You are standing at the helm of a sailing yacht, the wind is blowing almost in your face, and the boat stubbornly moves forward against the wind. It seems like magic that the sail allows the boat to go almost where the wind is coming from, instead of just pushing it backward. So what is the secret, how does a sail on a yacht work and why can it move even against the wind? There is a classical explanation based on Bernoulli's principle and a modern perspective grounded in Newtonian mechanics and the Coanda effect. Let's explore them in order so that the question of how a sail works on a yacht becomes understandable even for beginners. For more insights into sailing, explore our Sailing Theory articles.
Classical Explanation: Bernoulli Effect and Sail's "Lift Force"
Bernoulli's Principle in a Nutshell
The classical theory of how a sail works is largely analogous to the explanation of an airplane wing's lift force. It is based on Bernoulli's principle—a fundamental law of hydro- and aerodynamics. The essence of the principle is that in a fluid or gas flow, pressure decreases as the flow speed increases. That is, where the airflow moves faster, a region of reduced pressure is created. This principle was formulated by scientist Daniel Bernoulli in the 18th century and has since been successfully applied to explain various phenomena—from airplane flight to carburetor operation.
A simple demonstration of the Bernoulli effect is the paper sheet experiment. If you take a piece of paper by one short edge and blow over it, the sheet lifts up. The air passing over the sheet accelerates, the pressure above the sheet drops, and the higher pressure below pushes the sheet upward. Thus, the airflow seems to "suck" the light sheet upward—this is a manifestation of Bernoulli's principle.
The same idea applies to the sail. A sail can be imagined as a vertical "wing" spread out in the air. When the oncoming wind meets the sail at an angle, the airflow divides into two streams: one flows around the windward (convex) side of the sail, and the other around the leeward (concave) side. According to the classical approach, the air flows around the convex side of the sail faster than the concave side, resulting in lower pressure on the convex (windward) side than on the concave side. As a result, a pressure differential arises: the reduced pressure on the windward side seemingly "sucks" the sail forward, while the increased pressure on the leeward side pushes it. These forces together create a forward-directed force—the very thrust that drives the yacht. By analogy with a wing, it is said that the sail generates a lift force perpendicular to the oncoming flow. A component of this force pulls the boat forward.
Fig. 1: Diagram of forces on a sail.
The red arrow L – lift force (lift) of the sail, perpendicular to the oncoming wind VA.
The red arrow D – drag force.
The geometric sum of these aerodynamic forces (FT) is decomposed into forces acting on the boat: useful forward thrust FR and unwanted lateral force FLAT, attempting to shift the boat sideways.
The yacht's keel counters the lateral force, allowing the sail to accelerate the boat forward.
Indeed, the force generated by the sail is largely similar to the force from an airplane wing—it is directed perpendicular to the oncoming flow (see Fig. 1). This force can be decomposed into two components: one in the direction the yacht is moving forward, and the other sideward, pushing the yacht to the side. Sailors have long mastered handling the side component: a deep keel or a centreboard underwater creates a counteracting force, preventing the yacht from sliding sideways. As a result, when the forces are balanced, the sail pulls the boat forward, and the keel prevents it from drifting sideways.
Thus, the classical Bernoulli explanation describes the sail's operation as the sail generating lift due to the pressure difference on its sides, similar to an airplane wing. This lift force overcomes the resistance of water and wind, causing the vessel to move forward. At first glance, everything seems convincing, and for a long time, this was how "why the sail holds the wind" was explained. However, this theory has several nuances and weak points.
Problems and Paradoxes of the Classical Approach
Although Bernoulli's principle undoubtedly acts and the pressure difference on the sail is indeed observed, the purely Bernoullian explanation often suffers from simplifications. A classical example is the so-called myth of "simultaneous arrival of flows." Old textbooks claimed that the airflow split at the sail's edges must meet simultaneously at its trailing edge. From this, it was concluded that the flow traveling along the convex side must cover a greater distance in the same time, resulting in higher speed and lower pressure. In reality, nothing in nature forces the flows to "meet" simultaneously—experiments show that the upper flow arrives earlier than the lower one, not due to some mysterious agreement, but because the low pressure literally draws the airflow from above, accelerating its flow. In simpler terms, cause and effect are confused: the pressure difference does not arise because the flow is obliged to hurry somewhere, but because the shape and angle of the sail cause the flows to accelerate and deflect, creating a pressure differential.
Another drawback of the purely "pressure" approach: it's difficult to explain a flat sail or even a board set at an angle to the wind. After all, even a flat plate can create a lift force at a certain angle of attack—and in Bernoulli's concept, without surface curvature and path length differences, this is not so obvious. In practice, sails do not always have an ideal wing profile: their shape can be changed, they can be stretched quite flat. Nevertheless, even a relatively flat sail at the correct angle to the wind pulls the boat. The classical explanation through mere curvature and pressure difference does not provide an intuitive answer as to why this happens.
Finally, the Bernoullian model does not immediately explain why when turning closer to the wind, a yacht sometimes goes faster, even though the sail's area "facing the wind" decreases. It seems that the more the sail "catches" the wind, the stronger the thrust. But experienced sailors know that with optimal tuning on sharp courses (closer to the wind), the yacht can develop greater speed than on full courses with tailwind. How is this possible? The classical theory, relying solely on pressure differences, would predict the opposite. In such cases, it becomes clear that Bernoulli alone is insufficient, and other, more direct mechanisms are involved in the sail's operation.
All these paradoxes caused disputes for a long time. Different theories, sometimes contradictory to each other, were proposed in the sailing physics literature. Surprisingly, there was no single universally accepted model fully explaining the force that pulls the yacht against the wind until today. Many explanations were qualitative or relied on complex mathematical models but without a clear physical interpretation. However, in recent decades, an alternative approach based on Newton's laws and the Coanda effect has been gaining popularity. It provides a more intuitive picture and can resolve the very mysteries that remained unclear in the old theory.
Modern Explanation: Newtonian Approach and Coanda Effect
Reaction Action: A View Through Newton's Laws
The Newtonian approach considers the sail's operation not so much through pressures, but through the exchange of momentum between the sail and the airflow. Simply put, the sail causes the airflow to change direction and speed, and according to Newton's third law, "for every action, there is an equal and opposite reaction," the sail itself receives a reactive push from the air. In this understanding, the sail works similarly to a paddle pushing water or an airplane propeller throwing air backward.
Imagine that the sail is a paddle's blade in the air. When you paddle, you throw a mass of water backward—the boat moves forward. The sail does the same, but it doesn't throw water, it throws air. Every cubic meter of air redirected by the sail carries momentum backward, and the boat receives a push forward. This perspective immediately resolves many questions. It doesn't matter whether the sail has a particular surface curvature or is simply set at an angle—the mere fact that it deflects the oncoming flow means it receives a reactive force.
From a technical standpoint, the sail can be viewed as a device for pumping mass of air backward. A certain mass of air passes through the sail every second (denoted as m/dt)—effectively, the sail cuts a stream from the oncoming wind and redirects it behind, to the stern. Additionally, the sail imparts acceleration to this stream—it changes the airspeed by a certain amount dv (the difference between the incoming and outgoing speed relative to the boat). Then, according to Newton's second law, a force equal to the product of mass flow rate and speed change arises:
F = (m/dt) × dv
This force is directed backward—this is exactly the momentum per second that the air receives from the sail. According to the third law, the sail (and thus the boat) receives an equal and opposite force directed forward. This is how the thrust that accelerates the yacht arises. In modern research, for example in N. Landell-Mills' work (2020), it is shown that it is precisely the mass of air being deflected by the sail and the magnitude of its deflection (dv) that determine the force driving the yacht. You can find more information about different kinds of yachts in our article on types of sailing yachts.
It is important to emphasize: this approach does not contradict Bernoulli's principle—in fact, they describe the same process from two sides. The pressure difference on the sail is a consequence of the sail deflecting the flow and imparting acceleration to it (the connection is described by Euler's or Navier-Stokes equations for fluid flow). However, the Newtonian view is more intuitive in some situations. It directly states: to increase the force, you either need to increase m/dt (the mass flow rate of air through the sail) or dv (the stronger change in wind speed and direction). It is intuitively clear that the closer the sail is set to the wind, the higher the speed of the apparent wind (the headwind is stronger) and the greater the volume of air passing through the sail per second. Moreover, on sharp courses, the sail directs the flow more towards the stern, increasing dv. Hence, here's the solution to why when turning closer to the wind, the yacht can accelerate—the m/dt and dv increase, and the force F = m/dt × dv also increases, even though the sail's projection decreases.
For more yachting articles, please visit our blog. Our Navi.training blog offers a variety of resources for yachting enthusiasts.
Analogies are all around us. A helicopter hovers in the air because the rotor blades throw air downward—the helicopter flies up. A jet airplane surges forward because it expels a gas stream backward. Even a simple garden hose with a strong water flow will noticeably push you in your hands—the water shoots forward! The sail, of course, works more subtly and elegantly than a paddle or motor, but the essence is the same: it takes energy from the oncoming flow and redirects part of the air, gaining thrust as a result.
Coanda Effect: Stream Flows Around the Sail
But how exactly does the sail throw air backward? After all, air is not a dense fluid; it can more easily flow around obstacles, and the stream could simply separate from the sail, creating vortices instead of an organized flow along the surface. This is where the Coanda effect comes into play—a crucial part of the modern sail theory.
The Coanda effect means that a fluid or gas stream tends to follow a nearby surface. The jet "sticks" to the wall, especially if the wall is smoothly curved. This effect is named after the Romanian scientist Henri Coanda. It appears in many situations. For example, if you let a thin stream of water from a faucet and bring a convex surface (like a spoon or glass) nearby from the side, the water unexpectedly deflects towards the surface and flows along it. Even a light air stream can deflect similarly. This is demonstrated with experiments using ping pong balls and a hairdryer: the air stream from the hairdryer holds a lightweight ball in suspension, preventing it from falling—air flows around the sphere, creating a low-pressure area that keeps the ball within the flow. In both cases, the stream clearly adheres to the curved surface instead of immediately separating straight away. Before embarking on your sailing journey, make sure to familiarize yourself with essential yachting terminology.
Fig. 2: Demonstration of the Coanda effect.
A thin stream of water falling from above deflects and flows around the convex surface of a spoon instead of flowing vertically.
In real sails, the airflow similarly "sticks" to the sail's convex side, flowing around it and creating a thrust force.
On the sail, the Coanda effect manifests as follows: the airflow tries to flow along the sail's surface, even on the leeward convex side, instead of separating from it. The air follows the curvature of the sail, deflecting toward its plane. As a result, the sail directs the flow roughly along the sail's plane toward its stern (to the last furler). Without the Coanda effect, at a significant angle of attack, the airflow on the leeward side would immediately separate, creating a stall and a turbulent "wake" behind the sail—the force would decrease, and resistance would increase. But with proper tuning, the flow remains laminar and adheres to the sail along most of its length. This allows the sail to effectively deflect the air and generate a greater lift force. As noted in studies, the fluid (air) flow naturally follows the curved surface due to the Coanda effect. A classic illustrative example is the water stream and spoon (see Fig. 2): water flows around the spoon, showing how the flow "sticks" to the curved surface.
The Coanda effect is extremely sensitive to the sail's angle of attack and the flow's shape. If you set the sail too steeply into the wind, the flow will still separate—the sail will lose thrust and begin to flap (the "luffing" mode). On the other hand, on sharp courses (close to the wind), the Coanda effect is most pronounced: flows smoothly round the convex side of the sail, with fewer vortices, and a larger volume of air is redirected in an organized manner backward (thus increasing the m/dt). This is why with the correct angle of attack, the sail works more efficiently—it "sticks" to the airflow, extracting maximum momentum from it. On full courses (when the wind is almost behind), sails are often in a "flag-pole" mode: airflow is worse, separates behind them, and the lift force drops sharply—a frontal wind pressure remains, like on a flag's fabric.
Fig. 3: Flow around the sail at different angles of attack (α) relative to the oncoming wind VA.
Top image: α = 4° – flow fully adheres to the sail (attached flow), air smoothly rounds the convex side, creating lift.
Middle image: α = 6° – maximum lift mode: flow begins to separate (separation zone), but a significant portion of the stream still follows the profile.
Bottom image: α = 10° – sail set at a high angle, flow separated (stalled) – a detached turbulent flow forms on the leeward side, lift force sharply decreases.
Solving the "Unexplainable" Mysteries
The combination of the Newtonian approach and the Coanda effect not only provides an intuitive picture but also allows explaining a number of practical observations that were previously considered mysterious. Let's list the main ones and briefly analyze their essence:
-
Why can a yacht accelerate closer to the wind despite the reduction in the sail's projection?
Analysis: When transitioning from a full course to a sharper one (e.g., from beam reach to gybe and further to close-hauled beat wind), classical theory would expect a reduction in thrust—since the sail is more "hidden" from the wind. However, in reality, the yacht often moves faster. From the perspective of the modern model, everything makes sense: the sharper the boat heads to the wind, the higher the apparent wind speed (the headwind increases due to the sum of the true wind and the boat’s headwind from movement). Higher speed means a greater mass flux of air through the sail per second (m/dt). Additionally, an optimal slight angle of attack keeps the flow in adherence mode (see Coanda effect) and ensures significant deflection of the stream (dv). As a result, the product m/dt × dv increases, the thrust force grows until the boat encounters water resistance limitations. Therefore, on sharp courses, the sail works more efficiently, even though its projection area is smaller. -
Why are two sails (mainsail and jib) more effective than one of the same total size?
Analysis: Many yachts have multiple sails (e.g., a large mainsail and a front jib) instead of one enormous sail. The total sail area may be the same, but a combination of two sails pulls better. The modern explanation sees the reason in flow management: two sails placed sequentially create a special configuration in the stream between them—the "slot effect." Air accelerates in the narrow gap between the mainsail and the jib, enhancing the Coanda effect on the jib's leeward side and the mainsail's windward side simultaneously. Essentially, two sails process a larger volume of air (total m/dt) and deflect it more efficiently than a single wide sail, which might have a flow separation zone at the center. The Newtonian approach directly indicates that increasing the involved air mass increases the force—which is what we observe. In the classical "pressure-based" explanation, the advantages of multiple sails are harder to understand. Thus, two sails work like a compressor and ejector: the front sail optimally directs the flow for the rear sail, jointly increasing thrust. -
Why can a yacht exceed wind speed when the wind is on the bow (apparent wind), but not when it's a tailwind?
Analysis: This is a well-known paradox: on sharp courses, high-speed vessels (especially iceboats or hydrofoil boats) can develop speeds exceeding the true wind speed. But when sailing directly downwind, no classic sailboat can accelerate faster than the wind. From the perspective of the modern theory, there's no contradiction here either. When the boat accelerates against the wind, the headwind is intensified (apparent wind becomes stronger due to the sum of the true wind and the headwind from the boat's movement). Therefore, m/dt continues to grow, pulling the boat faster—up to the point where water resistance balances the thrust. There are practically no wind speed limits here, except for physical limitations of the hull and friction: ice boats can exceed wind speed five or six times. However, when moving directly downwind, the situation is different: as the boat accelerates, it "catch -
How to calculate the force, speed, and energy generated by the sail?
Analysis: Classical theory relied on aerodynamic coefficients of lift and drag measured in wind tunnels, providing a qualitative picture but making direct "by-hand" calculations difficult. The modern approach offers a simple model: knowing approximate flow parameters (sail coverage area, air density, stream deflection angle), one can estimate the force. For example, a 12-meter sail deflecting about 120 m³ of air per second at approximately 8 m/s would create a force of about 1150 N (about 115 kgf). These figures correspond to reality and provide an idea of how force changes with wind or angle variations. Additionally, knowing the force, one can estimate the sail's power (force × boat speed) and compare it, for example, with engine power. This approach makes sail physics more tangible. Of course, for precise calculations, complex models considering vortices, turbulence, etc., are still needed, but a "first estimate" can now be made even by a physics-savvy student. If you're new to yachting, our Yachting for Beginners articles can provide a strong foundation.
- Analogy with an airplane wing and the unity of approaches.
Analysis: Interestingly, debates about the nature of sail force are closely related to debates about the aerodynamic lift force of airplane wings. Until the 21st century, Bernoullian explanations dominated popular literature on lift, while many intuitive engineers (starting with Newton himself) leaned towards a reactive interpretation (air thrown downward—the wing goes upward). It is now clear that both approaches complement each other, and the key role is played by the Coanda effect, allowing the wing (and sail) to effectively deflect the flow. The modern sail theory is fully consistent with the current understanding of how airplane wings work. There too, part of the lift is generated by a pressure difference (Bernoulli) and part by the change in air momentum (Newton), and efficiency depends on the smoothness of the profile's airflow. It's no wonder experienced yacht captains often have a good understanding of aerodynamics, and aircraft designers have drawn ideas from sailing—since the laws are the same.
Conclusion
The sail is an amazing invention imbued with clever aerodynamics. The classical Bernoulli explanation helped understand that the sail creates force thanks to the pressure difference on its sides, similar to an airplane wing. However, this simplified view left much unclear and contradictory. The modern Newtonian approach, considering the Coanda effect, provides a more complete understanding: the sail accelerates and redirects the airflow, gaining reactive thrust, and the Coanda effect ensures the airflow adheres to the sail for maximum efficiency. This model successfully explains observations that the old theory could not adequately describe—from speed gains on sharp courses to the efficiency of double sails and the limitations of downwind movement.
It is important to emphasize that in reality, there is no "conflict" between Bernoulli and Newton—they are both correct, describing the same nature in different languages. Pressure drops where the air accelerates and deflects—and thus the sail is sucked into the low-pressure area. And why did the air accelerate there? Because the sail imparted acceleration to it, caused the flow to follow its surface (Coanda), and threw it backward (Newton). Thus, the modern view unites these explanations into a single picture.
If you are a beginner sailor, you can remember two images: first—"sail as a wing" (low front pressure pulls the sail forward), and second—"sail as a paddle" (deflecting air backward, the sail pushes the boat forward). Both descriptions are correct and complement each other. But in practice, it is more useful to understand the Newtonian approach: feeling how the flow rounds the sail and where it goes, you will better adjust the angle of attack, sheet twist, and sail shape. Watch the indicator tapes, catch the wind, imagine how air flows along the sail—and your yacht will fly against the wind, obeying the strict but beautiful laws of physics! To enhance your understanding, consider enrolling in yachting courses. Information on types of boat licences can also be helpful.
Sources and Literature
• N. Landell-Mills. “Sailing into Wind Is Explained by Newtonian Mechanics Based on The Mass-Flow Rate”. European Journal of Applied Physics, Vol. 2, Issue 4 (2020).
This scientific article proposes a Newtonian explanation of sail operation considering the Coanda effect and shows that it is precisely the mass of air deflected by the sail and the speed of its deflection that determine the sail's thrust. The article analyzes a number of paradoxes and concludes the advantages of the modern approach. You can also find useful tips for [yachting with children](https://navi.training/en/blog/yahting-s-det-mi-kak-podgotovit-sya-k-semeynomu-otp
Discussing yachting requires understanding navigational aspects and proper techniques, including anchoring a yacht and mooring. For more detailed information on staying safe, knowing the weather forecast is crucial. Also, consider how to avoid seasickness during your trips. If you are new to sailing, learning about yachting holidays can be a great starting point for planning your adventure. For advanced strategies, you might also be interested in Alongsidemooring.
• Forces on sails – Wikipedia.
Explains the decomposition of the sail's aerodynamic force into components (lift and drag) and their projections onto longitudinal and lateral forces acting on the boat. Describes the influence of the point of rotation, true and apparent wind, and other basics of sail theory.
• Physics StackExchange – Discussion: “Problem understanding basic sail mechanics”.
In answers and comments, the shortcomings of the purely Bernoullian approach are discussed. It is noted that the explanation through Bernoulli alone is not the primary cause and does not explain why even a flat sail at an angle generates force. Instead, it is proposed to view the sail as a device for deflecting the flow (references to the Coanda effect and Newton's action–reaction law).
• NASA Glenn Research Center – Aerodynamics Resources.
NASA's educational resources note that lift can be viewed in two ways: through pressure differences (Bernoulli) and through changes in air momentum (Newton), and both descriptions complement each other. This corresponds to the modern interpretation and applies to sails as well.