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Aerodynamics of boat sails: lift, lift-to-drag ratio and sail shape

The aerodynamics of boat sails is that of a deformable wing: a sail sails upwind thanks to its lift, and its quality is measured by its lift-to-drag ratio. Three factors govern it at equal area and apparent wind: the angle at which the wind meets the sail, the profile shape and the aspect ratio. This page describes these three factors and leads to modeling a sail in Heliciel.

On this page:

1: Why the lift-to-drag ratio of a sail matters

Sail shapes have evolved with techniques and with knowledge of aerodynamic phenomena. This search for the best lift coefficients and lift-to-drag ratios gave us the present shape of yacht sails. The lift-to-drag ratio represents the ability to sail upwind, hence the freedom of movement of the boat.

In the age of sail, this freedom relative to the wind direction was essential to the development of maritime transport. It provided:

2: The sail, a deformable wing

Far from being complete, the evolution of boat sails is close to that of wings and hydrofoils. A sail is a deformable wing, and its aerodynamics resembles that of a wing. Studying airfoils, then wings, is the first step to understanding the aerodynamic phenomena acting on sails.

3: Sail polar: aspect ratio and lift-to-drag ratio

The quality of a sail is determined by its lift-to-drag ratio, the ratio of the lift coefficient Cl to the drag coefficient Cd. A polar plots Cl against Cd for each angle of attack α of the wind on the sail. The polar below compares various sail shapes, from aspect ratio (AR) 6 down to 1/3.

Boat sail polars: lift coefficient Cl against drag coefficient Cd for aspect ratios AR of 6, 3, 1 and 1/3, with angles of attack in degrees

Polar of sails of aspect ratio 6, 3, 1 and 1/3: the more elongated the sail, the faster lift climbs for low drag. (Figure labels are in French: "Coefficient de portance Cz" is lift coefficient, "traînée Cx" drag coefficient.)

On the figure, the aspect ratio 6 sail reaches a Cl close to 1.2 around 15° of angle of attack while keeping a low Cd, whereas the aspect ratio 1/3 sail reaches that Cl only with a Cd above 1. We can see that the aspect ratio of triangular sails clearly improves close-hauled performance.

4: Angle of attack, profile and aspect ratio: the performance factors of a sail

At equal area and equal apparent wind speed, the performance of a sail depends on several factors:

  1. The angle of attack at which the wind enters the sail determines the drag and lift forces. Their ratio gives the lift-to-drag ratio of the sail, and we always look for the angle that gives the highest one.
  2. The profile shape: the lift-to-drag ratio varies with the camber of the profile and with the Reynolds number. This Reynolds number gives the type of flow for all profile sizes and fluid speeds: Re = (mean velocity × reference length) / kinematic viscosity of the fluid.
  3. The aspect ratio of the sail: the lift of a wing comes from the low pressure on its upper surface and the high pressure on its lower surface. At the wing tip, the air from the high-pressure side goes around the tip to the low-pressure side and forms a vortex proportional to the pressure difference. This phenomenon reduces lift at the wing tip. To limit this loss, we must avoid concentrating lift at the tip and spread it over a large span. To learn more, see wing aspect ratio.

Other factors, such as twist, roughness or the interaction between sails, are decisive too. But let us first concentrate on modeling a sail that takes these three factors into account: angle of attack, profile shape and aspect ratio.

5: Modeling a sail with Heliciel

The following video is a tutorial on designing and modeling a sail with Heliciel.

modeling of a sail with Heliciel

To go further, we can see how aspect ratio and the winglet limit wing-tip losses, or how a wing is modeled in 3D in Heliciel.