Flight Stability and Automatic Control SECOND EDITION Dr. Robert C. Nelson Department of Aerospace and Mechanical Engineering University of Notre Dame . Nelson Flight Stability and Automatic Control Second Edition ESTRATTO 4. Huy Lê. Loading Preview. Sorry, preview is currently unavailable. You can download . Control Robert C Nelson [PDF] [EPUB] The Second Edition of Flight Stability and Automatic. Control presents an integrated treatment of aircraft.
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3 Static Longitudinal Stability and Control. Control Fixed ..  Robert C. Nelson, Flight Stability and Automatic Control, McGraw-Hill, New York,. Second. Flight Stability and Automatic Control Second Edition Robert C. Nelson - Ebook download as PDF File .pdf) or view presentation slides online. Robert C. Airplane Stability and Automatic Control Nelson - Download as PDF File .pdf) or read Flight Stability and Automatic Control Second Edition Robert C. Nelson.
At very high altitude, air cannot be considered as a continuous medium and again the analysis breaks down. Several devices can be used to measure the angle of attack of an airplane, two of which are the vane and pressure-sensor type indicator.
The pivot vane sensor is a mass-balanced wind vane that is free to align itself with the oncoming flow. The vane type angle of attack sensor has been used extensively in airplane flight test programs. For flight test applications the sensor usually is mounted on a nose boom or a boom mounted to the wing tips along with a Pitot static probe, as illustrated in Figure 1. Note that a second vane system is mounted on the boom to measure the sideslip angle.
The angle measured by the vane is influenced by the distortion of the flow field created by the airplane.
Actually, the sensor measures only the local angle of attack. The difference between the measured and actual angles of attack is called the position error. Position error can be minimized by mounting the sensor on the fuselage, where the flow distortion is small.
The deflection of the vane is recorded by means of a potentiometer. A null-seeking pressure sensor also can be used to measure the angle of attack. The sensor consists of the following components: The device shown in Figure 1.
The pressures from the two slits are vented to air chambers by a swivel paddle.
If a pressure difference exists at the two slots, the swivel paddle will rotate. The paddle is connected by way of linkages so that, as the paddle moves, the pressure tube is rotated until the pressures are equalized.
The angular position of the probe is recorded by a poten- tiometer. The airspeed indicator has been calibrated for both instrument and position errors and reads a velocity of knots. The altimeter is a pressure gauge calibrated to the standard atmosphere. If the altimeter reads 10, ft, the static pressure it senses must correspond to the static pressure at 10, ft in the standard atmosphere. Using the standard atmospheric table in the Appendix, the static pressure at 10, ft is given as The ambient density can be calculated using the equation of state: Introduction A low-speed airspeed indicator corrected for instrument and position error reads the equivalent airspeed.
The true speed and equivalent airspeed are related by where a i s the ratio of the density at altitude to the standard sea-level value of density: For the comparison of flight test data and calibrating aircraft instru- ments, a standard atmosphere is a necessity: The U.
Standard Atmosphere provides the needed reference for the aerospace community. The standard atmo- sphere was shown to be made up of gradient and isothermal regions. Finally, we discussed the basic concepts behind several basic flight instruments that play an important role in flight test measurements of aircraft performance, stability and control. In principle these instruments seem to be quite simple; they in fact, are, extremely complicated mechanical devices.
Although we have dis- cussed several mechanical instruments, most of the information presented to the flight crew on the newest aircraft designs comes from multifunctional electronic displays. Color cathode ray tubes are used to display air data such as attitude, speed, and altitude. Additional displays include navigation, weather, and engine perfor- mance information, to name just a few items.
The improvements offered by this new technology can be used to reduce the workload of the flight crew and improve the flight safety of the next generation of airplane designs.
An altimeter set for sea-level standard pressure indicates an altitude of 20, ft. If the outside ambient temperature is -YF, find the air density and the density altitude. If the airplane is flying at a true airspeed of mls, determine the indicated airspeed.
References 33 1. A high-altitude, remotely piloted communications platform is flying at a pressure altitude of 60, ft and an indicated airspeed of ftls. Estimate the Reynolds number of the wing based on a mean chord of 3. An airplane is flying at a pressure altitude of 10, ft and the airspeed indicator reads knots. If there is no instrument error and the position error is given by Figure P1. Under what conditions are following relationships valid? Anderson, J. Introduction to Flight. New York: McGraw-Hill, Domnasch, D.
Sherby; and T. Airplane Aerodynamics. Pitman, Pallett, E. Aircraft Instruments. Putnam, T. One problem still beyond the grasp of these early investigators was a lack of understanding of the relationship between stability and control as well as the influence of the pilot on the pilot-machine system.
Most of the ideas regarding stability and control came from experiments with uncontrolled hand-launched gliders. Through such experiments, it was quickly discovered that for a successful flight the glider had to be inherently stable. Zahm, however, was the first to correctly outline the requirements for static stability in a paper he presented in In his paper, he analyzed the conditions necessary for obtaining a stable equilibrium for an airplane descending at a constant speed.
Figure 2. Zahm concluded that the center of gravity had to be in front of the aerodynamic force and the vehicle would require what he referred to as "longitudinal dihedral" to have a stable equilibrium point.
In the terminology of today, he showed that, if the center of gravity was ahead of the wing aerodynamic center, then one would need a reflexed airfoil to be stable at a positive angle of attack. In the 20 years prior to the Wright brothers' successful flight, many individuals in the United States and Europe were working with gliders and unpiloted powered models.
These investigators were constantly trying to improve their vehicles, with the ultimate goal of achieving powered flight of a airplane under human control. Lilienthal made a significant contribution to aeronautics by his work with model and human-carrying gliders. His experiments included the determination of the properties of curved or cambered wings.
He carefully recorded the details of over glider flights. The information in his journal includes data on materials, construction techniques, handling characteristics of his gliders, and aerodynamics. His successful flights and recorded data inspired and aided many other aviation pioneers.
Lilienthal's glider designs were statically stable but had very little control capability. For control, Lilienthal would shift his weight to maintain equilibrium flight, much as hang-glider pilots do today. The lack of suitable control proved to be a fatal flaw for Lilienthal. In , he lost control of his glider; the glider stalled and plunged to earth from an altitude of 50 ft.
Lilienthal died a day later from the injuries incurred in the accident. In the United States, Octave Chanute became interested in gliding flight in the mid s. Initially, he built gliders patterned after Lilienthal's designs. After experimenting with modified versions of Lilienthal's gliders, he developed his own designs.
His gliders incorporated biplane and multiplane wings, controls to adjust the wings to maintain equilibrium, and a vertical tail for steering. These design changes represented substantial improvements over Lilienthal's monoplane glid- ers.
Many of Chanute's innovations would be incorporated in the Wright brothers' designs. In addition to corresponding with the Wright brothers, Chanute visited their camp at Kitty Hawk to lend his experience and advice to their efforts. Another individual who helped the Wright brothers was Samuel Pierpont Langley, secretary of the Smithsonian Institution. The Wright brothers knew of Langley's work and wrote to the Smithsonian asking for the available aeronautical literature.
The Smithsonian informed the Wright brothers of the activities of many of the leading aviation pioneers and this information, no doubt, was very helpful to them. Around Langley became interested in problems of flight.
Initially his work consisted of collecting and examining all the available aerodynamic data. From the study of these data and his own experiments he concluded that heavier- than-air powered flight was possible. Langley then turned his attention to designing and perfecting unpiloted powered models.
On May 6, , his powered model flew for 1 f minutes and covered a distance of three-quarters of a mile. Langley's success with powered models pioneered the practicality of mechanical flight. Langley and his engineering assistant, Charles Manley, started work on their own design in For the next four years, they were busy designing, fabricating, and testing the full-size airplane that was to be launched by a catapult fixed to the top of a houseboat.
The first trial was conducted on September 7, , in the middle of the Potomac River near Tidewater, Virginia. The first attempt ended in failure as the airplane pitched down into the river at the end of the launch rails. A second attempt was made on December 8, ; this time, the airplane pitched up and fell back into the river. In both trials, the launching system pre- vented the possibility of a successful flight.
For Langley, it was a bitter disappoint- ment and the criticism he received from the press deeply troubled him. He was one of the pioneering geniuses of early aviation, however, and it is a shame that he went to his grave still smarting from the ridicule. Some 20 years later his airplane was modified, a new engine was installed, and the airplane flew successfully.
The time had come for someone to design a powered airplane capable of carrying someone aloft. As we all know, the Wright brothers made their historic first flight on a powered airplane at Kitty Hawk, North Carolina, on December 17, Orville Wright made the initial flight, which lasted only 12 seconds and covered approximately feet.
Taking turns operating the aircraft, Orville and Wilbur made three more flights that day. The final flight lasted 59 seconds and covered a distance of feet while flying into a 20 mph headwind.
The airplane tended to fly in a porpoising fashion, with each flight ending abruptly as the vehicle's landing skids struck tile ground. The Wright brothers found their powered airplane to be much more responsive than their earlier gliders and, as a result, had difficulty controlling their airplane. The first pho- tograph shows Orville Wright making the historical initial flight and the second shows the airplane after the fourth and last flight of the day. Notice the damaged horizontal rudder the term used by the Wright brothers.
Today we use the term canard to describe a forward control surface. The world canard comes to us from the French word that means "duck. They thought this airplane looked like a duck with its neck stretched out in flight. From this very primitive beginning, we have witnessed a remarkable revolution in aircraft development. In less than a century, airplanes have evolved into an essential part of our national defense and commercial transportation system. The success of the Wright brothers can be attributed to their step-by-step experimental approach.
After reviewing the experimental data of their contemporaries, the Wright brothers were convinced that additional information was necessary before a successful airplane could be designed. They embarked on an experimental pro- gram that included wind-tunnel and flight-test experiments.
The Wright brothers designed and constructed a small wind tunnel and made thousands of model tests to determine the aerodynamic characteristics of curved airfoils. They also con- ducted thousands of glider experiments in developing their airplane. Therefore, much of their work was directed toward improving the control capabilities of their gliders. They felt strongly that powerful controls were essential for the pilot to maintain equilibrium and prevent accidents such as the ones that caused the deaths of Lilienthal and other glider enthusiasts.
This approach represented a radical break with the design philosophy of the day. The gliders and airplanes designed by Lilenthal, Chanute, Langley, and other aviation pioneers were designed to be inherently stable.
In these designs, the pilot's only function was to steer the vehicle. Although such vehicles were statically stable, they lacked maneuverability and were susceptible to upset by atmospheric distur- bances.
The Wright brothers' airplane was statically unstable but quite maneuver- able. The lack of stability made their work as pilots very difficult. However, through their glider experiments they were able to teach themselves to fly their unstable airplane. The Wright brothers succeeded where others failed because of their dedicated scientific and engineering efforts. Their accomplishments were the foundation on which others could build. Some of the major accomplishments follow: They designed and built a wind-tunnel and balance system to conduct aerody- namic tests.
With their tunnel they developed a systematic airfoil aerodynamic database. They developed a complete flight control system with adequate control capa- bility. They designed a lightweight engine and an efficient propeller. Finally, they designed an airplane with a sufficient strength-to-weight ratio, capable of sustaining powered flight.
These early pioneers provided much of the understanding we have today regarding static stability, maneuverability, and control.
However, it is not clear whether any of these men truly comprehended the relationship among these topics. By stability we mean the tendency of the airplane to return to its equilibrium position after it has been disturbed.
The disturbance may be generated by the pilot's actions or atmospheric phenomena. The atmospheric disturbances can be wind gusts, wind gradients, or turbulent air. An airplane must have sufficient stability that the pilot does not become fatigued by constantly having to control the airplane owing to external disturbances. Although airplanes with little or no inherent aerodynamic stability can be flown, they are unsafe to fly unless they are provided artificial stability by an electromechanical device called a stability augmentation system.
Two conditions are necessary for an airplane to fly its mission successfully. Static Stability and Control to maneuver for a wide range of flight velocities and altitudes. To achieve equi- librium or perform maneuvers, the airplane must be equipped with aerodynamic and propulsive controls. The design and performance of control systems is an integral part of airplane stability and control.
The stability and control characteristics of an airplane are referred to as the vehicle's handling or flying qualities. It is important to the pilot that the airplane possesses satisfactory handling qualities. Airplanes with poor handling qualities will be difficult to fly and could be dangerous.
Pilots form their opinions of an airplane on the basis of its handling characteristics. An airplane will be considered of poor design if it is difficult to handle regardless of how outstanding the airplane's performance might be.
In the study of airplane stability and control, we are interested in what makes an airplane stable, how to design the control systems, and what conditions are necessary for good handling. In the following sections we will discuss each of these topics from the point of view of how they influence the design of the airplane. To discuss stability we must first define what is meant by equilibrium.
If an airplane is to remain in steady uniform flight, the resultant force as well as the resultant moment about the center of gravity must both be equal to 0. An airplane satisfying this requirement is said to be in a state of equilibrium or flying at a trim condition.
The subject of airplane stability is generally divided into static and dynamic stability. Static stability is the initial tendency of the vehicle to return to its equi- librium state after a disturbance.
An example of the various types of static stability is illustrated in Figure 2. If the ball were to be displaced from the bottom of the curved surface Figure 2. Such a situation would be referred to as a stable equilibrium point. On the other hand, if we were able to balance a ball on the curved surface shown in Figure 2.
In this case, the equilibrium point would be classified as unstable. In the last example, shown in Figure 2. Now, if the wall were to be displaced from its initial equilibrium point to another position, the ball would remain at the new position. This would be classified as a neutrally stable equilibrium point and represents the limiting or boundary between static stability and static instability.
The important point in this simple example is that, if we are to have a stable equilibrium point, the vehicle must develop a restoring force or moment to bring it back to the equilibrium condition. Static Stability and Control its equilibrium conditions. Note that the vehicle can be statically stable but dynam- ically unstable. Static stability, therefore, does not guarantee dynamic stability.
However, for the vehicle to be dynamically stable it must be statically stable. The reduction of the disturbance with time indicates that there is resistance to the motion and, therefore, energy is being dissipated. The dissipation of energy is called positive damping.
If energy is being added to the system, then we have a negative damping. Positive damping for an airplane is provided by forces and moments that arise owing to the airplane's motion. In positive damping, these forces and moments will oppose the motion of the airplane and cause the distur- bance to damp out with time. An airplane that has negative aerodynamic damping will be dynamically unstable. To fly such an airplane, artificial damping must be designed into the vehicle.
The artificial damping is provided by a stability augmen- tation system SAS. Basically, a stability augmentation system is an electrome- chanical device that senses the undesirable motion and moves the appropriate controls to damp out the motion. This usually is accomplished with small control movements and, therefore, the pilot's control actions are not influenced by the system. Of particular interest to the pilot and designer is the degree of dynamic stabil- ity. Dynamic stability usually is specified by the time it takes a disturbance to be damped to half of its initial amplitude or, in the case of an unstable motion, the time it takes for the initial amplitude of the disturbance to double.
In the case of an oscillatory motion, the frequency and period of the motion are extremely im- portant. So far, we have been discussing the response of an airplane to external distur- bances while the controls are held fixed. When we add the pilot to the system, additional complications can arise.
For example, an airplane that is dynamically stable to external disturbances with the controls fixed can become unstable by the pilot's control actions. If the pilot attempts to correct for a disturbance and that control input is out of phase with the oscillatory motion of the airplane, the control actions would increase the motion rather than correct it. This type of pilot-vehicle response is called pilot-induced oscillation PIO. Many factors contribute to the P I 0 tendency of an airplane.
A few of the major contributions are insufficient aero- dynamic damping, insufficient control system damping, and pilot reaction time. The same requirement exists for an airplane. Let us consider the two airplanes and their respective pitching moment curves shown in Figure 2. The pitching moment curves have been assumed to be linear until the wing is close to stalling.
In Figure 2. Suppose the airplanes suddenly encounter an upward gust such that the angle of attack is increased to point C. At the angle of attack denoted by C, airplane 1 would develop a negative nose-down pitching moment that would tend to rotate the airplane back toward its equilibrium point. However, for the same disturbance, airplane 2 would develop a positive nose-up pitching moment that would tend to rotate the aircraft away from the equilibrium point.
If we were to encounter a disturbance that reduced the angle of attack, say, to point A, we would find that airplane 1 would develop a nose-up moment that would rotate the aircraft back toward the equilibrium point.
On the other hand, airplane 2 would develop a nose-down moment that would rotate the aircraft away from the equilibrium point. On the basis of this simple analysis, we can conclude that to have static longitudinal stability the aircraft pitching moment curve must have a negative slope. That is, through the equilibrium point. Another point that we must make is illustrated in Figure 2.
Here we see two pitching moment curves, both of which satisfy the condition for static stability. However, only curve 1 can be trimmed at a positive angle of attack.
Although we developed the criterion for static stability from the C,,, versus a curve, we just as easily could have accom- plished the result by working with a C,,, versus C, curve. In this case, the require- ment for static stability would be as follows: The two conditions are related by the following expression: However, it is of interest particularly to airplane designers to know the contribution of the wing, fuselage, tail, propulsion system, and the like, to the pitching moment and static stability characteristics of the airplane.
In the following sections, each of the components will be considered separately. We will start by breaking down the airplane into its basic components, such as the wing, fuselage, horizontal tail, and propulsion unit.
Detailed methods for estimating the aerodynamic stability coefficients can be found in the United States Air Force Stability and Control Datcom [2.
The Datcom, short for data compendium, is a collection of methods for estimating the basic stability and control coefficients for flight regimes of subsonic, transonic, supersonic, and hy- personic speeds. Methods are presented in a systematic body build-up fashion, for example, wing alone, body alone, winglbody and winglbodyltail techniques. The methods range from techniques based on simple expressions developed from theory to correlations obtained from experimental data.
In the following sections, as well as in later chapters, we shall develop simple methods for computing the aerody- namic stability and control coefficients. Our emphasis will be for the most part on methods that can be derived from simple theoretical considerations. These meth- ods in general are accurate for preliminary design purposes and show the relation- ship between the stability coefficients and the geometric and aerodynamic charac- teristics of the airplane.
Furthermore, the methods generally are valid only for the subsonic flight regime. A complete discussion of how to extend these methods to higher-speed flight regimes is beyond the scope of this book and the reader is referred to [2.
In this sketch we have replaced the wing by its mean aero- dynamic chord F. The distances from the wing leading edge to the aerodynamic center and the center of gravity are denoted x,, and x,, respectively. The vertical displacement of the center of gravity is denoted by z,,. The angle the wing chord line makes with the fuselage reference line is denoted as i,.
This is the angle at which the wing is mounted onto the fuselage. If we sum the moments about the center of gravity, the following equation is obtained: With this assumption the following approximations can be made: Applying the condition for static stability yields For a wing-alone design to be statically stable, Equation 2.
Since we also want to be able to trim the aircraft at a positive angle of attack, the pitching moment coefficient at zero angle of attack, Cmi,, must be greater than 0.
A positive pitching moment about the aerodynamic center can be achieved by using a nega- tive-cambered airfoil section or an airfoil section that has a reflexed trailing edge. For many airplanes, the center of gravity position is located slightly aft of the aerodynamic center see data in Appendix B.
Also, the wing is normally constructed of airfoil profiles having a positive camber. Therefore, the wing contri- bution to static longitudinal stability is destabilizing for most conventional air- planes.
When the surface is located forward of the wing, the surface is called a canard. Both surfaces are influenced by the flow field created by the wing.
The canard surface is affected by the upwash flow from the wing, whereas the aft tail is subjected to the downwash flow. The wing flow field is due primarily to the bound and trailing vortices. The magni- tude of the upwash or downwash depends on the location of the tail surface with respect to the wing.
The contribution that a tail surface located aft of the wing makes to the airplane's lift and pitching moment can be developed with the aid of Figure 2.
In this sketch, the tail surface has been replaced by its mean aerodynamic chord. The angle of attack at the tail can be expressed as where E and i, are the downwash and tail incidence angles, respectively. The magnitude of 7 depends on the location of the tail surface. If LDt F. Such a situation could exist if the tail were located in either the slip stream of the propeller or in the exhaust wake of a jet engine. The pitching moment due to the tail can be obtained by summing the moments about the center of gravity: Usually only the first term of this equation is retained; the other terms generally are small in comparison to the first term.
From Figure 2. The downwash angle s can be expres- sed as where sois the downwash at zero angle of attack. The downwash behind a wing with an elliptic lift distribution can be derived from finite-wing theory and shown to be related to the wing lift coefficient and aspect ratio: The rate of change of downwash angle with angle of attack is determined by taking the derivative of Equation 2. More accurate methods for estimating the downwash at the tailplane can be found in [2.
An experimental technique for determining the downwash using wind-tunnel force and moment measurements will be presented by way of a prob- lem assignment at the end of this chapter.
Rewriting the tail contribution to the pitching moment yields Comparing Equation 2. Recall that earlier we showed that the wing contribution to C,, was negative for an airfoil having positive camber. The tail contribution to Cmocan be used to ensure that CmI1 for the complete airplane is positive. This can be accomplished by adjust- ing the tail incidence angle i,. Note that we would want to mount the tail plane at a negative angle of incidence to the fuselage reference line to increase Cmo due to the tail.
The contribution of Cmm, will become more negative by increasing the tail moment arm 1, or tail surface area S, and by increasing CLm. The tail lift curve slope C,,, can be increased most easily by increasing the kpect ratio of the tail planform. The designer can adjust any one of these parameters to achieve the desired slope.
As noted here, a tail surface located aft of the wing can be used to ensure that the airplane has a positive Cmoand a negative Cma. Static Stability and Control Estimate the horizontal tail area and tail incidence angle, i,, so that the complete airplane has the following pitching moment characteristics illustrated in Figure 2.
Assume the following with regard to the horizontal tail: Recall the Cmm, was developed earlier and is rewritten here: However, this can be estimated from the wing characteristics as follows: Next we can determine the tail incidence angle, i,, from the requirement for Cw,. The equation for C,, due to the horizontal tail was shown to be The tail incidence angle, i,, can be obtained by rearranging the preceding equation: The only quantity that we do not know in this equation is E,; that is, the downwash angle at the tail when the wing is at zero angle of attack.
Static Stability and Control the following expression: The horizontal tail is mounted to the fuselage at a negative 2. In summary we have shown that the level of static stability can be controlled by the designer by proper selection of the horizontal tail volume ratio.
In practice the only parameter making up the volume ratio that can be varied by the stability and control designer is the horizontal tail surface area. The other parameters, such as the tail moment arm, wing area, and mean wing chord, are determined by the fuselage and wing requirements, which are related to the internal volume and performance speci- fications of the airplane, respectively. The horizontal tail incidence angle, i,, is determined by trim angle of attack or lift coefficient.
For a given level of static stability, that is, slope of the pitching moment curve, the trim angle depends on the moment coefficient at zero angle of attack, C,,,,. The tail incidence angle, i,, can be adjusted to yield whatever C,,, is needed to achieve the desired trim condition. The canard surface has several attractive features. The canard, if properly positioned, can be relatively free from wing or propulsive flow interference.
Canard control is more attractive for trim- ming the large nose-down moment produced by high-lift devices. To counteract the nose-down pitching moment, the canard must produce lift that will add to the lift being produced by the wing. An aft tail must produce a down load to counteract the pitching moment and thus reduce the airplane's overall lift force.
The major disadvantage of the canard is that it produces a destabilizing contribution to the aircraft's static stability. However, this is not a severe limitation.
By proper loca- tion of the center of gravity, one can ensure the airplane is statically stable. The optimum shape for the internal volume at minimum drag is a body for which the length is larger than the width or height. The aerodynamic characteristics of long, slender bodies were studied by Max Munk [2. Munk was interested in the pitching moment characteristics of airship hulls. In his analysis, he neglected viscosity and treated the flow around the body as an ideal fluid.
Using momentum and energy relationships, he showed that the rate of change of the pitching moment with angle of attack per radian for a body of revolution is proportional to the body volume and dynamic pressure: Multhopp [2. A summary of Multhopp's method for Cmoand C,- due to the fuselage is presented as follows: The incidence angle is defined as negative for nose droop and aft upsweep. The correction factor k, - k , is given in Figure 2.
The local angle of attack along the fuselage is greatly affected by the flow field created by the wing, as was illustrated in Figure 2. The portion of the fuselage ahead of the wing is in the wing upwash; the aft portion is in the wing downwash flow. The fuselage again can be divided into segments and the local angle of attack of each section, which is composed of the geometric angle of attack of the section plus the local induced angle due to the wing upwash or downwash for each segment, can be estimated.
On the other hand, a station behind the wing is in the downwash region of the wing vortex system and the local angle of attack is reduced. Cmm due to the fuselage. If the thrust line is offset from the center of gravity, the propulsive force will create a pitching moment that must be counteracted by the aerodynamic control surface. The static stability of the airplane also is influenced by the propulsion system. For a propeller driven airplane the propeller will develop a normal force in its plane of rotation when the propeller is at an angle of attack.
Static Stability and Control contribution to Cmm. Although one can derive a simple expression for Cmm due to the propeller, the actual contribution of the propulsion system to the static stability is much more difficult to estimate. This is due to the indirect effects that the propul- sion system has on the airplanes characteristics. For example, the propeller slip- stream can have an effect on the tail efficiency 7 and the downwash field.
Because of these complicated interactions the propulsive effects on airplane stability are commonly estimated from powered wind-tunnel models. A normal force will be created on the inlet of a jet engine when it is at an angle of attack. As in the case of the propeller powered airplane, the normal force will produce a contribution to Cme. The center of gravity of an airplane varies during the course of its operation; therefore, it is important to know if there are any limits to the center of gravity travel.
Setting Cmaequal to 0 and solving for the center of gravity position yields In obtaining equation 2. We call this location the stick fixed neutral point. Movement of the center of gravity beyond the neutral point causes the airplane to be statically unstable. The influence of center of gravity position on static stability is shown in Figure 2. Given the general aviation airplane shown in Figure 2.
Also determine the stick fixed neutral point. For this problem, assume standard sea-level atmospheric conditions. The lift curve slopes for the two-dimensional sections making up the wing and tail must be corrected for a finite aspect ratio. This is accomplished using the formula where Cia is given as per radian. Static Stability and Control In a similar manner the lift curve slope for the tail can be found: The tail contribution to the intercept and slope can be estimated from Equa- tions 2. The fuselage contribution to C,,,,,and Cmm can be estimated from Equations 2.
To use these equations, we must divide the fuselage into segments, as indicated in Figure 2. The summation in Equation 2. Substitut- ing these values into Equation 2. Static Stability and Control Station Ax ft 1 3. In a similar manner Cmacan be estimated. A table is included in Figure 2. Cmqwas estimated to be The individual contributions and the total pitching moment curve are shown in Fig- ure 2. The stick fixed neutral point can be estimated from Equation 2.
The incremental lift force can be produced by deflecting the entire lifting surface or by deflecting a flap incorporated in the lifting surface. Because the control flaps or movable lifting surfaces are located at some distance from the center of gravity, the incremental lift force creates a moment about the airplane's center of gravity.
Pitch control can be achieved by changing the lift on either a forward or aft control surface. If a flap is used, the flapped portion of the tail surface is called an elevator. Yaw control is achieved by deflecting a flap on the vertical tail called the rudder, and roll control can be achieved by deflecting small flaps located outboard toward the wing tips in a differential manner.
These flaps are called ailerons. A roll moment can also be produced by deflecting a wing spoiler. As the name implies a spoiler disrupts the lift. This is accomplished by deflecting a section of the upper wing surface so that the flow separates behind the FIGURE 2. To achieve a roll moment, only one spoiler need be deflected. In this section we shall be concerned with longitudinal control.
Control of the pitch attitude of an airplane can be achieved by deflecting all or a portion of either a forward or aft tail surface. Factors affecting the design of a control surface are control effectiveness, hinge moments, and aerodynamic and mass balancing.
Con- trol effectiveness is a measure of how effective the control deflection is in producing the desired control moment. As we shall show shortly, control effectiveness is a function of the size of the flap and tail volume ratio. Hinge moments also are important because they are the aerodynamic moments that must be overcome to rotate the control surface.
The hinge moment governs the magnitude of force required of the pilot to move the control surface. Therefore, great care must be used in designing a control surface so that the control forces are within acceptable limits for the pilots. Finally, aerodynamic and mass balancing deal with techniques to vary the hinge moments so that the control stick forces stay within an acceptable range. As shown earlier, the pitch attitude can be controlled by either an aft tail or forward tail canard.
We shall examine how an elevator on an aft tail provides the required control moments. Although we restrict our discussion to an elevator on an aft tail, the same arguments could be made with regard to a canard surface. Notice that the elevator does not change the slope of the pitching moment curves but only shifts them so that different trim angles can be achieved. When the elevator is deflected, it changes the lift and pitching moment of the airplane. The change in lift for the airplane can be expressed as follows: The larger the value of Cmserthe more effective the control is in creating the control moment.
The change in lift of the airplane due to deflecting the elevator is equal to the change in lift force acting on the tail: The elevator effectiveness is propor- tional to the size of the flap being used as an elevator and can be estimated from the equation The parameter T can be determined from Figure 2.
An airplane is said to be trimmed if the forces and moments acting on the airplane-are in equilibrium. Setting the pitching moment equation equal to 0 the definition of trim we can solve for the elevator angle required to trim the airplane: If we substitute this equation back into Equation 2.
The elevator angle to trim can also be obtained directly from the pitching moment curves shown in Figure 2. The longitudinal control surface provides a moment that can be used to balance or trim the airplane at different operating angles of attack or lift coefficient. The size of the control surface depends on the magnitude of the pitching moment that needs to be balanced by the control.
In general, the largest trim moments occur when an airplane is in the landing configuration wing flaps and landing gear deployed and the center of gravity is at its forwardmost location. This can be explained in the following manner.
In the landing configuration we fly the airplane at a high angle of attack or lift coefficient so that the airplane's approach speed can be kept as low as possible. Therefore the airplane must be trimmed at a high lift coefficient.
Deployment of the wing flaps and landing gear create a nose-down pitching moment increment that must be added to the clean configuration pitching moment curve. The additional nose-down or negative pitching moment increment due to the flaps and landing gear shifts the pitching moment curve. Static Stability and Control the pitching moment curve becomes more negative the airplane is more stable. This results in a large trim moment at high lift coefficients. The largest pitching moment that must be balanced by the elevator therefore occurs when the flaps and gear are deployed and the center of gravity is at its most forward position.
Assume that the pitching moment curve for the landing configuration for the air- plane analyzed in Example Problem 2. Estimate the size of the elevator to trim the airplane at the landing angle of attack of 10". The elevator control power is a function of the horizontal tail volume ratio, VH, and the flap effectiveness factor, T: The flap effectiveness factor is a function of the area of the control flap to the total area of the lift surface on which it is attached.
By proper selection of the elevator area the necessary control power can be achieved. For a positive moment, the control deflection angle must be negative; that is, trailing edge of the elevator is up: The elevator area required to balance the largest trim moment is This represents the minimum elevator area needed to balance the airplane.
In practice the designer probably would increase this area to provide a margin of safety. This example also points out the importance of proper weight and balance for an airplane. If the airplane is improperly loaded, so that the center of gravity moves forward of the manufacturers specification, the pilot may be unable to trim the airplane at the desired approach CL.
The pilot would be forced to trim the airplane at a lower lift coefficient, which means a higher landing speed. Suppose we conducted a flight test experiment in which we measured the elevator angle of trim at various air speeds for different positions of the center of gravity. If we did this, we could develop curves as shown in Figure 2. Now, differentiating Equation 2. The hinge moment, of course, is the moment the pilot must overcome by exerting a force on the control stick.
Therefore to design the control system properly we must know the hinge moment characteristics. The hinge mo- ment is defined as shown in Figure 2. If we assume that the hinge moment can be expressed as the addition of the effects of angle of attck, elevator deflection angle, and tab angle taken separately, then we can express the hinge moment coefficient in the following manner: Wind-tunnel tests usually are required to provide the control system designer with the information needed to design the control system properly.
For simplicity, we shall assume that both 6, and Choare equal to 0. Then, for the case when the elevator is allowed to be free, Solving for 6, yields Usually, the coefficients Chatand Ch are negative. If this indeed is the case, then Z Equation 2. The lift coefficient for a tail with a free elevator is given by which simplifies to where The slope of the tail lift curve is modified by the term in the parentheses.
The factor f can be greater or less than unity, depending on the sign of the hinge parameters C, and Chc Now, if we were to develop the equations for the total pitching moment at for the free elevator case, we would obtain an equation similar to Equations 2. Substituting CL4 into Equations 2. Setting Ck- equal to 0 in Equation 2. Static Stability and Control The difference between the stick fixed neutral point and the stick-free neutral point can be expressed as follows: The factor f determines whether the stick-free neutral point lies forward or aft of the stick fixed neutral point.
Static margin is a term that appears frequently in the literature. The stick fixed or stick-free static neutral points represent an aft limit on the center of gravity travel for the airplane.
The forces exerted by the pilot to move the control surface is called the stick force or pedal force, depending which control is being used. The stick force is propor- tional to the hinge moment acting on the control surface: The work of displacing the control stick is equal to the work in moving the control surface to the desired deflection angle.
From this expression we see that the magnitude of the stick force increases with the size of the airplane and the square of the airplane's speed. Similar expressions can be obtained for the rudder pedal force and aileron stick force. The control system is designed to convert the stick and pedal movements into control surface deflections.
Although this may seem to be a relativey easy task, it in fact is quite complicated. The control system must be designed so that the control forces are within acceptable limits.
On the other hand, the control forces required in normal maneuvers must not be too small; otherwise, it might be possible to overstress the airplane. Proper control system design will provide stick force mag- nitudes that give the pilot a feel for the commanded maneuver. The magnitude of the stick force provides the pilot with an indication of the severity of the motion that will result from the stick movement.
The convention for longitudinal control is that a pull force should always rotate the nose upward, which causes the airplane to slow down. A push force will have the opposite effect; that is, the nose will rotate downward and the airplane will speed up.
The control system designer must also be sure that the airplane does not experience control reversals due to aerodynamic or aeroelastic phenomena. If such a provision is not made, the pilot will become fatigued by trying to maintain the necessary stick force. The stick force at trim can be made zero by incorporating a tab on either the elevator or the rudder. The tab is a small flap located at the trailing edge of the control surface.
The trim tab can be used to zero out the hinge moment and thereby eliminate the stick or pedal forces. Although the trim tab has a great influence over the hinge moment, it has only a slight effect on the lift produced by the control surface.
The stick force gradient is a measure of the change in stick force needed to change the speed of the airplane. If the airplane slows down, a positive stick force occurs that rotates the nose of the airplane downward, which causes the airplane to increase its speed back toward the trim velocity.
If the airplane exceeds the trim velocity, a negative pull stick force causes the airplane's nose to pitch up, which causes the airplane to slow down. The negative stick force gradient provides the pilot and airplane with speed stability. The larger the gradient, the more resistant the airplane will be to disturbances in the flight speed. If an airplane did not have speed stability the pilot would have to continuously monitor and control the air- plane's speed.
This would be highly undesirable from the pilot's point of view. Just as in the case of longitudinal static stability, it is desirable that the airplane should tend to return to an equilibrium condition when subjected to some form of yawing disturbance.
Static Stability and Control moment coefficient versus sideslip angle P for two airplane configurations. To have static directional stability, the airplane must develop a yawing moment that will restore the airplane to its equilibrium state. Assume that both airplanes are dis- turbed from their equilibrium condition, so that the airplanes are flying with a positive sideslip angle P.
Airplane 1 will develop a restoring moment that will tend to rotate the airplane back to its equilibrium condition; that is, a zero sideslip angle. Airplane 2 will develop a yawing moment that will tend to increase the sideslip angle. Note that an airplane possessing static directional stability will always point into the relative wind, hence the name weathercock stability.
The fuselage and engine nacelles, in general, create a destabilizing contribution to directional stability. The wing fuselage contribution can be calculated from the following empirical expression taken from [2.
Since the wing-fuselage contribution to directional stability is destabilizing, the vertical tail must be properly sized to ensure that the airplane has directional stability. The mechanism by which the vertical tail produces directional stability is shown in Figure 2.
If we consider the vertical tail surface in Figure 2. The moment produced is a restoring moment. The side force acting on the vertical tail can be expressed as where the subscript vrefers to properties of the vertical tail.
The sidewash angle is analogous to the downwash angle E for the horizontal tail plane. The sidewash is caused by the flow field distortion due to the wings and fuselage. The moment produced by the vertical tail can be written as a function of the side force acting on it: The contribution of the vertical tail to directional stability now can be obtained by taking the derivative of Equation 2.
A simple algebraic equation for estimating the combined sidewash and tail effici- ency factor qjis presented in [2. The rudder is a hinged flap that forms the aft portion of the vertical tail. By rotating the flap, the lift force side force on the fixed vertical surface can be varied to create a yawing moment about the center of gravity.
The size of the rudder is determined by the directional control require- ments. The rudder control power must be sufficient to accomplish the requirements listed in Table 2. The yawing moment produced by the rudder depends on the change in lift on the vertical tail due to the deflection of the rudder times its distance from the center of gravity. For a positive rudder deflection, a positive side force is created on the vertical tail. A positive side force will produce a negative yawing moment: The rudder must be able to overcome the adverse yaw so that a coordinated turn can be achieved.
The critical condition for adverse yaw occurs when the airplane is flying slow i. Crosswind landings To maintain alignment with the runway during a crosswind landing requires the pilot to fly the airplane at a sideslip angle. The rudder must be powerful enough to permit the pilot to trim the airplane for the specified crosswinds.
For transport airplanes, landing may be carried out for crosswinds up to Asymmetric power The critical asymmetric power condition occurs for a multiengine airplane condition when one engine fails at low flight speeds. The rudder must be able to overcome the yawing moment produced by the asymmetric thrust arrangement.
Spin recovery The primary control for spin recovery in many airplanes is a powerful rudder. The rudder must be powerful enouah to oppose the spin rotation. The rudder control effectiveness is the rate of change of yawing moment with rudder deflection angle: The restoring rolling moment can be shown to be a function of the sideslip angle P as illustrated in Figure 2. Each of these contributions will be discussed qualitatively in the following paragraphs. The major contributor to C, is the wing dihedral angle T.
The dihedral angle is defined as the spanwise inclination of the wing with respect to the horizontal. If the wing tip is higher than the root section, then the dihedral angle is positive; if the wing tip is lower than the root section, then the dihedral angle is negative. A negative dihedral angle is commonly called anhedral. When an airplane is disturbed from a wings-level attitude, it will begin to sideslip as shown in Figure 2.
Once the airplane starts to sideslip a component of the relative wind is directed toward the side of the airplane. The leading wing experiences an increased angle of attack and consequently an increase in lift. The trailing wing experiences the opposite effect. The pace of development in aerospace engineering during the decade that followed was extremely rapid, and The aircraft is only a transport mechanism for the payload, and all design decisions must consider payload first.
Simply stated, the aircraft is a dust cover. Aircraft Design" emphasizes that the science and art of the aircraft design Darcorporation, The book is aimed at junior, Thomas R. Yechout, Steven L. Morris, David E. Bossert, Wayne F. XV, p.