-two, and that’s what growing older is all about.

We pass in front of a flower shop. A small, warm air mass touches my skin. The asphalt is damp, and I catch the scent of roses. I can’t bring myself to speak to her. She wears a white sweater, and in her right hand she holds a crisp white envelope lacking only a stamp. So: She’s written somebody a letter, maybe spent the whole night writing, to judge from the sleepy look in her eyes. The envelope could contain every secret she’s ever had.

I take a few more strides and turn: She’s lost in the crowd.

Now, of course, I know exactly what I should have said to her. It would have been a long speech, though, far too long for me to have delivered it properly. The ideas I come up with are never very practical.

Oh, well. It would have started “Once upon a time” and ended “A sad story, don’t you think?”

Once upon a time, there lived a boy and a girl. The boy was eighteen and the girl sixteen. He was not unusually handsome, and she was not especially beautiful. They were just an ordinary lonely boy and an ordinary lonely girl, like all the others. But they believed with their whole hearts that somewhere in the world there lived the 100% perfect boy and the 100% perfect girl for them. Yes, they believed in a miracle. And that miracle actually happened.

One day the two came upon each other on the corner of a street.

“This is amazing,” he said. “I’ve been looking for you all my life. You may not believe this, but you’re the 100% perfect girl for me.”

“And you,” she said to him, “are the 100% perfect boy for me, exactly as I’d pictured you in every detail. It’s like a dream.”

They sat on a park bench, held hands, and told each other their stories hour after hour. They were not lonely anymore. They had found and been found by their 100% perfect other. What a wonderful thing it is to find and be found by your 100% perfect other. It’s a miracle, a cosmic miracle.

As they sat and talked, however, a tiny, tiny sliver of doubt took root in their hearts: Was it really all right for one’s dreams to come true so easily?

And so, when there came a momentary lull in their conversation, the boy said to the girl, “Let’s test ourselves – just once. If we really are each other’s 100% perfect lovers, then sometime, somewhere, we will meet again without fail. And when that happens, and we know that we are the 100% perfect ones, we’ll marry then and there. What do you think?”

“Yes,” she said, “that is exactly what we should do.”

And so they parted, she to the east, and he to the west.

The test they had agreed upon, however, was utterly unnecessary. They should never have undertaken it, because they really and truly were each other’s 100% perfect lovers, and it was a miracle that they had ever met. But it was impossible for them to know this, young as they were. The cold, indifferent waves of fate proceeded to toss them unmercifully.

One winter, both the boy and the girl came down with the season’s terrible influenza, and after drifting for weeks between life and death they lost all memory of their earlier years. When they awoke, their heads were as empty as the young D. H. Lawrence’s piggy bank.

They were two bright, determined young people, however, and through their unremitting efforts they were able to acquire once again the knowledge and feeling that qualified them to return as full-fledged members of society. Heaven be praised, they became truly upstanding citizens who knew how to transfer from one subway line to another, who were fully capable of sending a special-delivery letter at the post office. Indeed, they even experienced love again, sometimes as much as 75% or even 85% love.

Time passed with shocking swiftness, and soon the boy was thirty-two, the girl thirty.

One beautiful April morning, in search of a cup of coffee to start the day, the boy was walking from west to east, while the girl, intending to send a special-delivery letter, was walking from east to west, but along the same narrow street in the Harajuku neighborhood of Tokyo. They passed each other in the very center of the street. The faintest gleam of their lost memories glimmered for the briefest moment in their hearts. Each felt a rumbling in their chest. And they knew:

She is the 100% perfect girl for me.

He is the 100% perfect boy for me.

But the glow of their memories was far too weak, and their thoughts no longer had the clarity of fouteen years earlier. Without a word, they passed each other, disappearing into the crowd. Forever.

A sad story, don’t you think?

Yes, that’s it, that is what I should have said to her.

Arcjets (or, brrrt)

Like Faraday’s “The chemical history of a candle”, electric arcs have been studied extensively and recorded in Hertha Ayerton’s “The Electric Arc” (Which I obviously haven’t read because I am supposed to be studying propulsion) . This is partly due to their applications in various fields but mostly because they look (and sound) cool. The formation of an arc proceeds through the electric breakdown of the gas in which they operate (the propellant in our case). High voltages cause thermionic emission of electrons from the electrodes which ionise the propellant, heating it to the high temperatures required in an electrothermal thruster. Like all circuit elements, arcs have their own voltage-current characteristic and it’s a good idea to discuss it here.

screenshot-from-2016-12-25-10-28-34

The graph is divided into various regions, each with their own properties.

In region O-A, the voltage is small and the electric field just collects the stray charges (mostly electrons) created by other sources (like cosmic rays). Region A-B is called the first Townsend region and it is where the stray electrons acquire enough energy to ionise other atoms by collision. Region B-C, the second Townsend region, is where even the positive ions acquire enough energy to knock out electrons from the cathode by bombardment.

The dotted line at C-D indicates something interesting. This is where the discharge becomes momentarily unstable and the arc switches to a new lower voltage mode. The voltage Vc is called the sparking potential. Beyond C, a normal discharge called a glow discharge sets up which, while having no practical applications in propulsion, looks pretty.

The region F-G is where practically interesting things happen, the voltage near the cathode drops abruptly and a new type of discharge called an arc discharge develops. This discharge’s resistance drops rapidly as the voltage is changed, hence a ballast resistor is needed to protect the electrode from vaporisation. Ionisation is now vigorous with electrons flowing from the cathode to the anode and the propellant ions the other way. This is where the fun starts !

Now people might ask,

“You wanted high temperature not in contact with the metal, what about the electrodes.”

Well, all arcs have a profile that tells how a property changes along it’s length. A typical arc profile is given below. screenshot-from-2016-12-25-11-29-56

The positive column is where the most thermally excited particles are found. Temperature here can range anywhere between 5000 to 50,000 K depending on the current. So, now you have a way to heat the propellant to a much higher temperature than the melting point of the thruster body. The core of the propellant column can now be made much hotter than the part that touches the thruster directly thus greatly enhancing the exhaust speed. Good going !

The arc

In spirit of theoretical physics around the world, let us assume the arc to be a uniform cylinder. One of the various hand rules thought in your school will tell you that the magnetic field lines around the arc are in the form of concentric circles centred on the axis of the arc. This magnetic (self) field applies a force on the current that creates it, pushing the particles inwards. This is where things go wrong.

If the magnetic force exceeds the gas-kinetic pressure on the inside of the arc, the arcs starts contracting at the point where this happens. This is called pinching. Pinching is more adverse if the arc is allowed to bend.  Bending  (or kinking) increases the magnetic field on the concave side of the bend leading to even more pinching. (see diagram)

screenshot-from-2016-12-21-22-57-17

Pinching might lead to the breaking of the arc which is not a good thing considering the whole damned process we underwent to get an arc discharge. It’s a good idea to try to alleviate these problems while designing the thruster. This is usually done in two ways,

  • Vortex stabilization, where the propellant is injected into the thruster tangentially to the arc. This induces a spin and prevents both kinking and pinching by stabilising it centrifugally.
  • Constriction, where the arc is constricted to a small space so that it can’t bend. These techniques are almost always used together for maximum efficiency.

screenshot-from-2016-12-25-13-22-33

A typical thruster

The complete design of a 30-kw arcjet thruster is given in the diagrams below along with the operating conditions.

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screenshot-from-2016-12-25-13-33-19

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As can be seen in the last diagram above, the arc culminates in a spread over the anode nozzle. This also gives rise to a destabilisation problem.

The part where the arc attaches to the anode is quite creatively called  the “anode attachment”.  To prevent erosion of the anode, it must be spread symmetrically over the whole circular cross section . If the attachment is to collapse into a single spoke even for a second, it would mean the end of the anode due to high concentration of kinetic particles. An axial magnetic field is generally used to prevent this from happening. The magnetic field forces the particles to spread out uniformly over the cross section as they spiral along the field lines.

screenshot-from-2016-12-25-13-45-22

 

This was the basic breakdown of how arcjets work and the problems they face. As is seen in the thruster characteristic table, these are much more efficient than resistojets due to higher exhaust speeds. Frozen flow losses do exist but the efficiency of the thruster makes up for them.

Both of these thruster discussed use electricity to heat the propellant. However, there are better ways to gain high exhaust speeds without thermodynamics coming for the rescue.

So, I’ll leave ion thrusters for the next article.

Merry Christmas !

References

[1] Robert G. Jahn “Physics of Electric Propulsion”

Resistojets (or, The poor man’s electric thruster)

This post is the first in a N (will be stealthily replaced with an actual number) part series on electric thrusters. I decided it’s a good idea if I condense the knowledge I pick up in small articles. Firstly, it helps my other classmates easily pick up what they would otherwise have to scour books for. Secondly, it will help me in the future when I actually start working on these topics for my summer project. So, let’s start with a light topic – Resistojets, or the poor man’s electric thurster.


A resistojet is the bare minimum that is required for a thruster to be called electric. In fact, if you are a person like me who just likes the idea of ions and blue glows (Imperial destroyer engines), you will be really reluctant to call a resistojet a new type of thruster at all. The heat that is obtained from chemical reactions in conventional rocket engines is instead obtained from resistors that convert electrical energy into heat. The propellant is hence heated by passing it over the surface of these resistors and is then expanded through a conventional nozzle to provide thrust. The thruster design itself can be done in various ways, some of which are given below.

screenshot-from-2016-12-22-23-43-02

If it isn’t already clear, the things inside the cavity are differently shaped heating elements which are empirically tested for performance. As a matter of fact, the more interesting part of this whole device is the de Laval nozzle, which has nothing to do with electricity.

As is obvious from the overly simple design, this is not the most efficient type of electric thruster. Frozen flow losses refer to the fraction of input energy that is added to the propellant gas flow which does not appear in the form of exit kinetic energy and are quite significant in these thrusters. This may occur due to a variety of reasons (propellant dissociation, ionisation and unnecessary excitation being some of them). Radiation losses are also a problem, generally occurring through the heated body of the thruster.

However, the worst part of this business is the direct contact of heating element with the propellant. This means the highest temperatures (and hence the highest exhaust velocities) that can be attained are limited by the material used for making the body of the thruster. Various propellants can be used each with their own positive and negative points. Some thruster characteristics are given in the following table.

screenshot-from-2016-12-23-21-18-35

Tungsten is the obvious choice for the theoretical maximum performance that can be obtained from these thrusters. For lower temperatures, molybdenum is generally used. These materials hence restrict the exhaust velocities obtainable to below 104 m/s that correspond to specific impulses of about 1000 sec. This calls for better designs that can sustain higher temperatures without requiring breakthroughs in materials science.

Onto arcjets !

References

[1] Robert G. Jahn “Physics of Electric Propulsion”

[2] V. V. Subramaniam “Recovery of frozen flow losses in arcjets” 

Do notify me about any errors I might have made. Constructive criticism is always appreciated.

Murmurations

This poem was written as an assignment for one of the courses in my college. We were supposed to write a fable (i.e with some moral message) and correlate it with biology (somehow). At that time, I was really interested in swarm behaviour in birds,  especially starlings. So yeah, here’s a weird poem you might like.

Murmurations
Under the cloak of blue sky,
over the widening sea
lived a group of birds
called a murmuration.
Oh!
What a group it would be.
Day by day, they flew away
to search for food
in the rarest of places.
And all they left in their wake
was a spectacle enriched with traces
of spectacular beauty.
Wound like a fist they would fall
in a cacophony of beats
and none would stall
to follow the one that is nearest.
Three rules is all they need
and nothing else to heed
the herd’s call
and follow their dearest.

Say, wouldn’t it be pretty
if thousands of birds
descended over you at once
in a single instant.
Yes !
It would be awe-some,
It would be cool.
And in this process,
you would have been made
quite a significant fool.
For they don’t have a way to talk
and all they do is take a guess
at the nearest bird
in this flock’s untangling mess.
The three rules are all they need.
This is the law of the old bird’s creed.
One of them,
let’s call him Sam
is quite a curious character.
For he is brave like a soldier
as Shakespeare would say
ready to throw his life
into the fray
without a moment’s thought.
One day
on a foggy morning,
the birds took off from their nest
each being called a starling.
Sam being special (as he so thought)
took off away from the group at an opportunity he got.
Quite funny is the case with chance
‘cause a pergerine falcon spotted him
as he performed his freedom dance.

This bird swooped from up above
in a fit of enormous hunger.
And that’s when sam realized
he had made a great blunder.
The falcon hit him with all his might
but was unable to grab a bite.
Because the murmuration hereby intervened
and saved him from getting eaten.
For the confusion that their wake created
could never be beaten.
Since that day
Sam has never strayed
from the path of this group
however frayed.
And so should you realize
that strength lies in unity
for every member
however wise.
Some links for the interested
[1] A video of a murmuration in flight
https://www.youtube.com/watch?v= iRNqhi2ka9k
[2] Boids – A computer program that simulates starling behaviour using just 3 simple rules
http://www.red3d.com/cwr/boids/
[3] Boids Psedudocode- Explains the rules and how they are implemented
http://www.kfish.org/boids/pseudocode.html

Observing Andromeda and Orion in the middle of the winter.

As has been made clear in my older posts, the Orion nebula has evaded me for a long time. Last year, by the time my telescope arrived, it was already out of my visibility zone. Now however, I’ve finally managed to get a glimpse. It was quite underwhelming, as expected. For a long time now, I’ve noticed that the light pollution in my hometown is much worse than in Bangalore. This is made clear by the fact that even the bright star near the nebula is rarely visible here while it stands out quite clearly in Bangalore. So, in a hopeful bid to have better observing sessions I am taking my telescope to Bangalore to see what comes up. But for now, this is what I’ve got.

Orion Nebula

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I feel lucky to see the trapezium on the first glance. However, as my eyes adjusted to the dark, the cloudiness around the trapezium was quite clearly visible. Averted vision compounded the visibility even more. In my defence, I don’t think the sketch I’ve made is quite accurate because the bright white region at the bottom is not by design. That was a scanning fault.

(Also, to hardcore enthusiasts, I am really sorry for not drawing the headings or the FOV circle)

In the end, I’m really happy with the the result of my endeavour.

Andromeda Galaxy

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When I think about it now, this part should’ve been more difficult than the previous one due to a lack of M31’s proximity to any bright stars. The credit for making this task easier than expected goes to Mirach, Alpheratz and Shedir. These three stars were instrumental for me in approximating the position of the galaxy. Even then, it was just visible with averted vision. The sketch above is all I could draw after observing it for about an hour. Even then, I am not quite sure whether it’s M31 as of now. However, with a magnitude of 3.4, if my telescope could pick up anything in the light pollution of Jaipur, it’s Andromeda.

Horsehead Nebula

I am pretty sure that anybody who ever looked at M42 decided to choose Horsehead nebula as the next immediate target. Well, I was demanding too much of my scope here and these demands were not met (not unexpectedly).

That’s how I spent the last few nights in my hometown. Right now, I am most worried about how I am going to ship my scope to Bangalore. Furious use of padding and foam will be undertaken shortly.

Thanks for reading.