SP-367 Introduction to the Aerodynamics of Flight


- II. Background Information -



[5] As a background for the material presented, the reader is urged to examine the material presented in the appendixes. This information is basic and represents required background for the discussions throughout this paper. Appendix A contains aeronautical nomenclature concerning both general aeronautical definitions and descriptions of aircraft types. Appendix B discusses dimensions and units as used in this paper. A general discussion of vectors, scalars, and relative motion is also included. Appendix C describes the various coordinate systems used to define an aircraft's motion above the Earth's surface. The bibliography at the end of the paper will aid the reader in locating further information on the materials presented.


The Atmosphere


Nature of the atmosphere.- The aerodynamicist is concerned about one fluid, namely air. Air makes up the Earth's atmosphere-the gaseous envelope surrounding the Earth-and represents a mixture of several gases. Up to altitudes of approximately 90 km, fluctuating winds and general atmospheric turbulence in all directions keep the air mixed in nearly the same proportions. The normal composition of clean, dry atmospheric air near sea level is given in table I. Not included in the table are water vapor, dust particles, bacteria, etc. Water vapor, although highly variable, is estimated at 0.41-percent total volume. Interestingly, nitrogen and oxygen taken together represent 99 percent of the total volume of all the gases. That the local composition can be made to vary has been brought dramatically to light in recent times by the air pollution problem where in industrialized areas the percentages of carbon monoxide, sulfur dioxide, and numerous other harmful pollutants are markedly higher than in nonindustrialized areas.



[U.S. Standard atmosphere, 1962]

Constituent gas and formula

Content, percent by volume

Nitrogen (N2)


Oxygen (O2)


Argon (Ar)


Carbon Dioxide (CO2)


Neon (Ne), helium (He), krypton (Kr), hydrogen (H2), xenon (Xe), methane (CH4), nitrogen oxide (N2O), ozone (O3), sulfur dioxide (NO2), ammonia (NH3), carbon monoxide (CO), and iodine (I2)

Traces of each gas for a total of 0.003


[6] Above about 90 km, the different gases begin to settle or separate out according to their respective densities. In ascending order one would find high concentrations of oxygen, helium, and then hydrogen which is the lightest of all the gases.


Based on composition, then, there are two atmospheric strata, layers, or "shells." Below 90 km where the composition is essentially constant the shell is the homosphere. Above 90 km where composition varies with altitude, the shell is called the heterosphere. Although composition is one way of distinguishing shells or layers, the most common criterion used is the temperature distribution. In ascending order are the troposphere, stratosphere, mesosphere, thermosphere, and exosphere. Figure 6 shows both the composition- and temperature-defined shells. Figure 7 shows the temperature variation in the various shells.


It is the troposphere which is the most important atmospheric layer to aeronautics since most aircraft fly in this region. Most weather occurs here and, of course, man lives here also. Without the beneficial ozone layer in the stratosphere absorbing harmful solar ultraviolet radiation, life as we know it would not have developed. The ionosphere, a popularly known layer, begins in the mesosphere and extends indefinitely outwards. It represents the region in which ionization of one or more of the atmospheric constituents is significant. The exosphere represents the outer region of the atmosphere where the atmospheric particles can move in free orbits subject only to the Earth's gravitation. It is interesting to note that at these altitudes (greater than 500 km), the solar wind (streams of high-energy particles of plasma from the Sun) becomes a dominant influence so that one has an "atmosphere" which extends all the way to the Sun. The density of the solar wind, however, is negligibly small.


The standard atmosphere.- For purposes of pressure altimeter calibrations, aircraft and rocket performance and their design, and so forth, knowledge of the vertical distribution of such quantities as pressure, temperature, density, and speed of sound is required. Since the real atmosphere never remains constant at any particular time or place, a hypothetical model must be employed as an approximation to what may be expected. This model is known as the standard atmosphere. The air in the model is assumed to be devoid of dust, moisture, and water vapor and to be at rest with respect to the Earth (that is, no winds or turbulence).


The first standard atmospheric models were developed in the 1920's in both Europe and the United States. The slight differences between the models were reconciled and an internationally accepted model was introduced in 1952 by the International Civil Aviation Organization (ICAO). This new ICAO Standard Atmosphere was officially accepted by NACA in 1952 and forms the basis of tables in NACA report 1235. The tables extended from 5 km below to 20 km above mean sea level.


[7] With increased knowledge since 1952 because of the large scale use of high-altitude sounding rockets and satellites, extended tables above 20 km were published. Finally in 1962, the U.S. Standard Atmosphere (1962) was published to take into account this new data. For all practical purposes, the U.S. Standard Atmosphere (1962) is in agreement with the ICAO Standard Atmosphere over their common altitude range but extends to 700 km. Uncertainty in values increased with altitude as available data decreased.


Figure 6 - Atmospheric structure

Figure 6.- Atmospheric structure

Figure 7 - Atmospheric properties variation

Figure 7.- Atmospheric properties variation. (Based on U.S. Standard Atmosphere, 1962).


[9] With the expansion of this nation's space program requirements, a need was generated for information on the variability of atmospheric structure that would be used in the design of second-generation scientific and military aerospace vehicles.


Systematic variations in the troposphere due to season and latitude had been known to exist and thus a new effort was begun to take those variations into account. The result was the publication of the most up-to-date standard atmospheres-the U.S. Standard Atmosphere Supplements (1966). Essentially there are two sets of tables-one set for altitudes below 120 km and one for altitudes, 120 km to 1000 km. The model atmospheres below 120 km are given for every 15° of latitude for 15° N to 75° N and in most cases for January and July (or winter and summer). Above 120 km, models are presented to take into account varying solar activity. The older 1962 model is classified in the 1966 supplements as an average mid-latitude (30° N to 60° N) spring/fall model.


The 1962 U.S. Standard Atmosphere is the more general model and it is useful to list the standard sea level conditions:


Pressure, p0 = 101 325.0 N/m2
Density, p0= 1.225 kg/m3 [p = Greek letter rho]
Temperature, T0 = 288.15 K (15° C)
Acceleration of gravity, g0 = 9.807 m/sec2
Speed of sound, a0 = 340.294 m/sec


Figure 7 gives a multiplot of pressure, density, temperature, and speed of sound from sea level to 100 km. It is intended merely to indicate the general variation of these parameters. The temperature-defined atmospheric shells are also included.


In the troposphere (from sea level to 10 to 20 km in the standard atmosphere), it is seen that the temperature decreases linearly with altitude. In the stratosphere it first remains constant at about 217 K before increasing again. The speed of sound shows a similar type of variation. Both the density and pressure are seen to decrease rapidly with altitude. The density curve is of particular importance since, as will be seen, the lift on an airfoil is directly dependent on the density.


The real atmosphere.- It would be fortunate if the Earth's real atmosphere corresponded to a standard atmospheric model but thermal effects of the Sun, the presence of continents and oceans, and the Earth's rotation all combine to stir up the [10] atmosphere into a nonuniform, nonstandard mass of gases in motion. Although a standard atmosphere provides the criteria necessary for design of an aircraft, it is essential that "nonstandard" performance in the real atmosphere be anticipated also This nonstandard performance shows up in numerous ways, some of which are discussed in this section.


Winds and Turbulence


Unquestionably, the most important real atmospheric effect, and one receiving considerable attention of late, is the relative motion of the atmosphere. Although in the standard atmosphere the air is motionless with respect to the Earth, it is known that the air mass through which an airplane flies is constantly in a state of motion with respect to the surface of the Earth. Its motion is variable both in time and space and is exceedingly complex. The motion may be divided into two classes: (1) large-scale motions and (2) small-scale motions. Large-scale motions of the atmosphere (or winds) affect the navigation and the performance of an aircraft. Figure 8 illustrates one effect.


Figure 8a - Aircraft heading parallel to line AB. Wind drift causes actual flight path line AC

(a) Aircraft heading parallel to AB. Wind drift causes actual flight path AC.

Figure 8b - Aircraft yawed into wind angle [Greek letter psi] to account for wind drift

(b) Aircraft yawed into wind with angle [Greek letter psi] to account for wind drift.

Figure 8.- Effect of winds.


[11] In figure 8 (a) the pilot is attempting to fly his aircraft from point A to point B. He sets his heading and flies directly for point B but winds (representing large-scale motion of the atmosphere relative to the ground) are blowing crosswise to his intended flight path. After the required flight time which would have brought the pilot to point B if there were no winds, the pilot finds himself at point C. The winds, which were not taken into account, had forced him off course. In order to compensate for the winds, the pilot should have pointed the aircraft slightly into the wind as illustrated in figure 8 (b). This change would have canceled out any drifting of the aircraft off course. Compensation for drift requires knowledge of both the aircraft's velocity and the wind velocity with respect to the ground.


Statistical average values of horizontal wind speed as a function of altitude have been calculated and represent more or less a standard curve. Figure 9 represents one such typical statistical curve. Again, in the case of a real atmosphere, the real wind velocity at any particular time and place will vary considerably from the statistical average. In the case of wind drift then, rather than use a statistical curve, the pilot should consult local airports for wind conditions and forecasts along his intended flight path.


Figure 9 - A typical statistical maximum wind speed curve

Figure 9.- A typical statistical maximum wind speed curve. USAF Handbook of Geophysics.


[12] The small-scale motion of the atmosphere is called turbulence (or gustiness). The response of an aircraft to turbulence is an important matter. In passenger aircraft, turbulence may cause minor problems such as spilled coffee and in extreme cases injuries if seat belts are not fastened. Excessive shaking or vibration may render the pilot unable to read instruments. In cases of precision flying such as air-to-air refueling, bombing, and gunnery, or aerial photography, turbulence-induced motions of the aircraft are a nuisance. Turbulence-induced stresses and strains over a long period may cause fatigue in the airframe and in extreme cases a particular heavy turbulence may cause the loss of control of an aircraft or even immediate structural failure.


There are several causes of turbulence. The unequal heating of the Earth's surface by the Sun will cause convective currents to rise and make the plane's motion through such unequal currents rough. On a clear day the turbulence is not visible but will be felt; hence, the name "clear air turbulence (CAT)." Turbulence also occurs because of winds blowing over irregular terrain or, by different magnitude or direction, winds blowing side by side and producing a shearing effect.


In the case of the thunderstorm, one has one of the most violent of all turbulences where strong updrafts and downdrafts exist side by side. The severity of the aircraft motion caused by the turbulence will depend upon the magnitude of the updrafts and downdrafts and their directions. Many private aircraft have been lost to thunderstorm turbulence because of structural failure or loss of control. Commercial airliners generally fly around such storms for the comfort and safety of their passengers.


Figure 10 illustrates the flight path of an aircraft through the various turbulences described.


Another real atmospheric effect is that of moisture. Water in the air, in either its liquid or vapor form, is not accounted for in the pure dry standard atmosphere and will affect an aircraft in varying degrees. Everyone is familiar with the forms of precipitation that can adversely affect aircraft performance such as icing on the wings, zero visibility in fog or snow, and physical damage caused by hail. Water vapor is less dense than dry air and consequently humid air (air containing water vapor) will be less dense than dry air. Because of this, an aircraft requires a longer take-off distance in humid air than in the more dense dry air.


Air density is a very important factor in the lift, drag, and engine power output of an aircraft and depends upon the temperature and pressure locally. Since the standard atmosphere does not indicate true conditions at a particular time and place, it is important for a pilot to contact a local airport for the local atmospheric conditions.



Figure 10 - Flight path of an aircraft through various forms of turbulence. Relatively stable air exists above thunderstorms

 Figure 10.- Flight path of an aircraft through various forms of turbulence. Relatively stable air exists above thunderstorms.



From the local temperature and pressure readings, density may be obtained and, hence, take-off distance and engine power output may be determined.


The local pressure is important in aircraft using pressure altimeters. A pilot must zero his pressure altimeter to local measured sea-level pressure rather than to standard sea-level pressure if he is to obtain accurate altitude readings above sea level.


Although the preceding discussion considers only a few of the many effects of a nonstandard atmosphere on aircraft design and performance, the standard atmosphere still remains as a primary reference in the preliminary design stage of an aircraft.


The Airplane


Basic airplane.- Our attention will be centered mainly on that class of aircraft known as airplanes. Before proceeding into any discussion of aerodynamic theory and its application to airplanes, it would be well to consider in some detail the overall physical makeup of a typical airplane.


As figure 11 demonstrates in exploded view form, an airplane may be resolved into several basic components as follows: fuselage, wing, tail assembly and control surfaces, landing gear, and powerplant(s). The aerodynamics of these components are considered later in the discussion.


Fuselage.- The body of an airplane is called the fuselage. It houses the crew and the controls necessary for operating and controlling the airplane. It may provide space...



Figure 11 - Basic airplane components

 Figure 11.- Basic airplane components.



....for cargo and passengers and carry armaments of various sorts. In addition, an engine may be housed in the fuselage. The fuselage is, in one sense, the basic structure of the airplane since many of the other large components are attached to it. It is generally streamlined as much as possible to reduce drag. Designs vary with the mission to be performed and the variations are endless, as illustrated in figure 12.


Wing.- The wing provides the principal lifting force of an airplane. Lift is obtained from the dynamic action of the wing with respect to the air. The crosssectional shape of the wing is known as the airfoil section. The airfoil section shape, planform shape of the wing, and placement of the wing on the fuselage depend upon the airplane mission and the best compromise necessary in the overall airplane design. Figure 13 illustrates the shapes and placements often used.


Tail assembly and control surfaces.- The tail assembly (appendage) represents the collection of structures at the rear of the airplane. The tail assembly consists of (1) the vertical stabilizer (fin) and rudder which provide directional stability in yaw, and (2) the horizontal stabilizer and elevator which provide longitudinal stability in pitch. Figure 14 illustrates the numerous forms that a tail assembly may take.



Figure 12 - Various fuselage designs

 Figure 12.- Various fuselage designs.


Figure 13a - Examples of airfoil shapes

(a) Examples of airfoil shapes.
 Figure 13.- Wing shapes and placements.


Figure 13b - Examples of wing planform

(b) Examples of wing planform.
Figure 13.- Continued.


Figure 13c - Examples of wing placements

(c) Examples of wing placements.
Figure 13.- Concluded.

Figure 14 - Tail assembly forms

 Figure 14.- Tail assembly forms.


[19] Included in the control surfaces are all those moving surfaces of an airplane used for attitude, lift, and drag control. Yaw control (turning the airplane to the left or right) is provided by the rudder which is generally attached to the fin. Pitch control (nosing the airplane up or down) is provided by the elevators which are generally attached to the horizontal stabilizer. Roll control (rolling the wing to the right or left) is provided by the ailerons located generally near the outer trailing edge of the wing. Trim tabs are small auxiliary hinged control surface inserts on the elevator, rudder, and aileron surfaces whose functions are (1) to balance the airplane if it is too nose heavy, tail heavy, or wing heavy to fly in a stable cruise condition, (2) to maintain the elevator, rudder, or ailerons at whatever particular setting the pilot wishes without the pilot maintaining pressures on the controls, (3) to help move the elevators, rudder, and ailerons and thus relieve the pilot of the effort necessary to move the surfaces. Flaps are hinged or pivoted parts of the leading and/or trailing edges of the wing used to increase lift at reduced airspeeds. They are used primarily for landing and takeoff. Spoilers are devices used to reduce the lift on an airplane wing quickly. By operating independently on both sides of the wing, they may provide an alternate form of roll control. Figure 15 illustrates the attitude control surfaces and figure 16 shows a simple aileron and flap installation and a more complicated arrangement used on a large jet airliner.


Landing gear.- The landing gear, or undercarriage, supports the airplane while it is at rest on the ground or in water, and during the take-off and landing. The gear may be fixed or retractable. The wheels of most airplanes are attached to shock-absorbing struts that use oil or air to cushion the blow of landing. Special types of landing gear include skis for snow and floats for water. For carrier landings, arrester hooks are used. Figure 17 shows several of the gear arrangements found on modern-day airplanes.


Power plants.- With few exceptions an airplane must possess a thrust-producing device or power plant to sustain flight. The power plant consists of the engine (and propeller, if present), and the related accessories. The main engine types are the reciprocating (or piston type), and the reaction engines such as the ram jet, pulse jet, turbojet, turboprop, and rocket engine. Converting the energy of a reciprocating engine's rotating crankshaft into a thrust force is accomplished by the propeller. Figure 18 illustrates some of the many varied engine placements possible.


Forces on an airplane.- There are two general types of forces that may act on a body in unaccelerated or steady flight. They may be termed as body forces and surface forces. Body forces act on the body from a distance. For the airplane this is the gravitational force or weight. Surface forces act because of contact between the...



Figure 15 - Main control surfaces

Figure 15.- Main control surfaces.


Figure 16a - Simple flap arrangement

(a) Simple flap arrangement.

Figure 16b - Jet airliner aileron and flap assembly on wing

(b) Jet airliner aileron and flap assembly on wing.
Figure 16.- Flaps and ailerons.


Figure 17 - Landing gear forms

(a) Tricycle gear - nose wheel, two main wheels.
(b) Conventional gear- tail wheel, two main wheels.
(c) Unconventional gear - skis, skids, or floats.
Figure 17.- Landing gear forms. 


Figure 18 - Power-plant placement

Figure 18.- Power-plant placement.

Figure 19 - Forces on an airplane in normal flight

Figure 19.- Forces on an airplane in normal flight. 


[24] ...medium and the body, that is, between the air and the airplane surface. Lift, drag, and thrust, the other three main forces acting on an airplane, are all surface forces. Basically, the four forces acting on an airplane are weight, thrust, lift, and drag.


Weight: The weight includes the airplane itself, the payload, and the fuel. Since fuel is consumed as the airplane flies, the weight decreases. Weight acts in a direction toward the center of the Earth.


Thrust: The driving force of whatever propulsive system is used, engine driven propeller, jet engine, rocket engine, and so forth, is the thrust. It may be taken to act along the longitudinal axis of the airplane (except for vertical take-off airplanes).


Lift: This force is generated by the flow of air around the airplane, the major portion resulting from the wing. It represents the component of the resultant aerodynamic force normal to the line of flight.


Drag: Again, this force arises from the flow of air around the airplane but is the component of the resultant aerodynamic force along the line of flight.


In the simplest flight situation an airplane will travel in straight and level flight at a uniform velocity. Figure 19 shows the disposition of the four forces under these conditions. To maintain this basic flight situation, the lift equals the weight, and the thrust equals the drag. Weight and thrust are physical attributes of an airplane. They generally are known or can be easily determined and controlled. But lift and drag arise because of the dynamic movement of the airplane through the air. The major concern of aerodynamics is the manner in which the lift and drag forces arise. This subject is considered now in some detail.