Sail craft and apparent wind theory

[rcgldr]

TL;DR Summary

Sail craft and apparent wind theory

I created this thread for a separate discussion of apparent wind theory from the thread about sailboats providing their own wind, which is a bit mis-leading title, since the OP's question is about using a fan blowing against a sail to move the sailboat forwards. A quote of a post from that prior thread (that may get deleted) related to apparent wind theory, and my response.

Apparently, none of you are multi-hull sailors. Multi-hulls do create their own wind. And regularly exceed windspeed by two or three times. On a reaching course, the side-force pushed on the boat and via the centerboards, are converted into forward motion. As the air accelerates over the wing shaped sails, it creates apparent wind. As the apparent wind increases, the sails go faster and create more wind. The only limit is drag, which is why iceboats can exceed 120 MPH. Maritime architect Nat Herreshoff knew this more than a century ago when he designed the catamaran Amarylis in 1874. At around 20' it blazed past 120' yachts, so much so it was banned from racing. Even the lowly 40 year old Hobie 16 can easily exceed 2x wind-speed, and the big foiling Trimarans now racing across the Atlantic go 3x or more, on hydrofoils. https://sailinganarchy.com/2019/11/05/fantastique/

"Apparent wind" theory is mis-leading. For a better description of what occurs, separate the apparent wind into crosswind and headwind components, and note that for a given heading relative to the true wind, the apparent crosswind component is constant, the true wind speed · sin(θ), where θ is the heading relative to the true wind, independent of the sail crafts total speed. For example with a 10 knot wind and a heading of 30° offset from the true wind, the apparent crosswind is 5 knots, regardless of the sail crafts speed. The apparent headwind always adds to the total drag on the sail craft (it's never a benefit), and along with the other drag forces from the water, land, or ice, limits the maximum speed of the sail craft for a given true wind and heading relative to the true wind.

What also appears to be a dilemma is that the downwind or upwind component of an efficient sail crafts speed can exceed the true wind speed depending on it's heading relative to the true wind. The America's cup catamarans achieve over 1.5x component of speed downwind or upwind. In the case of tacking downwind with a net downwind component faster than the wind, a sail craft is not outrunning the wind that propels it, but instead sails into a continuing "fresh supply" of wind that is ahead of the sail craft.

Using the water/land/ice as a frame of reference, there are two requirements for a sail craft to maintain or increase speed:

1. The component of lift in the direction of the sail craft's heading must equal or exceed all drag factors that oppose the sail craft's forward motion.

2. The true wind must be slowed down due to the apparent wind's interaction with the sail, even when the sail craft's downwind component of speed is greater than the true wind. This because slowing down the true wind is how energy is extracted to propel the sail craft.

 

[anorlunda]

I don't see a question in your OP.

I recall a trick question from long ago. What is the theoretical maximum speed of a sailboat?
When sailing into the wind, it is undefined. Only drag limits speed and the drag of an unspecified sailboat is not defined. Ditto for how close the angle can be to the wind, not defined for an unspecified sailboat.

Sailing iceboats, can reach 10x windspeed.
https://en.wikipedia.org/wiki/Ice_boat

 

[A.T.]

Only drag limits speed

To be more precise, the lift/drag ratios of the the air and surface interactions limit the maximal ratio of vessel speed to true wind speed:

http://www.onemetre.net/Design/CourseTheorem/CourseTheorem.htm

 

[anorlunda]

The course page linked by @A.T. is very helpful. Perhaps it answers @rcgldr's points also.

@rcgldr , Every thread on PF should be free-standing, and not require people to read other threads. For every one of us who reads this thread today and perhaps replies, there may be 1000 people in future years who come here based on a Google search and read the thread. Old PF threads are a knowledge base. We need to respect those people too.

 

[anorlunda]

I can remove the link to the other thread

No don't do anything more. I was trying to explain why each thread should begin with a question. If it doesn't, you may get zero replies.

 

[A.T.]

To be more precise, the lift/drag ratios of the the air and surface interactions limit the maximal ratio of vessel speed to true wind speed:

http://www.onemetre.net/Design/CourseTheorem/CourseTheorem.htm

Equation 1 from the link below shows the simple relationship between the lift/drag ratios and the achievable windspeed multiple:

https://www.lehigh.edu/~inugrs/images/poster_pdfs_2010/stilsonyoder.pdf

For boats, the tire side force / tire drag force just becomes the lift/drag at the water interface (hull+keel combined).