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Why is beam reach (or near to it) the fastest point of sail?

59K views 65 replies 23 participants last post by  roverhi 
#1 ·
Hi,

I'm new to sailing and I'm trying to understand a little more about sailing theory.

Does anyone here know of a resource that explains exactly why the fastest point of sail for most boats is the beam reach (or close to it)? When I search on google I can find hundreds of site that state it as a fact, but I haven't found any that explain the reasons, preferably with vector diagrams.

I always find things easier to put into practice once I understand why I'm doing them....

Thanks,
 
#2 ·
Can't draw a diagram here, but I will take a crack.

To start, if you are sailing directly downwind, the faster you go, the lower the apparant wind on your sails. You are out running the wind. So far, so good? The faster you go, the less you have to work with heading downwind.

If you sail upwind, you actually create more wind to work with (increased apparent wind), because you compound the wind as you begin to move into it.

Therefore, it stands to reason that you will get more boat speed sailing into the wind, then away from it. Boy, there are exceptions to that, but let's stay simple.

So why a difference in close hauled and a beam reach? A beam reach remains the lowest point of sail, where you are still being pulled by the lift of the sail, rather than being pushed from behind. Therefore, you may still be creating some increase in apparent wind.

Now the vector part. If you thnk about where the boom is on a close haul vs. a beam reach, this may begin to make sense. Since you are creating a wing with your sail, the boom is much closer to the center of the boat on a close haul, as the wind is coming more directly at our bow. On a beam reach, your boom is eased out so the front of the wing (sail) is facing the wind coming from the side.

For illustrative purposes, imagine that the lift coming off the sail is heading perpendicular to the front of the boom. In a close haul, with the boom in tight, that lift is predominantly pointed off the side of the boat. You don't move sideways, because your keel or centerboard fights the sideways vector, leaving only forward motion. It's like pressing down on marble, but it squirts out from under your thumb. The vector of pressure is toward the table, but the table keeps it from moving in the direction of the pressure and it escapes to the side of least resistance. Your sails are the thumb and your keel is the table.

On a beam reach, the boom is eased out a bit further, so the vector is pointed more forward. The keel fights less, the boat heels less due to less sideward vector and there is more power remaining for forward motion. Sort of like your finger not pressing that marble directly into the table, but at a better angle toward the direction you want it to go.

Hope that wasn't too rudimentary...... or completely confusing. :). Thumbs, marbles and tables, what the heck?
 
#54 ·
To start, if you are sailing directly downwind, the faster you go, the lower the apparant wind on your sails. You are out running the wind. So far, so good? The faster you go, the less you have to work with heading downwind.
This is correct from a boat point of view. In reality of course, energy from the wind is being transferred to the boat and then bled off in hull drag. But, yes, from the sailor's point of view, the wind dies off as you accelerate downwind. There is less push on the sails and rigging. Naturally though, the rudder will still have good authority because you are moving. It's interesting that this is why a jibe is such a trap. You are heading downwind and the apparent wind seems very light, not any cause for worry. But if you veer off then the apparent wind speed picks up and hits your sails with unexpected force. You suddenly have your hands full.

If you sail upwind, you actually create more wind to work with (increased apparent wind), because you compound the wind as you begin to move into it.
Well, again, from a boat centered point of view this is correct. The increased wind will push harder on the sails and rigging. There will appear to be more energy available to drive the boat forward.

Therefore, it stands to reason that you will get more boat speed sailing into the wind, then away from it.
Yes, indeed, IF (and this is a big if) the apparent wind angle stayed the same.

So why a difference in close hauled and a beam reach? A beam reach remains the lowest point of sail, where you are still being pulled by the lift of the sail, rather than being pushed from behind. Therefore, you may still be creating some increase in apparent wind.

Now the vector part. If you thnk about where the boom is on a close haul vs. a beam reach, this may begin to make sense. Since you are creating a wing with your sail, the boom is much closer to the center of the boat on a close haul, as the wind is coming more directly at our bow. On a beam reach, your boom is eased out so the front of the wing (sail) is facing the wind coming from the side.
I think what you are saying is something like the following. If the boat were stationary and facing perpendicular to the wind then the wind would be coming directly over the side of the boat. And, in this position, 100% of lift from the sail would be used to push the boat forward. Here we have maximum potential (but of course the boat isn't moving yet).

As the boat begins to accelerate forward, the apparent wind will increase and this would theoretically give additional lift to the sail. And, it would if the wind angle stayed the same. However, it doesn't. As the boat accelerates the apparent wind will come more and more from the bow. It will shift forward. And, the apparent wind will shift more forward the faster the boat goes. This is bad because, as the wind shifts forward, it becomes less useful. Why? Because lift is perpendicular to the wind and therefore as it shifts forward an increasing amount of the apparent wind would only generate side force rather than forward propulsion. Also, the increasing side force will have to be countered by the keel and rudder so this will increase drag.

So, why is close hauled worse? As you pull towards the wind the apparent wind vector shifts even more towards the bow, so even though theoretically the apparent wind would increase, there is less and less lift to move the boat forward. More and more of the wind's energy simply goes to pushing the boat sideways which would result in more heel and more leeway but not more forward motion.

I think this is what you were saying and I agree. However, even though I tried to say it as simply as possible I still ended up with three fairly complex paragraphs. And without benefit of diagrams this can still be misinterpreted. I think this thread has included a lot of saying the same thing in different ways.
 
#3 ·
Minne is exactly right, but let me simplify it even further-

The beam reach is (usually) the point of sail that generates the most lift in the best direction or point of effort.

That was an intelligent question and I think you're off to a good start.
 
#4 ·
Simplistic answer. Think of a tidly wink; the boat is stuck between the force of the wind and the mass of the water. Squirting out to the side is fastest, though the exact angle depends on the sails set and the boat.

Full answer. Read a technical book on sailing, such as "Performance Sailing". Study engineering. Google isn't for long answers, and real understanding won't come in a few sentences.

Sorry.
 
#5 ·
If you are interested in looking deeper, then Magazine Articles is a good source. Although it is 40 years old, it shows that most school text books are even older. It explodes the myths about pressure differentials either side of the sail caused by different flow path lengths that most instructors propagate.

A beam reach is quickest because it is the point where you are still getting lift as well as push (draw yourself a small wind diagram and the vectors on the sail to convince yourself) and reduced resistance from component of the vector for windage from the boat's profile facing the wind in the direction of travel.

Hope that helps. The other answers are also correct and contain an element of simplification (as does my answer) but should all help your understanding of what is going on. Next stop is understanding how sail shape affects this question as well as the point of sail.
 
#7 ·
Minne you might have it but indulge me for a second while I try also.

"If you sail upwind, you actually create more wind to work with (increased apparent wind), because you compound the wind as you begin to move into it."

This is a common way to describe the process but I absolutely hate it. This should make every physics teacher cringe. Yes the boat creates wind when it moves forward but the wind it creates is entirely in the WRONG direction. This 'new wind' can't be harnessed for forward motion any more than pulling on your own bootstraps can be.

The best way to describe the ability of a boat to move faster than the wind is leverage.

Think about this just like doing calculations on prop pitch (inches per revolution). Given a pitch of a prop you can calculate, theoretically how far forward the boat should move for every revolution. So lets do the same exact thing for the sails of the boat except revolutions are replaced by how much the wind moves.

Picture the wind as some stiffer fluid that's determined to move forward and your boat as being friction less and only able to move straight forward back. Lets say the wind is coming from 90 degrees off starboard and your sail is trimmed to 45 degrees. Clearly the ratio is 1:1, if the wind moves 10 ft across your boat you'll move 10ft forward. Now imagine that you pull the sail in a bit, say to 50 degrees (with 90 being all the way in). Now the ratio is 1.2:1. You'll move forward 12ft for every 10 that the wind moves. The pitch of your sails could be said to be 1.2:1.

Theoretically you can pull your sail in to 89.999 degrees at which point for the wind to move 10ft you'll have to move almost infinity! (in our made up environment).

The vector math still works fine here. Lets go back to the 45 degree example with wind at 10knots . If you really did this what would happen is your boat would start moving forward creating wind off the bow. This would add into the wind coming from starboard. As this happens the apparent wind increases, but also changes direction so it's coming more and more from the bow. When it approaches 45 degrees, the angle of your sails, your sails will luff and you'll stop accelerating. In this example, with your sails at 45 degrees this would be exactly 10 knots forward speed (14 knots aparent), which is exactly what the 'leverage' example came to.

The point is that the 'new wind', the wind that you created, only hurt you because obviously this new wind is the wrong direction! Also note that there is no need for the concept of lift here. Personally I find lift to be extra confusing.

More broadly, sails on a boat can leverage only the wind that's coming from the sides. Any wind coming from the bow or the stern simply pushes or drags the boat in a simplistic fashion. But any wind coming from the sides can be leveraged and can theoretically be leveraged to infinity. The reason a broad reach is the best point of sail is because on a broad reach all the wind is coming from the side and all of it can be leveraged by the sails.
 
#8 ·
asdf: can you explain, without referring to lift, how camber and draft affect the sail's drive?

Why is it that increasing draft powers up a sail? Since increasing draft also decreases the angle of attack, in your model this should result in less leverage and therefore less drive.

Theoretically you can pull your sail in to 89.999 degrees at which point for the wind to move 10ft you'll have to move almost infinity! (in our made up environment).
I think this is pretty good evidence that your theory is not a good description of reality. Clearly the limiting forward component of the drive of the sails does not increase without bound as the boom approaches the centerline, and it has nothing to do with friction.

So here's my answer to the OP:

Recall that lift is defined as the component of the force exerted on a body by a fluid flowing around that body, in the direction perpendicular to the direction of distant upstream flow. Drag is the component in the parallel direction.

For example, with the wind a 45° off the port bow, the lift pushes the boat 45° to starboard, and drag pushes the boat 45° aft of the beam. Lift and drag are both contributing to leeway here. If you make your sails more efficient, increasing lift and decreasing drag, your keel is still resisting both of those; if drag was initially greater than lift, you might even be making more work for the keel.

With the wind abeam, the lift vector points straight ahead; the keel is only resisting drag now. If you maximize the lift-to-drag ratio, you're maximizing forward drive and minimizing the work your keel has to do to resist leeway. Also, there is no component of the wind that resists the forward motion of the vessel; drag is a purely lateral force and lift is a purely forward force.

With the wind abaft the beam, lift is reduced, but lift and drag are both contributing to forward acceleration. My understanding is that the fastest point of sail is not a true beam reach on most vessels, but rather a point somewhat aft beam.

This model ignores the keel, of course. The keel also generates lift and drag forces, and as long as the boat is making any leeway, some of the lift will be forward. It's less clear to me where this contribution is maximized, since it's not clear to me how the different factors (drive from the sails? windage? anything else?) contribute to leeway; maybe somebody else can weigh in on this aspect.
 
#9 ·
asdf: can you explain, without referring to lift, how camber and draft affect the sail's drive?

Why is it that increasing draft powers up a sail? Since increasing draft also decreases the angle of attack, in your model this should result in less leverage and therefore less drive.
No I can't! And that's part of my point. The aerodynamic effects of sail shape and lift are all secondary to what I'm describing just as propeller shape and hydrodynamics are secondary to the simple principle that the blades of the propeller are at an angle to the direction they are spinning! The ratio of that angle defines the basic behavior of the propeller. It's intuitive that while in theory the propeller can drive the boat to infinity the reality os obviously much different.

I think this is pretty good evidence that your theory is not a good description of reality. Clearly the limiting forward component of the drive of the sails does not increase without bound as the boom approaches the centerline, and it has nothing to do with friction.
Limiting forward component of the drive of the sails? I don't know what you mean.

But let's agree on one thing. When the apparent wind is in-line with the sails, the sails luff. This is true when you're in irons and it's true on any point of sail if you let it happen. As you increase speed the angle of wind changes to be coming from farther and farther forward. You're only option is to keep drawing in your sails. For any given angle of sail the maximum possible speed you can go is defined by the ratio, just like pitch on the propeller.

This is the be-all-end-all limit for any sailboat speed regardless of lift, sail type or any other factor. Because when this speed is reached the sails will luff and if it's exceeded they will backwind.

But we agree you'll never hit this speed. As your speed increases both the drag from the water and the drag from the wind will increase (because the 'new wind' is in the WRONG direction). At some point this drag equals the forward propulsion you're able to get from your sails and you stop accelerating and reach a steady state.

None of the sail lift or keel lift needs to be discussed to understand the basic dynamics here! The point of the keel is make it so the boat can only move forward or backwards and not sideways. Think about an iceboat with a flat steel sail - no airfoil, no hydrodynamics on the keel. Just a piece of metal to deflect the wind and blades in the ice to keep the boat moving forward or backwards only. It still sails and still sails with the principles of a sailboat.
 
#10 ·
Limiting forward component of the drive of the sails? I don't know what you mean.
I mean that as the boom gets closer and closer to the centerline, the forward drive from the sails does not increase to infinity as your model predicts.

[quote[But let's agree on one thing. When the apparent wind is in-line with the sails, the sails luff.[/quote]

Depending on what you mean by "in line", I'm not sure I agree. But whatever, I agree that there's some point near "in-line" at which the sails luff.

As you increase speed the angle of wind changes to be coming from farther and farther forward. You're only option is to keep drawing in your sails. For any given angle of sail the maximum possible speed you can go is defined by the ratio, just like pitch on the propeller.
Can you give a formula for the way in which maximum speed you can go is defined by the ratio? And the ratio of what to what? length of boom / distance from boom to centerline?

None of the sail lift or keel lift needs to be discussed to understand the basic dynamics here!
They absolutely need to be discussed. Here's the limits you've mentioned:

1) Ignoring drag, there's no limit. Put your boom on the centerline; your boat will travel at infinite speed. Maximum of speed is based only on the angle the boom makes with the wind.

2) Obviously we can't ignore drag. So drag puts a limit.

All of your dynamical discussions and your analogies to propellers are only interesting in the discussion of point 1. You don't actually state a speed limit due to drag; you just state that there must be point where drag balances forward drive. Your source for this forward drive is the leverage effect which, according to point 1, can be made arbitrarily large.

If you want to talk about drag, you have to talk about lift as well. Lift and drag are two components of the force that the wind applies to the boat.

I get what you're trying to do; you're trying to talk about the kinematics of sailing without talking about the mechanics. That is, you're trying to describe the motions (wind moves across sails, sails move in relation to the wind) without discussing the underlying mechanism that causes that motion. That's a valid thing to do, but your kinematics are completely wrong. Your kinematic statement is "speed is determined by this ratio", which is clearly not true, and then you get around the obvious flaw in the kinematic description by referring to a mechanical one.

My point is not that your understanding of drag is wrong, but that the formula you give for speed in the absence of drag, and the analogy that it's motivates it, are useless. Since the "ratio" rule doesn't describe anything we observe, why use it at all?
 
#17 ·
I mean that as the boom gets closer and closer to the centerline, the forward drive from the sails does not increase to infinity as your model predicts.

Depending on what you mean by "in line", I'm not sure I agree. But whatever, I agree that there's some point near "in-line" at which the sails luff.
Inline means that if the wind is moving paralel to the sail then the sail must luff and the boat can't accelerate.

Can you give a formula for the way in which maximum speed you can go is defined by the ratio? And the ratio of what to what? length of boom / distance from boom to centerline?
Just like pitch on a propeller, look more closely at how that's defined and you may understand what I'm saying. Technically it's the Tangent of the angle of the sail given that 90 is close hauled (tan=infinity), and 0 when the sails are let all the way out (hitting the spreaders perpendicular to the centerline).

Perhaps it wasn't useful to bring this up but this forms the upper bound on speed. The point is that only wind coming off the side of the boat can be leveraged in this fashion and on a beam reach (or close to it) the coponenet of wind in this direction is maximized. This is more technical than necessary.
They absolutely need to be discussed. Here's the limits you've mentioned:

1) Ignoring drag, there's no limit. Put your boom on the centerline; your boat will travel at infinite speed. Maximum of speed is based only on the angle the boom makes with the wind.

2) Obviously we can't ignore drag. So drag puts a limit.

All of your dynamical discussions and your analogies to propellers are only interesting in the discussion of point 1. You don't actually state a speed limit due to drag; you just state that there must be point where drag balances forward drive. Your source for this forward drive is the leverage effect which, according to point 1, can be made arbitrarily large.

If you want to talk about drag, you have to talk about lift as well. Lift and drag are two components of the force that the wind applies to the boat.

I get what you're trying to do; you're trying to talk about the kinematics of sailing without talking about the mechanics. That is, you're trying to describe the motions (wind moves across sails, sails move in relation to the wind) without discussing the underlying mechanism that causes that motion. That's a valid thing to do, but your kinematics are completely wrong. Your kinematic statement is "speed is determined by this ratio", which is clearly not true, and then you get around the obvious flaw in the kinematic description by referring to a mechanical one.

My point is not that your understanding of drag is wrong, but that the formula you give for speed in the absence of drag, and the analogy that it's motivates it, are useless. Since the "ratio" rule doesn't describe anything we observe, why use it at all?
[/quote]

No. I'm trying to describe the simplest way to understand the mechanics for why a boat moves forward when wind hits it (the sail is at an angle to the wind, the wind hits it and deflects backwards, the keel prevents the boat from moving sideways and the boat has to go forward). You ignored my example of the iceboat with the steel sail which strips the mechanics of sailing down to the basics, removes lift (in the sense that there are no foils, perhaps you will still use term), and yet we still have a vessel that we both agree will move (I think).
 
#12 ·
Such is often the OP's fate. That said, it's good to consider what lessons the OP can take from the discussion. After all, he's asking "why?", not, "What's the fastest point of sail?" If he's asking why, then maybe he's in a position to benefit from some understanding of the mechanics of sail trim.
 
#14 ·
the wright brothers are spinning in their graves.

as a graduate aerodymanicist it seems many sailors think my education took half an hour. no two things can complicate aerodynamics more than low speed and three dimesionality, and sailng has both. leave the junior high school diagrams alone and learn the wind and your sails. the reason s boat sails fatest on a broad reach are many and very complex - just believe and enjoy. i never think about aerodynamics when i sail or fly.
 
#19 ·
the wright brothers are spinning in their graves.

as a graduate aerodymanicist it seems many sailors think my education took half an hour. no two things can complicate aerodynamics more than low speed and three dimesionality, and sailng has both. leave the junior high school diagrams alone and learn the wind and your sails. the reason s boat sails fatest on a broad reach are many and very complex - just believe and enjoy. i never think about aerodynamics when i sail or fly.
No, but none of your degree needs to be applied, in my oppinion, to explain why a sailboat moves forward. For racers trying to maximize speed and tweak sail shape? You need a PHD in fluid dynamics for that.
 
#15 ·
It puzzled me at first, and still does.

I understand that it is possible to drop more pressure across the sail surface by accelerating the airflow across the leeward side than by (downwind) using the sail as a barn door and so decelerating the air past the sail barrier rather than accelerating it across a curved surface.

It is facinating to know that my ship is fastest when the apparent wind is slightly ahead of me. It can get a bit wet sometimes in deep water as those waves tend to be wet when they hit. Downwind, broad reaching, things are easier.
.
 
#16 ·
I understand that it is possible to drop more pressure across the sail surface by accelerating the airflow across the leeward side
That's what I had always understood as well. However, do you know about Arvel Gentry's ideas? He says that the slot effect actually decelerates airflow on the forward lee side of the main, and that this reduces the pressure gradient and thereby reduces separation of flow.

He bases this on actually measuring flow rather than the guessing that he accuses previous researchers of doing. Hm!

See Magazine Articles, especially "Another look at the slot effect".
 
#18 ·
Wow, my question generated some great responses, thanks everyone.

I wish I could have contributed, but I was suddenly invited out sailing, so I took that option instead :)

In any case, between all your answers I certainly understand better what's happening now. I also happened to stumble across another reference to "Performance Sailing" so I've ordered a copy for my amusement.

mortyd - I fully agree with what your saying. No amout of theory alone will make me a better sailer, for that I need to spend time in a boat. Nevertheless, I find the theory interesting and having a better understanding of the physics of what's happening can't do me any harm. It's the engineer in me.
 
#22 ·
I just thought it was because on a beam reach, you have both the "pull" of upwind work, and the "push" of downwind work.

So therefore better than either one by itself. Plus you're parallel to the seas.


The discussion reminds me of the story of the young kid, who asks, "mom, where did I come from?" Mom gives him "the talk", in all its scientific detail.

Kid says, "Oh. Billy says he came from Pittsburgh, I wanted to know where I came from".


It's fastest 'cause it's fastest. At least for displacement hulls. If you can get planing, then a broad reach. Please don't ask why ;-)
 
#26 ·
I've witnessed similar debates over the reason an aircraft wing works. Is it the pressure being applied to the underside of the wing, or the reduced pressure on the upper side that is causing lift?

Well, it seems to me that it is both.

Lift is simply a force applied perpendicular to the wing. The chicken and egg isn't relevant. Is it the pressure being applied below or the relative lower pressure above? Is it equal and opposite reaction of an applied force? It's all still defined as lift.

Regardless of how you explain why it happens, it's ultimately the differential in pressure that causes it to move. On the flat blade ice boat (trivial point.... all ice boats I've seen had a real sail), the pressure must be applied to the underside. However, that doesn't change what's happening on the upper side, it's just inefficient. Add sail/wing shape and improve efficiency. This seems to have as much to do with improving laminar flow over the top of the wing, as it does capturing pressure/wind underneath.

You get the most efficiency when the tell tales on both sides of our sails/wings are flowing straight back. Lift is both.
 
#29 · (Edited)
I've witnessed similar debates over the reason an aircraft wing works. Is it the pressure being applied to the underside of the wing, or the reduced pressure on the upper side that is causing lift?

Well, it seems to me that it is both.

Lift is simply a force applied perpendicular to the wing. The chicken and egg isn't relevant. Is it the pressure being applied below or the relative lower pressure above? Is it equal and opposite reaction of an applied force? It's all still defined as lift.

Regardless of how you explain why it happens, it's ultimately the differential in pressure that causes it to move. On the flat blade ice boat (trivial point.... all ice boats I've seen had a real sail), the pressure must be applied to the underside. However, that doesn't change what's happening on the upper side, it's just inefficient. Add sail/wing shape and improve efficiency. This seems to have as much to do with improving laminar flow over the top of the wing, as it does capturing pressure/wind underneath.

You get the most efficiency when the tell tales on both sides of our sails/wings are flowing straight back. Lift is both.
Yeah that's the basics of an airfoil as I understand them as well. I agree with all of this. Yes you can describe any hydrodynamic or aerodynamic force as being due to a pressure difference and that's one way of describing a simple metal sail at an angle to the wind. I just wouldn't chose to describe that with the term lift, just as I wouldn't use lift to describe a propeller or a fan blade which work on similar principles. They hit the air/water at an angle and push it forward. Every kid whose stuck their hand out the window on the highway and 'flew' it by tilting it forward and back to move up and down understands this principle as well. Hence the fact that I think it's an easier principle to explain and can go further towards producing an understanding than "lift".

Also, just to be clear, planes don't need the airfoil to fly. As you say with the flat metal sail, a plane wing could skip the airfoil and it could still fly. It would fly by creating an angle between it's wings and the ground such that as it flew forward it was deflecting air down just like a fan blade. This is how many simple balsa wood model planes fly, and you can see them flying with the back end lower than the front as they drag through the air.

Gosh, isn't it fun when someone oversimplifies an issue in an attempt to illustrate a point, then gets called out on their ovsimplification and spends pages and pages trying either to defend their original oversimplification or to prove that they do really know what they are talking about but that they were only trying to make it understandable to the Newb.........
Honestly I think part of the reason lift works as an explanation is because people vaguely know what it is but don't understand it well enough to ask any more follow up questions. And saying "a component of the forward propulsion of a boat is lift. Lift is maximized on a reach, therefore the boat goes fastest on a reach" is still entirely lacking quantification of the force of the 'lift'. Compared to going downwind why is the lift component gained on a reach more powerful than the simple "push from behind" component that exists running down wind. No one here has answered that including myself except I was able to explain one thing with my model that lift, without being quantified cannot - why a boat could travel faster than the wind.
 
#27 ·
Gosh, isn't it fun when someone oversimplifies an issue in an attempt to illustrate a point, then gets called out on their ovsimplification and spends pages and pages trying either to defend their original oversimplification or to prove that they do really know what they are talking about but that they were only trying to make it understandable to the Newb.........

May I ask a slightly different question but along similar lines to the OP?

What are the major factors that cause the differences in the polars for different boats? Sme seem to have maximum speed closer than a beam reach and others seem to have maximum slightly broader than a beam reach.

I am assuming that all polars are presented for the true, rather than the apparent, wind. Is that right and would that account for part of the difference - because a high performance boat will pull the apparent wind further back when on a beam reach than a more sluggish performer?
 
#38 ·
What are the major factors that cause the differences in the polars for different boats? Sme seem to have maximum speed closer than a beam reach and others seem to have maximum slightly broader than a beam reach.

I am assuming that all polars are presented for the true, rather than the apparent, wind. Is that right and would that account for part of the difference - because a high performance boat will pull the apparent wind further back when on a beam reach than a more sluggish performer?
No, this isn't related to relative wind. It's related to keel efficiency. A less efficient keel will reach maximum hull speed on a slight broad reach rather than a beam reach (because there is a bit less load on the keel).
 
#28 ·
AFAIK, apparent wind always moves forward on all boats.

A stab at your question (read guess) are the variety of differences in center of effort vs center of lateral resistance (keel design, mast placement, etc). There comes a point where, even if a given boat can make more power with her sails, that center of effort may not be well aligned with her center of LR and the compensating rudder slows you back down. I assume that sweet spot can't be maintained across every point of sail, so some boats find it in a slightly different place.

Well outside my bounds here, but curious if others agree.
 
#30 ·
asdf38 :

Compared to going downwind why is the lift component gained on a reach more powerful than the simple "push from behind" component that exists running down wind. No one here has answered that including myself except I was able to explain one thing with my model that lift, without being quantified cannot - why a boat could travel faster than the wind.

You have got more forward propulsive force on a reach because you drop more pressure by accelerating the air around the leeward side of that curved sail aerofoil.

When running downwind, you don't drop as much pressure. The air spills round the sail and eddies on its leeward side, and far more of the pressure is recovered on the leeward side. The net result is that there is less of a pressure difference across the sail when running downwind.

Also, when going upwind, your relative wind velocity is improving with boat speed (the relative wind angle will shift forward too). Of the wind, the reverse arguments apply.

Someting like that, anyway.
 
#35 ·
Wow, I should have checked in an hour ago.

Okay, so, brief comments on a variety of responses so far:

Luffing when wind "in line": I'm pretty sure the wind is "in line" with the luff of my sail when the telltales stream evenly aft on both sides. The sail isn't luffing because it's curved. The curve is maintained by the angled pull of the sheet.

Lift: perpendicular to freestream flow, not to the foil. Minor point; you could break down the force of the wind into any components you like, but only one is referred to as "lift" in the textbooks.

Acceleration on the lee side: my understanding is that faster flow separates sooner, which greatly increases drag, and that therefore you actually want to decelerate flow on the leeward side (while still keeping it faster than the windward flow), and that this is in fact how the slot effect works.

asdf38 said:
(paraphrased) The lift model lacks in quantification
No, that's patently false. Lift is given by a integral of forces over the surface of the sail. It's not especially useful for internet forum discussions, but it's there.

So yes, your "propeller pitch" model has an easy quantification --- which, as I keep complaining, is horribly wrong, because it predicts infinite speeds. Oh, except that you add drag, which you don't quantify. So your model either predicts infinite speeds, or is not quantitative, depending on which features you include :p

Here is a new point - think about how neat it would be if you could sail off apparent wind.
But, you do sail off apparent wind. If the apparent wind is in a direction that permits sailing, that is. Same goes for true wind.
 
#43 ·
Wow, I should have checked in an hour ago.

Okay, so, brief comments on a variety of responses so far:

Luffing when wind "in line": I'm pretty sure the wind is "in line" with the luff of my sail when the telltales stream evenly aft on both sides. The sail isn't luffing because it's curved. The curve is maintained by the angled pull of the sheet.
I said the boom/sail. Again the sail is only curved because wind is pushing it more to one side than the other. This is because the boom is at an angle to the wind. If the boom is inline with the wind the sails must luff.

Lift: perpendicular to freestream flow, not to the foil. Minor point; you could break down the force of the wind into any components you like, but only one is referred to as "lift" in the textbooks.

Acceleration on the lee side: my understanding is that faster flow separates sooner, which greatly increases drag, and that therefore you actually want to decelerate flow on the leeward side (while still keeping it faster than the windward flow), and that this is in fact how the slot effect works.

No, that's patently false. Lift is given by a integral of forces over the surface of the sail. It's not especially useful for internet forum discussions, but it's there.
That's not a quantification it's a trivial definition. Of course sum (integral) of the perpendicular forces over the sail tells you the lift. That doesn't help quantify the strength of this force relative to any other. It just defines how we'd find it.

So yes, your "propeller pitch" model has an easy quantification --- which, as I keep complaining, is horribly wrong, because it predicts infinite speeds. Oh, except that you add drag, which you don't quantify. So your model either predicts infinite speeds, or is not quantitative, depending on which features you include :p
Obviously the force is related to wind speed and sail size as well as how efficiently the sail is positioned. The force is not infinite but the mechanics of how the force is generated allow speed to theoretically hit infinity. A friction-less boat could reach infinite speed. Are you saying it can't? I think the "propeller pitch" or wind deflection model is the easiest way to explain this. Lift remains for most an imprecise term that doesn't contain the boundaries for what a sailboat can do.

For example why can't a sailboat sail into the wind? My explaination is that a boat sails when wind hits the sails and get's deflected. Well when it's pointed into the wind there is no wind to deflect and this is totally clear on a simple diagram.

On the other hand lift is less concrete. Why can't the sail generate lift when the wind is flowing straight over it when a boat is in irons someone might ask. Even you had trouble allowing that a sail will luff in this situation. However I'll admit this is my own opinion of the relative simplicity of these two models.

But, you do sail off apparent wind. If the apparent wind is in a direction that permits sailing, that is. Same goes for true wind.
I don't deny this but I don't think it's an effective way of explaining it. Once you allow for the fact that you're sailing off aparent wind, "A sailboat makes it own wind" is a phrase I've seen, you open yourself up to the kinds of mistakes that brehm62 points out. It becomes all to easy to get confused.
 
#39 ·
asdf38 and Adamlein. I keep wondering if you two are trying to say the same thing in a different way.

In an aerodynamic sense the sail only sees the relative wind. That is, everything that the sail does is related to relative wind, not true wind. This seems to be what Adam is saying.

However, in a motion sense, you can only get propulsive energy from the true wind, not the relative wind. In other words, the amount of energy available will remain constant if the wind speed remains constant. There is no change in the amount of energy available regardless of motion (although a naive assumption might be that as relative wind increases so too would the available wind energy) This seems to be what asf is saying.
 
#40 ·
However, in a motion sense, you can only get propulsive energy from the true wind, not the relative wind. In other words, the amount of energy available will remain constant if the wind speed remains constant. There is no change in the amount of energy available regardless of motion (although a naive assumption might be that as relative wind increases so too would the available wind energy) This seems to be what asf is saying.
I know I'm being a little hair-triggery and a little pedantic here. Actually I think it's an interesting question. I'd suggest that you can accelerate (gain kinetic energy) whenever the apparent wind is suitable (i.e. coming from a certain range of directions, and of a sufficient speed). If there's a 5 kt current, for example, setting due west, and your boat is pointed north and at rest relative to the current, she will experience a 5 kt beam wind that she can sail on. So, there's no true wind, but acceleration is still possible.

True wind is important for considering sailing in places your boat isn't in. It's also important for considering the implications of wind against current. But I'm confident that it is irrelevant for figuring out how much energy your boat can get from the wind (irrelevant in the sense that apparent wind tells you everything that you need to know, whereas true wind doesn't).

It's actually neither [low pressure above nor high pressure below]. An airplane wing gives lift because it deflects the wind stream downwards. While an aircraft is traveling, it constantly accelerates a certain mass of air downwards each second. Acceleration x mass = force.
And force x area = pressure. There absolutely is a pressure gradient across the wing and it absolutely does generate lift.

You are just discussing lift from the microscopic viewpoint, i.e., there are some particles with momenta and they transfer momentum from one to another when they interact. You're absolutely right, that is *all* that is going on, and there are no other effects that need to be considered.

However, it turns out that that's way more information than is really necessary or practical for actually calculating lift under a given set of conditions. If it were just air molecules bouncing of the airfoil, it wouldn't be okay, but it isn't... it's air molecules bouncing off the airfoil and off other air molecules. The airfoil gets momentum transferred to it from air that's still pretty far away. So instead of trying to work that into the equations, we take a macroscopic view of things and talk in terms of pressure. You can solve for the pressure field in a steady fluid flow around an airfoil, and then add up the pressures on the airfoil surface, to get lift.

So while your momentum-only description is valid, its best use is in deriving equations that tell us pressure at every point in the fluid.
 
#49 ·
Downwind with spinnaker can allow you to exceed wind speed
Yes, if you are using an asymmetric spinnaker on a broad run. If you are using a symmetric spinnaker running dead downwind then, no.

Of course, if the wind is not constant then whenever the wind drops you would still briefly be moving faster than the wind.
 
#48 · (Edited)
Let me see if I can explain this.
Wind Power = 1/2 * Rho * Velocity^3 * Area

Rho is the density of air which is about 0.0807 lbs / cubic ft.
If we are using cubic feet then we need Velocity in feet also.
Let's say the wind is blowing 6 knots.
That is about 6.87 mph or 10.08 feet / sec.
Let's just round that down to 10 ft/sec.
Let's say we have 200 square feet of sail area.

Okay: 1/2 * 0.0807 lbs / ft^3 * (10 ft/sec)^3 * 200 ft^2
0.04035 lbs / ft^3 * 1000 ft^3/sec^3 * 200 ft^2
8,070 lbs (ft^3 / ft^3) * ft^2/sec^3
8,070 lbs ft^2/sec^3
Now we have to divide by gravity which is 32 ft/sec^2
8,070 lbs ft^2/sec^3 / 32 ft/sec^2
252.1875 lbs (ft^2/ft) /(sec^3 *sec^2)
252.1875 lbs ft /sec
1 Horsepower is 550 ft lbs /sec so this is a little less than half a horsepower
0.46 HP
This is all we have to power the boat; there isn't any other source. Will we get more than this if the boat is moving? No. This is all there is.

But ... (someone might protest) HP doesn't move the boat, force does. Well, this is true. So, would it be possible to get unlimited force from a fixed amount of HP? No. The amount of force available is dependent on the speed of the boat. Let's say we sail 10 ft per second perpendicular to the wind.

252.1875 lbs ft/sec / 10 ft/sec
= 25.21875 lbs of force
If we sail faster we get less force, not more.
This is all boilerplate physics and engineering. There is no way to get around this.

Could we go faster than 10 ft per second? Yes, if the total hull drag is less than 25 lbs of force at that speed then we'll have thrust left over to go faster. Could we go faster than 10 ft per second downwind? Clearly not because at 10 ft per second there would be no relative wind so force would be zero. Okay, so why can't we use relative wind to sail faster upwind than when reaching?

When we are reaching, 100% of the lift force of the sail is in the direction we want to go. So, under normal circumstances this would give us maximum speed.

When we angle upwind then only part of the lift force is in the direction we are traveling. But what about relative wind? We keep hearing how the sails generate force in regard to relative wind, not true wind. Now, being quite familiar with physics I know that it makes no difference if we view wind relative to the boat, a fixed point, or to the water. So, let's try relative wind.

The simplest way to illustrate this is to just make assumptions. Let's assume that the wind is blowing out of the north at 10 ft per sec. Let's assume that we can travel in any direction at the same 10 ft per sec. Now, I'm sure at this point someone is screaming that we can't just make that assumption. Actually we can. The way you normally do this process is you make an initial assumption and see what happens. Then, if you wanted a good model you would take the result and use it as the second starting point and repeat this over and over until the results changed very little. This is iteration. However, in this case, I don't think we'll have to iterate this over and over to see the truth. So, let's start with our assumptions and see what happens.

I'm going to take a constant vector for the wind of 10 ft per second blowing south and this is -90 degrees. East is 0 degrees, and North is 90 degrees. We aren't going use west but if we did it would work the same as east. Now, if the boat could travel at a constant velocity of the same 10 ft per second in any direction, what would the relative wind be at each point?

Angle of travel : Rel Wind velocity
90 : 20 (north, directly into the wind)
80 : 19.92
70 : 19.7
60 : 19.32
50 : 18.79
40 : 18.13
30 : 17.32
20 : 16.38
10 : 15.32
0 : 14.14 (east, perpendicular to the wind)
-10 : 12.86
-20 : 11.47
-30 : 10
-40 : 8.45
-50 : 6.84
-60 : 5.18
-70 : 3.47
-80 : 1.74
-90 : 0 (south, directly downwind)

We see exactly what we would expect: the velocity is highest when pointing directly into the wind and lowest when running dead down wind. If you are still having problems with the notion that the boat can travel at this speed in any direction then just imagine that we are starting from a tow or by using the motor.

Now with the boat speed and course fixed what could we actually get out of the sails? What we care about here is that lift (which gives us thrust) is perpendicular to the relative wind. And, if the relative wind is not perpendicular to our direction of travel then what we care about is that part of the wind vector that is perpendicular. So, what do we see?

Angle of travel : Relative size of lift component
90 : 0 (north, into the wind)
80 : 0.09
70 : 0.17
60 : 0.26
50 : 0.34
40 : 0.42
30 : 0.5
20 : 0.57
10 : 0.64
0 : 0.71 (east, perpendicular to the wind)
-10 : 0.77
-20 : 0.82
-30 : 0.87
-40 : 0.91
-50 : 0.94
-60 : 0.97
-70 : 0.98
-80 : 0.996
-90 : 1 (south, directly downwind)

Here we can see that as we head into the wind that the actual part of the wind that produces lift gets smaller and smaller. If you prefer percents just multiply by 100. However, to see what the total is we need to multiply this by the relative wind speed.

Angle of travel : Forward thrust from sails
90 : 0 (north, into the wind)
80 : 1.74
70 : 3.42
60 : 5
50 : 6.43
40 : 7.66
30 : 8.66
20 : 9.4
10 : 9.85
0 : 10 (east, perpendicular to the wind)
-10 : 9.85
-20 : 9.4
-30 : 8.66
-40 : 7.66
-50 : 6.43
-60 : 5
-70 : 3.42
-80 : 1.74
-90 : 0 (south, directly downwind)

Here we can clearly see that thrust is at a maximum near 0 degrees which is a track perpendicular to the wind (or a beam reach). For the sticklers here, this is a linear comparison. The actual force due to wind velocity is squared so the curve would be even sharper. However, squaring the numbers won't change the fact that it is largest near the middle or perpendicular to the wind.

Does this explain why we can sail fastest on a beam reach?

Note: I can show more intermediate steps if necessary. You get the combined wind velocity by using the Law of Cosines as the angle sweeps from 0 to 180 degrees. You get the vector angle by using the fact that for all triangles the interior angles always add up to 180 degrees. And, for an equilateral triangle the remaining two angles are the same so each one is half of 180 minus the sweep angle. Then you subtract the wind angle from the boat's track angle to get the relative wind angle. The lift is 90 degrees to this angle. Then you use cosine to get the portion that is in the same direction as the direction of travel. Then you multiply this by the relative wind velocity. Again, if you wanted to be more precise you would square the velocity first. However, this is negated in practice since drag is also squared.
 
#50 ·
Brehm62 :

Let me see if I can explain this.
Wind Power = 1/2 * Rho * Velocity^3 * Area

Rho is the density of air which is about 0.0807 lbs / cubic ft.
If we are using cubic feet then we need Velocity in feet also.
Let's say the wind is blowing 6 knots.
That is about 6.87 mph or 10.08 feet / sec.
Let's just round that down to 10 ft/sec.
Let's say we have 200 square feet of sail area.

Okay: 1/2 * 0.0807 lbs / ft^3 * (10 ft/sec)^3 * 200 ft^2
0.04035 lbs / ft^3 * 1000 ft^3/sec^3 * 200 ft^2
8,070 lbs (ft^3 / ft^3) * ft^2/sec^3
8,070 lbs ft^2/sec^3
Now we have to divide by gravity which is 32 ft/sec^2
8,070 lbs ft^2/sec^3 / 32 ft/sec^2
252.1875 lbs (ft^2/ft) /(sec^3 *sec^2)
252.1875 lbs ft /sec
1 Horsepower is 550 ft lbs /sec so this is a little less than half a horsepower
0.46 HP


Well explained that man!
A word of caution.
My High School maths teacher woulde be jumping up and down like a hairdresser at THREE horrible sins within your explanation....

1 : Never, but never put units in the middle of equations. Write them above and below the equations if you wish but never within the equation.

2 : The unit you use for force should be the lbf ... do not forget the "f" after it.

3 : Worst sin of all, NEVER pluralise a unit. Units have, by definition, no plural. If you put an "s" after a unit, it denotes "second", so let's have none of this "lbs" stuff ever again.

Apart from three sins, it was a good explanation.

The thread has become rather confrontational. For me, I just put the sails up, choose a course, and trim the sails until they just stop flapping. My ship is fastest when the relative wind is ahead of beam.

One of the beauties of sailing, methinks. I am fastest when the wind is slightly against me.

Now there is a pleasant thought.

On my beloved Loch Ness, the wind is either right on my nose, or right on the back of my neck, as the land masses either side channel the wind right at me, or behind me. Unless I choose to sail across the Loch, that is. It's only about a mile wide.
 
#52 · (Edited)
Here's a graphical representation of the aerodynamic output of a sail in either a closehauled or beamreach orientation.

The "F" is the approx. resultant FORCE output due to the aerodynamics, "X" is the resultant in the direction of the boat and is the SOLE component vector that is responsible for boat speed. The distributed 'arrows' are the vectors of pressure gradient, the F vector is an approximate 'resultant' of all the 'arrows'.

You can see in the 'chart' between the two dwgs. that X1 is smaller than X2, beam reach is faster than closehauled.

The 'pumkin seed effect' AND the slip of the boat's lateral resistance toward leeward is ignored in this illustration, as 'relativistic math' would be quite complex for such a discussion; but however, since the Y vector is greater when closehauled - the pumpkin seed effect is actually GREATER when closehauled because the output in the Y direction (across the beam of the boat) is greater than when at a beam reach.

Simple Speak: just compare the 'length' of the resultant X Vectors in the drawing --- the beam reach produces a LARGER vector (all due to 'trigonometry').

FWIW - lower than beam reach (a high broad reach -- ~125°-135°) is actually faster on most boats because the sail is still or 'can be' in an aerodynamic flow regime and that resultant X vector is even larger than at when on a beam reach, and with less 'slip' , etc.
 
#57 ·
Does anyone here know of a resource that explains exactly why the fastest point of sail for most boats is the beam reach (or close to it)?
If you search for boat polars charts:

polar charts boat - Google Search

you will find that with sufficient windspeed the fastest course is broad reach. Especially for fast efficient boats or ice boats. It all depends on how your hydrodynamic efficiency compares to your aerodynamic efficiency. You can define a L/D ratio for both parts of the boat (below and above water). Combined they give you the polar charts and the fastest course.
 
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