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Physics of sailing

For the first time in my life, I could try what it means to pilot a yacht. My friend, the captain, took us to the Lake Lipno, the largest Czech-or-Slovak, 5000-hectare reservoir with a hydroelectric power plant built near the spring of the Moldau River in Southern Bohemia, miles from the Austrian border.

Bedřich Smetana, the Moldau. A decade ago, I tried to exploit the knowledge of which parts of our national river were described in various segments of Smetana's composition. Lipno is seen e.g. at 1:50, 1:58, 2:01. Smetana had predicted the big dams in the second part of the composition.

Our captain did almost everything for us – and he worked in his pub just minutes before our 21-hour-long sailing, as well as minutes after that. But I could at least enjoy to be the acting captain at night when I skipped sleeping. Unfortunately, our Yamaha motor stopped working minutes after we began our adventures. That got combined with another problem – there were many windless hours. You can imagine what it feels like to sit in the middle of the Bohemian Sea and be unable to do anything about it. The last 2 miles were impossible, too: We asked another yacht to bring us to the port which they kindly did.

It's fun to experience some practical physics. I have always found sailing counterintuitive. The practical experience has erased my doubts that it's possible, however. ;-)

What has always been my problem? I hope that some folks have shared this embarrassing mis-intuition with me. I would normally say that the wind has some velocity \(\vec v_{\rm wind}\) and this is where the sailboat may move, too. On top of that, the keel of the yacht may guarantee that the velocity \(\vec v_{\rm yacht}\) is either in the direction of the keel, or against it.

But one still expects the inner product \(\vec v_{\rm wind} \cdot \vec v_{\rm yacht}\) to be positive, right? It looks like the keel may at least project the wind velocity onto the direction of the keel. But the sail will still move in a direction that is more aligned with the velocity of the wind than anti-aligned. So it should be impossible to move against the wind, even slightly.

Sails and yachts have been successfully used to get anywhere, however. ;-) What's the problem with my proof that yachts don't work 50% of the time? Well, the problem is that I only considered forces in the direction of the wind.

They're enough to understand how the yachts "run downwind" – how they move in the direction of the wind or similar directions. In these contexts, the sail acts like a parachute. The most important force is the drag, the simple resistance of the air, and it determines the direction of the sailboat. The wind is simply pushing your boat or ship.

Yes, the mistake of my argument is that the drag isn't the only force. There's also the lift. It's a very similar force as the force that allows airplanes to fly. The sail – I mean the piece of clothes – acts almost just like a wing of an airplane. And the corresponding force (lift) is perpendicular to the direction of the wing. And this direction may easily be "mostly" against the wind.

So my argument that the sailboats can never "beat windward" was assuming that the drag is the only relevant force. It's enough to acknowledge that there also exists the lift and the no-go theorem is shown invalid. In fact, the lift may probably be greater in magnitude than the drag.

In practice, you need a bulge in the sail to be created by the wind. When it's there, the wind may come from Northeast, the keel may be oriented to North, and that's where you can move because the lift will point to Northwest and this force will be projected to the direction dictated by the keel.

We could feel the no-go zone shown in the image above. The bulge ceases to develop when your keel is oriented against the wind too accurately. Right on the boundary of no-go zone, you may feel some vibrations and noise because the sail is frequently changing its opinion whether it wants to keep the bulge or give it up. But you want to be right outside the no-go zone because that's where you probably maximize the lift-to-drag ratio, and that's probably optimum for the speed that you can get from the wind.

Gravistatics as a wrong theory of falling bikes

The way how I neglected the lift is analogous to my first incorrect physical prediction that was – thankfully – falsified when I was between 3 and 4 years old. My father was teaching me how to ride my Flash the Bike. OK, at some moment, my side wheels were removed and I was supposed to move without them – and without the stabilizing effect of my father's hand.

As you could have postdicted by now, I had predicted that it was clearly impossible to maintain the vertical direction of the bike. In other words, bikes without side wheels are worthless. Why? Because the vertical gravitational force will attract the bike to the Earth. A tiny deviation from the vertical direction will be exponentially growing and it's unavoidable that the bike will fall – along with me – onto the sidewalk in a logarithmically short time. In my original proof of the no-go theorem, I was using the baby talk synonym for the "logarithmically short time" and other phrases (a word taken from the Czech baby talk, of course, because at that time, I didn't have a clue how to say even simple words such as f*ck in English, let alone knowing what the verb meant).

OK, minutes later, the bike was moving – without side wheels, without any paternalistic hand, and it avoided falling for minutes. A miracle? No, it was a proof that something had to be wrong in my original proof. The original proof neglected the angular momentum of the bike and some corresponding forces that aren't vertical – they are horizontal. The stability of bikes is a topic that even adults (and physics PhDs!) at the Physics Stack Exchange often argue about vigorously.

My "theory" used to exclude the possibility of useful bikes without parents' hands and without side wheels was a form of gravistatics – I don't want to overwhelm you with translations of words such as "gravistatics" into the Czech baby talk. But there are also "gravidynamical" forces and, which is simpler, other forces that point in different directions than the simple vertical force of gravity, and forces that may depend on the velocity of the objects.

The analogy with the lift that was neglected above is obvious. In some sense, all the theorist's intuitive arguments always neglect a similar kind of forces, the "second most obvious ones".

The broader point I want to make is that it's great for someone to be an enthusiastic theorist – and it's critical for him or her to see his brilliant theory or argument being torn to pieces. The argument showing that "a bike without side wheels and hands must fall quickly" or "the yachts are only useful 50% of the time to get from A to B" may be formulated as very impressive, nearly rigorous arguments. They may be articulated in grammatically perfect sentences and their authors may feel self-confident.

However, it's enough to do a simple experiment – often an experiment that many normal people ignorant about deep theory are doing all the time – and the theory or the argument is immediately killed, anyway. It's very important that many such guesses are killed rather easily. And it's important for a scientist to immediately draw consequences.

The Pushbike Song, the Czechoslovak edition (lyrics by Karel Šíp) which has characteristically avoided erotic dimensions.

I am afraid that all the people who propose all the loop quantum gravities, alternative theories to the proper Copenhagen theory of quantum mechanics, and millions of other wrong things have never experienced the miracle of a stable bike or a sailboat that is beating windward. And maybe they experienced those effects but they had never produced any predictions what should have happened. They have never made wrong predictions about effects that are simple enough to be experimentally decided. That's why they may be so utterly wrong about some advanced physics and they don't even think that it's possible for them to be ludicrously wrong.

A physicist simply needs this experience to have been wrong – and to see that he's wrong – in order not to be wrong most of the time without actually seeing it.

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