Free to follow every thread. No paywall, no dead ends.
Lift (force): the story on HearLore | HearLore
Lift (force)
The Wright brothers' 1902 glider did not merely float; it pulled upward with a force so powerful it defied the common intuition of the era. When a fluid flows around an object, it exerts a force that is perpendicular to the oncoming flow direction, a phenomenon known as lift. This force is the invisible hand that keeps aircraft aloft, yet it is often misunderstood as a simple result of air moving faster over the top of a wing. In reality, lift is the component of the total aerodynamic force that acts perpendicular to the flow, contrasting sharply with drag, which acts parallel to the flow. While conventionally associated with upward motion to counter gravity, lift can act in any direction perpendicular to the flow, whether in air, water, or any other liquid. When the surrounding fluid is air, the force is termed aerodynamic, and when it is water, it is hydrodynamic. This distinction separates dynamic lift from aerostatic lift, or buoyancy, which relies on internal fluid density rather than movement and is used by balloons and submarines. Planing lift, used by motorboats and surfboards, involves only the lower portion of a body immersed in liquid flow, further diversifying the ways fluids can push against objects. The complexity of lift lies not just in its definition but in the subtle cause-and-effect relationships that govern how a fluid turns and how a solid body reacts to that turn.
The Newtonian Turn
The most fundamental explanation for lift begins with a simple observation: a wing pushes air downward, and the air pushes the wing upward. This is Newton's third law in action, where the reaction force of the deflected air mass acts on the wing to provide an equal and opposite upward component. When air flows over and under an airfoil inclined at a small angle to its direction, the air is turned from its course. As the airflow approaches the airfoil, it curves upward, but as it passes the airfoil, it changes direction to follow a path that is curved downward. According to Newton's second law, this change in flow direction requires a downward force applied to the air by the airfoil. The airfoil exerts a downward force on the air, and the air exerts an upward force on the airfoil, generating lift. This downward turning of the flow is not produced solely by the lower surface of the airfoil; the air flow above the airfoil accounts for much of the downward-turning action. In fact, the upper surface contributes more flow turning than the lower surface, and the pressure reaches its minimum value around 5 to 15% chord after the leading edge. Consequently, about half of the lift is generated in the first quarter chord region of the airfoil. This makes it critical to maintain a clean and rigid surface on the top of the wing, which is why most airplanes are cleared of any objects on the top of the wing. The misconception that the lower surface is the primary lift producer is a persistent error in popular understanding, as the upper surface is the dominant force generator.
What is the definition of lift force in fluid dynamics?
Lift is the component of the total aerodynamic force that acts perpendicular to the flow direction. This force keeps aircraft aloft and can act in any direction perpendicular to the flow whether in air or water.
How does the Wright brothers 1902 glider demonstrate lift force?
The Wright brothers 1902 glider pulled upward with a force so powerful it defied the common intuition of the era. This upward pull demonstrated that lift is a real force acting perpendicular to the oncoming flow direction.
Why is the equal transit time theory of lift incorrect?
The equal transit time theory is fundamentally incorrect because there is no physical principle that requires air particles to arrive at the trailing edge at the same time. Experimental results confirm that particles moving over the top arrive at the trailing edge long before particles moving under the airfoil.
When does an airfoil stall and what happens to lift?
An airfoil reaches its maximum lift at a specific angle of attack and then stalls when the angle increases beyond this critical point. At angles of attack above the stall lift is significantly reduced though it does not drop to zero.
What is the Kutta-Joukowski theorem used for in lift calculations?
The Kutta-Joukowski theorem relates the lift per unit width of span of a two-dimensional airfoil to the circulation component of the flow. This theorem provides a mathematical framework for understanding lift and resolving the indeterminacy of potential-flow solutions.
For decades, textbooks have taught that air travels faster over the top of a wing because it has a longer path to travel, and this speed difference creates lower pressure according to Bernoulli's principle. This explanation, known as the equal transit time theory, is fundamentally incorrect. There is no physical principle that requires air particles to arrive at the trailing edge at the same time, and experimental results confirm that the transit times are not equal. The air moving past the top of an airfoil generating lift moves much faster than equal transit time predicts, and particles moving over the top arrive at the trailing edge long before particles moving under the airfoil. The flaw in this explanation is that it does not correctly explain what causes the flow to speed up. A more accurate view involves the obstruction of the airflow, where the curved upper surface acts as an obstacle, forcing streamlines to pinch closer together. When streamtubes become narrower, conservation of mass requires that flow speed must increase. However, this obstruction explanation also fails to explain how streamtube pinching comes about or why it is greater over the upper surface than the lower surface. The real relationship between pressure and flow speed is a mutual interaction, not a one-way causation. Producing a lift force requires maintaining pressure differences in both the vertical and horizontal directions, and the Bernoulli-only explanations leave out the flow-deflection part of the interaction. The pressure difference which results in lift acts directly on the airfoil surfaces, but understanding how the pressure difference is produced requires understanding what the flow does over a wider area.
The Pressure Field
The true nature of lift is revealed when examining the pressure field around an airfoil. Pressure in a fluid is always positive in an absolute sense, meaning it must always be thought of as pushing, never as pulling. The pressure thus pushes inward on the airfoil everywhere on both the upper and lower surfaces. The flowing air reacts to the presence of the wing by reducing the pressure on the wing's upper surface and increasing the pressure on the lower surface. The pressure on the lower surface pushes up harder than the reduced pressure on the upper surface pushes down, and the net result is upward lift. This pressure difference is part of a larger pattern called a pressure field, which extends over a wide area around the airfoil. The non-uniform pressure exerts forces on the air in the direction from higher pressure to lower pressure. Air above the airfoil is pushed toward the center of the low-pressure region, and air below the airfoil is pushed outward from the center of the high-pressure region. According to Newton's second law, a force causes air to accelerate in the direction of the force. Thus, the vertical arrows in the pressure field diagram indicate that air above and below the airfoil is accelerated, or turned downward, and that the non-uniform pressure is the cause of the downward deflection of the flow. The changes in flow speed are consistent with Bernoulli's principle, but the cause-and-effect relationship works in both directions simultaneously. The air's motion is affected by the pressure differences, but the existence of the pressure differences depends on the air's motion. This mutual interaction is the key to understanding how lift is generated and sustained.
The Stall and The Vortex
As the angle of attack increases, the lift reaches a maximum at some angle, and increasing the angle of attack beyond this critical angle causes the upper-surface flow to separate from the wing. This is known as the stall, and at angles of attack above the stall, lift is significantly reduced, though it does not drop to zero. The maximum lift that can be achieved before stall is generally less than 1.5 for single-element airfoils and can be more than 3.0 for airfoils with high-lift slotted flaps and leading-edge devices deployed. The flow around a three-dimensional wing involves significant additional issues, especially relating to the wing tips. The vertical pressure gradient at the wing tips causes air to flow sideways, out from under the wing then up and back over the upper surface. This reduces the pressure gradient at the wing tip, therefore also reducing lift. The lift tends to decrease in the spanwise direction from root to tip, and the pressure distributions around the airfoil sections change accordingly in the spanwise direction. The wing is effectively flying in a downdraft of its own making, as if the freestream flow were tilted downward, with the result that the total aerodynamic force vector is tilted backward slightly compared to what it would be in two dimensions. The additional backward component of the force vector is called lift-induced drag. The wingtip flow leaving the wing creates a tip vortex, and as the main vortex sheet passes downstream from the trailing edge, it rolls up at its outer edges, merging with the tip vortices. The combination of the wingtip vortices and the vortex sheets feeding them is called the vortex wake. This horseshoe vortex system was recognized by the British aeronautical pioneer Lanchester in 1907, and it remains a critical factor in the design of modern aircraft.
The Mathematical Reality
Mathematical theories of lift are based on continuum fluid mechanics, assuming that air flows as a continuous fluid. The most relevant principles are conservation of mass, conservation of momentum, and conservation of energy. Conservation of momentum, which is a consequence of Newton's laws of motion, especially Newton's second law and third law, is central to understanding lift. The Navier-Stokes equations provide the potentially most accurate theory of lift, but in practice, capturing the effects of turbulence in the boundary layer on the airfoil surface requires sacrificing some accuracy and using the Reynolds-averaged Navier-Stokes equations. A RANS solution consists of the time-averaged velocity vector, pressure, density, and temperature defined at a dense grid of points surrounding the airfoil. The amount of computation required is a minuscule fraction of what would be required to resolve all of the turbulence motions in a raw NS calculation, and with large computers available, it is now practical to carry out RANS calculations for complete airplanes in three dimensions. In potential-flow theory, the flow is assumed to be irrotational, meaning that small fluid parcels have no net rate of rotation. A solution of the potential equation directly determines only the velocity field, and the pressure field is deduced from the velocity field through Bernoulli's equation. The Kutta condition, which states that the flow leaves the trailing edge smoothly, is a key element in resolving the indeterminacy of potential-flow solutions. The Kutta-Joukowski theorem relates the lift per unit width of span of a two-dimensional airfoil to the circulation component of the flow, providing a mathematical framework for understanding lift. These theories, while complex, are essential for predicting lift with high accuracy and designing aircraft that can fly safely and efficiently.