# The Physics of Sailing: How Does a Sailboat Move Upwind?

Have you ever wondered how a sailboat sails upwind?

 Sailboats racing upwind. Credit: Public domain

The sun is out, the wind is blowing, and I’ve been busy taking some sailing lessons. Turns out there’s an interesting bit of physics that allows sailboats to not only travel downwind, being pushed by the wind, but also to travel upwind, or nearly so.

 An 18th-century square-rigged ship sailing downwind. Credit: Public domain

But first let’s start with the downwind case. If the sailor wants to travel in the same direction as the wind, then all he or she has to do is hold the sail perpendicular to the wind and let the boat be pushed from behind.

This is the most basic point of sail, and was often used by ancient Egyptian, Greek, and Roman sailors. When they needed additional speed or wanted to travel upwind, they rowed.

The large square-rigged boats popular in the 18th and 19th centuries (the classic pirate ship, for instance) were also most effective on a downwind sail.

Modern sailboats can sail in any direction that is greater than about 45 degrees with respect to the wind. They can’t sail exactly upwind but with a clever boat design, a well-positioned sail, and the patience to zig-zag back and forth, sailors can travel anywhere.

To explore this, let’s draw a diagram that labels all the forces on the sailboat. If you haven’t seen a force diagram before, not to worry—it’s just a few arrows and triangles. By adding the forces together we will get the total force on the boat and thus the direction in which it will move.

Here’s a basic sailboat. The two parts we will focus on are the sail above the boat and the keel below the boat. The keel keeps the boat from tipping over and, as we shall see, plays a crucial role in moving the boat forward.

 A basic sailboat. Diagram credit: Tamela Maciel

Now let’s say we’re trying to sail upwind with the wind coming from the left or “port” over the front of the boat. This sketch shows the sailboat as if we were looking down on the boat as it moves towards the top of the sketch.

 Looking down on a sailboat, showing the equal and opposite forces on the wind and sail. Credit: Tamela Maciel

The wind fills the sail into the shape of a wing, but because the sail is held fast at both ends, the wind can’t push it out of the way. Instead the wind must change direction to flow parallel to the sail. The taut sail has created a force on the wind that causes it to change direction and Newton’s third law tells us that there is an equal and opposite force on the sail by the wind, as shown by the red arrows in the diagram above.

If this was the only force acting on the boat, then we would be in trouble: the boat would move forward but also to the right. But sailboats have a secret weapon hidden below decks: the keel.

 Keel and rudder below a sailboat. Credit: Paul Schultz

In addition to the force on the sail, the large area of the keel resists being dragged sideways through water. You can feel this resistance if you drag your hand palm-first through water compared to edge-on. The water applies a force to your hand that increases with greater surface area.

 Forces acting on a sailboat cancel each other such that the total force moves the sailboat forward. The downward pointing keel is outlined by the dashed rectangle. Credit: Tamela Maciel

This force on the keel is shown by the purple arrow in the diagram above. By combining the force on the sail and the force on the keel (triangle diagram), we see that the sideways forces are cancelled out and the total force on the sailboat is only in the forward direction (green arrow). The result is that the boat moves forward!

Some sailboats can even move faster than the wind itself. When sailing upwind, the relative speed of the wind on the sails is greater than the actual speed of the wind and this relative wind creates a larger force on the sails that can push sailboats faster than the actual wind speed.

There is a limit to how fast sailboats can move forward, of course. I have ignored boat drag in this example, but the boat also has an inherent friction as it moves forward through the water. The boat will accelerate until the force pushing the boat forward is balanced by the drag force pulling the boat back, and then the boat will travel at a constant speed.