Lift And Drag Coefficients Of Planes Engineering Essay

The term “fluid” in everyday language typically refers to liquids, but in the realm of physics, fluid describes any gases, liquids or plasmas that conform to the shape of its container.

Fluid mechanics is the study of gases and liquids at rest and in motion. It is divided into fluid statics, the study of the behavior of stationary fluids, and fluid dynamics, the study of the behavior of moving, or flowing, fluids. Fluid dynamics is further divided into hydrodynamics, or the study of water flow, and aerodynamics, the study of airflow.

Real-life applications of fluid mechanics included a variety of machines, ranging from the water-wheel to the airplane. Many of the applications are according to several principles such as Pascal’s Principle, Bernoulli’s Principle, Archimedes’s Principle and etc.

As example, Bernoulli’s principle, which stated that the greater the velocity of flow in a fluid, the greater the dynamic pressure and the less the static pressure. In other words, slower-moving fluid exerts greater pressure than faster-moving fluid. The discovery of this principle ultimately made possible the development of the airplane. Therefore, among the most famous applications of Bernoulli’s principle is its use in aerodynamics.

In addition, the study of fluids provides an understanding of a number of everyday phenomena, such as why an open window and door together create a draft in a room.

Wind Tunnel

Suppose one is in a room where the heat is on too high, and there is no way to adjust the thermostat. Outside, however, the air is cold, and thus, by opening a window, one can presumably cool down the room. But if one opens the window without opening the front door of the room, there will only be little temperature change. But if the door is opened, a nice cool breeze will blow through the room. Why?

This is because, with the door closed, the room constitutes an area of relatively high pressure compared to the pressure of the air outside the window. Because air is a fluid, it will tend to flow into the room, but once the pressure inside reaches a certain point, it will prevent additional air from entering. The tendency of fluids is to move from high-pressure to low-pressure areas, not the other way around. As soon as the door is opened, the relatively high-pressure air of the room flows into the relatively low-pressure area of the hallway. As a result, the air pressure in the room is reduced, and the air from outside can now enter. Soon a wind will begin to blow through the room.

The above scenario of wind flowing through a room describes a rudimentary wind tunnel. A wind tunnel is a chamber built for the purpose of examining the characteristics of airflow in contact with solid objects, such as aircraft and automobiles. 

Theory of Operation of a Wind Tunnel

Wind tunnels were first proposed as a means of studying vehicles (primarily airplanes) in free flight. The wind tunnel was envisioned as a means of reversing the usual paradigm: instead of the air’s standing still and the aircraft moving at speed through it, the same effect would be obtained if the aircraft stood still and the air moved at speed past it. In that way a stationary observer could study the aircraft in action, and could measure the aerodynamic forces being imposed on the aircraft.

Later, wind tunnel study came into its own: the effects of wind on manmade structures or objects needed to be studied, when buildings became tall enough to present large surfaces to the wind, and the resulting forces had to be resisted by the building’s internal structure.

Still later, wind-tunnel testing was applied to automobiles, not so much to determine aerodynamic forces per second but more to determine ways to reduce the power required to move the vehicle on roadways at a given speed.

In the wind tunnel the air is moving relative to the roadway, while the roadway is stationary relative to the test vehicle. Some automotive-test wind tunnels have incorporated moving belts under the test vehicle in an effort to approximate the actual condition. Its represents a safe and judicious use of the properties of fluid mechanics. Its purpose is to test the interaction of airflow and solids in relative motion: in other words, either the aircraft has to be moving against the airflow, as it does in flight, or the airflow can be moving against a stationary aircraft. The first of these choices, of course, poses a number of dangers; on the other hand, there is little danger in exposing a stationary craft to winds at speeds simulating that of the aircraft in flight.

Wind tunnel

Wind tunnels are used for the study of aerodynamics (the dynamics of fluids).

So there is a wide range of applications and fluid mechanic theory can be applied in the device.

– airframe flow analysis (aviation, airfoil improvements etc),

– aircraft engines (jets) performance tests and improvements,

– car industry: reduction of friction, better air penetration, reduction of losses and fuel consumption (that’s why all cars now look the same: the shape is not a question of taste, but the result of laws of physics!)

– any improvement against and to reduce air friction: i.e. the shape of a speed cycling helmet, the shape of the profiles used on a bike are designed in a wind tunnel.

– to measure the flow and shape of waves on a surface of water, in response to winds (very large swimming pools!)

– Entertainment as well, in mounting the tunnel on a vertical axis and blowing from bottom to top. Not to simulate anti-gravity as said above, but to allow safely the experience of free-falling parachutes.

The Bernoulli principle is applied to measure experimentally the air speed flowing in the wind tunnel. In this case, the construction of Pitot tube is made to utilize the Bernoulli principle for the task of measuring the air speed in the wind tunnel. Pitot tube is generally an instrument to measure the fluid flow velocity and in this case to measure the speed of air flowing to assist further aerodynamic calculations which require this piece of information and the adjustment of the wind speed to achieve desired value.

Schematic of a Pitot tube

Bernoulli’s equation states:

Stagnation pressure = static pressure + dynamic pressure

This can also be written as,

Solving that for velocity we get:

Where,

V is air velocity;

pt is stagnation or total pressure;

ps is static pressure;

h= fluid height

and ρ is air density

To reduce the error produced, the placing of this device is properly aligned with the flow to avoid misalignment.

As a wing moves through the air, the wing is inclined to the flight direction at some angle. The angle between the chord line and the flight direction is called the angle of attack and has a large effect on the lift generated by a wing. When an airplane takes off, the pilot applies as much thrust as possible to make the airplane roll along the runway. But just before lifting off, the pilot “rotates” the aircraft. The nose of the airplane rises, increasing the angle of attack and producing the increased lift needed for takeoff.

The magnitude of the lift generated by an object depends on the shape of the object and how it moves through the air. For thin airfoils, the lift is directly proportional to the angle of attack for small angles (within +/- 10 degrees). For higher angles, however, the dependence is quite complex. As an object moves through the air, air molecules stick to the surface. This creates a layer of air near the surface called a boundary layer that, in effect, changes the shape of the object. The flow turning reacts to the edge of the boundary layer just as it would to the physical surface of the object. To make things more confusing, the boundary layer may lift off or “separate” from the body and create an effective shape much different from the physical shape. The separation of the boundary layer explains why aircraft wings will abruptly lose lift at high angles to the flow. This condition is called a wing stall.

On the slide shown above, the flow conditions for two airfoils are shown on the left. The shape of the two foils is the same. The lower foil is inclined at ten degrees to the incoming flow, while the upper foil is inclined at twenty degrees. On the upper foil, the boundary layer has separated and the wing is stalled. Predicting the stall point (the angle at which the wing stalls) is very difficult mathematically. Engineers usually rely on wind tunnel tests to determine the stall point. But the test must be done very carefully, matching all the important similarity parameters of the actual flight hardware.

The plot at the right of the figure shows how the lift varies with angle of attack for a typical thin airfoil. At low angles, the lift is nearly linear. Notice on this plot that at zero angle a small amount of lift is generated because of the airfoil shape. If the airfoil had been symmetric, the lift would be zero at zero angle of attack. At the right of the curve, the lift changes rather abruptly and the curve stops. In reality, you can set the airfoil at any angle you want. However, once the wing stalls, the flow becomes highly unsteady, and the value of the lift can change rapidly with time. Because it is so hard to measure such flow conditions, engineers usually leave the plot blank beyond wing stall.

Since the amount of lift generated at zero angle and the location of the stall point must usually be determined experimentally, aerodynamicists include the effects of inclination in the lift coefficient. For some simple examples, the lift coefficient can be determined mathematically. For thin airfoils at subsonic speed, and small angle of attack, the lift coefficient Cl is given by:

Cl = 2

where  is 3.1415, and a is the angle of attack expressed in radians:

radians = 180 degrees

Aerodynamicists rely on wind tunnel testing and very sophisticated computer analysis to determine the lift coefficient.

Lift coefficient

The lift coefficient (  or ) is a dimensionless coefficient that relates the lift generated by an aerodynamic body such as a wing or complete aircraft, the dynamic pressure of the fluid flow around the body, and a reference area associated with the body. It is also used to refer to the aerodynamic lift characteristics of a 2D airfoil section, whereby the reference “area” is taken as the airfoil chord. It may also be described as the ratio of lift pressure to dynamic pressure.

Aircraft Lift Coefficient

Lift coefficient may be used to relate the total lift generated by an aircraft to the total area of the wing of the aircraft. In this application it is called the aircraft or planform lift coefficient 

The lift coefficient  is equal to:

where

 is the lift force,

 is fluid density,

 is true airspeed,

 is dynamic pressure, and

 is planform area.

The lift coefficient is a dimensionless number.

The aircraft lift coefficient can be approximated using, for example, the Lifting-line theory or measured in a wind tunnel test of a complete aircraft configuration.

Section Lift Coefficient

Lift coefficient may also be used as a characteristic of a particular shape (or cross-section) of an airfoil. In this application it is called the section lift coefficient  It is common to show, for a particular airfoil section, the relationship between section lift coefficient and angle of attack. It is also useful to show the relationship between section lift coefficients and drag coefficient.

The section lift coefficient is based on the concept of an infinite wing of non-varying cross-section, the lift of which is bereft of any three-dimensional effects – in other words the lift on a 2D section. It is not relevant to define the section lift coefficient in terms of total lift and total area because they are infinitely large. Rather, the lift is defined per unit span of the wing  In such a situation, the above formula becomes:

where  is the chord length of the airfoil.

The section lift coefficient for a given angle of attack can be approximated using, for example, the Thin Airfoil Theory, or determined from wind tunnel tests on a finite-length test piece, with endplates designed to ameliorate the 3D effects associated with the trailing vortex wake structure.

Note that the lift equation does not include terms for angle of attack – that is because the mathematical relationship between lift and angle of attack varies greatly between airfoils and is, therefore, not constant. (In contrast, there is a straight-line relationship between lift and dynamic pressure; and between lift and area.) The relationship between the lift coefficient and angle of attack is complex and can only be determined by experimentation or complex analysis. See the accompanying graph. The graph for section lift coefficient vs. angle of attack follows the same general shape for all airfoils, but the particular numbers will vary. The graph shows an almost linear increase in lift coefficient with increasing angle of attack, up to a maximum point, after which the lift coefficient reduces. The angle at which maximum lift coefficient occurs is the stall angle of the airfoil.

The lift coefficient is a dimensionless number.

Note that in the graph here, there is still a small but positive lift coefficient with angles of attack less than zero. This is true of any airfoil with camber (asymmetrical airfoils). On a cambered airfoil at zero angle of attack the pressures on the upper surface are lower than on the lower surface.

A typical curve showing section lift coefficient versus angle of attack for a cambered airfoil

Drag Coefficient

In fluid dynamics, the drag coefficient (commonly denoted as:   or ) is a dimensionless quantity that is used to quantify the drag or resistance of an object in a fluid environment such as air or water. It is used in the drag equation, where a lower drag coefficient indicates the object will have less aerodynamic or hydrodynamic drag. The drag coefficient is always associated with a particular surface area.

The drag coefficient of any object comprises the effects of the two basic contributors to fluid dynamic drag: skin friction and form drag. The drag coefficient of lifting airfoil or hydrofoil also includes the effects of lift induced drag. The drag coefficient of a complete structure such as an aircraft also includes the effects of interference drag.

Definition

The drag coefficient  is defined as:

where:

 is the drag force, which is by definition the force component in the direction of the flow velocity,

 is the mass density of the fluid,

 is the speed of the object relative to the fluid, and

is the reference area.

The reference area depends on what type of drag coefficient is being measured. For automobiles and many other objects, the reference area is the frontal area of the vehicle (i.e., the cross-sectional area when viewed from ahead). For example, for a sphere  (note this is not the surface area = ).

For airfoils, the reference area is the planform area. Since this tends to be a rather large area compared to the projected frontal area, the resulting drag coefficients tend to be low: much lower than for a car with the same drag, frontal area and at the same speed.

Airships and some bodies of revolution use the volumetric drag coefficient, in which the reference area is the square of the cube root of the airship volume. Submerged streamlined bodies use the wetted surface area.

Two objects having the same reference area moving at the same speed through a fluid will experience a drag force proportional to their respective drag coefficients. Coefficients for unstreamlined objects can be 1 or more, for streamlined objects much less.