Planning a short journey to windward, with a backing wind

[Jim Cate]

Matt, with a business model like that,you will join a long list of folks who meant well...

Seriously, I'll be interested in the product from an academic point of view, and hope that you have a good time nutting it out (one long past day I might have too, but now, not so much!).

We await developments!

Jim

[The Smokester]

Here's an analysis of a simplistic case for your amusement:


We have a destination directly upwind at distance L.


We have two identical boats which can sail at 45 degrees to the true (westerly) wind on either tack and the conditions are such that this gives the optimal upwind VMG.


If the wind speed doesn't change, the boat speeds don't change and the optimal course (for these boats) is to sail at 45 degrees to the wind on either tack until the destination is at 90 degrees, and then tack towards the destination. The routing is along the two short sides of an equilateral triangle, with the hypotenuse (L) pointed directly along the wind. The total distance traveled will be L*2^(1/2) and there is no preference for starting out on port or starboard tack.


Now, let's start again and send Boat 1 off to the SW on a starboard tack and Boat 2 off to the NW on a port tack.


But now, just as the destination appears at 90 degrees (off the beam) for each boat (which will happen at the same time in this simple case) the wind suddenly shifts 45 degrees to the SW.


Boat 1 now has a direct head wind and must tack. Its change in heading is 90 degrees to starboard and it heads directly to the destination on a port-side beam reach. Total distance for Boat 1 is L*2^(1/2).


With the new SW wind, Boat 2 has a 45 degree lift and can head up to a westerly course. Thing is, it is off to the NE of the destination which is now directly upwind. So now it must sail to the new lay line directly south a distance of L/2 and then west a distance of L/2 to the destination. The total distance for Boat 2 is L*(2^(1/2)/2 + 1).


Thus, Boat 2 goes about 20% farther than Boat 1. Plus, Boat 2 is close hauled the whole trip whereas Boat 1 enjoys a leisurely beam reach for the second half of the trip.


I just made this up so hoping it's both correct and useful.

[GILow]

Smokester, what you write is correct, and... yep... useful too.

Well done!

BUT, it just underlines the fundamental problem, which is the wind shift is the make or break, and with a bit of further thought, shows that WHEN the wind shifts is the really critical bit.

Simplest case, wind shifts after you are in the destination port... no problem.
Next case, wind shifts before you leave home port... no problem.
Next case, wind shifts some time between these two times... problem.

Anyway, I am making some progress now. I am busy tidying the code to calculate the polar diagram equations for boat speed. My code works, but it is clunky. The idea is to be able to tweak the various constants to get a polar that looks just like my boat. By extension, the constants can then be adjusted to suit the characteristics of any boat likely to be used by the person using the software. And, as previously alluded, that's gonna be a HUGE audience.

Matt

[bewitched]

Originally Posted by GILow

Out of this process will come a piece of very accurate, useable software that I WILL make readily available to all users of CF, with no restriction, at no cost,

Someone beat you to it. There's an OpenCPN plugin for weather routing already. I've been testing it against Expedition and there is good correlation between the two.

[bewitched]

Oh, and about the quickest way to do your route. I think Monte got it right. Tacking to stay near the rhumb line initially and then closehauled on port to the finish. It will normally be quickest and is a low risk strategy (if the expected shift doesn't come).

Being on starboard after the shift is going backwards. (hence the sail to the new wind advice)

Going all the way south on starboard tack initially is a high risk option and I only think it will pay off if you can hoist a zero or an A3 for the port reach....and I doubt may cruising boats carry those.

[Seasick Steve]