Posted in Science & Nature

## Airplane Game

You are cordially invited to a game that lets you earn money very easily. The game works like this:

1. You pay \$1000 to be recruited as a passenger to a plane.
2. There are 8 passengers, managed by 4 crew members, who have 2 co-pilots above them, co-ordinated by a captain at the top.
3. Everytime the “plane” is filled with 8 passengers, the captain retires and is paid out \$8000.
4. When the captain retires, the plane is split into two planes and everyone else is promoted one step higher (co-pilots each become a captain, crew become co-pilots, passengers become co-pilots).
5. When each plane fills with 8 new patients, the captain of each plane gets paid out \$8000 and retires.

This seems like a very easy way to earn money. Where else could you invest money and guarantee a 700% return, only needing to recruit 7 new people into the game?

The problem with the airplane game is that it is a classic example of a pyramid scheme. At first glance, it seems that the payout of \$8000 is guaranteed because it seems that the promotions will keep coming.

But if you look at the mathematics, 8 people need to participate before the first player wins. 16 people have to participate for the second player to win. 80 people have to participate for the tenth person to win. If you are the one-thousandth person to join the game, you need a total number of 8000 people to be playing the game before you are paid out. At the end of the game, 87.5% of people playing will have lost money because they will never be paid out.

This is how simple exponential growth can result in a very real fraud, resulting in thousands of people losing their hard-earned money.

Posted in Science & Nature

## Sonic Boom

When something moves through the air, it pushes the air in front and creates a sound. This sound spreads as a wave at the speed of 340m/s (1225km/h). As the object moves, it makes a series of pressure waves, which is why the Doppler effect happens. These pressure waves look like rings that are squashed to the side the object is moving towards. As the object moves faster, the more compressed these rings become. When the object moves at the speed of sound (340m/s), the pressure waves all overlap as the object makes a pressure wave on the same place as where the last wave reached. This is the sound barrier.

At this point, there is so much overlap of the waves that a shockwave is formed. This shockwave – made of compressed air – travels at the speed of sound (Mach 1) and originates from the front tip of the object (e.g. nose of the plane). If the object moves any faster than the speed of sound, the new wave is made even before the old wave has propagated that far. The rings are now no longer in a nice concentric pattern, but instead form a shockwave cone. Sometimes this can be seen physically if there is enough condensation in the air to create a vapour cone. The sudden change of pressure from the shockwave creates a large booming sound, which we call a sonic boom (in fact, there are two booms due to the pressure difference at the tail too).

Sound, like other waves, is a form of energy. Hence, the shockwave formed by breaking the sound barrier can cause physical damage. If a fighter jet were to fly over a building at low altitude at supersonic speeds, it may cause windows to shatter and people’s eardrums to rupture. The shockwave creates a significant problem in aircraft design, for if a plane’s wingspan is wider than the width of the shockwave cone, its wings will snap off. This is why fighter jets and the Concorde have a characteristic sleek, triangular shape. The faster the plane travels, the narrower the shockwave cone becomes and the thinner the plane’s wingspan has to be.

Then what was the first manmade object to break the sound barrier? The answer is surprisingly old and simple – a bullwhip. The crack from a whip is actually a small sonic boom made by the tip of the whip travelling beyond the speed of sound.

Posted in Science & Nature

## Bird Strike

An airplane flying across the sky faces many dangers. But a very common yet not well-known type of accident is the bird strike. Just as the name suggests, a bird strike is when a plane collides with a flying bird. This may not sound so dangerous, but considering a plane typically flies at 800~900km/h, the energy from the collision is quite significant. If a plane flying at 800km/h collides with a 5kg bird, the energy generated is 92 tonnes. This is not only enough to instantly kill the bird, but also enough to damage the plane.

The most common type of bird strikes is when a bird collides head-on with the windshield or gets sucked into the engine. The latter can cause severe damage to the engine and even cause it to fail. For example, in 1960 a plane flying above Boston collided with a flock of starlings, leading to all four of its engines failing and causing it to crash, killing 62 passengers. Since birds typically fly below an altitude of 9000m, bird strikes most often occur during take-off and landing. However, there are case reports of much higher altitude crashes, with the record being held at 11300m.

According to statistics, the most common type of bird involved are waterfowls and gulls, with 15% of bird strikes being severe. Bird strikes cause \$1.2 billion worth of damage annually worldwide and has cost 200 lives since 1988. The first bird strike occurred with the invention of the airplane, as recorded by the Wright brothers (inventors of the modern airplane). As bird strikes cause so much damage, airports place many countermeasures to prevent them. The most frequently used methods are driving away birds from runways by using scarecrows and other methods, or modifying the plane and engines to be more bird-resistant.