# Sail craft and apparent wind theory

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• rcgldr
In summary: The course page linked by @A.T. is very helpful. Perhaps it answers @rcgldr's points also."The equation is from Course Theorem, which explains that drag and lift forces acting on a sailboat determine the maximum speed that the sailboat can travel in a given wind and heading. For a sailboat to travel faster than the wind, drag would have to be reduced to zero, while lift would have to be increased to exceed the drag. For a sailboat to travel slower than the wind, drag would have to be increased to exceed the lift.
rcgldr
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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.

Catsailor said:
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.

Last edited:
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

anorlunda

@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.

rcgldr said:
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. said:
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).

## 1. What is the purpose of apparent wind theory in sail craft?

The purpose of apparent wind theory in sail craft is to understand how the wind affects the movement and speed of a sailboat. It takes into account the combination of true wind (the wind outside of the boat) and the wind created by the boat's movement, known as the apparent wind. This theory helps sailors optimize their sail settings and maneuver their boat efficiently.

## 2. How does the apparent wind angle affect sailboat performance?

The apparent wind angle, which is the angle between the direction of the true wind and the boat's heading, greatly affects sailboat performance. A sailboat can only move in the direction of the apparent wind, so the angle at which the sails are set can either increase or decrease the boat's speed and efficiency. Sailors must constantly adjust their sails to maintain the optimal apparent wind angle for their desired direction of travel.

## 3. What is the difference between true wind and apparent wind?

True wind is the wind that exists in the environment and is unaffected by the boat's movement. Apparent wind, on the other hand, is the combination of true wind and the wind created by the boat's movement. It is the wind that a sailor feels on their face and the wind that fills the sails. Understanding the difference between these two winds is crucial in sailboat navigation and performance.

## 4. How do sailboats use apparent wind to sail upwind?

Sailboats use apparent wind to sail upwind by tacking, which is the process of zigzagging the boat's direction against the wind. By tacking, the boat can effectively use the apparent wind to fill the sails and propel the boat forward. The angle of the sails must be adjusted accordingly to maintain the optimal apparent wind angle for upwind travel.

## 5. Can apparent wind theory be applied to other forms of transportation?

Yes, the principles of apparent wind theory can be applied to other forms of transportation, such as airplanes and cars. In these cases, the movement of the vehicle creates an apparent wind that affects its performance. For example, airplanes must take into account the apparent wind to maintain lift and cars may use the apparent wind to improve fuel efficiency. However, the application of apparent wind theory may vary depending on the specific vehicle and its design.

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