Lift (force)

The dynamic lift is a central factor in the fluid dynamics. It is the fraction of the forces acting on a body around which flow force, which is perpendicular to the flow direction. The dynamic lift is the physical rationale for the function of aircraft wings, propellers, Schratsegeln and turbines.

The emergence of buoyancy due to horizontal flow to be explained by the methodology of hydrodynamics. This is part of classical mechanics and therefore obeys Newton's laws and the resulting accounting conservation laws ( momentum and energy conservation ). In the compressible medium (gas ) is also a thermodynamic analysis of the processes is required.

Buoyancy body is formed correspondingly shaped, for example, airfoils with flow around. Here, the air is deflected downward, ie accelerated. Of downward force to the air corresponds to a reaction force, the upward force on the supporting surface, the buoyancy.

• 5.1 incompressibility
• 5.2 compressibility

• 6.1 The circulation - the observer on the ground
• 6.2 For Bernoulli

Introduction

During the movement of a body of a predetermined shape and position relative to a gas or liquid acting on the body forces which are caused by the flow around ( Bernoulli effect). In contrast to the buoyancy direction of the dynamic lift is not defined by the force of gravity, but rather by the direction of the flow. The total flow force is decomposed into two components: the resistance to the flow direction and the buoyancy perpendicular to it.

Each with:

The resultant of the two components is the amount and direction of force acting on the body. It attacks at the pressure point.

Principle of operation

For basic considerations to understanding the buoyancy of the air space of cubic air-filled space elements is assembled. Each of these air volumes must be supported by its environment, otherwise it would fall to the ground:

• Volumes that contain only air, carried by the buoyancy by Archimedes of the area. The pressure difference between the lower surface and the upper surface of a volume, which results from the decrease in pressure with increasing altitude, is the counter force to the gravity (see hydrostatic pressure).
• Volumes that contain all the aircraft ( the bird, ... ) must be worn along with the aircraft of their environment. The following remarks, that this on the air a pulse is generated within the volume down. The opposing force of the pulse production is the buoyancy. This momentum is conserved.

Easily understood experiments support this model of explanation:

• The table fan constantly blows fresh air felt in surprisingly large distances.
• A postcard moved horizontally and with angle of attack over a candle whose flame brings also astonishingly large amount of flickering.

Also in distances at which these effects are no longer felt, the rate of momentum conservation, the changing of the pulse only under the influence of forces applies. Mixes for example the fan vented to the ambient air, this process is pulse -preserving. By mixing a larger volume of air is probably involved in the pulse, and therefore the flow rate decreases. But there is no force acting on this air, and therefore, the pulse is maintained as a whole.

To preserve the conservation of energy mixing is important to note that by the decrease of the mean flow velocity decreases while the kinetic energy. However, this kinetic energy is converted into thermal energy, whereby the energy is maintained as a whole.

An analog of this from school physics is the inelastic collision.

On buoyancy involved physical quantities

This chapter first describes the flow field around a wing. Thereafter, the main forces and their contribution to buoyancy are discussed.

The flow field

An airfoil profile, which passes through a medium having a suitable angle, pushing the media not only to the side. In addition, the media is accelerated to the tangential movement. On the underside of a light acceleration occurs in the direction of movement as in a bow wave. Much stronger on the upper side of the profile of an acceleration against the direction of movement, that is to the rear.

The influence of the profile is the most close to the surface. This means that adjacent packs of the medium that have been separated from the front face of the profile do not come together again behind the profile. Rather, they continue to remain separated - in the example of a simulated flow by nearly a tread depth. This offset of the top flowing medium against the bottom can be observed experimentally by pulsed plumes.

The pressure

The sketch on the right shows the pressure field around a wing. It is characterized by low pressure over the wings upward with increasing pressure and high pressure under the wing with decreasing pressure downwards. Therefore, this pressure field exerts on the air located here from a downward force.

The image also shows two volumes ( green dashed lines), each of which contains the plane. Above and below the small central volume are two volumes that do not contain the plane. The vertical pressure forces on each volume resulting from the pressure distribution on the horizontal edge surfaces:

• The small central volume is replaced by the pressure of strong buoyancy. The pressure differences between the upper and lower limiting surface are large.
• According to the large volume has only weak to lift imperceptible. The edges are so far away from the wing that almost no pressure difference exists.
• The two volumes that do not include the plane view of the print output.

In this way any - even in front of and behind the wing - put together volumes after the block principle. The respective pressure force is generally always differ individually for each volume. Alone, therefore, the pressure force to describe the lift of an aircraft is inappropriate.

With increasing distance, the change in air pressure is decreased by the wing. This allows the definition of a sphere of influence as the area around the wings, within which the pressure has a significant share of the total lift. This influence is in any case small ( perhaps up to 100 m in commercial aircraft ) in relation to the achievable flight altitude of up to 20 km. This is due to that the pressure force is not mentioned in the summary. A principle maximum altitude there is no beyond.

Nevertheless, there are integrated in the motion equation or the second term to compensate for the weight of the aircraft, the pulse output of the air from the after integration of the impulse flow is through the volume surface.

The momentum flux

Get air particles in the above- specified area of ​​influence of the wing, they are accelerated according to the downwardly decreasing pressure down. According to their mass so vertical pulse is produced. After leaving the control of no force acts more on the air particles - their momentum is conserved.

Integrating this via a fixed volume, the pulse from the pulse output flow of the particles through the entire surface of the volume.

On volumes without a plane the pressure field exerts a total force when they are partially within the control of the wing - generally downwards. Since some of these in this Article are without force, and no other forces are present, the pulse production and thus the momentum flux out of the volume is the opposing force to the pressure force.

For volumes with aircraft, the aircraft will generally be borne by the sum of the pressure force and momentum production ( flow ). Since the pressure force with increasing volume is small, generally remains the only produced within the control pulse, which remains after leaving the sphere of influence. This pulse output is thus the reaction force, which supports the aircraft.

The viscosity

• Viscosity → zero or
• Reynolds number → infinity

The viscosity of the air has been largely ignored in the previous discussion. It was only demonstrated that the airflow around the wing in general by the production of the vertical pulse is the counter force to the force of gravity of the aircraft. However, it was excluded, why the air does, and the flow does not proceed, for example, as shown in the drawing, similar to flow past a plate transverse to the flow and this does not provide any buoyancy.

Viscous effects play an important role only in the boundary layer of the wing. This is also in commercial aircraft only a few centimeters thick. About the vertical shearing of the horizontal flow through the viscosity in the boundary layer, the flow here has a tendency to follow the direction of flow smoothly curved surfaces. Directly on the surface the velocity is exactly zero. It increases until it reaches with increasing distance from the surface of the flight speed. Through this shear the air has a vorticity in the boundary layer. The viscosity causes forces by which adjusted the speeds of the adjacent streamlines and the vorticity are homogenized.

The causal chain for lifting

Then leaves a particle having its vortex strength because of the curved surface, the boundary tangent, the viscosity is the shear homogenization of the velocity field and the eddy intensity remains at a medium value. Lack shearing it forces a curved trajectory in the direction back to the surface. As a counter- force for this purpose is reduced, the pressure at the surface. This low pressure also accelerates air above the boundary layer down. The pressure is also lower than the pressure along the vane upstream. Therefore, the flow is accelerated and tangentially over the wing to the rear.

Energy conservation

So far, no distinction was made between compressible and incompressible flow. For the analysis of the momentum balance under the influence of forces, this distinction is unimportant. When considering the energetics, however, the work against volume change important component in compressible flow. Here, however, is further from the viewpoint of the stationarity of the aircraft, and no friction ( outside the boundary layer ) is assumed.

Incompressibility

Initially applies for incompressible, steady flow of constant density along a trajectory that Bernoulli's law: the sum of the square of the velocity and the ratio of pressure and density is constant. For air particles that enter the sphere of influence of the wing, this means:

• With pressure decrease over the wing, the flow velocity increases.
• When the pressure increase under the wing, the flow velocity decreases.

The Bernoulli's law makes no statement about cause and effect, but it only describes a relation between the pressure and velocity field. The Bernoulli's law follows directly from the principle of conservation of energy. Here, the pressure field is a potential force.

Compressibility

For flow around an airfoil can be assumed with sufficient accuracy incompressibility, when the airspeed is small compared to the speed of sound. When commercial aircraft and large parts of the military flight, however, the compressibility must be taken into account.

When the pressure change along a trajectory a speed change according to Bernoulli is therefore no longer the only variant that to force conservation of energy. Alternatively, the air has the possibility to increase their volume, or to decrease the density. This work is done, which is compensated by decreasing the internal energy, ie in the absence of heat sources by adiabatic cooling. In this way, it can cause condensation and fog formation over the wing upper side come (pictured right).

Other explanatory models

The circulation - the observer on the ground

The observer on the ground sees a plane flying through still air. The flow from his vantage point, by subtracting the same everywhere airspeed (sketch, green arrow) of the previously considered flow from the perspective of the aircraft:

• Above the wing, the flow is from the perspective of the aircraft faster than the airspeed. The observer on the ground provides for a flow backwards against the direction of flight.
• Below the wing, the flow is from the perspective of the aircraft slower than the airspeed. The observer on the ground provides for a flow forward in the flight direction.
• The pressure field moves as previously observed with the wing with and causes from the perspective of an observer standing on the ground a vertical movement directly behind the wing down.
• For reasons of mass conservation, there is always an upward vertical motion in front of the wing. Because of the large surface to which it is distributed, it has no significance for the lift.

The result is a circulating flow, as outlined in the figure by means of current lines. A power line is obtained from a snapshot by connecting all points in the direction of the flow at this point and at the instant considered. Power lines are always closed or they end at the edge of the observed area. From the perspective of the aircraft is obtained on the same circulation of the speed difference and the flow under the wing.

This circulation is commonly used for explanation of the lift. The formation of the circulation is explained as a counter to the observed vortex behind the wing Anfahrwirbel and justified by the fact that the total circulation must be from Anfahrwirbel and circulation flow zero ( Helmholtz vortex shear rate). Mathematically, this method provides good results in 2D, but the full explanation of lift is inadequate:

• It reduces the problem to two dimensions because of the underlying integral Stokes' theorem requires.
• The Helmholtz vortex theorem says nothing about cause and effect of the vertebrae involved. In the present case the Anfahrwirbel the counter- vortex circulation to flow around the wing. For the strength of the vortex pair, the empirical Kutta condition is used, after the circulation around the wing is such that flow smoothly flows at the sharp trailing edge.

The mathematical model of an irrotational circulation flow around the wing flying with airspeed provides, however, in many cases, good quantitative results for the lift. This is especially true for wings with a large extension in the subsonic range, eg gliders. The reason lies in the similarity of the simplifications of a general flow, so that they can be described by Bernoulli or as irrotational potential flow.

Although called Kutta condition fulfilled its purpose in the practical calculation of the lift, but is not physically justifiable. The physically correct justification lies in the viscosity of the air through which the air is in the few millimeters thick boundary layer forced to follow gently curved surfaces. As a result, the air flows from the sharp trailing edge according to the Kutta condition.

For Bernoulli

The Bernoulli equation is a simplified form of the Navier -Stokes equations. It applies along a trajectory in steady, incompressible and viscosity- free flow in an area that contains no vertebrae. Because of the limitations, the Bernoulli equation is only limited to the explanation of flows suitable for buoyancy extraction:

• Insect and bird flight eliminated because the flow around the wing by wing beat is not stationary.
• Commercial and military flight excrete because here the speed of sound is reached or exceeded. The compressibility is thus to be considered mandatory.

In classic sailing, motor and model aircraft and the flight of birds sailing the conditions are met for the application of Bernoulli's equation in the flow around the wing outside the boundary layer. However, it is no statement about cause and effect, but only describes the relationship between the pressure and velocity field.

Steady and unsteady flows

In steady flow shall, as the flow around from the perspective of the aircraft describes very well. In steady flow, for example, an aircraft is therefore only the weight of the aircraft by surface forces thus balanced by the boundary conditions of the observed volume. This volume is as large as desired, but have the limitation of being in time for this discussion constant from the perspective of the aircraft. Bird flight ( with flapping wings ) can not be discussed with them. Even with temporal averaging over the period of a wing beat is very careful to discuss because of the nonlinearity of the momentum flux of this term.

At stationarity, rotating airfoils ( rotors of helicopters, propeller fans, table fans ) are excluded in this form of the equation of motion first. In then rotating frame of reference the centrifugal and Coriolis inertia forces are to discuss their importance in the play of forces. These forces are, however, perpendicular to the axis of rotation and therefore play in the discussion of buoyancy not matter because these forces show parallel to the axis of rotation.

Then as a mathematical model for the description of non-stationary case to use the Euler or Navier-Stokes equations.