Looking for the magic number in wind vs tide...

Now you have explained it a bit more, I think you are unlikely to come up with a universal factor. Most of the reasons have already been aired.

Take a typical windward passage with a favourable Spring tide. Cowes to Poole, around 30 miles. Reasonably possible in one tide, but with prevailing SW wind, speed through water likely to be nearer 4 than 5. Conditions will vary enormously over the passage. For example Cowes to Hurst will likely be 4 or 5 long tacks into steepish short seas. At Hurst you have a choice - Needles Channel or North Channel. Both very different and give you a different course and sea conditions across Christchurch and Poole Bay. The tide at that point is running hardest and has more effect on the boat than other factors. The next change will be at Christchurch Ledge where the seas will become steeper again because of the shallow reef. Next choice is go inshore to take East Looe or stay out to use the main channel. Tide effect generally weaker closer inshore, but often wind less favourable. Ideally want to avoid entering the harbour against the last of the ebb as on springs it can run 3-4 knots.

Over the years I have used just about every combination on this passage. My boat is slow to windward and adversely affected by wind over tide chop, but quite enjoys going through the longer waves that you get in the Needles Channel. On the other hand the tide squirts you out much quicker through the North Channel and the mackeral are usually better on this course, particulalry as I usually have to motor sail and this presents the spinner at the right speed.

Guess what I am confirming is that there are so many variables, but some of them, particularly tidal streams are predictable, but speed through the water and VMG for the average cruising boat are so variable from boat to boat, from skipper to skipper, and more importantly dependent on the interplay of three unpredictable variables, wind speed/direction, tidal rate and water depth, further complicated by time - prolonged period of wind from a constant direction will have a different effect from short periods or variable wind.

My preference is always for making maximum use of a favourable tide as this moves you reasonably predictably over the ground independent of what is happening through the water. I then adjust my sailing strategy to get the best out of the wind conditions.

A cross tide passage such as Poole Cherbourg is much more predictable and easier to model, except at either end where tide/wind interplay can still be an issue.

Good luck with your project.
 
I assume you have the maths to support this quest..

If you can solicit some GPS plots off boats in the Round Island race you could compare their speeds in the fisrst leg to Cowes Wind Vs tide with the last leg ( wind with tide).

There will be at least two separate boat effects, the effect of the wave on the hull, (stopping or slowing some shapes more than others) and the effect on the rig (disturbing the efficiency more on small boats than larger ones).

Shore effect and Depth effects are other influences you may have to consider.

I doubt you would get enough useful data , you could perhaps employ dimensional analysis like Froude did towing planks to deduce the Froude no (and Reynolds), but they were giants in the world of fluid dynamics.

Still, standing on the shoulders of giants we learn to see afar.
Isaac Newton I think

Good Luck in your quest.
 

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