To complete the system of equations defining the standard atmosphere, it is assumed that the temperature is a known function of the altitude. The assumed temperature profile for the first three layers of the U. Standard Atmosphere Ref. An is shown in Fig. The initial conditions for the first layer of the stratosphere are obtained by applying Eqs.
Values of these quantities are presented in Table 3. The same quantities can be derived for a nonstandard day by shifting the temperature profile in Fig. Exponential Atmosphere 47 mathematically decimal exponents that their use will not lead to an- alytical solutions. An approximate atmosphere which may lead to ana- lytical solutions is the exponential atmosphere or isothermal atmosphere. This form is motivated by the statosphere formulas where the temperature is constant and exponential is exact.
To achieve more accuracy, it is possible to assume that each layer of the atmosphere satisfies an exponential form. Here, Table 3. Atmosphere, Aerodynamics, and Propulsion Table 3. Aerodynamics: Functional Relations 49 Table 3. Atmosphere, Aerodynamics, and Propulsion The lift and the drag are the components of the resultant aerodynamic force perpendicular and parallel to the velocity vector.
In practice, Reynolds number effects are neglected in the expression for the lift coefficient so that Eqs. Plots of the angle of attack and drag coefficient are shown in Fig. It is interesting to note that the lift coefficient has a maximum value. Aerodynamics: Functional Relations 51 CLmax 1.
Dimensional expressions for the angle of attack and the drag can be obtained by combining Eqs. Plots of the angle of attack and the drag for the SBJ are shown in Fig.
Note that at each altitude the angle of attack decreases monotonically with the velocity and there is a velocity for minimum drag which increases with altitude.
Angle of Attack 53 1. It has been observed that the lift of a wing-body combination can be replaced by the lift of the entire wing including that portion which passes through the fuselage.
The lift of the horizontal tail is neglected with respect to that of the wing. Hence, the lift of the airplane is approximated by the lift of the entire wing. Geometrically, the wing is defined by its planform shape, its airfoil shapes along the span, and the shape of its chord surface. The only wings considered here are those with a straight- tapered planform shape, the same airfoil shape along the span, and a planar chord surface no bend or twist.
If a wing does not meet these conditions, it can be replaced by an average wing that does. For example, if the airfoil has a higher thickness ratio at the root than it does at the tip, an average thickness can be used. The aerodynamic characteristics of airfoils and wings have been taken from Refs. AD and Ho. Over the range of lift coefficients where aircraft normally op- erate, the lift coefficient of the wing can be assumed to be linear in the angle of attack see Fig.
Atmosphere, Aerodynamics, and Propulsion of the wing. First, airfoils are discussed, then wings, then airplanes. The geometry of a cambered airfoil is defined by the geometries of the basic symmetric airfoil and the camber line shown in Fig. The basic symmetric airfoil and the camber line are combined to form the cambered airfoil. The resultant aerodynamic force is resolved into components parallel and perpendicu- lar to the velocity vector called the drag and the lift.
From this figure, it is seen that the angle of attack varies linearly with the lift coefficient and the drag coefficient varies quadratically with cl over a wide range of cl. A systematic study of airfoil aerodynamics has been conducted by NACA.
Collections of airfoil data can be found in Refs. While the numbers are presented in terms of degrees, all of the formulas use the numbers in radians. Each of the numbers in the designation means something. The 6 denotes a 6-series airfoil which indicates a particular geometry for the thickness distribution and the camber line. Table 3. Angle of Attack 57 3. The mean aerodynamic chord is the chord of the equivalent rectangular wing.
It has the same lift and the same pitching moment about the y-axis as the original wing. Assuming that the lift coefficient is linear in the angle of attack Fig. From Table 3. It is close to unity, as it is for most airfoils. For a passenger airplane, the xb axis is usually parallel to the cabin floor. The wing is attached to the fuselage at an incidence iW , the angle between the wing chord plane and the xb axis. Since all of the lift of the airplane has been assumed to be produced by the wing, the airplane lift-curve slope is given by Eq.
A and are presented in Fig. Atmosphere, Aerodynamics, and Propulsion -3 6. The former is the sum of the equivalent parasite area of each airplane component multiplied by 1. Hence, 1. Drag Coefficient 61 where each term is defined below. The average skin friction coefficient Cfk is computed from the equation for the skin friction coefficient for turbulent flow over a flat plate, that is, 0.
The form factor F Fk accounts for thickness effects. Lifting surfaces can be assumed to be flat plates; bodies can be made up of cones and cylinders; and nacelles can be represented by open-ended cylinders. The total equivalent parasite area is the sum of the component equivalent parasite areas plus ten percent of this total to account for miscellaneous contributions. Shock waves cause the bound- ary layer to separate, thus increasing the drag. Wave drag begins at the Mach number for drag divergence which is shown in Fig.
The wave drag coefficient is included only if the free-stream Mach number is greater than the drag divergence Mach number. If it is less than the drag divergence Mach number, then the wave drag coefficient is equal to zero.
It is called vortex drag, drag due to lift, or induced drag. Atmosphere, Aerodynamics, and Propulsion The induced drag of the horizontal tail is neglected. The wing tip tank diameter dT accounts for the tendency of tip tanks to reduce the induced drag because of an end plate effect. In Fig. Hence, the change in the Reynolds number has only a small effect on the value of CD. If the Reynolds number which is selected for the computation is around the lowest value expected to be experienced in flight, the drag coefficient will be on the conservative side slightly higher.
This relationship is given by Eq. Parabolic Drag Polar 65 1. Atmosphere, Aerodynamics, and Propulsion of CL , the drag coefficient can be assumed to be a parabolic function of the lift coefficient.
The lift coefficient range for which these approxi- mations are valid includes the values of CL normally experienced in flight. One form of the parabolic drag polar is given by see Prob. To obtain the parabolic drag polar for a given Mach number, the actual polar is fit by the parabola 3. Parabolic Drag Polar Atmosphere, Aerodynamics, and Propulsion Figs. This range of Mach numbers defines the flow regime known as subsonic flow.
This flow regime is called transonic flow. This explains why the velocity for minimum drag equals the velocity for maximum lift-to-drag ratio. Next, approximate expressions are presented for the thrust and specific fuel consumption. The point of view taken here is that engine data is available from the engine manufacturer so that no formulas are presented for estimating these quantities. The numbers for these figures are given in Table 3. Propulsion: Thrust and SFC 71 2. Propulsion: Thrust and SFC 73 3.
These formulas are more valid near the tropopause than they are near sea level. The fitting of Eqs. Next, Eqs. In the interest of developing analytical performance results, it is observed from Fig. Atmosphere, Aerodynamics, and Propulsion 2. Ideal Subsonic Airplane 75 The fitting of Eqs. Note that they are the same as the statosphere values. In the interest of developing analytical performance results, it is observed from Figs. Hence, the Tt and Ct in the above approximations can be rewritten as Eqs.
Values of Tt P and Ct are given in Table 3. Atmosphere, Aerodynamics, and Propulsion 1. Each turbofan engine weighs about lb more than the turbojet. Problems The answers to the problems involving the computation of the SBJ ge- ometry or aerodynamics are given in App. A to help keep you on track. Once you have completed an assignment, you should use the numbers given in App.
A instead of those you have calculated. The wing planform extends from the fuselage centerline to the outside of the tip tanks. Starting from the measured values for the root chord, the tip chord, the span, and the sweep angle of the quarter chord line App. A calculate the planform area, the aspect ratio, the taper ratio, and the sweep of the leading edge. Also, calculate the length of the mean aerodynamic chord.
Atmosphere, Aerodynamics, and Propulsion 3. Compute the Mach number for drag divergence. Calculate CD0 and K for this flight condition. In doing this calculation, remember that there are two nacelles and two tip tanks. If the Mach number is given, find the lift coefficient for maximum lift-to-drag ratio and the maximum lift-to-drag ratio for this polar. Chapter 4 Cruise and Climb of an Arbitrary Airplane In the mission segments known as cruise and climb, the accelerations of airplanes such as jet transports and business jets are relatively small.
Broadly, this chapter is concerned with methods for obtain- ing the distance and time in cruise and the distance, time, and fuel in climb for an arbitrary airplane. These functional relations can represent a subsonic airplane powered by turbojet engines, a supersonic airplane powered by turbofan engines, and so on.
In order to compute the cruise and climb performance of a particular airplane, the functional relations are replaced by computer functions which give the aerodynamic and propulsion characteristics of the airplane. There, approximate analytical formulas are used for the aerody- namics and propulsion. Analytical solutions are obtained for the dis- tance and time in cruise and the distance, time, and fuel in climb.
The airplane is a controllable dynamical system which means that the equations of motion contain more variables than equations, that is, one or more mathematical degrees of freedom MDOF. Cruise and Climb of an Arbitrary Airplane mission leg. Then, the performance of an airplane can be computed for a particular velocity profile, or trajectory optimization can be used to find the optimal velocity profile. This is done by solving for the distance, time, and fuel in terms of the unknown velocity profile.
After selecting distance, time or fuel as the performance index, optimization theory is used to find the corresponding optimal velocity profile. An example is to find the velocity profile which maximizes the distance in cruise from one weight to another, that is, for a given amount of fuel.
Besides be- ing important all by themselves, optimal trajectories provide yardsticks by which arbitrary trajectories for example, constant velocity can be evaluated. This chapter begins with a discussion of how flight speeds are represented and what some limitations on flight speed are.
The velocity of the airplane relative to the atmosphere, V , is called the true airspeed. This airspeed is im- portant for low-speed flight because it can be measured mechanically. The air data system measures the dynamic pressure and displays it to the pilot as indicated airspeed. The indicated airspeed is the equivalent airspeed corrupted by measurement and instrument errors. To display the true airspeed to the pilot requires the measurement of static pres- sure, dynamic pressure, and static temperature.
Then, the true airspeed must be calculated. For high-speed flight, it has become conventional to use Mach number as an indication of flight speed. High-speed airplanes have a combined airspeed indicator and Mach meter. In this chapter, the performance of a subsonic business jet the SBJ of App.
A is computed to illustrate the procedures and results. Because this airplane operates in both low-speed and high-speed regimes, the true airspeed is used to present performance. Other conversion formulas are useful. Flight Limitations 81 1. A kt is one nautical mile per hour. Hence, the lower the speed of the airplane is the higher the lift coefficient must be.
Since there is a maximum lift coefficient, there is a minimum speed at which an airplane can be flown in steady level flight. This limit can affect the best climb speed of the airplane as well as the maximum speed. At high speeds, some airplanes may have a maximum operating Mach number.
Note that the stall speed and the maximum dynamic pressure speed are actually constant equivalent airspeeds. Cruise and Climb of an Arbitrary Airplane 4. These problems can be solved by a branch of mathematics called Calculus of Variations, which in recent times is also called Optimal Control Theory. It is known that the curve y x which maximizes the integral 4. It is possible to verify the nature maximum or minimum of the optimal curve by looking at a plot of the function f x, y versus y for several values of x.
Because of the simple form of Eq. The integral is the area under the integrand. To maximize the integral, it is necessary to maximize the area. At each value of the variable of integration, the area is maximized by maximizing F with respect to y. The conditions for doing this are Eqs. In the calculation of atmospheric properties, drag, thrust, and specific fuel consumption, it is assumed that the altitude h, the velocity V , the weight W , and the power setting P are known.
Flight Envelope 83 The first function contains the standard atmosphere equations of Sec. The second function computes the drag. The third function calculates the thrust and specific fuel con- sumption of the turbojet.
Then, the corrected thrust and the corrected spe- cific fuel consumption are obtained from Table 3. Finally, T and C are computed using the formulas at the beginning of Sec. For a subsonic airplane, the drag has a single minimum whose value does not change with the altitude see for example Fig.
Cruise and Climb of an Arbitrary Airplane altitude increases. As the altitude decreases thrust increases , there is some altitude where the low-speed solution is the stall speed and at lower altitudes ceases to exist. As the altitude increases thrust decreases , there is an altitude where there is only one solution, and above that altitude there are no solutions.
The region of the velocity-altitude plane that contains all of the level flight solutions combined with whatever speed restrictions are imposed on the airplane, is called the flight envelope. It is shown in Fig. The region enclosed by these curves is the flight envelope of the SBJ. The highest altitude at which the airplane can be flown in steady level flight is called the ceiling and is around 50, ft. Note that the highest speed at which the airplane can be flown is limited by the maximum dynamic pressure or the maximum Mach number.
Next to be discussed are the distance and time during cruise. These quantities have been called the range and endurance. Quasi-steady Cruise 85 the range, for example, could be defined as the sum of the distance in climb and the distance in cruise. For a constant altitude cruise, the velocity vector is parallel to the ground, so that the equations of motion for quasi-steady level flight are given by Eqs. Since there are four equations, this system of equations has one mathematical degree of free- dom, which is associated with the velocity profile V t.
The general procedure followed in studying quasi-steady air- plane performance is to solve the equations of motion for each of the variables in terms of the unknown velocity profile. Then, given a veloc- ity profile, the distance and the time for a given fuel can be determined. Since there are an infinite number of velocity profiles, it is desirable to find the one which optimizes some performance index.
For cruise, there are two possible performance indices: distance range or time endurance. Hence, the optimization problem is to find the velocity profile which maximizes the distance or the velocity profile which max- imizes the time. This process is called trajectory optimization. Then, Eq. Once a velocity profile has been selected, the distance and the time for a given amount of fuel can be obtained.
Cruise and Climb of an Arbitrary Airplane In general, the number of intervals which must be used to get a reason- ably accurate solution is small, sometimes just one. While the distance and time can be computed for different velocity profiles such as constant velocity or constant lift coefficient, it is important for design purposes to find the maximum distance trajectory and the maximum time trajectory.
For a fixed altitude, this can be done by plotting F and G versus velocity for several values of the weight. Regardless of the weight interval [W0 , Wf ] that is being used to compute distance and time, F and G can be com- puted for all values of W at which the airplane might operate. The use of F and G to compute the distance and time for a given velocity profile V W and a given weight interval [W0 , Wf ] is called path performance, because a whole path is being investigated.
Point performance for the SBJ begins with the solution of Eq. Note that the power setting is around 0. Then, P is substituted into Eqs. These quantities are plotted in Figs.
It is observed from Fig. This maximum has been found from the data used to compute F. At each weight, the velocity that gives the highest value of F is assumed to rep- resent the maximum. Note that V and Fmax W are nearly linear in W.
This maximum has been found from the data used to compute G. Cruise and Climb of an Arbitrary Airplane 1. Note that V and Gmax W are nearly linear in W. The other is to find the velocity profile V W that optimizes the distance or that optimizes the time. Because distance factor has a maximum, the optimal distance trajectory is a maximum. Similarly, because the time factor has a max- imum, the optimal time trajectory is a maximum.. Optimal trajectories are considered first because they provide a yardstick with which other trajectories can be measured.
Optimal Cruise Trajectories 91 Table 4. Cruise and Climb of an Arbitrary Airplane. This velocity profile is then used to compute the maximum distance factor which is used to compute the maximum distance and to compute the time factor which is used to compute the time along the maximum distance trajectory. The values of Fmax and G shown in Table 4. Similarly, the time along the maximum distance trajectory is obtained from Eq.
This happens because Fmax Fig. Optimal Cruise Trajectories 93 Table 4. If it is not available, the optimal path can only be approximated. Other velocity profiles are possible: constant lift coefficient, constant velocity, constant power set- ting, etc. The importance of the optimal profile is that the usefulness of the other profiles can be evaluated. For example, if a particular velocity profile is easy to fly and it gives a distance within a few percent of the maximum distance, it could be used instead.
It can be shown that the maximum distance is almost independent of the velocity profile V W. Cruise and Climb of an Arbitrary Airplane the weight see Sec. This velocity profile is then used to compute the maximum time factor which is used to compute the maximum time and to compute the distance factor which is used to compute the distance along the maximum time trajectory.
Then, the maximum time and the corresponding distance are obtained from Eqs. For the maximum time of the SBJ, the maximum time has been found by using four intervals to be 2. These results have also been obtained using only one interval mi and 2. The agreement between the results using one interval and the results obtained by using four intervals is very good.
The maximum distance path requires that the velocity change as the weight changes Table 4. Since there is no weight meter on an airplane, the pilot cannot fly this trajectory very well.
At constant altitude, the indicated airspeed is proportional to the airspeed. Hence, the pilot can fly a constant velocity trajectory fairly well even though the controls must be adjusted to maintain constant velocity. To obtain the distance for a particular velocity, the values of the distance factor F for that velocity for several values of the weight are used with Eq. Similarly, the time along a constant velocity path is obtained by using the values of the time factor G for that velocity for several values of the weight and by using Eq.
The results are shown in Table 4. With regard to the distance, note that there is a cruise velocity for which the distance has a best value. This speed can be calculated by computer or by curve fitting a parabola to the three points containing the best distance. Hence, the airplane can be flown at constant velocity and not lose much distance relative to the maximum.
It is emphasized that this conclusion could not have been reached without having the maximum distance path. As an aside, it is probably true that the airplane can be flown with any velocity profile for example, constant power setting and get close to the maximum distance. A similar analysis with similar results can be carried out for the time. Note that the term maximum distance is applied to the case where all possible velocity profiles are in contention for the maximum.
On the other hand the term best distance is used for the case where the class of paths in contention for the maximum is restricted, that is, constant velocity paths. The maximum distance should be better than or at most equal to the best distance. Table 4. Hence, it has two mathematical degrees of freedom. Experience shows that it is best to climb at maximum continuous thrust so the power setting is held constant leaving one degree of freedom, the velocity. Hence, it is possible to assume that the weight of the aircraft is constant on the right-hand sides of the equations of motion.
Then, the integration of the weight equation gives an estimate of the fuel consumed during the climb. Quasi-steady Climb 97 where all variables are now functions of h.
Once the velocity profile is known, the distance, the time, and the fuel can be obtained by approximate integration. The flight path angle is presented in Fig. This value of the velocity is used to compute the rate of climb and the fuel factor. The rate of climb is shown in Fig. This value of the velocity is used to compute the flight path angle and the fuel factor. Because it is not possible to fly at the airplane ceiling, several other ceilings have been defined.
The reason is the electronic devices divert your attention and also cause strains while reading eBooks. The author develops the theory of stability and control of aircraft in a systems context.
Topics cover: systems of axes and notation, static equilibrium and trim, the equations of motion, longitudinal dynamics, aerodynamic modelling, and aerodynamic stability and control derivatives. Cook detailed in the below table…. Step-1 : Read the Book Name and author Name thoroughly.
Kermode Mechanics of Flight by A. Kermode Mechanics of Flight A. Kermode pdf Summary: Mechanics of Flight is an ideal introduction to the basic principles of flight for students embarking on courses in aerospace engineering, student pilots, apprentices in the industry and anyone who is simply interested in aircraft and space flight.
Cancel Preview Save Page. Cancel Keep Editing Save Page. Rich Text Content. Page Comments. Click here to download. Using an ePortfolio Introduction ePortfolios are a place to demonstrate your work. They are made of sections and pages. The list of sections are along the left side of the window show me. Each section can have multiple pages, shown on the right side of the window show me. The content you see on a page is the same content any visitors will see.
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It covers trajectory analysis, stability, and control. I strive to illustrate the beauty and complexity of avian flight. A white-tailed eagle plummeting through a Japanese sky, a brown pelican striking a silhouette against an Ecuadorian sunset, an Atlantic puffin carrying its fish dinner above the Scottish coast, or a keel-billed toucan gliding through a Costa Rican jungle canopy; readers will marvel at the splendor of birds in flight while learning the techniques to capture these gravity-defying moments from a world-class nature photographer.
For each picture, author and photographer Peter Cavanagh shares his most evocative thoughts: the challenges of the shoot, the beauty of the location, and the curiosities of the species. Bird people will enjoy the bird photographs and facts, travelers will gobble up the tales of distant parts, and photographers will absorb the technical details.
For instance, readers might be surprised to see that a very slow shutter speed can freeze the motion of hummingbird wings. Peter Cavanagh has collected beautiful photos spanning a wide range of species. Author : Thomas R. The course is usually taken after a fundamental course in aeronautics. Annotation c Book News, Inc. Author : Ulla M. The most difficult problem was deciding what to exclude among so many interesting things, because the available material usually exceeded the space.
Because a book like this covers so many aspects, each component must be limited. This book is intended for graduate and undergraduate students as well as professional scientists who want to work with animal flight or to gain some insight into flight mechanics, aerodynamics, energetics, physiology, morpho logy, ecology and evolution.
My aim has not been to give the whole mathe matical explanation of flight, but to provide an outline and summary of the main theories for the understanding of how aerofoils respond to an airflow. I also hope to give the reader some insight into how flight morphology and the various wing shapes have evolved and are adapted to different ecological niches and habitats.
Author : Jitendra R. A text that provides unified coverage of aircraft flight mechanics and systems concept will go a lon. Author : Barnes W. Covers the fluid mechanics and aerodynamics of incompressible and compressible flows, with particular attention to the prediction of lift and drag characteristics of airfoils and wings and complete airplane configurations.
Following an introduction to propellers, piston engines, and turbojet engines, methods are presented for analyzing the performance of an airplane throughout its operating regime. Also covers static and dynamic longitudinal and lateral-directional stability and control. Includes lift, drag, propulsion and stability and control data, numerical methods, and working graphs. A single comprehensive in-depth treatment of both basic and applied modern aerodynamics.
The fluid mechanics and aerodynamics of incompressible and compressible flows, with particular attention to the prediction of lift and drag characteristics of airfoils and wings and complete airplane configurations. This book captures some of the new technologies and methods that are currently being developed to enable sustainable air transport and space flight. It clearly illustrates the multi-disciplinary character of aerospace engineering, and the fact that the challenges of air transportation and space missions continue to call for the most innovative solutions and daring concepts.
Itstopicoriginallywasthemotion of planets, moons and other celestial bodies in gravitational? Newton - gave then, with the devel- ment of his principles of mechanics, the physical explanation of these motions.
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