Dear Captain KH Lim,


A Journey of Science Fantasy from Kuala Lumpur to Macau in an Air Bus A320

(Hind thought from ‘Alice in Wonderland’)


By: JB Lim


I know you are extremely busy with your work, and also having to answer so many seemingly endless questions from air-travelers posted in your blog. So I did not want to trouble you with unnecessary questions. Instead, I begin to dream of a journey from Kula Lumpur to Macau, and finally I decide to cross the almost infinite dimension of our Universe in an Air Bus.

So instead of troubling you, I decided to search the Internet myself for some basic facts, and from there I began to build up my calculations into a world of fantasy.

This was some very basic but interesting information about the Airbus A320 from which I made some conclusions, albeit only assumptions about my flight from Kuala Lumpur International Airport (KLIA) to Macau International Airport (MIA). I also made some assumptions about the cost of an air ticket.

Fuel consumption of an Airbus A320 is:

665 Imperial gallons (3,025 litres / 2,420 kg) per hour

Cruising speed:

530mph (853 kph / Mach 0.78) at 35,000ft (10,668m)

Range between KLIA and Macau International Airport:

2321 miles: (3717km):

This was based purely on theoretical calculation using coordinated geometry along a Great Circle as I do not have the benefit of using an onboard plane computer. I only have a scientific calculator, and some knowledge on spherical geometry.

However, a website gave a typical range with 150 passengers for the A320-200 as about 2,900 nautical miles (5,400 km). Yet another website gave the range as 2,650 miles (4,900km). I do not know which is correct, so I rely solely on my calculations which I think is safer.

Engine thrust:

Powered by two CFMI CFM56-5 or IAE V2500 with thrust ratings between 25,500 to 27,000 pounds force (113 kN to 120 kN). Another website said it is powered by two IAE V2527-A5 power plants with a thrust of 26,500lb (117.8 k N) per engine. I don’t know which is which?

Take off and landing speed:

160 mph (258 kph)

Seating Capacity:

150 passengers (Air Asia gave the figure as 180 passengers)
From the above Internet info, we can derive the following:

Density of jet fuel = 0.799 kg per litre

There are many grades of aviation fuels for jet engines. But I am unsure what type of fuel was used to power the jet engines of an Airbus A320? The general info I got from a website concerning the energy value of jet fuel for Boeing 767, the one that crashed into the New York World Trade Centre, the net calorific value of the jet fuel is between 42-44 MJ / kg.

Energy value of jet fuel:

Other sites gave the energy values of jet fuel (aviation kerosene) as between 43.28-43.71 MJ / kg (average 43.49 MJ / kg). So the energy values do not differ very much from each grade. Let us use the average caloric value of 43.49 MJ / kg for the different grades of jet fuels.

This means, the total energy used by the Airbus A320 to fly the plane from Kuala Lumpur to Macau was 43.49 MJ x 2,420 kg x 3.346944 hours (3 hrs 20 min 49 sec) = 352252 Mega joules. This is equivalent to 8099 kg of fuel used up.

Of course this was only an average estimate since the actual amount depended entirely on the weight of the plane with the number of passengers and their luggage, the amount of fuel that has to be burnt to provide the necessary thrust exerted by the engines to lift it up into the air, the forward motion at the required speed against the varying wind velocities blowing against, or helping it from behind, the air resistance at varying attitudes – probably much less energy needed at cruising heights where the air density, humidity and oxygen availability were much less.

Fuel consumption:

But if we assume the average fuel consumption at 2420 kg per hour remained the same throughout the journey with a full passenger load, and that the power of the engines were also constant (117.8 k N per engine) to keep the plane afloat at cruising height, then the only thing that will be affected, as far as I can see is, the velocity of plane due to varying wind resistance for reasons given above.


Fuel needed from KLIA to Macau:

This means that the total amount of fuel used up for my flight from Kuala Lumpur International Airport to Macau International Airport must have been around:
2420 kg x 3 hrs 20 min 49 sec (actual time) = 8099 kg. This is equivalent to a volume of:
Volume of fuel (v) = weight of fuel used up (w) ÷ density of fuel (d) = 10136 litres (10.17 cubic metres) calculated from first principle

This is almost similar to the 10125 litres (10.13 cubic metres) figure calculated directly from the info given in the Internet. I do not know the shape of the fuel tank, but it is equivalent to a cube of at least 2.16 meters on each side to store just sufficient fuel for the entire journey.

All the above calculated assumptions are based on whatever basic info I could get about A320 from the Internet, but in practice it may vary, and I do not know. Only Captain KH Lim can tell us exactly.

Now, the Air Fare, Cost of Transportation and Revenue:

In recent years, air fares offered by a lot of carriers are becoming ridiculously cheap. Air Asia operating in this region is one of them. The air fare from Kuala Lumpur to Macau by Air Asia is 319.99 MYR per person one way, as sited in Air Asia’s websites. If Air Asia can take in 180 passengers, and if we assume a maximum passenger load of 180 per flight, then the maximum fare collected is RM 57,598.
However, normally I found there a lot of empty seats on each flight.

But let us assume Air Asia got only 150 passengers, which is the seating capacity for an A 320 operating in European routes, then the revenue ought to be 47,998 MYR for the distance between KL and Macau (3 hours 20 minutes) for 1356 nautical miles (1561 statute miles = 2512 km). This distance was what you gave. This means it is just 20.5 cents per passenger per statute mile (12.74 cents per kilometer per passenger). Even the taxi fare in Kula Lumpur is already RM 3.00 for the first two kilometers and 10 cent for every 200m there after. This means if we were to travel 20 km by taxi, the fare will already cost us some RM 12.

What if we drive from Kuala Lumpur to Macau?

Even if we use the national car, say the Proton Savvy that recorded a fuel consumption rate of about 24 km / L (or about RM 0.08 / km of fuel), making the car as the most fuel-efficient Malaysian car as verified by Malaysian Book of Records. At the current price of petrol in Malaysia, this means that even for a Proton Savvy, the most fuel saving Malaysian car, for it to travel all the way to Macau (assuming theoretically possible) 2512 km away, the petrol itself would have already cost RM 200, without counting the cost of wear and tear, servicing, and the maintenance to the car along the way. But Air Asia charges only RM 319.99 for the same distance, and 10 times faster too without any stop. At some destinations say to Johore Bahru, they charge only a ridiculous RM 9.99? How did Air Asia do it? I always wonder?

Aviation Fuel Prices:

I really do not know the price of aviation fuel (high grade kerosene?) used by Air Asia compared to car petrol in this country. I have tried to search, but could not find the answer on current price. There was not much information about the prices of aviation jet fuel, their grades, and the one actually used by the engines of Air Bus A320. So it is not possible for us to give exact figures.

But I know that jet fuel prices have fallen by about 26% since the record high of US$93 (325.17 MYR) per barrel last August. But Air Asia said the high cost of jet fuel remains a concern, yet their air fares are so low. How do they then make money? Was it by imposing fuel surcharges on passengers?
Based on oil prices averaging US$47 (164.335 MYR) a barrel for the year (Taipei Times, AFP, Singapore reported on Monday, Sep 05, 2005 – rather outdated figure due to lack of current info, I admit), Malaysia Airlines imposed a fuel surcharge on all international routes from 1 June last year due to the “surging price of jet fuel”. I really do not know what all this means to a poor and ignorant passenger like me – whether they are really offering low air fares but ‘with extra fuel surcharges’ added or what? But all I know after all the taxes, the fare is no longer cheap.

But I know there are 42 US gallons or 159 litres in a barrel of oil. Since it takes about 10,125 litres (63.68 barrels) of jet fuel to fly from KL to Macau, the fuel itself would have cost the airline RM 10,465 per flight over the distance of KL to Macau at a price of US $47 (RM 164.335) per barrel of oil. 1 USD = 3.4965 MYR, if this is aviation fuel at that price.

Other Expenses:

Then what about other operating costs – high salaries of the management staff, the pilots, air and ground crew, the engineers, the office staff, the rentals of office, the agents, the mechanics, maintenance staff, the engineering maintenance of the aircraft, the landing fees, etc, etc? From revenue of 47,998 MYR from 150 passengers per flight, there will be a surplus of RM 37,533 to pay for all these other expenses. But how much are there left after deducting all other operating expenses? But Air Asia claims they are making money, while Malaysian Airline which charges far more for their air-fares claims they are operating at a loss. I believe both the carriers’ stories. But if this is true, there is something seriously wrong somewhere, but I do not know what and where.

Beyond A Scientist to Answer:

This question is far beyond me and Science to answer. I need to pass this question to the Business Management people in the airline industry. Maybe my friend Captain KH Lim can answer as he is a Senior Pilot with AirAsia even though not in the management division to manage policy matters.

This is a puzzle a scientist cannot solve. Only the smarter business people knows how to tackle problem without incurring losses, albeit sometimes with disastrous results

My imagination:

More pleasant thoughts for a scientist than trying to figure out commercial and financial headaches would be to answer my own original question as to how long it will take for a A320 commercial jet to transverse across the diameter Universe estimated to be 40,000 million light years, or 3.78 x 1023 km (378 sextillion km) across. Of course we will have to imagine that was possible as if it was flying in an atmosphere like ours with unlimited fuel.

The answer is 4.2 x 1020 hours at a maximum speed of 900 km per hour. This would be 4.79 x 1016 or 47.9 quadrillions (47.9 pentallions) Earth Solar years. But how much fuel it would use up, as if it was flying through atmosphere 10,000 metres high where the air pressure is 26.5474 kPa (26.157 % of 1 atmosphere), a density of 0.414403 kg/m3 and an air viscosity of 1.45787e-05 kg / m.s

The answer is 1.0164 x 1024 kg (1.0164 x 1021 metric tons) or 1 sextillion metric tons of aviation kerosene will be needed. The mass of Earth is 5.97 x 1024 kg. Thus the amount of fuel required is 17 % that of the mass of Earth.

Just a dreamy fantasy:

Of course all these are just not possible. A scientist fantasizes just for theoretical fun sake only. In the outer reaches of space, in between the galaxies it is almost an absolute vacuum, containing just one hydrogen atom per cubic metre of space. There is almost no matter to encounter any resistance that will require fuel and energy. In fact there will be just about 4 x 1026 hydrogen atoms the air-craft or space ship will encounter once it is in deep outer space between the stars and the galaxies (inter-stellar and inter-galactic space). With our Solar System there are much more matter to encounter between the planets, particularly in the asteroid belt between Mars and Jupiter with the myriads of asteroids, meteors, meteoroids, inter-planetary dust, micro-meteorites, particles from solar winds, and other space debris floating there. Once the plane leaves our Solar System, there will be just darkness, emptiness, and complete void with just one hydrogen atom from interstellar dusts to encounter for every cubic meter of space. The density of air at 10,000 metres at minus 50 degrees Celcius – the cruising height of a jet liner is about 0.38696 kg/m3.

Cruise along without fuel:

With almost no resistance to slow it down, the plane will just have to obey Newton First Law of Motion, provided it does not accelerate to near the speed of light, that it will remain in that state of motion in a ‘straight’ line at a uniform velocity of 900 km per hour till it reaches the end of the observable Universe from end-to-end.

At sea level and at 20 °C dry air has a density of approximately 1.2 kg/m3 varying with pressure and temperature. Air density and air pressure decrease with increasing altitude. The density of dry air at sea level is about 1/800th the density of water." The density of air at sea level is about 1.25 kg / m3 (1.25 g/L) at 10 km, d is about 1/4 its sea-level value.

Amount of molecules per cubic metre:

A cube meter of space at ground (sea) level contains about 45 moles of air. Since 1 mole or Avogadro’s number = 6.022 x 1023, hence at ground level, there will be 2.7099 x 1025 ‘air molecules’ per cubic meter.

Bear in mind there is no such specific entity as ‘air molecules’ since air is roughly 78% nitrogen (normally inert except upon electrolysis by lightning), 21% oxygen, 0.93% argon, 0.04% carbon dioxide, and trace amounts of other gases, in addition to about 3% water vapor. This mixture of gases is commonly known as air. But for the sake of simplicity let us call a mixture of these molecules as ‘air molecules’

Since the density of air at ground level is 1.25 kg / m3 (1.25 g/L), each ‘air molecules’ will have a mass of 4.6127 x 10-26 kg. That same cube at 10 km altitude will contain just over 13 moles of air (7.8286 x 10 24 air molecules). Therefore the density of air at 10,000 will be 0.36 kg. m3. or just about 28.9 % that at sea level. This figure varies of course depending on humidity, temperature and pressure up there. It can be as high as ¼ that of sea level. Clearly, number density declines with altitude.

The hydrogen atom:

The hydrogen atom consists of a proton of mass mp=1.7 x 10-27kg + an electron of mass m e= 9.110-31kg. Hence the mass of a neutral hydrogen atom = 1.70091 x 10-27 kg. This means an ‘air molecule’ will have an average mass 27 times that of a single hydrogen atom. A hydrogen atom is 0.0369 times lighter than an air molecule based on the average air density. But there is no such thing as an ‘air molecule’ since air is a mixture of gasses, namely: nitrogen 78.084%, oxygen 20.946%), argon 0.9340%, carbon dioxide 0.0387%, neon 0.001818%, helium 0.000524%, and numerous other trace gasses. But just to make this story simple we shall call it ‘air molecules’.

Volume of air sucked in by a jet-engine:

I do not know how much of air is being sucked in by an engine of an Airbus A320, but from an information I got some years ago from a newspaper, it was reported that an RR Trent Engine empties 945.12 cubic meters or 1.2 Imperial tons (1.2192 tonne / metric tons) of air per second during take off.

Size of Malaysian residential houses:

Houses in Malaysia come in all shapes, sizes and prices. They range from mansions, istana-like, bungalows, apartments, terrace and lined houses to small squatter living spaces. But most urbanites in the middle income group live in linked or terrace houses, either double or single storey. Whether double or single the land area is about the same except the height.

From several architectural as well as real estate websites, sales and purchase agreement with floor plan measurements, and actual measurements from all these sources, and all the data put together for statistical analysis to derive their mean values, below is a summary of the dimensions of most of the houses in Malaysia.

Approx total land space = 1600 square feet
Length & breadth of house inside = 48 ft x 20 ft = 960 sq ft
Length & breadth of backyard = 8 ft x 20 ft = 160 sq ft
Area of car porch = 11 ft x 12 ft = 132 sq ft
Area of driveway = 24 ft x 20 ft = 480 sq ft
Hence total area = 960 + 160 + 480 = 1600 sq feet
Height of floor to ceiling = 130 inches (10.8 feet)
Volume of built up indoor area of house = 960 x 10.8 = 10368 cubic ft = 293.589 cubic metres

Hence, the dimension inside the house of an average single storey or a double storey terrace house in Malaysia is 48 ft x 20 ft of floor space, with a standard indoor ceiling height of 130 inches (10.8 feet). Hence the average volume of either a single storey house or the volume of either downstairs or upstairs of a double-storey house within its enclosed area is only 10368 cubic feet or 293.589 cubic metres.

How fast and how much can it sucks?

This mean a single RR Trent Jet Engine of a plane on take off can completely empty all the indoor air of 3.22 houses put together in one second just to get enough oxygen to ignite its fuel to provide the thrust it requires for lift-off.

But a plane has two engines. The emptying rate will be 6.44 single-storey houses per second on take off. It is like having nearly 7 houses imploding together when all its air inside is emptied within one second - if the air is not replaced fast enough from outside. Quite a thought!

The atmosphere at sea level will exert a pressure of 101.3 kPa (kilopascals) = 14.7 psi (pounds per square inch) = 760 torr = 29.9 inches of mercury on all its exterior walls and roof and instantly cause all the walls and the roof to collapse instantly (implode inwards) if air flow into the house through its doors and windows is not fast enough to replace what was sucked out by the jet engines. Just imagine the power of the jet engines and fancy that. I never thought of this without this simple calculation.

Let us now assume two RR Trent Engines were used. The density of air at 10,000 meters = 0.36 kg / m3 At this density, there are 13 moles or 7.8286 x 10 24 of air molecules. Both the engines would have sucked in (2 x 1.2192 metric tons x 1000 kg x 7.8286 x 10 24) ÷ 0.36 kg = 5.30 x 1028 air molecules per second. The kinetic energy generated by the plane’s two engines per second as they strike against 5.30 x 1028 molecules, each with a mass of 4.6127 x 10-26 kg. will be ½ mv2 = ½ (5.30 x 1028 x 4.6127 x 10-26) x (236.9 meter per second)2 = 137 202 239 joules (137 megajoules) provided the molecules are stationary before being sucked in – which is not possible of course.

Fluid dynamics: Bernoulli's principle

This is the minimum energy expenditure against the two engines since we are assuming that the speed at which the air molecules were being sucked in is the same as the speed of the plane at 853 km. per hour, which of course is not true. The speed of the air intake has to be a lot faster than the forward thrust velocity of the whole plane which also has to suffer the impact of other air molecules covering the much larger surface of the entire plane. I do not know how large the surface area of the plane is, so we cannot determine how many more molecules the plane will have to strike. The ejection of the mass of gasses behind the jets has to be equal to the thrust forward against air resistance (Newton 3rd Law of Motion)

Furthermore, an increase in the speed of the fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid's potential energy (Bernoulli's principle).

We can easily calculate this out if we have some very basic info from Captain KH Lim about the plane’s surface area especially the wings which give it the thrust forward and lift upwards against gravity. But Captain Lim is such a busy pilot, and I do not wish to trouble him. So I like to work things on my own. Of course I was only conducting medical research all along, but this should not hinder me from trying to figure out problems in aeronautical or molecular physics.

We can guess:

However we can make a guess indirectly. Since the fuel consumption of an Airbus A320 is 665 Imperial gallons (3,025 litres / 2,420 kg) per hour or 0.672 kg per second, and since the energy values of jet fuel (aviation kerosene) given as between 43.28-43.71 MJ / kg (average 43.49 MJ / kg), the energy expenditure is 29.225 MJ per second. The net velocity of the plane is 236.9 meters per second, and the mass of each air molecule is 4.6127 x 10-26 kg, the total number of air molecules the plane has strike in other areas excluding those sucked in by the engines each second, can be determined by:
E = ½ mv2
2E = mv2
m= 2E / v2 = 2 x 29 225 000 joules / 236.92 = 1041.48 kg of air molecules
= 2.2578 x 1028 molecules per second.

Much slower:

But we know the velocity of the plane is very much slower than that of the air-intake and the velocity of the jets of gases ejected behind.

The calculations I gave showed that the engines alone suck in 5.30 x 1028 molecules or 2444.7 kg of air per second, not counting other air molecules encountered by the wings and fuselage. Hence the plane will require 0.6722 kg of fuel per second at the rate of 2420 kg per hour at a cruising height and speed of 10 km per second and 853 kph respectively to be equivalent to the striking kinetic energy against the non-engine parts of the plane.

Let us use the figure 2,2578 x 1028 molecules or about 1040 kg of air per second against the moving plane in still air. This is equivalent to encountering about 6.12 x 1029 hydrogen atoms per square meter in deep intergalactic space. We assume below there are about just 10 hydrogen atoms per cubic meter in deep intergalactic space.

This means our plane can afford to travel for 6.12 x 1026 km or 6.469 x 1013 light years before encountering the same mass of resistance and energy usage as a plane traveling for one second or to a distance of about 237 meters in our Earth’s troposphere (1 light year = 9,460,730,472,580.8 km).

No more fuel needed:

In short, we assume our A320 has already left the Solar System, and is now cruising without the need of anymore fuel in the emptiness of deep space except an encounter with just 10 hydrogen atoms per cubic meter or per square meter of space it scooped up. It will continue in that state in a ‘straight’ line at 530mph (853 kph / Mach 0.78) for all eternity as if it was flying at 35,000ft (10,668m) in our own atmosphere, unless acted by an external force such as interstellar and intergalactic dust and molecules to resist that state as prescribed by Newton First Law of Dynamics.

The void of interstellar space:

The interstellar medium (ISM) is usually extremely tenuous, with densities ranging from a few thousand to a few hundred million particles per cubic meter, and an average value in the Milky Way Galaxy of a million particles per cubic meter. Other estimates gave it as 300,000 atoms per cubic meter. The elemental composition of interstellar clouds is much like that of the sun, about 90 percent of hydrogen, and 9.99 percent helium. The heavier elements make up the remaining 0.01 percent. The average density of the Universe is just 10 to 100 hydrogen atoms per cubic meter. But deep between the galaxies, there may be just one hydrogen atom most of the time.

In the Cold Neutral Medium (CNM) of space where the temperature is just 50 – 100 Kelvin, there are just 1 - 103 neutral hydrogen atoms per cubic cm of space. The density at different locations of the Universe varies enormously. It is very much denser within a galaxy than in between the galaxies, much, much more dense in the centre of a galaxy where the black holes are, than in the peripheries where the stars are scattered apart, and the interstellar densities are so much more tenuous. Cosmology and astrophysics is a very complicated subject and the data on densities and amount of matter from the dark matter to the derived varies so greatly. In the above calculation, we assumed we only encounter an average of just 10 hydrogen atoms per cubic metres or per sq. metre of our plane.

Interstellar density:

In the solar neighborhood, the stellar density is about one star per cubic parsec (one parsec is 3.26 light-years). At the Galactic core, around 100 parsecs from the Galactic center, the stellar density has risen to 100 per cubic parsec, crowded together because of gravity, let alone where ‘neutron stars’ exist. These stars have a radius of only 10 km, and the density is about 100 million tons per cubic centimeter. This is insignificant compared to a black hole or a super black hole where volume and mass collapsed into a singularity. Here the density is infinite. Because of all these variations let us steer our plane far, far away from these grotesque cosmic events, well away from any event horizons Let our plane drift through the immense intergalactic valley, end to end, an immense abyss of space spanning 40,000 million light years, or 3.78 x 1023 km (378 sextillion km) across.

An eternal cruise:

For that, it will take the plane almost 48000 million, million Earth years to achieve. Fancy that! I salute the super-pilot who can live and endure that kind of journey. To solve that, he may have to marry abroad, bear children over 1.6 x 1015 (1600 million, million) generations to take over the piloting once each child attains the age of 30 years, taken as the span of one generation.

A better idea:

But I have a better idea. This is not possible. But it is possible for his sperm and his wife’s eggs be frozen in liquid nitrogen as they are left to drift into the frigid coldness and darkness of space where the temperature is almost 0 Kelvin. The pilot may either remain back on Earth, or kept in suspended animation if he wishes to follow his genes aboard. A robot is programmed to take over which will only be activated towards the end of the journey. The awaken robot will then take out the sperm-ovum in deep freeze, fertilize them. It will then nurse them, and bring them up. It will teach them where they came from, their language, culture and civilization, and what their world looked like.

A voyage guided and narrated by a robot:

It will tell him or her purpose of their voyage, their fate, destination, and destiny. They will pictures and images of their world, their parents, other humans, plants, animals and all other living things. All the images of this world will be beamed towards the plane for their benefit from the day it left Earth and the Solar System. All scenes of Earth will be continuous with time, such that the entire length of 40,000 million years of history from the beginning to the edge of this Universe could be shown.

The TV transmissions will not be broadcast the usual way. This will ‘dilute’ the energy of transmission over a wider and wider volume into space as the plane leaves planet Earth. The entire energy of the signals will have to be concentrated into just a very narrow beam in the direction of the plane in order to focus the pictures clearly on arrival without being spread out. It would be like a laser beam.

The transmission should be continuous so that there is no gap in time in receiving the images. Even then, towards the end of the journey, all the images would have been at least 40,000 millions years out of date for the far-away pilot. He will perhaps never be able to learn of his / her origin, and the world he came from.

Time needed even by light to cross the chasm:

The distance across the horrendous chasm of the Universe from one end to the other is: 299792458 metres ÷ 1000 (to change into km / sec) x 60 sec (to change to km per min) x 60 min (to change to km per hour) x 24 hr in a day x 365.25 days in a year x 40,000, 000,000 years = 3.78 x 1023 km (378 sextillion km).

This will take light 4 x 1010 (40 billion) years to cross this grotesque time
space corridor. How long would my Air Bus A320 take?

‘Ask Captain KH Lim’ in his fantastic website I highly recommend you to visit if you ‘Ctrl & Click’ on my articles above. They are linked to his.

http://askcaptainlim.com/index.php?option=com_content&view=category&id=74&Itemid=89

What a journey? Fancy that! Have a safe trip.

JB Lim