# The meaning of circulation

Circulation is one of the most misunderstood terms in sailing. Yet, circulation is essential to understand lift and why sails, wingsails, keels, rudders, foils, etc., work. We can safely say that sailing is possible, at least when beating windward, thanks to circulation.

This content is for Pro members only.

## Flows in sailing

Sailing boats interact with flows of two very different fluids: air and water. Moreover, sailing boats are able to make their way through the water surface only because they work at the interface of these two fluids which are moving relative to one another at different speeds and directions. Before we dive into other aero-hydrodynamic considerations like lift generation, drag, etc., it is essential to describe first the nature and characteristics of these flows that make sailing possible.

This content is for Pro members only.

## Bernoulli’s principle

The physical significance of Bernoulli's equation is what is known as Bernoulli's principle. It states that when the velocity of a fluid increases, the pressure decreases, and when the velocity decreases, the pressure increases.

This content is for Subscriber, Advanced, and Pro members only.

## The Reynolds number

The Reynolds number is the ratio of inertia forces to viscous forces involved in the flow. Reynolds understood that while inertia forces were dominant in a turbulent flow, viscous forces were prevalent in a laminar one. In this way, the Reynolds number can be used to determine whether a flow is laminar or turbulent.

This content is for Subscriber, Advanced, and Pro members only.

## Understanding the boundary layer

In 1904, Ludwig Prandtl introduced an approach to understanding and analyzing flows around bodies that produced a massive breakthrough: the boundary layer. This concept would eventually lay down the foundations of modern aeronautical engineering, and today is at the base of most modern calculations of skin friction, heat transfer, and flow separation.

This content is for Subscriber, Advanced, and Pro members only.

## Wind triangle

The wind experienced by a fixed observer (true wind) is not the same wind an observer on a moving yacht will feel (apparent wind). The wind triangle helps us understand what the true and apparent winds are and how they are related.

This content is for Subscriber, Advanced, and Pro members only.

## Unswept Wings: coefficients and forces (calculation)

Calculation template How does it work? This calculation template uses Prandtl’s classical Lifting-line Theory. All the results are available for angles of attack from 0…