Calculus lesson for 2010

Every now and then, some event comes along in life that makes us happy. However, like most things on earth, such an event is finite and runs out eventually, this makes us sad. If we integrate the happiness over the time of the event all the way till the time we eventually forget about it, is the resulting integral positive or negative?

Beautiful Summer - Kalokairi

Fig 1. Summer BBQ

I learnt a new word to describe summer:

“kalokairi comes from two Greek words meaning fine or beautiful (kalos) and time or moment (kairos). Now “fine time” might not seem an especially insightful formulation for summer, but you need to remember that kairos is not just any old time. Kairos is the proper time, the unique, unrepeatable, propitious moment, as opposed to chronos, that deadly kind of time which grinds on relentlessly, linear, unstoppable, consuming all things.” FT weekend 9th Aug 2008.

Fig 2. Chilling in the shade

So chronos marches on but kairos are seared in your mind forever. Measured chronologically, summers are short, but it also opens up the possibility of kairological time. Can you remember how you felt as a child at the beginning of the summer holidays? Golden, lazy, full-leafed days, stretching on for 8 to 10 weeks – an eternity.

Fig 3. the joys of gelato

As a “responsible” adult, summer holidays don’t happen anymore, but my kairological memories “effortlessly put to flight all those deadly intervening stretches of mechanical routine, boredom and anxiety”, and brings me back to the redemptive moments.

Fig 4. Home made jeopardy games

What brings on this transition from chronology to kairology? One of my favourite is the half an hour after a football game. Lounging around in the leafy-shade with your football pals, talking nonsense, the cicadas make their usual cacophony, a mild breeze stirs the leaves, the joker amongst us plays his pranks, laughter-laziness-contentment all round. Moments like these have pretty much retained the same essence regardless of chronological time.

Fig 5. Apres footie

I was told that animals have no concept of chronological time: “nothing more pitiful than a dog trudging in the wake of a clock-time-obsessed master, not allowed to sniff that tempting tree or lamp post for fear of putting out the schedule that the dog will never comprehend.”

Fig 6. Paper chase

As I sit in the office today, I bring on my kalokairi to break free from the leash of my chrono-obsessed masters. The long shadows at summer’s dusk, treehouses and secret dens, climbing walls, codes and missions, homemade explosives, Nintendo wrestling, smokey arcades, Pims and lemonade by the Cam, Mayballs and garden parties, swimming in Walden Pond, paper plane competitions, strawberry picking… Moments like these will ensure that I never grow up.

Fig 7. Summer!

What are your kalokairi moments?

Eh Trrrrevoorrrrr… siu hoongkee

I stopped a week ago.

Just a few thoughts:

When I first lit up, it never occurred to me that I will end up smoking for so long. Somehow, I imagined that one day, I will magically stop smoking… I guess I assumed smoking is like a hobby, something that I will eventually lose interest in.

I worked hard to pretend to be a casual smoker, that I’m not really addicted. This became a bit comical after a while, when I had to hide in corners to I smoke. I always washed my hands and chewed gum after I smoke. But yeah, I smoked a lot more than I admit to.

I felt patronized when told how bad it was for my health… like I did not know. I already know better than any of you fuckers. I experienced it first hand! Aspects of life which I used to take for granted, things that I used to excel in, there was a slow decline. Can't do anything without thinking, gosh, I need a cigarette to boost my morale. I was lethargic for years! This is the main reason I’m quitting now.

The weird thing was that it was not really the nicotine I was addicted to, I think. The nicotine definitely contributed somewhat to it, but it was more of a psychological addiction. I needed it to gain confidence, to tide me through bad patches, to relieve the monotony of sitting in a fucking office. And these were for me, the scary things about living without cigarettes… what will I do in these situations? I was very afraid, worried that without cigarettes, I will be someone else.

Okay, I admit, I read a fucking self-help book to assist in the quitting (grudging thanks to Su-Ming). Nicotine gums were too disgusting… see earlier article.

There are two situations when I get the most severe withdrawal pangs. One is when I’m out drinking, all the bloody smokers are taunting me by blowing smoke into my face. Another is during football. Lungs feel like they are made of lead, and the heart seems to explode with every beat… gasp

However, I am surprised by how "not bored" I am when in the office. As stated earlier, I wondered what will I do if I didn't go for a smoke when I'm bored. Turns out that yes, I still think that I want to have a fag when I'm in the office, but somehow not doing it is surprisingly bearable. In fact, I feel less bored than when I used to smoke... I always came back from smoke breaks wishing they were longer, and can't wait till the next one, it's this constant process of waiting and hoping which made things miserable.

So anyway, instead of immersing myself with work to distract myself from thoughts of smoking, I decided to relieve my boredom by learning as much as I can about smoking... Here are some statistics:

Men smoke a lot more than women. I actually didn't know this. In Singapore, male smokers outnumber female smokers 7 to 1.

The most popular tobacco in Hong Kong and Singapore are made by Phillip Morris, these include the infamous Marlboro (my companion for 16 years), and Virginia Slims (for ah Kuas), other than these I don't recognize other Phillip Morris brands. Coming in second is the British American Tobacco Company, they don't seem to have one single blockbuster brand, but have a whole series of quite recognizable ones: Dunhill, Kent, Lucky Strike, Pall Mall, Benson and Hedges, John Players, Viceroy etc...

The price of a pack also varies significantly between countries:

Mind you, this is old data from 2002, the last packet I bought in HK was only $29 ~ USD$3.7. In the US, it varies from state to state, in Massachussetts, I think it was USD$4.05 for Marlboro lights, the first time I bought cigarettes in Singapore in 1995, it cost SGD$2.80 and the last time (2008) it was SGD$12 ~ that's around USD $8.

I still get pangs… hmmm won’t it be nice to squat in the yellow box with some ah bengs? Or perhaps rush to the bogs between classes to meet my Russian pal to share a muscovite-no-filter?








See also my literary masterpiece

The Dragonfly

As discussed in our previous meeting, your correspondent was tasked to source for an appropriate research subject. This is what I came home with:


The Flytech Dragonfly! This is a radio controlled ornithopter.

An ornithopter is a machine that propels itself through the air by flapping its wings, as opposed to more conventional fixed-wing aircraft, or the rotating wing helicopter. The four wings are powered by cams; the wings on each side of the airframe flaps in the opposite direction, i.e. each stroke squishes air out between them to give forward thrust and lift. Yaw control is activated by a tail rotor that swings the dragonfly around.

This vehicle certainly has superior maneuverability when compared to similar 2 channel helicopter models, in fact flight characteristics is closer to a 2 channel fixed wings craft: the airframe launches forward in a series of stalls and dives.

This is a really well thought out design. It is robust, all the structural components are made from carbon fibre. It has survived repeated crashes and rough handling by research assistant #1. It is easy to repair, one of the wing struts were snapped into two by an obnoxious neighbour kid, but luckily the kit comes with two spare wings. One can also fine tune the handling characteristics through a selection lever, and attaching a tail ribbon.

Turns out this toy was designed by teenagers (Dan Getz and Sean Frawley) who sold the rights to WowWee (the toy company). They went onto study at Embry-Ridle Aeronautics University but remained as consultants for WowWee.

Here is a video of the dragonflyer in action at the WowWee office:



Black Mamba, you got to get one of these!

Research meeting

I had a brief research meeting with my nephews last week. This was what went down:

your correspondent, the principal researcher (PI): "I propose that we upgrade our research equipment. We have gained a reasonable understanding of passive gliders, and now is time for us to move onto the next level: remotely controllable, powered flight."

Research assistant #1, (nephew #1), singing: "Helicopter and aeroplane, aeroplane, aeroplane, helicopter aeroplane, and sometimes a motorboat."

Research assistant #2, (nephew # 2): "ball! addaaaaaah!" throws a ball across the conference room.

PI: "I have done a brief literature review in the relevant publications, (takes out toys'R us catalogue). In the short term, I propose we move up to radio controlled devices. As #1 correctly pointed out, we should focus our efforts on airborne vehicles, maybe dabble in a bit of hydrodynamics if it is financially feasible. In the long run, we will like to get our hands on some autonomous machinery."

#1, flicks through the catalogue, points at the barbie dolls, and pronounces: "Pink is for girls, hehehehe."

#2 supports the proposal through action by crushing our previous research equipment (a paper airplane).

PI: "I will head over to the stores and start sourcing for parts."

Fig 1. Picoo Z. A radio controlled helicopter. 2 channels. Controls for this airframe is much sharper compared to the previous acquisition. This was one of the candidates I considered as a research subject. However, after some additional scouting, I decided on something a bit more unusual, standby for a detailed report.

Back from the dead

My computer recently underwent a near death situation.

Two nights ago, I spilled a cup of water onto the keyboard and it pretty much seeped through to the innards while the computer was running. Most laptop users will agree that this is a serious situation, it is unlikely that a computer can recover from such disaster.

I tried switching it off, but it gave a long distress beep and crashed. the next day was spent attempting to dry and power it up. The fan ran but the CPU refused to boot up.

However, last night, a miracle occurred! After another frantic drying attempt with a hair-dryer, it sounded the welcome tone and booted up!!! Currently, all systems are go and there seems to be no ill effects!

Get a mac!

errata

After more experiments. The authors conclude that delta wings are not as bad as they have supposed (see previous entry). My team of researchers (nephews aged 1 and 3) and I have managed to construct a number of delta wing aircrafts that have very satisfactory gliding performance.

This means the drag performance of the airframe is not as important as we have assumed (based on a rigid airframe glide ratio calculation). Instead, the structural integrity and improved balance of delta wings probably compensate any drag penalty from using them.

Further investigations will be the subject of future work.

I believe I can fly

Paper airplanes are one of the greatest inventions of the modern world. With some cheap and readily available scrap paper, any 3 year old child can become an aeronautical engineer. Your correspondent has whiled away a large portion of his childhood folding these little devices; I have been completely mesmerized by how a well-designed airplane glides across a room. Having two nephews these days once again allows me ample excuse to design and fold planes to my heart's content without being accused of engaging in childish pursuits.

Fig 1. Aerodynamicist #1 with design #23

Typically, I set myself these rules when designing the aircraft:
1. One sheet of paper per aircraft only.
2. No additional material, i.e. paper clips, staples
3. No adhesives
4. No tearing

However, I will break these rules as quick as you can say Wright brothers if the result is a more spectacular flight. In fact, I frequently tear little ailerons on the wings for fine tuning.

After some initial calculations, experiments and literature review, I will like to share the following observations:

Induced drag: to minimize induced drag, the wings should be of high aspect ratio, i.e. long and slender in the direction perpendicular to the fuselage. it might be tempting to suppose the sharp delta wing (space shuttle/triangular wings) might be more efficient for "cutting" through the air. However, they are actually inefficient lifting geometries at these speeds. (You need to be well over the speed of sound for delta wings to be efficient).

Fig 2. Delta Wing Paper Dart: inefficient aerodynammics

Balance: a head heavy plane is more dynamically stable; but will have a strong tendency to nose down. Generally speaking, trimming the the centre of gravity to be slightly less than 1/4 chord length from the leading edge of the wing is ideal. The quarter chord point is both the centre of lift and neutral point; the trimmed aircraft will fly at a steady angle of attack. This thin airfoil theory was derived in the 1920s by the greatest aerodynamicist, my hero: Prof. Ludwig Prandtl, who amongst other things, also brought us boundary layer theory. It is amazing what a man sitting at a desk can come up with.

Fine tuning is key: Little adjustments to the ailerons, and dihedral makes a large difference. While the effect of ailerons are pretty obvious, it is not obvious how dihedral affects flight characteristic. A positive dihedral increases the lateral stability: the plane is less likely to roll over. However, it does increase the tendency to swerve to the side. I recommend a very gentle positive dihedral: less than 10 deg +ve for optimal flight.

The world record for paper airplane flight endurance is 27.6s! His strategy is to throw the plane as high and fast as possible, and let it glide down slowly. Hence the design has two conflicting requirements, one is a low drag stage in which the plane needs to acquire altitude as rapidly as possible, while the other is a high lift-drag ratio stage in which the plane glides slowly down. A 8s flight is considered a crash by this guy.

Fig 3. Ken Blackburn breaking the world record.

I don't think I have managed more than 5s.