What's in a shape

A sail forms a 3-dimensional surface whose shape is ever changing, and can be changed at will. The sail does not have one single shape: It stretches under loading, but it can change shape without stretching, too. In fact, a sail can have a multitude of shapes without stretching (but not any shape whatsoever!).

In an isometric deformation, the distance between points on the sail surface remains unchanged. In other words, the sail does not stretch, shrink or rip. Although stretching does influence the shape of the sail, isometric deformations are by far more important. As an extreme example, consider the shape of the sail folded in its bag or up and flying in the wind. These large deformations (shape variations) are for the most part isometric.

Gaussian curvature & sail shape

Any shape is not possible without stretching the sail, since isometric deformations are limited by a factor called Gaussian curvature. According this law discovered by the famous mathematician, the product of the largest and smallest radius of curvature in each and every point of the surface remain the same, as long as the deformations are isometric (i.e. there is no stretching or shrinking involved). In sail terms, if the sail gets more curved in the vertical direction, it will get less curved (flatter) in the horizontal direction. This is what happens when you lift the spinnaker pole, for instance. This Gaussian curvature is unique to every sail, defining its shape and remaining unchanged through all major deformations the sail will undergo on its way from the bag to the top of the mast.

The flying shape

Gaussian curvature is meaningful to the sail designer. Basically, it makes no difference whether the designer designs the sail folded in its bag or up and flying in the wind. In practice it is useful to try to find, from the almost infinite amount of possible shape variations, the one that corresponds as closely as possible to the actual shape when sailing (in the wind the sail is designed for). This is known in sailmaker's jargon as the flying shape of the sail - a good hype-term for a crew member or sail consultant who wants to appear smarter than he is. When the designed shape of the sail closely resembles its flying shape, it is easier for the designer to grasp how small variations will affect the sail shape in a future design. Photographs taken from down below will give a direct comparison with the design. And it is much easier for the sailor to communicate his thoughts to the designer and understand effects of various trim control lines, as he discusses the sail with the sailmaker. Clearly, there is a strong case for the design to mimic the flying shape.

Sails for the real world

The regular sail design program is geometrical, it does not understand a thing about the flying shape of the sail. The desired Gaussian curvature can be achieved with an infinite amount of shapes. It is quite possible to design shapes that cannot be achieved in the real world with a sail cut from fabric-material. Creases and wrinkles may form when the sail is finding its natural shape in the sailing situation.

This is where DynaSim fits in. Dynamic simulation of sail shape complements and takes the traditional, purely geometrical design a step further. Dynamic simulation allows for the stress-strain (stretch) characteristics of the fabric or laminate, not only in the warp and fill direction, but also in the diagonal. In-plane bending stiffness, weight, porosity (spinnaker fabrics), wind pressure and even friction when the sail is touching the rigging can be taken into account. Since DynaSim is physically based, gravity is a factor especially when dealing with spinnakers in light winds & manoeuvres. The sailcloth can be varied in different parts of the sail, to mimic real sail design and to investigate the effect of substituting heavier and stiffer material in parts of the sail.

DynaSim is based on a particle metaphor: The sail surface is represented by "particles", attached to each other with flexible springs. The stiffness of the springs can be varied, defining the physical stiffness of the model. DynaSim performs its magic in small steps, adjusting the flying shape of the sail until a balance is found between the internal stresses and the external forces: wind pressure, gravity and motion generated accelerations. The constraints set by sheet and halyard tension, forestay sag and mast bend are all met, making it possible to study effects of sail trim on the designed shape. The end result can be a 24 frames per second animation of the sail behavior, where every frame is a product of thousands of iteration steps. The aerodynamic model used for DynaSim is fairly coarse, to perform the calculations in a reasonable time. But that is unimportant, since from the flying shape point of view, external forces transmitted through the mast, rigging, halyards and sheets are much larger and far more important than details in the wind pressure distribution. The final shape can be fed back into a more accurate aerodynamic simulator, to obtain more exact forces & moments if desired.

Wrinkles and creases

Wrinkles play a significant role in real world sail behavior and trimming. Wrinkles and creases usually influence much more the sail shape than stretch. Wrinkles are due to local compression in the fabric. Low compression stiffness is characteristic to fabric materials - in engineering terms sail cloth buckles easily under small compressive loads, due to its low bending resistance. Sailcloth, on the other hand, has a very high strain resistance, or ability to resist stretch when pulled. Bending stiffness is usually increased in the corners of the sails by adding several layers of fabric, patches, to avoid excessive wrinkles. On the other hand, wrinkles are useful in light airs. Sails are usually designed and cut for medium, 10 to 12 knot winds. In light winds, fuller sails are more efficient, and fullness can be significantly increased by allowing the luff of the sail wrinkle in a suitable fashion. Modeling wrinkles in fabrics is no simple task - it demands a dense "grid" and setting the mesh in a such a manner that it hinges correctly allowing for natural wrinkling. DynaSim is capable of predicting wrinkling fairly realistically, as comparisons to real world sails show, but there is still a lot to be learned in this particular area. Patches and battens are simulated in DynaSim by adding elements with a large bending stiffness.

Looks nice, but what is it good for?

So how can dynamic simulation help to create better sails? It has a large field of application for the sail designer:

• assessing the flying shape of the sail
  
• simulating the effects of various trim lines (halyards & sheets, forestay sag, mast bend etc.)
  
• appreciating the deformation of sails under load, to help choices of materials
  
• setting apparent wind speed (AWS) limits for a given sail
  
• estimating apparent wind angle (AWA) limits for spinnakers, gennakers and asymmetricals
  
• educational purposes, coaching and for illustrating trimguides

You don't need to be a sailmaker to understand that the list above represents a major step in sail design. Sail dynamic simulation is still in its early stages, but expect it to be a "standard issue", fully incorporated into saildesign software within 5 years or so. As it is now, DynaSim completes one of the runs shown on this page in a couple of minutes... but setting up the simulator can take days for one particular boat and sail. On the other hand, once the setup is ready, investigating the effects of trimming the sheet or increasing the wind from 10 to 20 kn is a matter of minutes. Very cheap compared to actually physically making the sail, going sailing and
photographing it.

Scale effects - size does matter

Dynamic simulation clearly demonstrates that the size of the sail has an important effect on its behavior - something that has been more or less ignored in the past. So you cannot draw too much parallel between an America's Cup boat's 500+ sqm. asymmetrical and a 40 ft IRC- boat's 100 sqm A-sail. Notwithstanding the apparent wind angle differences with the height (very important per se, they too..), there is considerable differences in the dynamics of different sizes of sails. For downwind sails, often the same materials are used for big and small boats. The bending stiffness affects significantly the dynamics in different scale: Think about a 10x10 cm piece of spinnaker cloth at the tip of your finger, and compare it to a 100x100 cm piece. They will wrinkle & drape completely differently.

The scale effect applies for small dinghies and one design boats jibs, too, where often a stiff "Polykote" or "HTP" fabric is used. The bending stiffness of these materials is so appreciable that it affects their shape. Similar designs in Polykote fabrics for bigger boats will behave differently, due to scale effects in sail dynamics.

The largest source of error due to fabric scaling is probably in windtunnel tests - like the ones performed at the famous twisted flow tunnel of Auckland University. Dynamic simulation predicts that the models will behave differently from their real world counterpart. In wind tunnels, predictions and even direct conclusions have been drawn for full scale AC-gennakers and spinnakers, with models only 1 meter high, while the real sails (cut in the same fabric) hover at 35 m heights. Researchers maintain, however, that while the sail dynamics may be different, the order of merit still remains the same when comparing the performance of small models to full size sails in a wind tunnel.