Aerodynamic force components for two points of sail. Left-hand boat: Down wind with stalled airfow— predominant drag component propels the boat with little heeling moment. Study Of Abrupt Transitions in Two-Dimensional Flows PDF on sails depend on wind speed and direction and the speed and direction of the craft.

Författare: Sergiy Kravchuk.

Swirling and stratified flows demonstrate a complex

behaviour with rich spectrum of possible regimes and

sudden changes in the pattern of flow. It is known

that these flows may become sensitive to small

perturbation in boundary conditions and form an

internal jump-like transition from one flow pattern

to a different one a hydraulic jump in stratified

and a vortex breakdown in swirling flows. Analysis of

the motion equations for such flows reveals

singularly perturbed nature of the problem; this

explains the abruptness and sensitivity of

transitions. The book reviews the model flows,

develops a theoretical framework for handling the

singularity at the point of transition, and provide a

procedure for finding the transition point. A

generalisation of the Tikhonov s boundary function

method is developed to study the problem. This

approach is illustrated by calculating of parameters

of an internal hydraulic jump for a model stratified

fluid flow. The book is aimed for graduate students

and professionals in fluid mechanics and applied

mathematics.

For apparent wind angles aligned with the entry point of the sail, the sail acts as an airfoil and lift is the predominant component of propulsion. For apparent wind angles behind the sail, lift diminishes and drag increases as the predominant component of propulsion. Various mathematical models address lift and drag by taking into account the density of air, coefficients of lift and drag that result from the shape and area of the sail, and the speed and direction of the apparent wind, among other factors. This knowledge is applied to the design of sails in such a manner that sailors can adjust sails to the strength and direction of the apparent wind in order to provide motive power to sailing craft. The combination of a sailing craft’s speed and direction with respect to the wind, together with wind strength, generate an apparent wind velocity. When the craft is aligned in a direction where the sail can be adjusted to align with its leading edge parallel to the apparent wind, the sail acts as an airfoil to generate lift in a direction perpendicular to the apparent wind. To understand forces and velocities, discussed here, one must understand what is meant by a „vector“ and a „scalar.

Driving force overcomes resistance to forward motion. Apparent wind and forces on a sailboat. As the iceboat sails further from the wind, the apparent wind increases slightly and the boat speed is highest on the broad reach. The sail is sheeted in for all three points of sail. Sailing craft B is on a beam reach. Sailing craft C is on a broad reach.