How do sailing boats go against the wind?

FRITZ sails [sails info]


When a sail is surrounded by a flow, forces arise that enable a boat to be sucked to windward at an angle to the wind.

Every child understands that a boat can sail before the wind. Because a bundle of straw drifts in front of the wind. The sail offers resistance to the wind, a surface that it can "press" against, thereby pushing the boat in front of it. Very pictorially expressed.
The fact that a boat can sail higher than 90 degrees to the wind has to do with different pressures. There is negative pressure on the leeward side and overpressure on the windward side. The negative pressure can be up to be three times greater than the overpressure. The sail is sucked leeward (see Figure 1).
Both pressures act along the sail in different directions, but can be represented as a resultant force that is concentrated in the sail pressure point and acts exactly perpendicular to the apparent wind. It is called lift or transverse drive. At the same time, however, the sail offers resistance to the wind, which the wind tries to carry it away with it. Usually the lift outweighs the drag. The resulting total force "pulls" the sail slightly backwards, viewed from the apparent wind (Figure 2). This effect can be checked by taking the sword and rudder out of the water on a dinghy. The boat drifts across the wind, but also sails a little in the direction of the course, overall in the direction of the total force. Reason: The total force, viewed from the apparent wind, acts slightly diagonally backwards, but when viewed from the boat it acts diagonally forward.
If, on the other hand, a sword or keel and rudder are present, they, together with the hull, oppose a resistance in the water to the overall transverse force. The boat can no longer drift and converts the force into propulsion and heeling. The propulsion force only makes up a quarter to a third of the total force.
At the same time, the keel and rudder form a configuration similar to a sail and create lift that increases speed.
The question that remains is what causes the pressure differences on the sail. According to the Bernoulli principle (Swiss mathematician, 1700-1782), the pressure in the air decreases with increasing speed and vice versa. The air flows faster on the leeward side and slower on the windward side.
The next logical question: Why does it flow at different speeds? To explain this, a comparison with the airplane wing is often used, which one or the other is still familiar with from physics lessons at school. A wing is arched at the top and flat at the bottom, so it has a profile thickness. The air that flows over the curved side has to travel a longer distance than that which flows over the flat side. So you have to hurry - flow faster - in order to arrive at the rear edge of the profile at the same time as the underside.
The same is said to be true of a sail. So far understandable and plausible - but unfortunately not logical.
Because the sailing profile is not thick. An average Dacron cloth is about 0.3 millimeters thick. With a sail width of three meters, which corresponds to an average cruising size, there is a barely measurable difference in distance between windward and leeward. And thus no slower or faster flow around, no pressure difference, no propulsion. In addition, an airplane can fly on its back, which should not be possible according to this theory, because it would be sucked down.
And yet a sailboat can cross. To put it in one sentence, it should be correct: the sail tries to get you out of its direction.
Wind, i.e. accelerated air, has inertia (mass times acceleration). If the air hits the sail, it actually wants to continue flowing in the old direction, but does not manage to do so because it cannot pass through the sail. She is forcibly distracted. According to Sir Isaac Newton's third law of motion, every action (deflection) has an equally large reaction in the opposite direction, which here means a force on the surface - the suction.

The air is deflected by the angle of attack of the sail. Result: buoyancy

But what is preventing the air from simply flowing past the sail in the old direction? A quality that is most welcome to sailors: viscosity. This means a certain toughness that can best be compared, albeit greatly exaggerated, to thick honey. If this thick honey flows around the deployed sail, it is not only deflected by it, but also braked, because even the smoothest cloth causes frictional resistance. It brakes the honey layer that is directly adjacent to it down to zero, the layer above it a little less and so on until the current is unchecked. The current hugs or sticks to the sail.
Which still doesn't explain why the air accelerates leeward and decelerates on windward. This is done by the so-called start-up vortex. At the very first moment when the sail is hauled tight, when the boat is not yet moving, the following happens: The flow around the top of the sail On its way to the leech, the current is slowed down more and more by the friction on the cloth and at the same time it is deflected out of its path by the angle of attack. She does not like it. She wants to go back to her old direction. The air slides out of the track like a sports car where the brakes are stepped on in a curve, tearing off the leeward side of the sail prematurely (Figure 3 a). A hole is created in the air on the remaining area, from the tear-off point to the leech. That must be replenished, so the laws of nature want it.
But where do you get it from? The current from the windward side steps in to help. The honey upwind tries to get around the leech to the leeward side to fill up the hole. But it is tough and sluggish and although it just manages to get around the corner, it stops and forms a vortex, the starting vortex. It is carried away by the current on the leeward side (Figure 3b) and thus sets in motion a phenomenon called circulation. The sail "notices" that the void on leeward side cannot be removed by filling around the leech. So it tries to branch off air via the leading edge that was actually intended for the windward side (Figure 3c). The air is divided into two streams a long way in front of the sail.
Now you have to imagine that the sail is in a canal. This is formed by the external air masses. The stream that leads over the leeward side is pressed as if through a nozzle that forms the sail and the canal wall. This nozzle accelerates the air the first third of the sail so strong that it results in a negative pressure (Figure 3d). This weakens again due to the friction-related reduction in speed along the sail to the aft.
At the same time, an overpressure arises in the windward direction, as the little air has a lot of space to distribute and therefore flows more slowly. At the leech, both currents ideally have the same speed again, so that the air flows around the sail cleanly and without vortices.
Decisive for the development of different pressures on the sail and thus the propulsion are not very long distances. But the fact that more air is led over the leeward side than the windward side of the sail.

Lars Bolle

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