# The Earth is smoother than a billiard ball

Earth the billiard ball

The Earth may seem all bumpy and uneven, with molehills, mountains, trenches, buildings and what nots. But really if you shrank it to the size of a billiard ball, it’s smoother! The standard set by The World Pool-Billiard Association requires a billiard ball to have humps or bumps no more than 0.002 times the diameter of the ball. For a 5.72cm ball, that’s about 0.1mm. The Earth is roughly 12, 500km. The deepest point on Earth is the Mariana Trench, about 11km deep. That’s deeper than the height of the tallest point on Earth – Mount Everest at around 9km. So… The deepest bump on Earth is roughly 11/12500 = 0.0009 times the diameter of Earth. Less than half the largest allowable bump:diameter ratio for a competition-standard billiard ball! Regrettably, the Earth is probably not spherical enough.

# How planes do NOT fly

Many people claim that Bernoulli’s Principle is the main factor contributing to lift in an airplane. For those unfamiliar with the principle, it states that a fluid (like air) that flows faster exerts a lower pressure than a fluid that flows slower. The wings of airplanes are usually curved at the top surface and flat at the bottom. As it cuts through air, it forces the air at the top surface to move at a higher velocity than the air at the bottom surface. This is so since the air on top has to “catch up and join back” with the air at the bottom, by the time both flows reach the end of the wing. Therefore, higher pressure on the underside of the wings, lower pressure on the top side, results in lift. (See here for explanation of Bernoulli’s Principle with diagrams: http://www.grc.nasa.gov/WWW/k-12/airplane/wrong1.html) Some physics teachers/texts aerospace museums cite this as the reason why planes fly.  This was Fact, till Jiahuang (who has the ability to change Facts) asked during Mr Wee’s lesson “how then do planes fly upside down then?” That got us all thinking. Well, turns out this very popular and very pervasive reasoning (called theory of Equal Transit Time) on how planes fly is wrong! Xkcd did up an interesting comic strip summarizing everything that I just said (and everything I’m about to say):

In the first place, nobody ever said that the top flow and bottom flow must meet at the end of the wing (which was the assumption we made when we said the air flow at the top is faster than the air flow at the bottom). Fact is they don’t.

Sounds like the Bernoulli’s argument is simply wrong. But actually it’s not so simple (as the comic suggests). It turns out that the earlier argument was wrong on 2 fronts, but correct on one. Wrong firstly that “Bernoulli’s Principle is the main reason for lift”. Wrong secondly that “the airflow meets again at the end of the wings”. From the video, the airflow clearly does not meet again. However, the theory is right when it says that “Bernoulli’s Principle generates lift”. From the video, clearly the speed of the top flow is much higher than the speed of the bottom flow (in fact much higher than required for the two flows to meet again at the end of the wings). So, the lift generated due to the pressure difference would actually be more substantial than what the wrong textbooks would have calculated. BUT, it is still nowhere near enough to lift a plane. It might suffice to end off with “So there, the most common and most appealing (probably because it’s the simplest) myth on how planes fly debunked.” But then the entire conclusion would be based on the claim that “BUT, (the lift generated by pressure differences between the top and bottom of the wing) is still nowhere near enough to lift a plane.” Not very convincing eh? Considering I didn’t provide any figures. Haha if you want figures based on simple maths can just go google/estimate yourself.

A more convincing way to disprove this myth would be to ask what Jiahuang and the xkcd person asked “how then, do planes fly upside down?” If the myth were true, then the wings flown upside down would definitely produce a force downwards, plunging the plane to the ground right? Er… I wasn’t joking when I said that the xkcd comic strip summarized everything I’m about to say – It’s really not that simple. A normal wing flown upside down CAN still generate lift. According to some dude from the xkcd forum, the point where the front of the wing cuts the air changes when you turn the wing upside down. The result is that the airflow on the underside (now the top of the upside down wing) of the wing is still faster than the airflow on the other side. Thus, lift is still generated by the wings even when the plane is flying upside down. So… The answer to the question “how then, do planes fly upside down?” really does not provide a convincing argument against the myth of Equal Transit Time.

At the end of the day, xkcd is correct. How planes fly is not that simple. What’s 100% wrong is that Bernoulli’s Principle is the main reason for the lift. There are many reasons that generate lift. But they are too chim for me to understand, thus I will not attempt to touch on them. (Thus the title of this section).

Interesting side fact: A B2 stealth bomber is basically a flying wing. No tail to stabilize, no fuselage. It’s so unstable that it’s not flyable by a human. It requires 4 computers to constantly make adjustments every split second in order to keep that flying wing in the air. So it’s really the computers doing the flying, not the pilot. Well, such technology for the price of twice its weight in gold.

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