# Free body diagram of a sailboat

Gold Member
This is a practical issue I've trying to resolve by understanding the physics. While I talk sailing jargon, ultimately this is a question of simple torsional forces on a body.

So: In a high wind, when heeled over, my boat does what's called "rounding up"; it turns sharply into the wind - despite rudder hard over to stop it - and stalls.

Granted, this is a good safety failsafe, automatically preventing the boat from being knocked down. But it is not always desirable. It should not occur when the boat is controlled (actively being prevented from doing so). It definitely should not occur when I have only the foresail up. Mainsail is completely doused. That essentially puts all the force forward, meaning there is no way the boat should be able to turn toward the wind.

Naively viewed, if all force is forward of the point of rotation (the keel) there should be no way for it to turn toward the force.

I'm in discussions with sailors and one of the suggestions is that a giant sail (Genoa 150%) extends well aft of the keel, almost to the cockpit, this means there is force on the stern of the boat (the cleat, abeam of the cockpit), pushing the stern downwind.

So the suggestion is to take in enough foresail so that the aft edge of the sail does not go aft of the keel.

I've drawn a diagram, and I think, in doing so, I see why this is the case. I want to confirm.

What's giving me doubts is that the sail area has been moved forward, but the cleat (the point of attachment at which the boat is physically pulled through the water) has not moved forward.

I was thinking this causes the whole boat to act as a single, solid structure, and it should not matter where you attach the line/cleat.

But if I am to believe my diagram, I see that the distance from point of rotation to point of force is shorter, therefore - like a short-handled wrench versus a long-handled wrench - it provides less torque. Which is what I want.

So did I just confirm this bit of nautical wisdom?

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Gold Member
This is a practical issue I've trying to resolve by understanding the physics. While I talk sailing jargon, ultimately this is a question of simple torsional forces on a body.

So: In a high wind, when heeled over, my boat does what's called "rounding up"; it turns sharply into the wind - despite rudder hard over to stop it - and stalls.

Granted, this is a good safety failsafe, automatically preventing the boat from being knocked down. But it is not always desirable. It should not occur when the boat is controlled (actively being prevented from doing so). It definitely should not occur when I have only the foresail up. Mainsail is completely doused. That essentially puts all the force forward, meaning there is no way the boat should be able to turn toward the wind.

Naively viewed, if all force is forward of the point of rotation (the keel) there should be no way for it to turn toward the force.

I'm in discussions with sailors and one of the suggestions is that a giant sail (Genoa 150%) extends well aft of the keel, almost to the cockpit, this means there is force on the stern of the boat (the cleat, abeam of the cockpit), pushing the stern downwind.

So the suggestion is to take in enough foresail so that the aft edge of the sail does not go aft of the keel.

I've drawn a diagram, and I think, in doing so, I see why this is the case. I want to confirm.

What's giving me doubts is that the sail area has been moved forward, but the cleat (the point of attachment at which the boat is physically pulled through the water) has not moved forward.

I was thinking this causes the whole boat to act as a single, solid structure, and it should not matter where you attach the line/cleat.

But if I am to believe my diagram, I see that the distance from point of rotation to point of force is shorter, therefore - like a short-handled wrench versus a long-handled wrench - it provides less torque. Which is what I want.

So did I just confirm this bit of nautical wisdom?

View attachment 209953
In your diagrams, you do not show the force at the front attachment point of the sail (the tack), and so the story is incomplete.

The sail attachments are irrelevant to the overall moments applied to the boat. They are just internal structure, like triangulation on a tower. If I held the aft point (clew) of the sail rigidly in position with a girder, the location of the hull attachment of the girder would alter the internal forces but not change the moment applied to the boat. What matters is the relative positions of the centre of pressure (CP) of the sail and the that of the immersed boat (the centre of lateral resistance, CLR). Which one is more forward?

If we want to find the actual moments, we need more detail, so we also need to find the size and direction of the wind force on the sail and the water force on the immersed boat. The sail force is usually plotted as lift, at right angles to the wind, and drag, in line with the wind. So we have to combine these into a resultant and find the moment it exerts.

The water flow acting on the boat is treated in a similar way. But I must just mention that to resist sideways motion, the boat (and keel in particular) generates lift. To do this it must point at a slight angle to windward the direction of travel, and this creates the required angle of attack. As a matter of interest, this angle of attack corresponds to glide angle for an aeroplane and to leeway angle for a sailing boat.

The position of CLR is very difficult to ascertain without experiment; just pushing the boat sideways is a bit different from the CLR when water flows over the surfaces. It is not half way along an aerofoil, for instance. And of course, the CP of the sail also moves around a bit depending on shape, angle of attack and wind speed.

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A.T.
Tech99 is basically correct. The CP or what I have come to know it as the center of effort CE of a sail is that point which the total force due to the sail relative to the hull may be considered to be located. It is perpendicular to the sail surface. It is usually resolved into two components, a heeling component perpendicular to the hull ( tipping the boat ) and a drive component parallel to the hull moving it forward. In a fully rigged sloop the CE of the Main is so far aft of the CLR (the fulcrum) and the CE of a Genoa is too forward to counteract the turning moment of the main.

In going to windward the CE of a Genoa is roughly about 1/3 of its length aft.and by itself should not be able to cause the boat to round up without the mainsail.
The CE of a main is usually about 1/2 of the length of the foot of the sail aft..

The CLR is in the vicinity of a point below and aft the mast but this changes as the boat increases speed. moving forward (I think). How much depend on the hull shape and heel of the boat.

Usually the rounding moment is adjusted by changing the shape/size of the main or reefing it. Increasing the size of the genoa also decreases this tendency. Centerboard, swing keel, or drop keels position also change this behavior.

As you noted this tendency causes the helm to be held to windward (weather helm) and the rudder usually induces more drag and slows the boat. So adjusting the weather helm so it is minimal can be used to assess how well you have reduced the rounding tendency and give you a bit more speed.

Staff Emeritus
Your diagram does not show the rudder, and loss of effectiveness of the rudder with heeling.

If also doesn't account for the change of shape of the wetted hull area with heeling. Nor the forces on sail and keel.

I guess what I'm saying is that your free body diagram with the boat not heeled is inadequate. The same rounding up occurs with mainsail only. It is more pronounced with fin keel and spade rudder than full keel and skeg rudder. That is a clue that forces below the water line dominate.

PaulK2
Gold Member
Tech99 is basically correct. The CP or what I have come to know it as the center of effort CE of a sail is that point which the total force due to the sail relative to the hull may be considered to be located. It is perpendicular to the sail surface. It is usually resolved into two components, a heeling component perpendicular to the hull ( tipping the boat ) and a drive component parallel to the hull moving it forward.
If we want to refer to typical aerofoil characteristics, we need to look at lift, at right angles to the wind, not the hull, and drag, in line with the wind, not the hull. These forces can then be combined to provide the components you mention.

Homework Helper
Gold Member
As a sailor rather than mechanical engineer, I would attribute your luffing or rounding up to the heel of the hull. I have little experience of keel boats, but would expect at least short keel boats to behave like dinghies. In dinghies, particularly with rounded cross-section rather than hard chines, any departure from flat balance (mast vertical) results in a strong turning force. This is generally attributed to hydrodynamic effect, but there is also movement of the sail CE relative to the centreline of the boat. It seems to work also when dinghies are being towed with sails lowered, so the hydrodynamic explanation gets my vote,

For straight running on a reach to a beat it is generally regarded as desirable to keep the boat as flat as possible. In dinghies we hike or sit out or even trapeze to windward. In a keel boat crew sit on the windward gunwale (with their torso inside the guard rail to comply with racing rules), but I'm not sure it makes much difference.
Downwind, when the sail is well out to the side, there is clearly a strong turning force from the sail. In some classes, particularly singlehanded classes such as the Laser, many helms heel the boat well to windward: some say this is to bring the CE closer to the centreline of the boat, but I believe it also causes significant lee helm to counteract the weather helm of the sail, even before the CE reaches the CL..
The aim is normally to have the boat run true with the helm centred for minimum resistance.

When making a turn, heeling in the appropriate way steers the boat into the turn and reduces the need for strong rudder. Trying to gybe (turn away from the wind) in strong winds is often very difficult unless the boat is well heeled to windward. After a tack (turn through the wind) in strong winds it is important to get the boat back on an even keel asap, else the boat, being heeled to lee by the wind, will try to turn back to the wind and stall.

Rudderless sailing is a common exercise for intermediate dinghy sailors. With no rudder the effect of balance is much more noticeable. In light winds, balance of the boat is generally the most effective steering control when moving. In stronger winds, balance of the sails becomes more significant, but boat balance is still essential. (The last coach I saw teaching this suggested reducing sails in stronger winds and still rely on balance to steer.)

CWatters
Homework Helper
Gold Member
I did a bit of dinghy racing 30 years ago...when sailing upwind you want the V shape front end dug into help the keel reduce the sideways slip. When going cross wind you want the weight rearwards for planing. This moves the centre of the wetted area (i know that's probably not the right term?) forwards and backwards just as the centre of effort for the sails can be moved forward and backwards. I'm wondering if you design a boat to sail upwind well then perhaps this movement is just the price you pay?

If we want to refer to typical aerofoil characteristics, we need to look at lift, at right angles to the wind, not the hull, and drag, in line with the wind, not the hull. These forces can then be combined to provide the components you mention.

Just to be clear by the hull I meant the midline of the hull.

The sails and the jib in particular are not a perfect airfoil as you find on an airplane because of the way it is mounted on boat and the way its shape is modified by sheets. The sail is trimmed so that the apparent wind is parallel to the leading edge. And unlike a plane wing the sails windward and leeward side are the same shape. The keel on the other hand is more like and acts more like an airfoil. providing lift to help the boat point more toward the wind as the boat moves faster. This is very noticeable as the boat speeds up and you find yourself changing your compass direction toward the wind.

The drag on a sail is primarily do to the imperfect airfoil shape due to the way the sail is mounted and trimmed. In particular due to the trimming arrangement the aft half of the sail often significantly curls to windward increasing aft directed forces.

As a sailor rather than mechanical engineer, I would attribute your luffing or rounding up to the heel of the hull.

My experience is very limited with dinghies. But I believe that the underwater asymmetric hull shape produced when heeled does produce a turning moment. even for keel boats. One design dinghies that have only a mainsail do not have many problems with helm issues as they are not adjustable except by sail/hull trim. For boats than can have a multitude of sail combinations then one has to work to and pay attention to the weather helm issues.

Gold Member
In your diagrams, you do not show the force at the front attachment point of the sail (the tack), and so the story is incomplete.
Yes. I probably shouldn't have used the term free body diagram so freely, since I am deliberately not considering all forces.

What I am trying to do is isolate the force I'm interested in and treat (in theory) all other factors as unchanged.

As all these contributors have pointed out, the physics of sailing is a complex and very dynamic process, and frankly, well beyond the scope of a single thread.

So I am examining a single factor - that of moving the leach of the foresail forward, close to the axis of rotation - while leaving all other factors (ideally) unchanged.

In practice, of course, all things affect all others, but that is a rabbit hole down which this thread would go and never return.

The sail attachments are irrelevant to the overall moments applied to the boat. They are just internal structure, like triangulation on a tower. If I held the aft point (clew) of the sail rigidly in position with a girder, the location of the hull attachment of the girder would alter the internal forces but not change the moment applied to the boat.
That is exactly my thinking, which is why I started to diagram it.

What I think I've determined is that it is not the location of the attachment points, but the length of the moment arm from the axis of rotation. If I were to manage to shorten that moment arm to near zero (i.e. virtually attach it to the mast) there would be zero force pushing the stern to lee.

Your diagram does not show the rudder, and loss of effectiveness of the rudder with heeling.

Dual rudders. You could be knocked down to 90 degrees, have the keel high and dry, and the lee rudder will simply be even deeper.

My experience is very limited with dinghies. But I believe that the underwater asymmetric hull shape produced when heeled does produce a turning moment. even for keel boats.
This is a 26 foot power sailor. Neither fish nor fowl. It has a hull shape halfway between keelboat and powerboat.

There's no doubt that hull shape changes with heeling. But that is a known factor. These boats should be able to compensate. Others of the same design do. The only question is: how is my particular boat configured differently? (There could be a dozen ways, but right now, I'm examining sail plan.)

Usually the rounding moment is adjusted by changing the shape/size of the main or reefing it.
In this case main is not merely reefed, but fully doused. It is not in-play at all. This is why rounding up is a mystery.

Increasing the size of the genoa also decreases this tendency.
You would think wouldn't you? But that is not what is happening.

The sailor's rationale is that, with a large enough jenny, essentially it can take on the role of the main, since it sweeps all the way back to the 'pit, well aft of the mast.

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Homework Helper
Gold Member
Can you lean the mast forward a bit?

So I am examining a single factor
Then choose a useful one, like the total force by the sail on the boat, not just at one of the attachments.

Gold Member
Imagine a beam balancing on a fulcrum, and beneath the beam you suspend a mass using some strings, so that the CG of the mass is directly below the fulcrum. The beam is in balance still. Now if you move the strings around, the beam will remain in balance provided the mass remains in the same position.

Homework Helper
What about the effects of the keel itself? I browsed a few articles, and it seems that keels are typically located where they would tend to turn a sailboat into the wind.

This is a 26 foot power sailor. Neither fish nor fowl. It has a hull shape halfway between keelboat and powerboat.

Could you post pictures of it under sail and on the hard?

Gold Member
What about the effects of the keel itself? I browsed a few articles, and it seems that keels are typically located where they would tend to turn a sailboat into the wind.
The design objective would be to get the vessel balanced as near as can be predicted but with a slight tendency to round up into the wind, called weather helm. This means that if the tiller is released, the boat will come up into the wind and stop. Most helmsmen prefer this.
However, if a comparison is made with an aeroplane, it is common for the tail plane to press down, not up. This would correspond to the opposite action, which is lee helm, or a tendency to bear off. For an aeroplane the CG is placed a little forward of the CP of the wings, so that it is nose heavy. The tail then holds the nose up by pressing down. This condition is found to be stable when hands-off, because if the nose goes down, the angle of attack of the tail increases and raises it again. So there is a theoretical case that a sailing boat with lee helm will tend to self steer.

Homework Helper
aeroplanes

However, if a comparison is made with an aeroplane, it is common for the tail plane to press down, not up. This would correspond to the opposite action, which is lee helm, or a tendency to bear off. For an aeroplane the CG is placed a little forward of the CP of the wings, so that it is nose heavy. The tail then holds the nose up by pressing down. This condition is found to be stable when hands-off, because if the nose goes down, the angle of attack of the tail increases and raises it again. So there is a theoretical case that a sailing boat with lee helm will tend to self steer.
Normally the angle of attack of the elevator remains nearly fixed. If the aircraft noses down, it picks up speed, generating more downforce at the tail due to the combination of increased speed at the same angle of attack, so that the aircraft pitches upwards to correct. If the aircraft noses up, it loses speed, and pitches down due to the same effect. In the case of radio control gliders, assuming some amount of positive pitch stability (CG in front of CP), then elevator trim adjusts the glide speed. For full scale powered aircraft with direct control of the elevator, trim tabs are used to adjust the elevator angle of attack so that it takes zero pressure on the yoke to maintain level flight at the current altitude and speed.

Staff Emeritus
When a sailboat heels, the rudder's force is divided into components. One component moves the stern port and starboard. The other component lifts the stern and pushes the bow down. It is simple trigonometry that the rudder becomes less effective as steering as heel angle increases.

The same trigonometry reduces the forces on the sail, reaching zero at 90 degrees heel.

The same trigonometry also alters the shape and the center of force of water on the portion of the hull below the water line.

@DaveC426913 , it is time to think about things other than the sail.

Gold Member
When a sailboat heels, the rudder's force is divided into components. One component moves the stern port and starboard. The other component lifts the stern and pushes the bow down. It is simple trigonometry that the rudder becomes less effective as steering as heel angle increases.
Good point. In retrospect it is obvious that a rudder tilted from vertical must provide less steering force, no matter how much of it is in the water.

As a matter of fact, the more one turns such a rudder to steer the boat off the wind, the more the rudder actually acts as a lifting force on the stern.

The same trigonometry reduces the forces on the sail, reaching zero at 90 degrees heel.
Yes. Which is why excessive heel is to be avoided, since it merely spills off wind.

Gold Member
@DaveC426913 , it is time to think about things other than the sail.

To be clear to all: it was not my intention to try to solve the rounding up problem in this thread. There's no doubt there are many forces involved. There's no way to solve it in the specific case of my boat (i.e. pathological) without looking at every one of those aspects with regards my boat. (Remember, other boats of this same design (allegedly) do not behave this way ).

My intention was to examine the plausibility of one specific proposed change, leaving all other factors alone, and see if that one change makes a difference.

This why I presented it as a physics problem, rather than a sailing problem. We should be able to find an answer to the simple problem as specified in the OP without any consideration of the other factors.

Pretend the object in the OP is a simple wedge-shaped block of wood - no rudder, no main sail, no water. It has a point of rotation, a force of wind, and a sail-like appendage.

I mean, I definitely appreciate the feedback I'm getting; it is great food for thought and experiment, but I suspect the scope is so large that the thread will inevitably spiral toward 'unanswerable without more information', and die with a whimper.

Is your boat a Macgregor 26 or something like it? If so one can see that the rudders are quite small and might not be capable of controlling boat in high winds especially with one mostly out of the water.

Do you have any additional canvas as a dodger or bimini? This would move the CE aft. The boat has a water ballast and if the tank is not totally filled then the water can shift and change the hull trim.

As @anortunda suggested sails should not figure in the possible solution to your problem. I think the boat should not be sailed at a heel of greater than 15- 20 deg as it keeps both rudders submerged and besides it can be dangerous when moving about. Also when heeled the centerboard which is suppose to provides a good amount of lateral resistance becomes less effective compared to the hull under the water. Also the problem that anortunda noted about the rudder lifting the stern when heeled too much forcing the bow down would be a factor.

But all that said, the Macgregor website show picture of the boat sailing nicely in gale force winds with reefed main as a spit of or no jib.? Have you asked one of your experience sailor friend to go out with you and see for themselves the problem?

Pretend the object in the OP is a simple wedge-shaped block of wood - no rudder, no main sail, no water. It has a point of rotation, a force of wind...
That's all fine, but the force of the wind on the boat, is not the one shown in the OP.

Gold Member
I have just found this thread. Interesting. I had exactly the same sort of problems.
I had a Westerly Centaur for several years and, although they say it's got good performance for a cruiser from the 60s, it had several things against it. Firstly, there is a lot of windage, especially with the spray dodgers and spray hood in place. Without full reefing, it was difficult to run in a 5 or above and I often couldn't manage to Gybe on my own. I would need to do a coat hanger turn instead
The design was from a time when neither forms of protection were in common use (look at the original adverts for such boats). Here's one for the original Centaur. (Do you have a similar reference that you could post, Dave?) Add at least 1m2of extra canvas towards the stern and take nearly all the sails away and you have a significant contribution aft of the mast. Also, in the Centaur design, see how much more of the forward hull is in the water and how shallow the aft section is. That all puts the centre of pressure further forward than the centre of the keel - especially when she heels.
I have heard that it could be solved by tipping the mast forwards by a few degrees. With no sails, the mast windage will be significant.

Gold Member
That's all fine, but the force of the wind on the boat, is not the one shown in the OP.
The OP diagram does not show force of wind.
It shows wind direction. And it shows the force on the cleat/sheet.

Gold Member
Is your boat a Macgregor 26 or something like it?
Maaaaybeeee...

Do you have any additional canvas as a dodger or bimini? This would move the CE aft.
This year, no dodger. And I douse the bimini to reduce parachute effect.
But Mac does have a high freeboard, which contributes to windage.

As @anortunda suggested sails should not figure in the possible solution to your problem.

Well then I have to abandon my sailor's advice that rounding up is not normal, and is peculiar to my boat.

I think the boat should not be sailed at a heel of greater than 15- 20 deg
20 degrees is the max ideal heel for performance. But when a boat should not be sailed is a matter of skipper experience. There is no doubt that the boat itself can handle rough weather.

Have you asked one of your experience sailor friend to go out with you and see for themselves the problem?
Working on that.

Is here an owners association which you can contact for other person's experience with this boat.? If it is characteristic of the design then everybody should have the problems.

Gold Member
The design was from a time when neither forms of protection were in common use (look at the original adverts for such boats). Here's one for the original Centaur. (Do you have a similar reference that you could post, Dave?)
http://sailboatdata.com/viewrecord.asp?class_id=4090

I have heard that it could be solved by tipping the mast forwards by a few degrees.
This is not the first time such an idea has come up. Mast rake on this boat should be 4 degrees.

sophiecentaur
Gold Member
Is here an owners association which you can contact for other person's experience with this boat.? If it is characteristic of the design then everybody should have the problems.
Yes, I am in lengthy discussions with sailors on the forum specifically for this boat.
It is they who are making the suggestions of adjustments that I am bringing here for validation.

This page, documenting a test by Roger MacGregor (the designer himself) suggests:
If the boat wants to round up into the wind, unroll a bit more genoa, or let the mainsail out. This will move the center of pressure on the rig forward, and make is less likely to round up into the wind and waves.
http://www.macgregor26.com/photo_ga... winds/photo_gallery_page_4_heavy_weather.htm

Gold Member
The situation as described poses a problem under really bad conditions as it implies that you need to heave to and can't run before a storm.

Yes, I am in lengthy discussions with sailors on the forum specifically for t
his boat.
It is they who are making the suggestions of adjustments that I am bringing here for validation.

This page, documenting a test by Roger MacGregor (the designer himself) suggests:

MacGregor's suggestions are typical for any boat in heavy conditions. He even suggest that the boat might even have excessive lee helm under certain conditions. Can you ever produce lee helm? If yes when at what point can't you?

sophiecentaur
Gold Member
I don't think the Physics approach will help too much here. After all, even with a lot of computing power and know how, there's still a need for physical testing on cutting edge hydro and aero dynamics designs. So - no shame in a practical approach here.

Gold Member
The situation as described poses a problem under really bad conditions as it implies that you need to heave to and can't run before a storm.
How so? The boat will round up. That's what you want, if you want to stop sailing.

Gold Member
I don't think the Physics approach will help too much here. After all, even with a lot of computing power and know how, there's still a need for physical testing on cutting edge hydro and aero dynamics designs. So - no shame in a practical approach here.
Well, this is what I was afeared of. See post 19. ... and post 1. You guys are expanding the scope beyond answerability.