Of sailing and relativity and titillating patterns

[DaveC426913]

(This is about SR. Really.)

While learning sailing the other day, I was told I was understeering when tacking. Here's my problem:

1] "Close haul" is a Point-of-Sail less than ~30 degrees (or so) from head-to-wind. (i.e. if the wind is coming an angle less than 30 degrees off the bow, you are on a Close Haul PoS.)
2] "Tacking" is the act of turning the boat through the wind from a Close Haul on one side, to a Close Haul on the other side.

Thus, in performing a successful tack, you will change direction by (30 +30) = no more than 60 degrees, right?

Wrong!

3] A successful tack will have you pass through a full 90 degrees. It will do this without violating rules 1 and 2.

How can this be? When does 30+30=90?


When the axes of wind direction do not stay fixed wrt the boat as it turns.

(Let's take just one half of the tack for simplicity) Even though I rotate the boat from "30 degrees from head-to-wind" to "zero degrees from head-to-wind", the boat must actually rotate a full 45 degrees to do this.

Why? Because (forget the turn for a minute, let's look at a boat going straight) the forward motionof the boat changes the angle of the wind wrt the boat itself, moving the angle from an actual 45 degrees to an apparent 30 degrees. When the wind was coming across the bow at 30 degrees, that was wrt and obnserver in the boat's frame of reference. An observer in the water would calculate an angle of wind wrt boat as 45 degrees.

Thus, on the boat, a 60 degree wind-direction-change requires a 90 degree boat-direction-change.

As my skipper explained it, the wind angles "scissor together". And the faster you are travelling, the more they scissor together.

This was a moment of Zen. This "scissoring axes" is a term I've heard elsewhere, in physics texts, and in threads discussing time dilation, explaining the distortion of spatial and temporal axes at relativistic speeds.

But I can't quite get the thought to gel in my head.

Sometimes my brain can smell a personal higher understanding of the universe - but on the whim of a breeze, it is lost. Damn you middle-aged brain.

 

[Jorrie]

(This is about SR. Really.)
...
This was a moment of Zen. This "scissoring axes" is a term I've heard elsewhere, in physics texts, and in threads discussing time dilation, explaining the distortion of spatial and temporal axes at relativistic speeds.

But I can't quite get the thought to gel in my head.

Sometimes my brain can smell a personal higher understanding of the universe - but on the whim of a breeze, it is lost. Damn you middle-aged brain.

I guess what your "Zen moment" was directing you to was Minkowski spacetime diagrams. There the spatial and temporal axes of a fast moving object, as viewed from an inertial reference frame, "scissor together" as speed increase. As the speed of light is approached, the scissor approaches a "closed state".

Actually, the above (simplified) description is not quite true, because it implies acceleration, in which case the object’s world-lines are curved. It is more correct to view a number of objects, all moving inertially, but at different speeds relative to an inertial reference frame. As viewed from the reference frame, each object's spatial and temporal axes are at an angle to each other, with the angle becoming close to zero for an object moving at near the speed of light.

Sorry for a somewhat convoluted explanation, but I hope it brings it all back!

 

[DaveC426913]

I think I want to take some courses.

Start with a refresher of HS Calculus, then move on to post-secondary physics.