Andrew M.H. Alexander

Notes on sailing

July 2016

Some notes on sailing, after taking Cornell’s “Adult Sailing Camp.”

(Always important to remember first impressions when learning new things. I mean, I HAVE sailed before, plenty of times, but not since Clinton was president. Bill Clinton. Gotta get ready for the next Clinton administration!)


The most amazing thing about sailboats is that you can sail upwind. I mean, you can’t sail directly upwind, but you can sail pretty far upwind. That’s amazing, because where’s the energy coming from??? You’re basically going backwards with respect to the vector that’s powering you! The wind is blowing south, so how can you possibly use it to make yourself go north??! (Or at least northwest/northeast.)

There’s a strong analogy in my mind between sailing and skiing. In skiing, we use the force of gravity to make us move; in sailing, we use the force of wind to make us move. By cleverly manipulating that force we can do cool things, in both sailing and skiing. We don’t just ski directly downhill, following the same path a soccer ball would take if we let it free. Likewise, in sailing, we aren’t totally at the mercy of the wind: we don’t always (or even usually) sail in exactly the direction the wind is pointing.

And yet: gravity controls us in skiing a lot more than the wind controls us in sailing. We can’t ski uphill. So why can we sail upwind?

The answer is that boats actually have two sails. I mean, they might have a bunch of sails up above. But the distinction I mean is: a boat has some sails up above, and one sail down below (which we call the keel). The sails up above translate the force of the wind into forward momentum, and the sail down below translates the (resisting) force of the water into forward momentum. Sailing is, in a sense, the result of balancing out the force of the wind with the force of the water. The keel is the reason we can sail at all. If we didn’t have a keel, our boat would just move in the direction of the wind, regardless of which direction the boat was facing. (Like a hot-air balloon.) That’s not very useful! Motorboats don’t have a keel, because in order to change their direction they just change the direction of their propellers.

So when we’re sailing we can ski uphill.

So in principle, I guess the movement of the boat is just the vector sum of the wind, the translating force of the sails, and the resisting force of the keel? Which means that in principle, we can sail in any direction except for directly into the wind. (In practice, of course, it’s usually impossible to sail any boat much closer than pi/4 into the wind.)

I want to see some vector diagrams of all these forces acting together. I want to see, like, an interactive visualization of all this. I want to be able to play with a wind vector and a sailboat direction and see the resulting vectors.

I have this idea in my mind now of “vector-field-powered sports.” Sailing is powered by the vector field of wind; skiing is powered by the vector field of gravity. (Or slope, maybe, since I guess gravity is the same everywhere.)

Two open questions I have:

  1. How does this relate to the maximal speeds of the boat, and the optimal sail positions at the 2pi wind positions? The Cornell sailing manual says that boats are fastest when sailing perpendicular to the wind. Why is that? Why isn’t it when they are sailing directly downwind? Is this just a linear algebra/physics problem?

  2. What determines the relative size of the keel and the sail? Obviously wind speed is probably the primary factor, but modulo wind speed, what determines the relative size? Does it have to do with the relative viscosities of water and wind? Water is denser than air—is that why I can have a smaller keel than sail?


The fact that we can sail both upwind and downwind means that there are two distinct ways we can turn.

Think about skiing. If you’re skiing really slowly, carefully switchbacking down a slope, there’s going to be a moment at the end of every switchback where you have to turn, and your skis will be pointing directly downhill for a moment. But with sailing, you can either turn like that, or ski uphill, and have your skis pointing directly uphill for a moment at the end of every switchback. Because you can ski uphill. In sailing, you can either ski uphill or downhill. I.e., you can sail upwind (not directly upwind, but more-or-less upwind, by tacking back and forth), or you can sail downwind. (The wind vector in sailing replaces the gravity vector in skiing.)

So, when you’re turning, and you’re going downwind, the front of the boat will for a moment be pointing directly downwind. If you’re sailing upwind and you’re turning, the front of the boat will for a moment be pointing directly upwind. (There are all sorts of fancy words and names for the wind directions and boat directions and boat parts; I think this language is appropriately clear for my introductory purposes.)

Of course this is only relevant for turns where you’re passing through what in skiing we’d call the “fall line” of the slope. i.e., making a switchback, as opposed to just turning a few degrees but still going the same general direction w/r/t the wind. I’m not sure what the more general word for that point/line/direction. The gradient? Maybe that’s the linear algebra word but the vernacular meaning is a bit different.

Anyway, if you’re turning like this and going upwind, that’s called tacking (a word which I’ve known since I was seven!); if you’re turning like this but going downwind, that’s called jibing.

But there’s an asymmetry in tacking vs. jibing. Namely, when sail is along the axis of the boat, and the boat is pointed directly into the wind, it’s at a stable equilibrium. If the sail shifts a little bit aport or astarboard, the force of the wind will push it back to center. But when the boat is pointed directly downwind, it’s just the opposite. The sail being aligned along the axis of the boat is an unstable equilibrium. If it moves a little bit aport or astarboard, the wind will try to push it further in that direction.

(A simple animation would go really well here.)

This has a few implications.


Boats are different than cars. Not just because one of them stays on land. With cars, you can press on the gas pedal, or you can press on the brake. You have both positive and negative control. You can make the car go faster, and you can make it go slower. But with boats, you don’t have both those choices. You can only make it go faster. You can make it go faster by changing the orientation of the boat or the tightness of the sails, but there’s no way that you can actively slow the boat down. Boats don’t have brakes.

So how do you slow a boat down? Well, how would you slow a car down if it didn’t have brakes? It would slow down by itself if you just took your foot off the gas pedal, from friction. That might take a while. If you were going uphill, it would slow down faster. How often do you use the brake when driving from downtown Ithaca to Cayuga Heights? Not very often. There are plenty of stops, sure, but you just glide into those by taking your foot off the gas. You don’t bother to push down on the brake pedal. If you were driving over an arbitrary 2D surface, you would stop by turning uphill. (In practice, of course, you can’t do this, because you have to stay on the 1D road.)

But with boats, we don’t have roads. You can go wherever you like! Two dimensions of freedom! So if you want to stop, you just turn upwind. You have momentum in a certain direction, and by turning around, you zero out your momentum vector in that direction. I guess you could let your sails out, and then glide to a stop, alternatively, but turning upwind erases your momentum (all of it, if you had been running downwind before).

This is relevant especially when you need to stop in a specific place: i.e., you’re trying to dock, or you’re trying to pick up the person who just fell overboard. So the way to do that is to sort of make a J-shaped approach: approach from upwind (sailing downwind), and then hook around and turn to lose momentum and stop. If you approach from downwind, then you won’t be able to stop! You’ll be sailing upwind, and maybe you can let the sails out, but you’ll still be zooming forwards! You need to delete your momentum, and making a 180 degree turn (or close to it) is the way to do it.