# What exactly is the 'lift' of a sailboat as explained by Bernoulli principle

I have heard that when a sailboat is sailing against the wind, it operates on the principle of 'lift'. I am unable to understand the explanation, based on Bernoulli principle, completely. My question is, when it says 'lift', it literally means that the boat is being 'lifted' out of the water? Like when we throw a stone across the lake and it skims and hops on the water?

• The Bernoulli principle applies here as much as to airplane wings (that is to say, not at all). But this is orthogonal to the question of sailing against the wind, which has nothing to do with "lift" (which can be said to be there, though horizontally) and everything to do with the keel. – user10851 Dec 29 '15 at 11:18

Bernoulli's Principle is one very small piece of a large mathematical theory that explains lift. Unfortunately, most attempts to explain lift using Bernoulli's principle without the overall mathematical context (i.e. vector calculus, partial differential equations, boundary conditions, the Navier-Stokes equation, etc.) are either so confusing that few readers can follow them, or they are just out and out wrong. Often both.

From a layman's perspective, Bernoulli's principle does more to obscure the issue than it does to enlighten. US Sailing does not use Bernoulli's principle in their instruction materials to explain how sailboats move and we do not use it in our instruction program (I am the manager of a learn to sail program with ten US Sailing Certified Instructors). It's a red herring that confuses students without giving them any insight into how to sail.

To answer your question, "lift" is a defined term in aerodynamics with a different meaning than usual usage. When a solid object is immersed in a moving fluid, the fluid exerts a force on the object and the object exerts a force on the fluid that is equal in magnitude but opposite in direction. "Lift" is the component of this force perpendicular to the fluid flow. For a sailboat sail, the fluid is air and the "lift" is a horizontal force that propels the boat forward (and also makes it lean). So "lift" doesn't push the boat up, it pushes it forwards and sideways.

As for Bernoulli, there's nothing wrong with Bernoulli's principle, it just doesn't do a very good job of explaining why sailboat sails and airplane wings develop lift. Lift is the result of unequal air pressure on one side vs the other. An airplane wing has lower pressure on the top side of the wing and higher pressure on the bottom. A sail has lower air pressure on the front (leeward) side and more pressure on the rear (windward) side. If you look at the derivation of Bernoulli's equation, it concerns itself with pressure gradients parallel to the air flow, while lift is the result of air pressure gradients perpendicular to the air flow. So Bernoulli's equation doesn't get at the reason for the lift - to understand lift you need to understand why there is a pressure difference perpendicular (not parallel) to the air flow.

Fortunately there is an equation that deals with pressure gradients perpendicular to the air flow. It doesn't have a name, but was derived at the same time as Bernoulli's equation so it's been around for centuries. It is:

$$\frac{dp}{dz} = \frac{\rho v^2}{R}$$

where $p$ is the pressure, $dp/dz$ is the pressure gradient perpendicular to the air flow, $\rho$ is the density of the fluid, $v$ is the velocity and $R$ is the radius of curvature of the airflow. (BTW, the derivation of this formula is just a straightforward application of Newton's 2nd law to the kinematics of centripetal acceleration - Physics 101 stuff)

This equation shows that whenever air follows a path that is curved there are pressure gradients perpendicular to the airflow, the tighter the curvature the higher the pressure gradients, and for straight flow (R -> infinity) there is zero pressure gradients and therefore no lift.

Lift comes from curved air flow. Sails are curved. When air follows the curve of the sail, you get pressure differences. That's what drives the boat. Bernoulli's principle tells you that the air speeds up as it flows through the region of reduced pressure, but it doesn't tell you why the low pressure is there, and while the air speeding up may be an interesting side effect of lift it's not very important to understanding how a sail works.

If you know a little bit of calculus, Babinsky's paper "How Do Wings Work?' (http://iopscience.iop.org/0031-9120/38/6/001/pdf/pe3_6_001.pdf) is a good overview. Or check out NASA's site:

http://www.grc.nasa.gov/WWW/K-12/airplane/wrong1.html

An important point that is often overlooked is that sails do not just generate 'lift', but generate lift in a direction. The pressure differential across the sail's surface is typically much larger near the leading edge, which results in more forward force than you might expect. The two sails (with a sloop) also interact in a way that generates more forward force.

You can see some simulations with different sail configurations, and comparison to the performance of a real sailboat at this site:

• NB: the link is dead – Kyle Kanos Dec 29 '15 at 11:29

Unfortunately the link is broke with no forward link. However the effect is the same as an airplane wing, where lift is generated on the upper or slightly rounded surface. This in effect "Pulls" the aircraft up at a constant rate of assent as long as the upper surface continues to receive the "flow" at a constant rate. Now imagine the airplane wing sitting im the vertical position. The air flow will do the very same thing to the wing as it does to the sail. Now to make matters more complicated, Airplane wings have "airflow disrupters called ailerons, which disrupt the air flow in a certain section of the wing. Now if the flow remains constant, then the disturbed air will cause an area of increased or decreased pressure which causes certain areas of the wing to either slow down or speed up depending on the pressure flow.

The Wikipedia article on wingsails explains the use of a fixed wing/sail and the way airflow flowing around the wing creates the force needed to push the boat. These are essentially airplane wings that have been turned from a horizontal position to a vertical position. The effect is the same because the sailboat with a center keel assumes the characteristics of a plane. The lower centerboard or keel act as a wing in the same way as the fixed wing above decks.

This explains the relation between the Bernoulli principal and how a boats sail works. Aviators are trying to build a stunt plane with both horizontal as well as vertical wings for never before seen stunts. (See this gizmag article for more information)

Well, according to this Bernoulli effect is NOT the cause of lift.

Basically planes fly because they push enough air downwards and receive an upwards lift thanks to Newton's third law.

It is clear that blowing over a piece of paper pulls it up (video). Here: fast air => lower pressure => paper pulled up. Right.

But that IS NOT the case for sails and wings. Wind arriving to a sail/wing goes ALL of it at the SAME speed. The air above the wing / on leeward of a sail does not spontaneously accelerate up. It gets speeded up by a a lower pressure in that zone. Thus, the "fast air" is not the cause but THE CONSEQUENCE.

What does it cause the low pressure zone above a wing / on leeward of a wing?

What is for sure is that wings/sails deflect air. Then for wings and sails:

Main cause: air deflection => change of pressure => changes in air speed.

That's it.

Don't get confused by the fact that Bernoulli equation can be effectively used to measure lift. It's perfectly right to estimate the real cause (air deflected downwards) by a direct effect (change of pressure).

• The argument from momentum has an element of truth, but it misses out the significant fact that a continuous entity such as air can transmit force just by pressure differences, similar to the way a solid rod can. The force exerted by a rod is not directly to do with the motion of the rod. The same goes for a fluid. – Andrew Steane Sep 16 '20 at 9:34
• @AndrewSteane Totally true. But there are 2 cases. Fast air => lower pressure OR lower pressure => fast air. Unlike the case of lifting a paper (fast air => lower pressure); for sails and wings we have lower pressure => fast air; because unlike the lifting paper case, air arrive at same speed to the sail/wing. Think of a wing flying through still air (i.e. air speed = 0), that is not the case of the lifted paper (there is a `previous airflow over the paper). – cibercitizen1 Sep 16 '20 at 9:41
• @AndrewSteane See this video youtube.com/watch?v=zp1KzGQdouI. – cibercitizen1 Sep 16 '20 at 9:52