Let's Get to the Bottom of the Lee-Bow Effect Once and For All

[Dockhead]

Originally Posted by Seaworthy Lass

But you sail to true wind. And true wind is the sum of ground wind and wind due to current (and leeway, but that complicates this too much at the moment).

The boat does not know if the true wind is changing due to a change in ground wind or current. But it IS changing, so there is a favourable tack to be on, just as there is if ground wind is changing.

Yes, absolutely! But does putting the lee bow into the current always or even often put you on the "favourable tack" under the circumstances? I don't know; let's think about it. It will be interesting if you can think of a reason why it would. Let's leave aside the fact that lee bowing will keep you closer to the rhumb line to your windward mark -- from our CTS discussion we positively know that this is irrelevant.

I earlier said that you should lee bow to increase the true wind, windward bow to reduce it. The idea being that if you need more wind, you'll get a lift by lee bowing.

But that is only really true in a very limited set of circumstances. First of all -- if the ground wind direction is perpendicular to the current, the current will have no effect on true wind speed.

And if the true wind direction deviates from perpendicular by more than half of your tacking angle for max VMG to windward, then you can lay the mark in one tack and thus there is no choice of tack, and the question is moot.

So the range of cases where the effect of changes of true wind speed will be noticeable is extremely narrow, because at or around perpendicular, the effect of current on true wind speed will be nil or very small, and so the effect on true wind speed will be greatest - but still very small (if you have a narrow tacking angle), when you can almost but not quite lay the mark in one tack.

OK, but there's not just the question of wind speed, but also wind direction. The true wind direction will also change when the current changes. I guess this is the key fact here. When the lee bow is in the current, the true wind will be freerer than the ground wind. So you're getting a lift from a ground-referenced point of view:



We can easily imagine cases where the current is strong enough that we can sail a constant COG by tacking with the current, keeping the lee bow into the current:




I bet this is what a lot of people are thinking about, when they think about the supposed Lee Bow Effect.

BUT! This is all ground referenced. We don't want to be sailing a constant COG, as we know from our CTS discussion. We want to be sailing a constant heading, or tacking around a constant average heading at our optimum tacking angle.

So the way I have drawn it is fundamentally the wrong way to look at it.

[Dockhead]

A devilish note:

Heading is also ground referenced (!).

So constant heading is also not precisely ideal! This applies to our CTS discussion as well as to this one, and I only just now thought of it. To sail an ideal straight line through water, heading would also need to change somewhat during a passage across moving water, even without a change in current (!).

I think it's a tiny, tiny effect because of the great distance from us to the North Magnetic Pole. Of theoretical interest only.

[Dockhead]

Yep, that's it

Here is a precise formulation of the problem:

True wind direction changes when the current changes, so why not get a lift by tacking with the current, to catch the freerer wind every time.

Problem with this is that it assumes that the boat is moving along a constant COG. Since we will moving along (or tacking towards) a point along a constant heading, our COG changes with the changes in the current and nullifies the Lee Bow Effect.

At a given constant heading, our boat's keel will be aligned at a constant angle to the True Wind, not a constant angle to the Ground Wind, because the direction at which the boat moves in relation to the land is changed by the same current vectors which change the direction the wind moves in relation to the land.

So the most efficient path through the water will always have the same angle to the True Wind, notwithstanding the changes in current. The True Wind will change compass direction, but will not change direction in relation to our boat's keel (and therefore her sails) while we are sailing on a constant heading.

To say it another way -- and this is really funny!!! The True Wind will change when the tide changes. But the Apparent Wind Will Not change!!! Because the current imparts the same vectors to our boat's motion in relation to land, as it does to the wind.



QED. This version of Lee Bow Effect is obliterated, as far as I'm concerned. The problem is caused by failing to compare apples to apples -- by confusing ground and water referenced vectors. It would be right to now run some scenarios and do some numbers to double check.

[Seaworthy Lass]

Originally Posted by Dockhead

Yes, absolutely! But does putting the lee bow into the current always or even often put you on the "favourable tack" under the circumstances? I don't know; let's think about it.

It will be interesting if you can think of a reason why it would. Let's leave aside the fact that lee bowing will keep you closer to the rhumb line to your windward mark -- from our CTS discussion we positively know that this is irrelevant.

Yes, it does I think. You need to split the wind components due to current into two vectors - perpendicular to the ground wind and parallel to it. The bit that affects which tack to be on is the bit perpendicular to the ground wind. I think this will always coincide with the lee bow, but I may be wrong.

The easy way to look at it is relative to the CTS, you need to pick the tack that gives you a heading that is closest to the CTS.

Originally Posted by Dockhead

I earlier said that you should lee bow to increase the true wind, windward bow to reduce it. The idea being that if you need more wind, you'll get a lift by lee bowing.

But that is only really true in a very limited set of circumstances. First of all -- if the ground wind direction is perpendicular to the current, the current will have no effect on true wind speed.

No, you cannot increase or decrease the true wind by putting your bow either way. The true wind has nothing to to with what tack you are on. The effect has nothing to do with increasing the true wind strength, instead it is because of the future alteration in true wind direction when the current flips.

Originally Posted by Dockhead

And if the true wind direction deviates from perpendicular by more than half of your tacking angle for max VMG to windward, then you can lay the mark in one tack and thus there is no choice of tack, and the question is moot.

What if you can't lay the mark until the current changes direction, but you can sail either side of the CTS as you are no longer close hauled. What then? Not sure about this yet. I need to think about it.

Originally Posted by Dockhead

So the range of cases where the effect of changes of true wind speed will be noticeable is extremely narrow, because at or around perpendicular, the effect of current on true wind speed will be nil or very small, and so the effect on true wind speed will be greatest - but still very small (if you have a narrow tacking angle), when you can almost but not quite lay the mark in one tack.

Yes, the effect may be small. It depends on the amount of current and the angle, as only the component perpendicular to the ground wind is relevant in deciding what tack to be on. If the current is exactly with and against the ground wind, there is no preferred tack.

Will post this before before going further, so you can follow my train of thought.

[Seaworthy Lass]

Originally Posted by Dockhead

A devilish note:

Heading is also ground referenced (!).

So constant heading is also not precisely ideal! This applies to our CTS discussion as well as to this one, and I only just now thought of it. To sail an ideal straight line through water, heading would also need to change somewhat during a passage across moving water, even without a change in current (!).

I think it's a tiny, tiny effect because of the great distance from us to the North Magnetic Pole. Of theoretical interest only.

That is plain mean to throw that in LOL .

[Dockhead]

Here is what cancels out the Lee Bow Effect:



How cool is that?

So what will happen is this:

The current changes, and God will know that the True Wind has changed with it.

HOWEVER, bizarrely, you will find that your instruments cannot see this change. Your instruments will stubbornly continue reporting True Wind and Apparent Wind as the same as they were (if the Ground Wind has not changed and your speed through water has not changed).

Why? Because neither in relation to land, nor in relation to the compass, your boat is not moving along the axis of its keel. The direction (I hesitate to call it "heading") your boat is moving is affected by the very same vector which has changed the True Wind and to exactly the same degree.

Thus your instruments are deceived, since they use the axis of your keel as a reference.

And thus the Lee Bow Effect is exactly cancelled.

[Seaworthy Lass]

Continued:

Originally Posted by Dockhead

OK, but there's not just the question of wind speed, but also wind direction. The true wind direction will also change when the current changes. I guess this is the key fact here. When the lee bow is in the current, the true wind will be freerer than the ground wind. So you're getting a lift from a ground-referenced point of view:

Yes, that is the key factor (in fact the only factor) here.

Originally Posted by Dockhead

We can easily imagine cases where the current is strong enough that we can sail a constant COG by tacking with the current, keeping the lee bow into the current:

Nothing to do with COG. It is your heading relating to the CTS, not the COG.

Originally Posted by Dockhead

BUT! This is all ground referenced. We don't want to be sailing a constant COG, as we know from our CTS discussion. We want to be sailing a constant heading, or tacking around a constant average heading at our optimum tacking angle.

So the way I have drawn it is fundamentally the wrong way to look at it.

Yes .

Will address your post following this next (much harder doing this not knowing how much you have not read of my previous posts and vice versa).

[Dockhead]

Originally Posted by Seaworthy Lass

Continued:



Yes, that is the key factor (in fact the only factor) here.



Nothing to do with COG. It is your heading relating to the CTS, not the COG.



Yes .

Will address your post following this next (much harder doing this not knowing how much you have not read of my previous posts and vice versa).

The way I drew it the first time, the one which I described as "wrong", is a statement of the Lee Bow Effect. I was showing that is wrong, because it only works in relation to COG. That was what I was getting at.

[Seaworthy Lass]

Originally Posted by Dockhead

Yep, that's it

Here is a precise formulation of the problem:

True wind direction changes when the current changes, so why not get a lift by tacking with the current, to catch the freerer wind every time.

Problem with this is that it assumes that the boat is moving along a constant COG. Since we will moving along (or tacking towards) a point along a constant heading, our COG changes with the changes in the current and nullifies the Lee Bow Effect.

At a given constant heading, our boat's keel will be aligned at a constant angle to the True Wind, not a constant angle to the Ground Wind, because the direction at which the boat moves in relation to the land is changed by the same current vectors which change the direction the wind moves in relation to the land.

So the most efficient path through the water will always have the same angle to the True Wind, notwithstanding the changes in current. The True Wind will change compass direction, but will not change direction in relation to our boat's keel (and therefore her sails) while we are sailing on a constant heading.

To say it another way -- and this is really funny!!! The True Wind will change when the tide changes. But the Apparent Wind Will Not change!!! Because the current imparts the same vectors to our boat's motion in relation to land, as it does to the wind.

Attachment 70166

QED. This version of Lee Bow Effect is obliterated, as far as I'm concerned. The problem is caused by failing to compare apples to apples -- by confusing ground and water referenced vectors. It would be right to now run some scenarios and do some numbers to double check.

Originally Posted by Dockhead

Here is what cancels out the Lee Bow Effect:

Attachment 70168

How cool is that?

So what will happen is this:

The current changes, and God will know that the True Wind has changed with it.

HOWEVER, bizarrely, you will find that your instruments cannot see this change. True Wind and Apparent Wind will remain the same (if the Ground Wind has not changed and your speed through water has not changed).

Why? Because neither in relation to land, nor in relation to the compass, your boat is not moving along the axis of its keel. The direction (I hesitate to call it "heading") your boat is moving is affected by the very same vector which has changed the True Wind and to exactly the same degree.

Thus your instruments are deceived, since they use the axis of your keel as a reference.

And thus the Lee Bow Effect is exactly cancelled.

No LOL. I don't know where to start with all you have written, but the boat WILL experience the shift in true wind direction when the current changes in direction. You have that wrong.

Consider this: If the ground wind was steady, the boat dropped its sails it would know when the current had reversed as their would be be a change in the true wind direction (which would be the apparent wind for the boat if its speed relative to the water was zero because the sails were down).

Maybe before I go and poke holes in the above post, forget about the fixation with lee bow at the moment. Maybe simply initially think about the issue "is there a preferred tack to be on when the current is changing direction during a journey."

The answer is yes (later worry about whether or not the current is on the lee bow to achieve this).

[Dockhead]

Originally Posted by Seaworthy Lass

What if you can't lay the mark until the current changes direction, but you can sail either side of the CTS as you are no longer close hauled. What then? Not sure about this yet. I need to think about it.

Let me explain.

You are confusing the mark with Point B in the water.

You're sailing to Point B, not to the mark.

Either you can lay Point B or not; it's not a question of coordination with the current. Point B, unlike your mark, is a constant heading away from you whatever the current does.

Following from the last bit of discovery in my previous post -- which I think is the last remaining piece of the puzzle -- Point B will also be constant True Wind from you, despite any changes in the current, as measured by your instruments, as long as Ground Wind doesn't change.

Deviation TW1 and TW2 is precisely the same as the deviation TW-GEV and TW-BIV.

Where TW1 is True Wind before current change
TW2 True Wind after current change
TW-GEV -- True Wind after the current change, God's Eye View
TW-BIV -- True Wind after the current change, Boat's Instruments View.


And one other thing -- if at any point in trying to lay a point which you can't lay in one tack, you deviate from close hauled, that is, deviate from your optimum tacking angle, you have screwed the pooch. It means you've sailed a loop around your ideal path through the water and ended up too far upwind of where you want to go, losing time.

[Dockhead]

Originally Posted by Seaworthy Lass

No LOL. I don't know where to start with all you have written, but the boat WILL experience the shift in true wind direction when the current changes in direction. You have that wrong.

Consider this: If the ground wind was steady, the boat dropped its sails it would know when the current had reversed as their would be be a change in the true wind direction (which would be the apparent wind for the boat if its speed relative to the water was zero because the sails were down).

Maybe before I go and poke holes in the above post, forget about the fixation with lee bow at the moment. Maybe simply initially think about the issue "is there a preferred tack to be on when the current is changing direction during a journey."

The answer is yes (later worry about whether or not the current is on the lee bow to achieve this).

Poke away! If I screwed something up, you'll save me time by finding it.

[Seaworthy Lass]

Originally Posted by Dockhead

Let me explain.

You are confusing the mark with Point B in the water.

I am not LOL.

Originally Posted by Dockhead

You're sailing to Point B, not to the mark.

Yes, you are sailing to point B on the water. This is your destination point on the water. This will wander all over the ground when you have any current. However, when you arrive at your destination point on the ground, point B will at that instant coincide with it

Originally Posted by Dockhead

Either you can lay Point B or not; it's not a question of coordination with the current. Point B, unlike your mark, is a constant heading away from you whatever the current does.

Yes, your heading to point B does not depend on current at all. We both agree on this. But when you can't steer the CTS to B because you are close hauled, then it is a case of coordinating with the current, as the current alters the direction of your true wind. If the true wind is due to shift because the ground wind changes, then you have a favoured tack. The same applies if it due to change because of current.

[Seaworthy Lass]

Originally Posted by Dockhead

Poke away! If I screwed something up, you'll save me time by finding it.

Hey, that's cheating. That is not how this game works .

I need a cuppa, maybe address what I have just written while I make one

If it hasn't sunk in I will then go and poke holes.

[Seaworthy Lass]

OK, here is the main poke:

Originally Posted by Dockhead

Here is a precise formulation of the problem:

True wind direction changes when the current changes, so why not get a lift by tacking with the current, to catch the freerer wind every time.

Problem with this is that it assumes that the boat is moving along a constant COG. Since we will moving along (or tacking towards) a point along a constant heading, our COG changes with the changes in the current and nullifies the Lee Bow Effect.

No, forget about COG. You can only look at that if you consider ground wind, not true wind. If you look at true wind (which is relative to the water and which is what the boat experiences and you feel if your sails are down and you have no leeway), then you can't consider the boat's motion relative to the ground because of current. You must consider the boat's position relative to the water. Current does not alter this postition.

So you can't cancel out the effect of the current on the boat's position and the effect of the current on the wind, as they are not in the same planes of reference.

Originally Posted by Dockhead

QED. This version of Lee Bow Effect is obliterated, as far as I'm concerned. The problem is caused by failing to compare apples to apples -- by confusing ground and water referenced vectors. It would be right to now run some scenarios and do some numbers to double check.

No not QED LOL. You are failing to compare the same fruit in your "proof" .

[AndytheSailor]

My only comment, while agreeing with Seaworthy, is that if you are crossing a tide on a tack, if the tide is on the lee bow then you can lay you course less close to the wind, thus sail faster and still make your destination. I know this doesn't deal with the maths but it does offer the logic.