Trigonometry of racing to a windward mark with a cross tide.

[BlueSkyNick]

I become engrossed in a conversation today with one of the top RYA Race Management guys, and still dont fully understand the sums!

The hypothetical race start is in a ground wind of 6kts from 000degs, with a steady tide of 1 kt from west to east. On what bearing should the windward mark be laid from the centre of the start line to provide a true beat on the first leg?

RYA-man explained that the sailing wind due to the tidal vector is from approx 010 degs. He then went on to say that the tide will ALSO affect the COG of the boats and the two effects are added. So the Windward mark needs to be laid on a bearing of approx 025degs. On the downwind legs the two effects are subtractive.

It is almost 40 years since I struggled through both Physics and Maths A'levels and the theory hasnt changed in that time, but my ability to compute it has seriously dropped.

My view is that the tidal vector which changes the effective angle of the wind, ie the sailing wind. and the vector which affects the COG of the boats is one and the same thing so the two affects should not be added. Not wanting to get into an argument with an RYA International RO, I have to take his word for it.

Where I am going wrong?

 

[lpdsn]

I become engrossed in a conversation today with one of the top RYA Race Management guys, and still dont fully understand the sums!

The hypothetical race start is in a ground wind of 6kts from 000degs, with a steady tide of 1 kt from west to east. On what bearing should the windward mark be laid from the centre of the start line to provide a true beat on the first leg?

RYA-man explained that the sailing wind due to the tidal vector is from approx 010 degs. He then went on to say that the tide will ALSO affect the COG of the boats and the two effects are added. So the Windward mark needs to be laid on a bearing of approx 025degs. On the downwind legs the two effects are subtractive.

It is almost 40 years since I struggled through both Physics and Maths A'levels and the theory hasnt changed in that time, but my ability to compute it has seriously dropped.

My view is that the tidal vector which changes the effective angle of the wind, ie the sailing wind. and the vector which affects the COG of the boats is one and the same thing so the two affects should not be added. Not wanting to get into an argument with an RYA International RO, I have to take his word for it.

Where I am going wrong?

It will be more than just the effect of the tide on the true wind (assuming the most common interpretation of true wind as the combination of wind over the ground and tide wind). As well as sailing in the modified wind, boat will be set off by the tide. Not sure you can precisely calculate it with trig though - the effect will depend upon boat speed for a start and there's bound to be variations in the tide across the course. Not to mention wind shifts of various types.

I reckon all you should really aim for is a beat that is not highly skewed to one tack (or even worse a close reach) and a start line that is reasonably straight against the true wind modified by the tide. And if you own the committee boat you may also want to introduce a bit of pin end bias

 

[flaming]

He's right.

Think of it like this. The wind as experienced by a drifting boat is, as he says, about 010 because of the tide. Now, if you laid your windward mark on 010 and I came off the line on starboard doing, say, 3 knots at 45 degrees to the wind I will pointing at 325 at 3kts through the water but going over the ground more like 345/350 at probably 2.5 due to being taken East by the tide. Similarly if I was on port I would be pointing 055 at 3 knots but going more like 065/070 at nearly 4 knots over the ground. Since your mark laying team have done a good job of actually securing the thing to the bottom you can see that you're making progress at 20/25 degrees off course on Starboard but 55/60 on port. So to get to the top mark if it was laid at 010 would mean a lot more starboard tack than port.

 

[Pinnacle]

And if you own the committee boat you may also want to introduce a bit of pin end bias

All other things being equal, I would expect that lots of crews will wish to start from the up-tide end of the line.

 

[bedouin]

The way I would look at it is that you want to set the mark so the course through the water is in the opposite direction to the wind - that is the 10 degrees.

Then you need to place the mark in the position over land that corresponds to that water track - which adds a second effect, assuming the boats will do about 6 knots at 45 degrees to true wind (including leeway) that would add a further 14 degrees - so 25 degrees is reasonable (but very dependent on the performance of the boat)

 

[Yacht Yogi]

Something exactly like this happened one day in the Hamble Winter Series last season. A Northerly wind and a West going tide. The Sigma 38 fleet set off in a tight bunch with the leaders going off down-tide on starboard tack. The laggards were left nearer to the committee boat and tacked off onto port to get clear air. The port tackers all got a massive lift and arrived at the windward mark well ahead of the boats that had led them off the line. The following week the wind was the same but the tide going the opposite direction so starboard tack had the advantage. Everyone had figured it out by then, including the race officer who placed the windward mark in a more unbiased direction.

 

[BlueSkyNick]

He's right.

Think of it like this. The wind as experienced by a drifting boat is, as he says, about 010 because of the tide. Now, if you laid your windward mark on 010 and I came off the line on starboard doing, say, 3 knots at 45 degrees to the wind I will pointing at 325 at 3kts through the water but going over the ground more like 345/350 at probably 2.5 due to being taken East by the tide. Similarly if I was on port I would be pointing 055 at 3 knots but going more like 065/070 at nearly 4 knots over the ground. Since your mark laying team have done a good job of actually securing the thing to the bottom you can see that you're making progress at 20/25 degrees off course on Starboard but 55/60 on port. So to get to the top mark if it was laid at 010 would mean a lot more starboard tack than port.

Yes that's much the same as he explained it. My thinking is that the offset you experience 'due to be taken East by the tide' is the same as what causes the wind experienced by the drifting boat. The boat can either be drifting or sailing to the mark, not both, so the tide can only be counted once - albeit that I realise I am wrong!

 

[DJE]

If you had some sort of strange boat that could sail dead to windward you would set off heading 010 degrees but making something like 025 degrees COG (depending on boat speed). So despite sailing dead to windward you would miss the windward mark if it was laid 010 degrees from the start. Hence a real boat would sail more on one tack than the other.

 

[Angele]

If you had some sort of strange boat that could sail dead to windward you would set off heading 010 degrees but making something like 025 degrees COG (depending on boat speed). So despite sailing dead to windward you would miss the windward mark if it was laid 010 degrees from the start. Hence a real boat would sail more on one tack than the other.

A difficult concept to get your head around, but that is a good way of explaining it :encouragement:

 

[lw395]

First you need to define 'true beat'.
A beat in a cross tide cannot be made exactly like a true beat in no tide, because the mark is moving through the water.
So if I were RO, I might aim to make the average boat spend an equal time on each tack.
Let us say the WW mark is to be 2 miles upwind.
Let us say the average boat will do 5 knots through the water.
Let us say the boats sail 42 degrees from the true (sailing wind) wind.

Then look at the COG and SOG for each tack.
Port tack CTS is 52deg and stbd its -32
Take the sines of those angles and multiply by boat speed. Average them to get the net boatspeed west of 0.625 knots. Then add the 1 knot of tide
Then average the cos's to get the VMG north 3.66 knots
So the true bearing to the mark needs to be invtan (1.625/3.66) or 24 degrees.

Changing boat speed, pointing angle etc will change things a bit.
It's nonsense anyway, the tide will be generally weaker offshore, or something more complex will be happening. Or the wind will shift 15 degrees...

 

[BlueSkyNick]

Let us say the boats sail 42 degrees from the true (sailing wind) wind.

Then look at the COG and SOG for each tack.
Port tack CTS is 52deg and stbd its -32
....
Take the sines of those angles and multiply by boat speed. Average them to get the net boatspeed west of 0.625 knots. Then add the 1 knot of tide

.

Here is my mental block.

You have offset the COGs on each tack because of the tide, so why add the 1 knot of tide again to get the VMG ? Hasnt the tide been taken into account twice?

 

[BlueSkyNick]

If you had some sort of strange boat that could sail dead to windward you would set off heading 010 degrees but making something like 025 degrees COG (depending on boat speed).

Why?

 

[lw395]

Here is my mental block.

You have offset the COGs on each tack because of the tide, so why add the 1 knot of tide again to get the VMG ? Hasnt the tide been taken into account twice?

Unfortunately I looked at a mirrored version of the original problem, I was reading it as westgoing tide.

The hypothetical race start is in a ground wind of 6kts from 000degs, with a steady tide of 1 kt from west to east. On what bearing should the windward mark be laid from the centre of the start line to provide a true beat on the first leg?


The wind seen by the boat is a combination of the ground wind and the tide.
Imagine there is no ground wind, a yacht in the tide taking it left feels wind apparently coming from the left.
So the north wind in the left going tide will be bent to the left, relative to the water.
So the boat is steering more left, plus the tide is taking it left.

Imagine a more extreme case, 3 knots of Eastgoing tide, 3 knots of North wind.
A boat will head due east on starboard, and have a cog of boat speed plus tide
On Port it will head due north, making boatspeed to the north, plus tide to the east.

 

[DJE]

Why?

Beacuse you are sailing in a cross tide. So the boat isn't going where you are pointing her. Even though the apparent wind is right on the bow the tide is pushing you sideways.

 

[flaming]

Why?

Think of it another way. Do the true wind calculation, and you get a True wind angle of 010.

Now imagine that all the time the boats are beating back and forth there is a film boat motoring directly up the middle of the beat filming the action, and it's going 010 straight into the true/sailing wind at the same speed as your fleet's VMG to windward. (I know some people call it sailing wind, but I think True is better)

Now do an old school traditional ded reckoning calculation with the known tidal stream for where that boat will be when it's gone the distance you want the windward mark. And if your aim is to have the boats spend the same amount of time on each tack, then that's where to put the mark.

 

[johnalison]

The way I read the problem, without using numbers, was that the requirement is to provide a starting line where boats from each end have an equal chance of reaching the mark at the same time. Ignoring port and starboard rules, this would only happen in the example if the line were slanted "towards" the tide when viewed from above.

 

[flaming]

The way I read the problem, without using numbers, was that the requirement is to provide a starting line where boats from each end have an equal chance of reaching the mark at the same time. Ignoring port and starboard rules, this would only happen in the example if the line were slanted "towards" the tide when viewed from above.

Not quite - that's about the setting of the start line, which is a different subject. This is about the location of the 1st mark, which should ideally be set so that boats spend an equal amount of time on each tack, thus making more tactical options available and thus helping spread the fleet out a bit, as well as making it a more interesting race for the competitors. A race where 80% of the 1st beat is spent on one tack just turns into a drag race and so in handicap racing favours those who can point higher and in OD racing can lead to some pretty epic pileups at the 1st mark.

 

[Keen_Ed]

ISAF race management guide on currents: Basically, slow boats take a long time to make it to the windward mark, so get swept a long distance down current, so need the windward mark further down current for a fair beat.

L.7.3 Effect on the windward leg
A current parallel to the wind changes the velocity but not the direction of the apparent wind. It also alters the track of close-hauled boats but no course adjustment is necessary to ensure equal times on each tack to reach the windward mark, compared to faster boats in the same conditions.

The correct bearing to a mark may be altered drastically by a cross-current. A cross-current carries boats downstream while they are beating and therefore the windward mark should be located downstream to ensure boats sail equal times on each tack and fulfil the ideal of maximum sailing area.

The correction required in a cross-current varies with the speed of the boats. The faster the boats the less time they take to reach the top mark and therefore the smaller correction required. In our example in paragraph L.8.1 above, with a true wind of 7 knots and a crosscurrent of 1 knot the apparent wind was from 8° downstream of the true wind.

If boat speed in these conditions is 4 knots and boats sail at 45° to the apparent wind, the windward mark should be set 26° down the current of the Race Committee Signal Boat. This leads to a rule of thumb for a cross-current. Assess the difference between the wind directions for sailing boats and the Committee boat by observing boats luffing. Multiply by three and set the windward mark at that angle downstream. For fast boats the correction would be less, to have equal times on each tack while beating to the top mark.

Obviously, from the example above, corrections may become very large. The Race Officer must decide what changes in tidal current will occur during the leg and during the race and set a course to allow for these keeping in mind the effects of the current on the off-wind legs.

 

[DJE]

Cowes is just about due south of Hill Head SC but in a southerley wind, with the west-going ebb running we sail it in one tack.
With a southwesterly against the ebb it's a reach!