Day 3: STT -> Azores - Motor vs. Motor sailing

Blue Note
Marco M.
Tue 30 Apr 2013 16:14
Date: Tuesday 30/04/13 - Time: 12:00 EDT
Position 23:25.87N  61:40W
COG 30T SOG 4.5 kt, Wind 90T 12 kt, Barometer 1009.2 stable
Temperatures: Air 25.0C, Sea 22.7C
Last 24h Sailed Distance: 108 NM
Sailed distance since departure: 380 NM
Time since departure: 3d 3h 00m
Average Speed since departure: 5.06  kt
Intention: sail to Horta
Distance to End on rhumb line: 1913 NM
ETA: Saturday May 18
Diesel consumption: 18% diesel burned with 15% of passage done.
Detailed Track (50 is the maximum number of point, i.e. once the last point reaches 50, the last point always is 50):

So far this has been the slowest passage that Blue Note every made. There are still many more miles to go and the opportunity to bring up the speed but so far we have an average sailing speed of 5.06 kts and an average VMG of only 4.4 kts.

A part from two hours, right before coming up to region of rain, when the wind increased to 13 kts yesterday we have been running
the engine constantly. Luckily, since 9am a bit of wind fill up from the East and we are back sailing on a closed hauled course.

Yesterday afternoon the choice was between:
        1) dousing down the sails and motoring on the rhumb line
        2) Motor sailing at a close hauled course.

Since our destination is still very far (let's say far in the infinite) the choice was between which of the two option was giving the highest VMG.
It's obvious that the answer must be function of the wind speed (if no wind #1 is the right choice) and of the angle between
the wind and the rhumb line (if the angle is greater than the minimum sailing angle of the boat, #2 is the obvious choice).
So the real problem exist when the wind is within the dead sailing angle, that is when Jeff Lewis rule is true "the arrow on top of the mast always point to your destination".
It should be possible to write some equations to solve the problem.
I started to work on it but the too many distractions of the failed fishing attempts of Damien prevented me to concentrate sufficiently....
I believe in most cases many erroneously choose opt #1.
Due to the lack of a mathematical theory to guide us we followed an empirical approach and tried the two options.
Evidences seems to suggest that with an angle between wind and rhumb line of +/- ten degrees , as long as there is 8 or more kts of wind Blue Note is better off by motor sailing.
I hope we will not have many more chance to experiment the motor vs motor sailing choice and we are looking forward to the wind to shift to the west.
Unfortunately the grib file downloaded this morning does not show that for another 48 hours.

No fish to report but only lots of sargasso.