Boats sailing faster than the wind

Cecil's Columns/Staff Reports
1

In this column http://www.straightdope.com/columns/read/2908/how-can-racing-yachts-sail-faster-than-the-wind , Cecil tries to explain how a boat can sail (i.e. move by wind power only) faster than the wind driving it.

This explanation might be aided by a general explanation of how a boat can sail into the wind in the first place. How does the wind push the boat into itself?

I know, it has to do with the water and the keel. But I think the explanation of how the wind pushes on the sail is necessary for understanding how the wind can push the boat faster than itself.

2

For the most part, unless you are sailing straight downwind, goose-winged, the air isn’t pushing the boat but rather pulling upon it. The airflow across the front of the sail is faster than that on the backside, causing a pressure differential that draws the bunt of the sail out and drawing the boat forward. The c.p. (center of pressure) is typically well-aft of the mast, which applies a torque that would tend to turn the boat into the wind (which would cause this force to decrease) unless counteracted by another force; in the case of a sailboat, the keel and rudder provide a balancing torque by the drag of water across them. The balance of these two forces provides the ability to orient the boat, and by trimming the sail(s) you can optimize speed in any direction.

The use of a foresail or jibsail, rather than just adding more aspect area, tends to force air across the front of the mainsail faster by creating a jetting effect, especially when close-hauled, thereby enhancing the performance of the mainsail and also providing more controllability in windward directions. Trimmed properly on a racing boat, the foresail can actually give extra torque when changing tack to prevent the lost of momentum when going across the wind (straight upwind or “in irons”), whereas its contribution in a downwind situation is modest and requires a jibing pole to extend it far enough outboard to be of any use whatsoever. Most true racing boats use a very baggy spinnaker sail (the big poofy ones that are deployed on downwind legs) to maximize the force of the wind.

Stranger

3

I’m not sure that explanation helps. Why is the airflow across the front of the sail faster than across the back?

Like the airplane wing explanation, I think a more intuitive explanation is the deflection of air.

4

The air moving faster across one side than the other creates a pressure differential. You can demonstrate this for yourself by putting a small sheet of paper on a desk, blowing over it, and watching it rise off the desk.

Unlike an airplane, in which the engines create a forward thrust that is converted to a downward thrust by deflection of air from the angle of attack of the wing and resulting reaction that gives lift, a sailboat has no self-motive force and is reliant on air flow over the wind to both draw the sail into an aerofoil and generate “lift” in a forward-ish direction. The sail doesn’t push back on the wind; it is pulled forward by the partial vacuum created by differential flow.

I’m sorry if this isn’t intuitive, but this the phenomena that occurs. Like orbital mechanics (“To slow down, you speed up; to speed up, you slow down,”), you just have to accept it for what it is.

Stranger

5

All of the responses here are really really complicated, but the “physics” is quite simple. Assuming everyone here has had 12th grade physics, we all know that every force can be resolved into its combined vectors.

If you’re looking down at a boat, and there sail is perpendicular to the wind, then the resultant force vector is a single line pushing the boat along. Note the ASCII drawing:
-------> --|–
(10 mph E wind) (sailboat being pushed east)

Thus, the wind pushes the boat along at 10mph, as already explained.
But now lets assume the wind is traveling at 45 degrees to the boat:

---- (sailboat pushed Northeast due to sail direction + wind direction)

^
|
| (10 mph N wind)
|
Now the resultant force being applied to the sail of the boat perpenducular to the direction of the sail is 14.15 mph. If you assume a frictionless surface, the boat’s going to go alot faster.

That’s when all the other complex stuff like drag and so forth comes in, since the water isn’t frictionless. But the faster the boat goes, the greater the eastward push due to wind, current velocity, minus drag (ie, the coefficient of sliding friction).

6

I think you multiplied by sqrt(2) when you should have divided by it. The total wind speed is 10 mph, which is 7.07 mph “forward” and 7.07 mpg “sideways” relative to the sail.

7

But my question was why does the air move faster across one side than the other? That’s not at all intuitive.

And maybe you don’t see it the same way, but I think the airplane wing deflecting air is the best way to explain a sail. It’s deflecting the wind towards the rear of the boat.

8

Woops. You are correct.

9

The air moves faster over the forward size because it is free to expand and detach from the sail (although in order to maintain the aerofoil shape you want it to hold until it gets to the edge) while on the back side it tends to collect in the bunt, which offers resistance and increases pressure. There is very little air deflected to the rear by the sail, especially on a beam reach; the air basically stagnates, and the boast is drawn forward by the negative pressure differential.

Stranger

10

Cecil shouldn’t have dismissed P. McCartney like that at the end of the column. I’m sure he can work it out. With a little luck.

11

But he may need a little help from some friends.

12

If there is very little air being deflected to the rear of the boat, then (necessarily) the sail is producing very little forward force. By conservation of momentum, the momentum given to the boat’s forward motion is exactly equal to the momentum of the air deflected backwards.
ETA: Similarly, if an airplane wing is not deflecting air downwards, then it’s producing zero lift.

13

I too think it seems weird. I need to trust in the physics and the reality.

{Failed Example Here}
So with a wind going north to south and the boat facing south to north, the wind blows, the sails flap, and the boat goes nowhere. With the sail tipped 40 degress, part of the wind suddenly slams into the sail and gets a headache. It slows and imparts its loss of energy to the sail, and piles up like a train wreck(higher pressure).

Meanwhile, the wind that missed the forward point of the sail goes around just past the mast. Suddenly it finds its neighbor wind is not at its side. It is lonely (and it is in a partial vacuum). It spreads out (and creates a low pressure area).

So the sail has high pressure on the wind side and low pressure on the downwind side. This is where I understand vectors but wonder how it applies here. Part of me sees the high pressure wind exerting its pressure on the sail only in the direction of the wind. Another part sees the high pressure area on one side of the sail pointing toward the low pressure area on the other side of the sail. Both seem to exert a force from high pressure (wind-side) to low pressure (downwind-side) that points downwind.

If the boat were then on a frictionless surface, wouldn’t it move downwind?

{Better Example Here}
Then I check the simulator and realize that I’ve been pointing the boat into the wind and it doesn’t matter how much I angle the sail, I still can’t sail into the wind. So I turn the rudder and point the boat 40 degrees to the wind and have the sail in line with the wind. Nothing. Then I angle the sail closer to the boat’s angle and suddenly I start moving. So I’ve got this:



\   \   \   \   \   \   \   \   \   \   \   \   
 \   \   \   <IIII((IIIIIIIII>   \   \   \   \
  \   \   \   \   \ ((    \   \   \   \   \   \
   \   \   \   \   \  ((   \   \   \   \   \   \
    \   \   \   \   \   ((  \   \   \   \   \   \

Now what’s happening? The wind hits the mast. The wind on the stern-side of the sail piles up and causes high pressure. The wind missing the mast and going around to the bow-side sees low pressure because his buddies have train wrecked on the other side of the sail. So, and this is where it’s weird, the wind packed like Coney Island in June pushes the sail to the bow of the boat! Well, a bit to the bow and a bit port (downwind).

{Question Here}
So why doesn’t the piled up wind just exert all its effort in the direction the wind was going (down and right in the picture). I think that’s the big question. Maybe it’s because it piles up and its high pressure center then points right to the center of the low pressure area. That would be left and down. Maybe that’s the Bernoulli Principle part. Can someone help on this point?

But since there is a left-and-down vector of force, the boat would move that way but the rudder/keel dampens the downward part of the vector. All that’s left is the forward part, so the boat moves.

I haven’t run any numbers so I can’t get how it can go faster than the wind. Also, that part about why the wind doesn’t just push on the sail directly downwind is puzzling.

{Simulator}
Maybe this simulator can help.

14

You persist in trying to define the physics to fit your conception, rather than deal with them as they are. The primary momentum transfer comes from “pulling” on the wind in front of the sail (by developing a partial vacuum) rather than the sail pushing at the wind that flows behind it. You can see this very clearly by looking at the reefing lines on the mainsail with the jib drawn crisply, where the ones in front are flailing around frenetically on a beam reach or higher, while in the back they’re only moving slightly.

Stranger

15

Simple airplane airfoil dynamics - you can find all sorts of explanations online, but basically wind across a convex surface has the following result…
The wind on the convex side (top of airplane wing) travels farther, hence faster - it gets to the same point after a curved path. Wind on the bottom - flat or bypassing the concave side - just travels the same speed, usually straight line. The sail captures a bit of the wind on the bottom/backside curve to keep the sail conves at the front.

A sail is a wing turned on its side. As the wind flows around it, it pulls the boat forward instead of up like a plane.

the classic experiments:

  • blowing over the top of a paper and watching the air pressure from underneath make it rise up.
    -hold a piece of paper near/below your bottom lip and blow across over top. It will rise up, even though you are not blowing UNDER it. This is the Bernoulli effect, which is how carburetors worked before fuel injection. The faster air flows, the lower the air pressure it has perpendicular to the air stream.

Why does the ship not just blow downwind in the direction of the wind? This is where keel and rudder come in handy. The keel does a job not much different than a skater on ice - it digs in and limits the movement except in the direction along the keel, where it’s thinnest and has least resistance. Fancy sailbots have pretty decent keels to ensure they don’t go off course.

So then your high-school physics vector math comes back into play. The force on the sail is roughly perpendicular to the wind, like lift on an airplane is up. There’s also the push-downwind vector (like drag on the airplane wing) but the keel handles that.

The pull perpendicular to the sail means a sailboat using the wing effect will be most efficient at about 90 degrees to the wind. However, sometimes you want to go into the wind. Then, you turn a bit into the wind depending onhow efficient the sail is. The perpendicular force of the sail translates into a vector along the keel - which moves the boat forward - and a 90-degree perpendicular vector force pushing the boat sideways, which the keel controls.

Fine tuning the balance between keel effectiveness against sideways drift, sail efficiency, hull shape efficiency, etc. - that’s why the Americas Cup yatch designers are masters and work in secrecy.

IANAS (I am not a sailor) but iIRC I have heard that good sailboats will do 45 degrees into the wind. To go upwind, you tack (aahrr, matey!) By zig-zagging back and forth against the wind. As mentioned in the previous posts, you need the momentum of the ship to allow you to turn about from the wind coming at you from 45deg left to 45d right or vice versa. That’s also when the boom swings over to catch the wind the other way (reversible!!) thus providing many comedic moments in cinematic history.

16

This is where you’ve gone off the rails. An airplane doesn’t generate all it’s lift from deflection. Most off the lift comes from the airfoil effect due to the curvature of the wing. In other words, an airplane wing is pulled upwards rather than pushed, in the same way that a sail is. Searching for ‘lift’ and/or ‘airfoil’ will provide better explanations.

17

This sounds a lot like the old explanation that the air above and below the airplane’s wing want to rejoin at the trailing edge, and the path over the top is longer, therefore the air above must travel faster. This is wrong: there is no reason why the two flows should rejoin and in fact the air flowing over the top essentially always reaches the trailing edge sooner.

18

Newton insists (correctly) that you can’t have a one-way force. If the wing is being pushed in one direction (e.g. up) then air is necessarily being pushed in the other (e.g. down). Same story with the sail.

19

I just wanted to note that (a) the explanation by “Stranger on a Train” (above) confirming that the wind is rather pulling the sailboat is easier to conceptualize, for me. However, if true, (b) aren’t we also saying that an airplane would prefer a headwind to a tailwind? Or, ideally, a headwind at 45 degrees across the nose??? Surely, it is known from personal flying experience a tailwind is best, true?

20

To answer your comments, doesn’t a free body diagram on an airplane wing show that the lift (Fl) and weight (Fg = mg) are the equal and opposite forces to which you refer?

Also, regarding your previous comment about the top air rushing to meet the bottom air divided by an airplane wing: If this did not happen, wouldn’t there be a vacuum? Having studied airflow profiles in general applications, perhaps the simplest explanation for the layman represents the ideal case with 100% perfect air match-up, so to speak, at the trailing edge (i.e., perfectly laminar). However, I would say there could be some tolerance for inefficiency here and achieve flight - almost in keeping with the layman description. We know flying in a plane’s wake is a bad idea. I am no expert, but isn’t it possible the air off the trailing edge exhibits (what’s it called?) “Street Turbulence”, I think, is the exact term? i.e., a form of turbulent air with small air pockets (that are unsustained). If correct, it may be because of what you say - the story presented to the public may be oversimplified.

I’ll see if I can find out more about airflow at the trailing edge of a wing. If I learn something of interest, I’ll repost here to share. I’ll check some Fluids books. I know they have sketches of airflow profiles across different airfoils…