Lift is the force that holds an aircraft in the air and directly opposes the weight of an airplane. It is the mechanical aerodynamic force produced by the motion of the airplane through the air.It is generated by the difference in velocity between the solid object and the fluid. There must be motion between the object and the fluid: no motion, no lift. It makes no difference whether the object moves through a static fluid, or the fluid moves past a static solid object. Lift acts perpendicular to the motion and Drag acts in the direction opposed to the motion.

But how is lift generated?

Lift is generally generated by every part of the airplane, but most of the lift on an aircraft is generated by the wings. Because lift is a force, it is a vector quantity, having both a magnitude and a direction associated with it. Lift acts through the center of pressure of the object and is directed perpendicular to the flow direction. There are several factors which affect the magnitude of lift.

There are many explanations for the generation of lift found in encyclopaedias, in basic physics textbooks, and on Web sites. Unfortunately, many of the explanations are misleading and incorrect. Theories on the generation of lift have become a source of great controversy and a topic for heated arguments for many years.

These arguments arise because people mis-apply Bernoulli and Newton’s equations and they over-simplify the description of the problem of aerodynamic lift.

1. “Equal transit time” or “longer path” : The most popular incorrect theory of lift arises from a mis-application of Bernoulli’s equation. The theory is known as the “equal transit time” or “longer path” theory which states that wings are designed with the upper surface longer than the lower surface, to generate higher velocities on the upper surface because the molecules of gas on the upper surface have to reach the trailing edge at the same time as the molecules on the lower surface. The theory then invokes Bernoulli’s equation to explain lower pressure on the upper surface and higher pressure on the lower surface resulting in a lift force. The error in this theory involves the specification of the velocity on the upper surface.

In reality, the velocity on the upper surface of a lifting wing is much higher than the velocity which produces an equal transit time. If we know the correct velocity distribution, we can use Bernoulli’s equation to get the pressure, then use the pressure to determine the force. But the equal transit velocity is not the correct velocity.

“It is often said that the lift on a wing is generated because the flow moving over the top surface has a longer distance to travel and therefore needs to go faster. This common explanation is actually wrong.” Here, aerodynamics expert Professor Holger Babinsky from the University of Cambridge’s Department of Engineering debunks a popular, yet misleading, explanation of how wings lift.

2. Venturi flow : Another incorrect theory uses a Venturi flow to try to determine the velocity. But this also gives the wrong answer since a wing section isn’t really half a Venturi nozzle. The Venturi analysis cannot predict the lift generated by a flat plate. The leading edge of a flat plate presents no constriction to the flow so there is really no “nozzle” formed.

3. Skipping stone: There is also an incorrect theory which uses Newton’s third law applied to the bottom surface of a wing. This theory equates aerodynamic lift to a stone skipping across the water. It neglects the physical reality that both the lower and upper surface of a wing contribute to the turning of a flow of gas.

The proponents of the arguments usually fall into two camps:
(1) People who support the “Bernoulli” position that lift is generated by a pressure difference across the wing, and
(2) those who support the “Newton” position that lift is the reaction force on a body caused by deflecting a flow of gas.

Interestingly, neither Newton nor Bernoulli ever attempted to explain the aerodynamic lift of an object. The names of these scientists are just labels for two camps.

The real details of how an object generates lift are very complex and do not lend themselves to simplification. For a gas, we have to simultaneously conserve the mass, momentum, and energy in the flow.

Newton’s laws of motion are statements concerning the conservation of momentum. Bernoulli’s equation is derived by considering conservation of energy. So both of these equations are satisfied in the generation of lift,  both are correct.

The conservation of mass introduces a lot of complexity into the analysis and understanding of aerodynamic problems. For example, from the conservation of mass, a change in the velocity of a gas in one direction results in a change in the velocity of the gas in a direction perpendicular to the original change. This is very different from the motion of solids, on which we base most of our experiences in physics. The simultaneous conservation of mass, momentum, and energy of a fluid (while neglecting the effects of air viscosity) are called the Euler Equations after Leonard Euler. Euler was a student of Johann Bernoulli, Daniel’s father, and for a time had worked with Daniel Bernoulli in St. Petersburg. If we include the effects of viscosity, we have the Navier-Stokes Equations which are named after two independent researchers in France and in England. To truly understand the details of the generation of lift, one has to have a good working knowledge of the Euler Equations.

When a gas flows over an object, or when an object moves through a gas, the molecules of the gas are free to move about the object; they are not closely bound to one another as in a solid. Because the molecules move, there is a velocity associated with the gas. Within the gas, the velocity can have very different values at different places near the object.

Bernoulli’s equation, which was named for Daniel Bernoulli, relates the pressure in a gas to the local velocity; so as the velocity changes around the object, the pressure changes as well. Adding up (integrating) the pressure variation times the area around the entire body determines the aerodynamic force on the body F = P*A .

Now adding up the velocity variation around the object instead of the pressure variation also determines the aerodynamic force. The integrated velocity variation around the object produces a net turning of the gas flow. From Newton’s third law of motion, a turning action of the flow will result in a reaction (aerodynamic force) on the object. So from a Newtonian perspective, lift is generated by turning a flow of air. The flow turning creates a downwash from the wing which can be observed in flight. For a body immersed in a moving fluid, the fluid remains in contact with the surface of the body. If the body is shaped, moved, or inclined in such a way as to produce a net deflection or turning of the flow, the local velocity is changed in magnitude, direction, or both. Changing the velocity creates a net force on the body.

It is very important to note that the turning of the fluid occurs because the molecules of the fluid stay in contact with the solid body since the molecules are free to move. Any part of the solid body can deflect a flow. Parts facing the oncoming flow are said to be windward, and parts facing away from the flow are said to be leeward. Both windward and leeward parts deflect a flow. Ignoring the leeward deflection leads to a popular incorrect “Skipping Stone” theory of lift.

So both “Bernoulli” and “Newton” are correct. Integrating the effects of either the pressure or the velocity determines the aerodynamic force on an object. We can use equations developed by each of them to determine the magnitude and direction of the aerodynamic force.

Newton and Bernoulli do not contradict each other. Explanations which are based on Newton’s and on Bernoulli’s principles are completely compatible. Air-deflection and Newton’s Laws explain 100% of the lifting force. Air velocity and Bernoulli’s equation also explains 100% of the lift. There is no 60% of one and 40% of the other. One of them looks at pressure forces, the other looks at F=mA accelerated mass. For the most part they’re just two different ways of simplifying a single complicated subject.

 

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