Saturday, March 15, 2014

Mystery of Missing Planes like MH 370 - A Probability of Meteorite Strike



Can a plane be brought down by a meteorite – just an academic thought!  

Reading all the conflicting reports of the missing Malaysian Airlines jetliner MH 370 on how it could escape the network of radar surveillance of Malaysia and neighboring countries, I couldn’t help thinking of other possibilities. One is a plane could be hit by a meteorite from space.

Normally, we would look at some of the most commonly thought of possibilities of a missing plane first. Such as mechanical failure, pilot’s error, hijacking, terrorism and explosions on board, bad weather and thunderstorms, psychological factors among the crew and / or with passengers are among the most possible causes. These causes should be the first step as they are the most common and simplest.

But if we are unable to find these causes to explain the mystery of a missing plane in flight, we need to look at other avenues of possibilities.

We will then need to adopt the ‘blue ocean strategy’ to look at a wider picture.  Our thoughts need to widen and we need to start thinking out of the box.

One possibility I am thinking is that a plane could be brought down by a meteorite in space.

Straight away from this beginning I am not implying the Malaysian Airline MH 370 was hit by a meteorite. No, not at all! I am talking about a possibility for any plane that takes to the sky. The risk, albeit very rare as I shall explain, can still happen if we cannot account for its mysterious disappearance from the sky.

First, let us look at some approximate data  to work on from there.

Area of a Boeing 777:

I do not know the exact surface areas of a Boeing 777 or the Boeing 777-200 version.  The best I could get was some data from the Internet, and sort it out from there.  So it is only an approximate for the sake of calculations.

The wingspan of a Boeing 777 was expected to increase from the current 64.8 metres to 71.3 metres for a Boeing 777-200.  Let us say it is about 68 metres, with a fuselage length of about 69.5 metres for convenience. That means if the aircraft was somewhat a square or rectangular, its area would be:

64.8 x 69.5 = 4503.6 sq. metres

Of course this is not. An aircraft is not a square. It is tube-like with wings. Its shape has to be as slim as possible in order for it to be streamline and aerodynamic in action. Assuming for the sake of calculation, the total surface area was just 20 % of this.

Hence as an assumption, the total surface area of Boeing 777 would be 900.7 sq. metres. It could be more, it could be less. I have no figure on this.

Let us now assume the Boeing 777 was cruising at about 900 kph or 250 metres per second.

If a plane like Boeing 777 was cruising at 900 kph (250 metres per second), it would then sweep over its own wing and fuselage area equivalent to 900.7 sq. m x 250 m /sec = 225,175 square metres  per second.

The Area Swept:

This sweep exposes it to a greater chance of being strike by a meteoroid. This of course is a virtual area as it was flying, and not at rest on the ground.

It would virtually increases its chance by 250 times each second of being strike by an oncoming meteorite as if it was rushing “to catch a falling star”

Suppose there were 1000 planes flying up there all over the world at any one time. The virtual coverage would be 225,175,000 square metres per second.  This area is 4.4 x 10-5 or 0.000044 percent of the entire Earth’s surface. What then is the Earth’s surface? Let’s check this out.

The equatorial radius of Earth is about 6,371 kilometers or 6,371,000 metres. Its surface area would then be 4 pi r 2 = 5.1 X 10 14 square metres.

Out of this, only ½ or one half of the Earth’s sphere will be exposed to a direct head-on collision with any meteorite and meteoroid as it revolves around the Sun. The rest trails or are left behind as the Earth moves in its rotation about its axis and revolves around the Sun in space. It is during this forward motion that the Earth is more likely to collect and collide with space debris.

Since Earth also rotates around its axis, it will encounter more meteorites after midnight until dawn because it is during this period of the Earth’s forward motion that gives it a greater chance of a head-on encounter.

The meteorites trailing and left behind on the other half of the Earth surface will have to chase after Earth from the back. The speed of a tail on collision from behind will be greatly reduced. 

In short, it is always the forward movement, be it rotation, or rotation of the Earth that enhances a greater risk of a head-on collision, not a tail-on collision from the behind.

Forward half of Earth:

Hence we shall consider only one-half of Earth where the chances of collisions after midnight will be most likely. This means only 2.55 x 1014 sq. metres of the Earth are more likely to encounter a meteoroid or a meteorite fall.

A meteor is what we see as a streak of light in the night sky when a small piece of interplanetary debris burns up as it enters through our atmosphere. In other words, it is a “shooting star”

A meteoroid is a large piece of interplanetary matter that is smaller than a kilometer, frequently only millimeters in size. Most meteoroids as they enter the Earth's atmosphere are so small they vaporize completely and never reach the Earth’s surface.

But if a meteoroid survives being burnt up through the atmosphere and lands on Earth, it is called a meteorite

Space debris and Chances:

Having said that, let us now go back to what astronomers tell us. They tell us that about 10 -100 millions meteors peppers the Earth every day, most of them as dust. 

But let us be conservative. Let us begin by assuming only 10 million meteoroids rain down on the Earth every day. Let us assume that out of the 10 million, only 100 of them are the size of a brick each weighing 10 kg. That is, there is only a 100/10 million, or 10-5 (0.00001) chance for a meteoroid of such size surviving our atmosphere each 24 hours-day.

The chance per second is even less. It would be 10-5 / 24 hrs-day x 60 min x 60 sec

= 1: 10, 000, 000,000

Most are micro meteorites or dust particles. Most sizable meteorite will fall over the oceans since ¾ of the Earth’s coverage is over the oceans. So we never get to see or detect them.

So do planes. If a plane flies all over the Earth’s surface all the time, including the oceans, the chances one of them being hit by a meteorite is even more remote.

Furthermore, there will be a 75 % chance it would fall into the oceans or seas. We can never hope to see or find them again. It just vanishes from the radar.

Probability:

However with tens of hundreds of planes spreading their wings up in the air all over the world - over the oceans, land, across mountains in its 115 years of aviation history since 1909, the chances of at least one of them being hit by a meteoroid one day at any moment albeit slim, is a possibility. It is a matter of the law of chance or probability that – that day shall surely come. 

But what are the chances of a plane being hit by a meteorite compared with the wide surface of the Earth?  Let us check this out.

If half the Earth’s surface is 2.55 x 1014 sq. metres, and if there is only a 10-10 chance of a 10 kg meteorite falling over Earth at any single second, then we can expect an even lesser chance of an airplane similar to Boeing 777 being hit by one.

Let’s check this out:

Chance x surface areas of planes / half the surface area of Earth:

10-10 x (225,175,000 square metres ÷ 2.55 x 1014) = 10-10 x 9 x 10-7 = 9 x 10-17    

(Where, 225,175,000 square metres is the total virtual wing spread of 1000 planes the size of Boeing 777 flying all over the world each second).

This is the calculated chance of a “cosmic brick” hitting one of these 1000 flying planes at any moment in time.

But so far we are talking about the chance per second. This chance naturally increases with each passing second.

For instance in a 24-hour day (86400 seconds) the chances increases to 8 x 10-12,  in a Solar Year (86400 x 365.25) the chance increases to nearly 3 in a billion, and in 115 years of aviation history, the chance of an occurrence increases to 3 in 10 million

This is very rare indeed, so rare that perhaps it has never occurred in the entire history of flying.
Yet…!

Yet in statistics, the law of chance or probability is always there, and is it is real. The probability is only zero when there is totally no plane around and totally and no meteorite at all slamming down on Earth. This of course is not true. We all know that 10 – 100 million cosmic dusts and pebbles rain down on Earth every day.

Kinetic Energy of Collision:

What if it does? How powerful will be the collision? Let us check this out.

Let us assume that of this, 10 million cosmic particles the size of a pebble, only 100 of them are the size of a brick each with a mass of 10 kg.

This means there is only a 10 -5 (0.00001) chance of a “cosmic brick” 10 kg in mass raining down on us.

The figure may be much higher, but let us be conservative in our thoughts.

Such a “brick” traveling at around 30 km/s would develop a whooping kinetic energy of:  

½ mv2   = ½ x 10 kg x (30,000 metres / sec)2  = 4,500,000,000 Joules of energy
(where, m = mass, v = the velocity).

The power of a Boeing 777 in flight:

That not all. Consider the jet plane also travelling at 900 kph to meet this collision. Let us calculate how much would be the total energy of collision.

Its gross weight of a Boeing 777 I understand is about 352,000 kg (775,000 lb). I really do not know if this includes the fuel as I am not an aviation engineer. My area of expertise is in nutrition, food science, medicine and in medical research which are all so very remotely distant from aviation physics. But just for the fun of it, let us try to work this out.

But let us assume the plane gross weight includes the fuel. Let us just take an example of the missing Malaysian Airlines MH 370 with its passenger abroad.

The missing MH 370 Boeing 777-200 has 239 passengers + 12 crew + 2 infants on board.

Let us assume the passengers + 12 crew members each weighs 65 kg, plus the 2 infants who were 20 kg each. Their total body mass would be 16355 kg.

Add on to the luggage of a max of 20 kg each for the 251 adults on board. That would be 5020 kg in total (ignore ‘luggage’ of the two infants)

The total mass would have been:

(352,000 + 16,355 + 5020) = 373,335 kg

Hence the kinetic energy of the aircraft flying at 900 kph (250 metres / sec) =

½ x 373,335 kg x (250) 2 = 1.17 x 1010 Joules

Imagine the power of this collision when a falling meteorite meets it?

How powerful will that be?

Consider when a meteoroid strikes, it is never a head-on horizontal collision. A meteorite must come from above in space at an angle. Let us assume a midway angle between 0 and 90 degree, namely at 45 degree.

The energy of impact would then be the cosine of this angle of attack.
Hence it is:

= cosine 45 degrees x energy of the meteorite + the kinetic energy of the plane.

This works out to be:

0.707 x 4,500,000,000 + 1.17 x 1010 = 1.49 x 1010 Joules   (where cosine 45 deg = 0.707)

Imagine this power of collision!

A 10 kg meteorite collision coming from an angle of 45 degrees to meet a Boeing 777 travelling at 900 kph with a load of 239 passengers + 12 crew + 2 infants and their luggage inside will deliver an energy of impact equivalent to 3.56 tons of TNT

(A ton of TNT delivers a punch of 4.184 x 109 Joules of energy)

What need to say about a plane under such catastrophe?  It will completely be disintegrated into smithereens. There will be nothing left.

It will just disappear in the sky and from radar and perhaps scattered into the oceans never to be seen again. The radar will not even to detect the meteorite coming as it is far too small – just the size of a brick, but with that power

Fortunately such an event occurring is so rare that we need to look at other much more common possibilities.

Once again I am not implying MH 370 was struck by a meteorite from space.  I am merely thinking of astronomical and statistical possibilities for any plane that mysteriously disappeared from the sky that we cannot account for.  It is just my academic thought to pen an article for my blog
Don’t take me seriously that the plane was hit by a cosmic rock from space.

The search goes on!

lim juboo


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