A few months ago, Cantabria económica published an article discussing whether Santander would be a good host for the America’s Cup. Even dropping in the article that the lack of infrastructure would make a hypothetical candidacy difficult, I couldn’t contain my excitement at the thought of seeing America’s Cup sailboats live in the Santander bay.

But Juan, what makes these sailboats special? Well, the AC75 or the F50 are true works of engineering. As a sailing enthusiast, I will try to explain in this post how we went from only being able to sail downwind to getting speeding tickets from speed cameras 😉.

Our engine? The wind

Points of sail

One of the vital pieces of knowledge in sailing is understanding how the wind affects our boat. Let’s start with some basic nomenclature about the points of sail:

• Running: This is the point of sail we all imagine when we think of a sailboat. The wind reaches us from the stern of the boat and we sail downwind.
• Reaching: This is a boat’s point of sail when the wind hits it on its beam, that is, perpendicular to the direction it is heading.
• Broad reach: The intermediate course between running and reaching, that is, we receive the wind on the boat’s quarter.
• Close-hauled: This is the most counterintuitive point of sail. The boat moves against the wind, receiving it on its bow, meaning we receive it between the beam and the bow.
• In irons: In this point of sail, you cannot move forward. The wind reaches us from the bow, meaning the front of the boat, and we are heading windward.

If you have to take anything away from this article, it’s that when Jack Sparrow says “set sail windward”, as epic as it may sound, he’s telling his crew to stop the boat since they will go in irons and won’t catch any wind.

But how does the boat behave on each of the points of sail? The force vector, which defines how the boat will move, can be divided into 3 components that will make our analysis easier. Taking some naming liberties, we will call them the bow component, the stern component, and the beam component:

As can be seen, to produce the boat’s forward movement we need to minimize the stern and beam components as much as possible on the different points of sail so that the bow component makes the boat move forward. On points of sail like running, it is not particularly problematic, but on reaching and, especially on close-hauled, these components cause us problems as they deviate the boat too much from the desired direction.

The stern component is easy to explain how to mitigate. Simply, boats are wide at the stern and narrow towards the bow. That is, the stern is much less hydrodynamic than the bow, generating a lot of drag to backward movement and canceling, to a large extent, the stern component that would push the boat backward. However, the beam component deserves its own section:

The keel and heeling

How do we prevent the beam component from taking the boat far away from our destination (leeway)? The answer is the keel. This part of the boat is an underwater extension of the boat that generates resistance to the boat’s lateral movement. However, as a counterpart, the boat heels and, if not controlled, can capsize.

But, if the keel is so small compared to the sail, how is it possible that it opposes so much resistance to leeway? The answer is the difference in density between the 2 fluids: the air/wind that acts on the sail and the water that exerts resistance on the keel. The weight of the displaced water, even having little volume, acts as a counterweight to the force exerted by the wind on the sail, balancing the boat.

The apparent wind problem

Having mitigated the two wind components of stern and beam, we can now conclude the fastest point of sail for the boat. As is obvious, the fastest point of sail is the one that maximizes the bow component. Therefore, we can conclude that it is when the boat is running, right?

Not quite, if we watch a SailGP race we can see that the course they take when the next mark is to leeward is a broad reach and not running:

Why does this happen? Well, as our friend Albert Einstein would say, everything is relative. So far in our explanation, we have talked about absolute wind speed, that is, assuming the boat is stationary. However, the force exerted by the wind on the boat depends on the wind speed relative to the boat’s speed, called apparent wind.

What does this mean? That a boat moving downwind loses apparent wind since it gets weaker by subtracting the wind speed from the boat speed. And conversely, a boat that sails against the wind has an increasingly stronger apparent wind as its speed increases.

Taking this into account, we realize that depending on the absolute wind speed and the boat speed, we are interested in taking one course or another to reach our destination. For example, if we want to reach a point that is to leeward from a resting position, the optimal course will be to gain speed with a running course and, as we lose apparent wind when gaining speed, luff towards a broad reach to continue having apparent wind and maintain a higher maximum speed.

To represent these maximum speeds as a function of the wind, polar diagrams are used, which are intrinsic to each boat model. We will use as an example measurements taken from a Volvo Open 70:

(Credits to orc.org for data collection)

As can be seen, to get to a leeward point as soon as possible, the fastest course is not running(in fact, in the data this course is not even included because it is unstable) due to the loss of apparent wind but a broad reach.

Now, let’s look at the speed record obtained in the SailGP competition:

Quite counterintuitively, the fastest speed is achieved with a reaching wind and it coincides with the diagram data! Being more precise, the top speed is achieved after bearing away a few degrees downwind after having managed to accelerate while reaching.

Although it seems strange, after explaining how apparent wind and the components of force work, it makes perfect sense! By going totally perpendicular to the wind, we don’t lose wind as we move forward and therefore the force of the wind remains, ideally, constant, being able to achieve, in our simplified frictionless model where cows are spherical and PI=3, whatever speed we want.

The challenge? The sea

We’ve already seen how to squeeze the most energy out of the wind by playing with the points of sail and the apparent wind to generate the greatest possible force. However, unfortunately in the real world friction exists and there is a great physical wall that slows us down: the sea.

Drag

Water is approximately 800 times denser than air. No matter how much force we manage to capture in our sails, pushing a boat’s hull through such a heavy fluid generates colossal friction.

Historically, the speed of a traditional sailboat was conditioned by its “hull speed”, a hydrodynamic limit at which the boat gets trapped by the very wave train it generates as it moves.

As the boat accelerates, the wave generated by its bow becomes longer and longer. When hull speed is reached, the length of this wave equals the boat’s length, leaving the bow riding on the crest and the stern falling into the trough. Physically, this slope causes an aft shift of the submerged volume and, with it, the delay of the “center of buoyancy” (the center of hydrostatic thrust). As the center of buoyancy shifts, the stern sinks drastically, forcing the sailboat to perpetually sail “uphill” against its own wave and exponentially multiplying the drag.

Although lighter boats manage to mitigate this effect by planing (skimming over the surface of the water instead of pushing it aside), the large surface in contact with the sea still slows the boat down enormously.

So, if friction with the water is the problem… why not avoid the water?

Hydrofoil

This is where spectacular modern engineering comes into play with hydrofoils. If you look closely at the F50 catamarans of SailGP or the AC75 monohulls of the America’s Cup, you will see large carbon appendages submerged in the shape of ‘L’, ‘T’ or ‘Y’.

Their operating principle is exactly the same as that of airplane wings, but applied to a much denser fluid. As the boat accelerates pushed by the wind, the water flow passes through the asymmetrical profiles of the foils, generating a great upward lift force.

Upon reaching a certain critical speed, this lift becomes greater than the boat’s own weight, lifting the hull completely and lifting it out of the water. From one moment to the next, hydrodynamic drag drops drastically, since the only surface in contact with the sea becomes the bottom part of the foils themselves and the rudder blades.

Thanks to this massive reduction in friction, combined with the multiplying effect of the apparent wind we saw earlier, the boat is “freed”. The sailboat continues accelerating until it multiplies the real wind speed by three or four, catapulting the crew to reach the mind-boggling figure of 100 km/h (almost 55 knots) over the surface of the ocean. Pure physics working in perfect harmony!