Quote:
Originally Posted by CaptForce
I agree that the dabate is not a question of position fixes or the use of navigation tools or of ant behavior. The debate is about calculating elapsed time. We can not dispute that the variables of speed and distance are direcly proportional to time. If speed and distance are increased or decreased proportionally, then time remains the same.
The debate is wether the choice of the constant heading or the shortest distance course GPS track results in a disproportional change in speed an distance.
I remain with the opinion that the time elapsed would be the same; however, as with any valid endeavor, I would be eager to hear convincing opposing opinions supported by good data.

All right, let's try again.
1. Distance sailed through the
water does not necessarily equal distance over the ground. If the
water is moving, it will ALWAYS be different.
2. The shortest path between any two points is a straight line.
3. Since we sail in water, we care about distance through the water, not over ground. Therefore, the shortest distance across moving water for a
boat is a straight line through the water.
4. A straight line through water is a constant heading. NOT a constant COG, which will vary according to the motion of the water.
Therefore, the shortest distance across moving water is a constant heading calculated to put you in that bit of water which will be in front of your
destination when you get there.
A corollary to this  a straight line across the ground, following the GPS approach, will ALWAYS be the wrong way across, unless either (a) the water is not moving; or (b) the water is moving at a constant speed and direction for the entire
passage (in both cases, constant heading and straight track across ground coincide).
OK, is that more clear? It boils down to this  you have a choice to go straight with regard to the ground, or straight with regard to the water. You need to choose the latter if you want to sail less distance and get there sooner. Sailing a straight line over ground means sailing a crooked path through water, which will add miles to your
passage. Except only exceptions (a) and (b) above, where the shortest paths through water and over ground are in the same place.
There are specific examples in Post 253 by Noelex, with calculations showing the difference in time and distances:
Distinct Activities: Shackled by a Common Name?
And in Post 237:
Distinct Activities: Shackled by a Common Name?
Let me give another example showing how different water and ground distances can be:
You are crossing a river one mile wide with a 6
knot current which runs due North and South. You are on the W bank of the river in a
boat capable of making 6 knots. You want to sail to a
dock on the E bank of the river which is one mile downstream from your point of departure.
You point your bow directly across the stream, and in 10 minutes you are there. You sailed 1.4 miles over ground but only 1 mile through the water, which is why you got there in 10 minutes although you were only going 6 knots.
That is to illustrate the difference in water distance and ground distance. In that example, you never feel the 0.4 miles extra over ground  you don't sail in the bottom.
Now another example  exaggerating the effect to underline  let's suppose you're crossing a tidal body of water, 60 miles across, on Mars, say, with the tide exactly perpendicular to your course. On Mars the tides run only for two hours at a time, then an hour pause, then two hours in the other direction, then 10 hours of slack water. They run at 10 knots. You are sailing W to E and the tide runs N and S.
What's the fastest way to get there? Go full speed ahead against the tide, when it's running, in order to stay closer to the rhumb line and minimize distance over ground? Or forget about the tides since they cancel each other out? If you hold a constant heading of 90, you will sail 60 miles through water and get there in 10 hours at 6 knots, although you will have sailed 100 miles over ground as the tide swept you back and forth. Sailing to your GPS and staying on the rhumb line you will sail a shorter distance over ground, but longer through the water. If you can make 10 knots at full revs and stem the tide when its running, then you will have sailed 60 miles over the ground, but you will have added 40 miles of useless sailing through the water, at redline to boot, and you will get there 4 hours later, by following the GPS approach.
In Post 237, you have a choice between sailing 60 miles through the water on a constant heading (although this is a huge "S" curve over ground, taking you 12 miles off the rhumb line at one point), or 75 miles through water on the rhumb line and 60 miles over ground. Since your boat can only sail in water, the constant heading saves you 15 miles and three hours of sailing, compared to staying on the rhumb line over the shortest distance over ground following the GPS approach.
Again, the shortest distance over ground will NEVER be the shortest distance through the water except for the two cases above. You never feel ground distance; you only feel distance through the water since that's what your boat
sails in. The shortest distance across a moving body of water is ALWAYS a constant heading.