Zezo forum: Orthodromy vs loxodromy around the poles

Orthodromy vs loxodromy around the poles

Post by Valou | 2020-11-27 | 08:50:12

Hello,
As we are arriving soon on VR around the poles, the ortho/loxo routes becomes more different; shoud we consider now the loxo and if so, is it by aligning now the bleu line on the route but considering the red/ortho cap value?
Alors is there a correction to apply on the TWA?
Thank you :-)

5 Comments

Post by zezo | 2020-11-27 | 10:44:08

There is a way to sail the blue line - place a waypoint 12 or 24 hours ahead, with heading to it equal to the one indicated by the track tool. And yes, it matters after few hours.

TWA is twa. You are going for the optimum if sailing up/downwind everywhere in the wordld.

Post by Paul Shore | 2020-12-15 | 17:58:22

Zezo tells me to go mostly for 150� in the first two hours, doing here and there a few short sections of 10 min at 145�; then a bit more than 4 hours at 150, before jibing for 155. So I checked the green line TWA and set it for 149 in the first two hours and then I programmed to go untiul the jibe at 150.
Now my point is:
What if I take the coordinates of the jibe and set a waypoint there?
I know it will follow loxodromy, so a shorter route.
I did it and of course my bearing is 147�, and a guess that it will progressively rise until something around 153� (it could be ok given the strong wind that rises the VMG bearing up until around 155�).
But then I wonder: is this a smart move? The router calculates routes with orthodromy. How can I be sure that that following a loxodromy my route shoud still head to that point for a jibe?
Can you please help me clarifying the point?

Post by BooBill | 2020-12-15 | 19:26:20

Think you have ortho and loxo mixed up, or at least the way WP work.

Orthodrome is the great circle route, which is the shortest distance around a sphere.

Loxodrome is a constant compass bearing or rhumb line.

Waypoints in the game follow an orthodromic path. Setting a WP at the coordinates of your intended gybe point will sail the shortest distance to that point. However, that may not be the fastest as you may not be at the best wind angle.

In this case, the wind will be lifting you as you proceed to the gybe point. Be careful that your path will not have you exceeding max VMG angle. I've found trying to calcuate wind angles when using WPs extremely difficult to do and will tend to use TWA instead.

Post by Paul Shore | 2020-12-15 | 23:30:00

Thank you BooBill.
I was writing constantly inverting ortho and loxodromy. But, beside that, the concepts were quite clear but I needed a confirmation to my hypothesis. Your answer was super clear and very helpful. Thanks, again.

Post by zezo | 2020-12-16 | 12:21:25

We've been sailing mostly VMG angles in the past days, but once the desired direction falls inside those for a while the router will tend to sail orthodromy. Unless there are dips in the polars, in which case it will sail TWA around the dip.

For example see the polars between 27 and 30 knots TWS. It will probably try to avoid 135 and instead alternate between 130 and 140.