Can a sailboat sail directly upwind?

Can a sailboat sail directly upwind?

Thank you for reading.
First, I will give you the answer.

The answer to the question "Can a sailboat sail directly upwind?" is "No."

However, as shown in Figure 1, by using tacking navigation which involves repeating close-hauled sailing at 40° to 50° toward the wind, you can progress in the upwind direction, albeit in a zigzag pattern rather than a straight line.

Bernoulli's principle

Bernoulli's principle is, simply put, the principle that "as the speed of a fluid increases, its pressure decreases."

For steady flow of an inviscid, incompressible fluid under uniform gravity, the following equation holds along a streamline:

$${\displaystyle {\frac {1}{2}}v^{2}+{p \over \rho }+gz=\mathrm {constant} }$$

Here, $${\displaystyle v}$$ represents speed, $${\displaystyle p}$$ pressure, $${\displaystyle \rho }$$ density, $${\displaystyle g}$$ the magnitude of gravitational acceleration, and $${\displaystyle z}$$ the vertical coordinate.

In other words, it means that when the fluid speed is high, the pressure is low, and conversely, when the speed is low, the pressure is high, meaning fluid speed and pressure are inversely proportional.

Lift

As shown in the conceptual diagram of lift in Figure 2, due to Bernoulli's principle, when a wing or sail is designed such that the speed of the fluid below is slower than the speed of the fluid above, the pressure below becomes greater than the pressure above, and a force due to the pressure difference acts upon it. That force is decomposed into drag and lift, and a force acts to lift the wing or sail by the amount of lift.

Sailboat structure and forward force

A sailboat has a hull, a sail (an airfoil in the air), and although it is not visible when the sailboat is floating on water, there is a keel (an underwater wing) at the bottom of the sailboat.

In an actual sailboat, the speed of the air differs between the front and back of the sail, creating a pressure difference, which becomes lift.

That lift, as shown in Figure 1, becomes a force directed diagonally forward relative to the direction of travel.
The lateral component of that lift (lateral force) is mostly canceled out by the water resistance (drag) acting on the underwater keel.
Only the longitudinal component of that lift (forward force) remains, and the sailboat's hull is propelled forward.

Sailboat propulsion direction and the stroke direction of Kanji characters

While researching sailboats, I learned that it is impossible to sail straight in the 0° to 40° direction from the wind.

When we began our research on Kanji, we found that the three directions ←, ↖, and ↑ in Kanji strokes are Inhibit Directions.
Then, I realized that by assigning the remaining five directions to the five vowels: ↗(O), →(A), ↘(E), ↓(I), and ↙(U), it might be possible to turn logographic Kanji into phonetic characters.

Finally, starting next time, I will write about Kanji pixels. Please look forward to it.

I would appreciate it if you could write your opinions and impressions in the comments section.