Flows in sailing

Sailing boats interact with flows of two very different fluids: air and water. In fact, sailing boats can make their way through the water surface only because they work at the interface of 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.

One first important point is the distinction between flow and fluid:

  • Flow is the movement of a fluid. 
  • Fluid is any substance that can flow with relative ease and tends to assume the shape of its container.

1. Continuum or free molecule flow

A fluid consists of individual molecules moving around in random motion. These individual molecules collide with their neighboring ones after traveling a distance. We call mean free path to the average distance a molecule moves between collisions.

A body immersed in a flow with a much smaller mean free path than its size will not distinguish the individual molecular collisions over its surface. These collisions will happen very frequently. The flow will appear to the body as a continuous substance, and the body will feel the fluid as a continuum flow.

On the contrary, when the mean free path is in the same order of magnitude as the body’s size, the collisions with the body will be much more infrequent, and the body will feel each molecule’s impact separately. Such a flow is called free molecular flow.

Free molecular flow can be found in situations where the air density is very small, for example, when a space shuttle is at the outer edge of the atmosphere. It is also possible that the flow displays both continuum and free molecule flow characteristics, as is the case in “low-density flows.”

When studying continuum flows, instead of focusing on molecules, we focus on fluid elements. A fluid element is a very small element of fluid that can be identified and followed while moving within the flow. 

As a fluid element moves, the mass within the fluid element remains constant, although its volume can change (as is the case for compressible flows, see below) or stay constant (as is the case for incompressible flows, see below). Moreover, even if the mass remains constant, a fluid element would not always consist of the same molecules.

The advantage of working with fluid elements is that they describe the properties of fluid particles, averaged over a length scale that is large compared to the mean free path but small compared to the typical length scales of the specific flow under consideration.

Fluid elements are very useful when describing flow fields like the velocity field, which is the velocity value at each point of a fluid in space and time. Another example would be the density field.

In sailing

In sailing, flows (water and air) over hulls, keels, rudders, hydrofoils, sails, airfoils, and wings are always continuum flows.

2. Viscous or inviscid flows

An important property of fluids is viscosity. Viscosity is the measure of the fluid’s resistance to shear force (a force acting in a direction parallel to the fluid’s surface or a fluid’s layer), and its value depends on the temperature of the fluid.

The origin of the viscosity lies in electrostatic attraction forces that arise when two or more molecules are in proximity. Since these forces have a very short range (they are negligible when molecules are separated by just a few molecular diameters), a molecule feels an attraction only for those immediately surrounding it.

When a fluid flows, its molecules move from one point to another, giving rise to the phenomena of viscosity (friction), mass diffusion, and thermal conduction. Such flows are called viscous flows.

However, although real-life flows are always viscous flows, the influence of these phenomena is very small in many aero-hydrodynamic flows. For such cases, the flow is modeled as not exhibiting these phenomena. Such flows, which do not truly exist in nature, are called inviscid flows.

In fact, when a fluid flows around a body, the influence of viscosity (friction), diffusion, and thermal conduction is only limited to a very thin region adjacent to the body called the boundary layer. Thus, the flow around a solid is usually divided into two different regions:

  • The boundary layer where the flow is considered viscous.
  • The remainder of the flow outside of the boundary layer where the flow is considered to be inviscid.

This classical model of a thin viscous boundary layer along a body’s surface, surrounded by an inviscid flow field, has produced important engineering results for most practical aero-hydrodynamic problems.

Two regions of flow: viscous boundary layer and inviscid flow outside the boundary layer.

For flows over slender bodies, such as keels, sails, or air- or hydrofoils, the application of inviscid fluid theory to the region outside the boundary layer adequately predicts the pressure distribution, lift, and induced drag on the body. However, these inviscid theories cannot adequately predict drag since viscosity (friction) is a major source of it.

Similarly, when the boundary layer separates from the body surface, as is the case for sails trimmed with a high incidence angle (angle of attack) to the flow, or in the case of very blunt bodies, the separated flow is mainly dominated by viscous effects. Therefore, inviscid theory cannot predict the dynamics of such flows since they do not consider the viscous effects.

In sailing

The boundary layer and the inviscid flow outside of it are both very important flows for sailing, yacht design, and performance analysis.

3. Compressible or incompressible flow

In an incompressible flow, the density of the fluid remains constant. In contrast, in a compressible flow, the fluid’s density varies.

In real life, all flows are compressible. However, flows of liquids such as water and gases moving at a low Mach number (M, ratio of flow velocity to the speed of sound) can be considered incompressible without any loss of accuracy of the results.

In fact, for gases moving at Mach Numbers less than 0.3 (M < 0.3 or M < 370.44 km/h), it is safe to consider a constant density value.

In sailing

As a result of what has been mentioned above, water and air flows are always considered incompressible in sailing.

4. Rotational or irrotational flow

A flow is called irrotational if, at every point, the fluid elements move through space without spinning. On the contrary, the flow is called rotational if the fluid elements move through space with rotation. Irrotational flows are much easier to analyze than rotational one.

Rotational and irrotational motion of a fluid element.

In sailing

In sailing, water and air flows inside the boundary layer are highly rotational, while flows outside of it are essentially irrotational.

5. Steady or unsteady flow

The field variables (e.g., density, velocity) vary in unsteady flows (turbulent) depending on spatial location and time. That means that if we focus on a fixed point in space, the value of these variables will change with time. On the other hand, in steady flows, the field variables are a function of spatial location only. They do not change with time.

The vast majority of practical aero-hydrodynamic problems can be tackled considering steady flow.

In sailing

The flow (water and air) is considered steady in the majority of sailing applications and analyses.

6. Flow visualization

Flow visualization allows seeing the nature of the flow over a body, which helps to understand what is happening and provides guidance for improvement (e.g., reducing the drag). It can be used in either experimental (flow over an actual body) or numerical (post-processing operation in computational fluid dynamics) contexts.

There are three main sets of lines used to visualize flows:

  • Pathline: line that describes the trajectory that an individual fluid element follows on space over a certain period of time. 
  • Streaklines: line connecting the position of different fluid elements that have previously passed through a common point at a particular instant in time.
  • Streamlines: line that is everywhere parallel (tangent) to the velocity field. Since the velocity (speed and direction) at any point in the flow is unique, streamlines cannot cross (otherwise, the flow element would display two different velocities at the intersection point). In other words, no flow crosses a streamline.

In steady (no turbulent) flows, pathlines, streaklines, and streamlines are fixed in space and time and perfectly match one another. On the other hand, in unsteady flows, they differ, and their forms change with time.

Streamlines in a steady flow.

Furthermore, in steady flows, the flow rate (volume of fluid that passes per unit of time) between two streamlines is constant. That means that the flow speeds up where the streamlines get closer together and slows down where the streamlines get farther apart. Moreover, considering Bernoulli’s equation, we can also say that the pressure goes down where the streamlines get closer (the flow speeds up), and the pressure goes up where the streamlines get farther apart (the flow slows down).

Do you want to read more articles like this?


Some of the links shown below are affiliate links and we may earn a commission at no additional cost to you:


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.

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.

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.

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.

What is the Froude number?

The Froude number is a dimensionless number used to quantify the influence of gravity on the motion of a fluid. It is the ratio of the inertia forces to the gravitational forces related to the mass of water displaced by a floating boat.

The air-water interface

Water and air are two different fluids that enter into contact at the ocean’s surface at what is called the air-water interface. This interface plays an important role in ship hydrostatics and in describing the flow of water around a vessel.


Go to Courses


Go to Merch

Send us a Message