Chapter 20

Flying QuaZities Flight Test Simulators Chapter 20 Contents

.. Flying Qualities Flight Test Simulators

20.1 Types of Flying Qualities Simulators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20-2 20.1 . 1 Non Real-Time Flying Qualities Simulators . . . . . . . . . . . . . . . . . . . . . 20-3 20.1.2 Piloted. Ground-based Flying Qualities Simulators . . . . . . . . . . . . . . . . . 20-3 20.1.3 Hardware-in-the-Loop Simulators . . . . . . . . . . . . . . . . . . . . . . . . . . . 20-6 20.1.4 Iron Bird Simulators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20-7

20.1.6 Flight Control System Test Stand . . . . . . . . . . . . . . . . . . . . . . . . . . 20-10 20.1.5 Piloted Inflight Simulators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20-8

20.2 Simulator Fidelity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20-10 20.2.1 Motion Fidelity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20-10 20.2.2 Visual Display Fidelity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20-12 20.2.3 Risk Fidelity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20-13 20.2.4 Cockpit Controls Fidelity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20-13

. 20.2.5 Aerodynamic and Flight Control System Fidelity . . . . . . . . . . . . . . . . . 20-15 20.2.6 Equations of Motion Fidelity . . . . . . . . . . . . . . . . . . *. . . . . . . . . . . 20-15 20.2.7 Cockpit Fidelity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20-15

20.3 Uses and Benefits of a Flight Test Simulator . . . . . . . . . . . . . . . . . . . . . . . . . 20-16 20.3.1 Education . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20-16 20.3.2 Handling Qualities Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20-16

20.3.4 Creating Programmed Test Input Signals . . . . . . . . . . . . . . . . . . . . . . 20-17 20.3.5 Pilot Proficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20-18 20.3.6 Data Reduction Checkout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20-18 20.3.7 Test Planning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20-18 20.3.8 Safety . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20-18 20.3.9 Analyzing and Correcting Deficiencies . . . . . . . . . . . . . . . . . . . . . . . 20-19 20.3.10 Augmenting Test Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20-19 20.3.11 Hardware Verification and (Limited) Validation . . . . . . . . . . . . . . . . 20-20 20.3.12 Dress Rehearsals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20-20

20.4 Justifying a Flight Test Simulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20-20

20.3.3 Developing New Test Maneuvers and Analysis Techniques . . . . . . . . . . 20-17

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20.5 Building a Flight Test Simulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20-23 20.5.1 Defming Flight Test Simulator Requirements . . . . . . . . . . . . . . . . . . . 20-24

20.6 Aerodynamic Models for Flight Test Simulators . . . . . . . . . . . . . . . . . . . . . . . 20-26 20.6.1 Wind Tunnel Aerodynamic Data . . . . . . . . . . . . . . . . . . . . . . . . . . . 20-28 20.6.2 Coefficient Aerodynamic Models . . . . . . . . . . . . . . . . . . . . . . . . . . 20-39 20.6.3 Stability Derivative Aerodynamic Models . . . . . . . . . . . . . . . . . . . . . 2 0 4 20.6.4 Pseudo Stability Derivative Aerodynamic Models . . . . . . . . . . . . . . . . 20-53 20.6.5 Summary of Advantages and Disadvantages . . . . . . . . . . . . . . . . . . . . 20-66

Flying Qualities Testing 20-i

Flying Qualities Flight Test Simulators Chapter 20 Contents

.. 20.7 Flight Control System Models for Flight Test Simulators . . . . . . . . . . . . . . . . . .

20.8 Configuring a Flight Test Simulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

20.9 Waypoint: Fiying Qualities Flight Test Simulators . . . . . . . . . . . . . . . . . . . . . . 20-68

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204 Flying Qualities Testing

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Chapter 20

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Flying Qualities Flight Test Simulators

The use of simulators was largely pioneered and developed in the world of aviation. During World War 11, for example, tens of thousands of pilots were introduced to instrument flying procedures in small simulators called Link trainers (built by a company namd Link). These small simulators had enclosed cockpits, a pneumatically driven motion system that moved the cockpit in response to the pilot’s control inputs, and stubby wings and tails that made them look like enlarged copies of a child’s toy airplane. Today, simulators are still used extensively by airlines, the military, and general aviation for pilot training and proficiency. But the use of simulators in the world of aviation has grown to encompass much more than pilot training and proficiency. Simulators are now deeply embedded in the design and testing of airplanes at every level, including flying qualities, avionics, propulsion, performance, subsystems, and so on.

In this chapter we will focus exclusively on the use of simulators in flying qualities design and testing. We will leave other uses of simulation to other areas of your coursework.

Flying qualities simulators are an indispensable tool for designing and testing complex new airplanes and for designing and testing extensive modifications to existing airplanes. During flying qualities design, simulators serve as handling qualities testbeds, giving pilots their first opportunity to evaluate the predicted handling qualities of the airplane. During ground and flight testing, flying qualities simulators provide a wide range of capabilities which are essential to conducting a safe and productive test program at the lowest possible cost. They are used to prepare for ground and flight testing, to conduct certain ground tests, to explore problems encountered during testing, to augment test data, and so on.

Flying Qualities Testing 20-1

Flying Qualities Flight Test SimuZutors 20.1 Types of Flying Qualities Simulators

.. Because piloted simulators are so heavily used in preparing for and conducting a flying qualities test program, it is important that they should be available at the test site. This is why the Flight Test Center has its own flying qualities simulation capability. The Flight Test Center simulators are so important to flying qualities testing that we commonly refer to them as flight test simulators.

In this chapter we will explore several topics that are directly related to flight test simulators. We will begin by introducing the kinds of simulator you are likely to encounter during a flying qualities design and test program. Next, we will discuss the importance and pitfalls of simulater fidelity. Then we will explore some of the uses of a flight test siinulator and show why it is important that a test program have an independent flight test simulator. Finally, we will explore the broad topic of building a simulator, including a discussion of simulator aerodynamic models.

Much of the material presented in this chapter is adapted from Reference 20-1, an excellent seminar on simulation.

20.1 Types of Flying Qualities Simulators There are many ways to categorize sinhators. At the most fundamental level, we may divide them into real-time simulators and non real-time simulators. Real-time simulators produce the simulated airplane response in exactly the amount of time it takes for the real airplane to produce it. If a 360 degree turn requires one minute in the real airplane, it will also require one minute in a real-time simulator. To the pilot or observer, there is no distinguishable difference between the flow of simulator time and the flow of clock time. Non real- time simulators, on the other hand, are not constrained by this requirement. A non real-time simulator might be either faster or slower than clock time, depending on the complexity of the simulation and the performance of the computer.

Real-time flying qualities simulation is necessary only when the simulator will be flown by pilots or when it must be connected to flight control computers or other equipment. Otherwise, a non-real- time simulation will prove adequate.

Real-time flying qualities simulators may be further categorized in several ways. One way is according to the purpose, or purposes, the simulator serves. In this case, we might speak of handling qualities evaluation simulators, or flight control system test simulators. Another way to categorize simulators is according to their physical attributes. In this case, we might speak of large amplitude motion simulators, or inflight simulators. But because simulators come in so many forms and serve so many purposes, it is difi'icult to find a single, entirely satisfying way to categorize them.

In the following sections, we will introduce you to six flying qualities simulators you are likely to encounter during the course of a design and test program. We will refer to them by the labels that are commonly associated with them. But be wary: often the labels refer to different functions performed by the same simulator over the course of the program. We will introduce these simulators in the chronological order in which you are likely to use them. As Test Pilot School students you will have an opportunity to use or observe examples of these simulators. As working flying qualities test aircrew and engineers, you will work with them extensively.

20-2 Flying Qualities Testing

Flying Qualities Flight Test Simulators 20.1.2 Piloted, Ground-based Flying Qualities Simulators

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20.1.1 Non Real-Tie Flying Qualities Simulators The first simulator a designer is likely to use is a mn real-time simulator. Non-real-time simulators are software models of the airplane that run on desktop, mini-, or mainframe computers. Non real-time simulators are sometimes referred to as butch simulators. (The term "batch" is rooted in years gone by, when digital computer programs were run by feeding batches of coded cards into the computer.) Non real-time, or batch, simulators run at the speed of the computer, rather than the speed of the airplane motion.

When used for flight control system design and flying qualities testing, non-real-time simulators include models of the aerodynamics and flight controls, and may also include a model of the structural dynamics. The complexity of a non real-time simulator depends on the purpose it serves. If the purpose is to simulate the airplane response to a gust, or to small doublet inputs, a simple "point" model of the aerodynamics at a single flight condition, together with a simplified model of the flight control system, might be adequate. If the purpose is to simulate more complex responses (such ;\s aero-servoelastically coupled responses) over a broader expanse of the flight envelope, more comprehensive models are necessary. *

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There are a number of commercially available non real-time simulators, and most of these include an impressive array of analytical capabilities as well. These analytical capabilities may include identifying the roots of the characteristic equation, drawing root locus and frequency response plots, and so on. Often, non real-time simulators are written by airplane designers to serve special purposes.

Much may be accomplished with a non real-time simulator, but an important drawback is that pilots cannot fly them and evaluate the simulated handling qualities. For this reason, designers also work with real-time, pilot-in-the-loop simulators, which are often referred to as piloted simulators. There are two main categories of piloted simulators: ground-based and inflight. As the names imply, a ground-based simulator is tied to the ground, whereas an inflight simulator is one that flies. We will discuss ground-based simulators first.

20.1.2 Piloted, Ground-based Flying Qualities Siulators Piloted, ground-based, flying qualities simulators are real-time simulators that are used throughout the process of designing and testing an airplane. During the design phase, they are used primarily to help designers and pilots evaluate and hone the predicted handling qualities of the airplane. During flight testing, they are put to many uses, some of which are described in section 20.3. As the name implies, ground-based simulators are fixed to the ground.

Piloted, ground-based, flying qualities simulators consist of a cockpit, a visual display, an aerodynamic model, a flight control system model, and perhaps a motion system. In some cases, a structural dynamics model might also be present. The complexity of these components can span the gamut from spartan to very elaborate, depending on the purpose the simulator serves.


Flying Qualities Flight Test Simuhtors 20.1.2 Piloted, Ground-based Flying Qualities Simulators

At the spartan end, the cockpit might be nothing more than a folding chair and a simple joystick. A mid-range level of complexity might include generic, all-purpose, "typical fighter" or "typical transport" cockpits, such as those used at the Flight Test Center. At the elaborate end of the scale we might find a complete replica of the test airplane cockpit, including high fidelity control stick and rudder pedal dynamics.

The level of complexity of visual displays can be equally broad. At the spartan end of the scale, the visual display might consist of no more than the primary cockpit instruments. Near the middle of the scale we might find a simple target presented on a monochrome TV screen, or perhaps a narrow field of view, color, "out-the-window" display of moderate resolution. At the elaborate end, we might find an all-aspect, high resolution, "out-the-window" view of the world.

The aerodynamic and flight control system models can also span a wide range of complexity. At the spar& end of the scale, the aerodynamic model might take the form of stability derivatives that are valid only at a single flight condition, or perhaps over a narrow range of flight conditions. Near the middle of the scale, the aerodynamic model might be expanded to include larger portions of the flight envelope. At the elaborate end of the scale, the aerodynamic model might include the entire flight envelope. A spartan flight control system model might consist of a simplified version of a single flight control mode together with a simplified, linear actuator model. An elaborate flight control system model might fully replicate the flight control laws and sensor dynamics, and use high-fidelity, nonlinear models of the actuators.

Ground-based simulator motion also runs the gamut from the spartan to the very elaborate. At the spartan end are simulators that do not move at all. At the elaborate end of the scale are motion systems that produce large amplitude, sixdegree-of-freedom motion. Ground-based simulators that do not move are calledfied-base simulators. Ground-based simulators that move are called mtion- based sirnularors.

The level of complexity of the simulator cockpit, visual display, aerodynamic and flight control models, and motion system is determined by the purpose (or purposes) the simulator serves. It is not unusual to find a mixture of complexity. For example, a mid-range, generic cockpit might be coupled with a mid-range visual system, elaborate models of the aerodynamics and flight controls, and a spartan motion system (that is, no motion at all). Figure 20-1 depicts two fixed-based flying qualities simulators used at the Flight Test Center. These simulators use a mid-range, generic cockpit, a mid-range limited field of view display, aerodynamic and flight control system models that can range from spartan to elaborate, and no motion system. Figure 20-2 depicts a simulator that uses a mid-range, generic cockpit, an elaborate visual system, aerodynamic and flight control system models that can range from spartan to elaborate, and a motion system that can range from spartan (no motion) to elaborate (large amplitude, sixdegree-of-freedom motion). This simulator, called LAMARS, is located at the Flight Dynamics Laboratory at Wright-Patterson Air Force Base. LAMARS is an acronym for Large Amplitude Multi-mode Aerospace Research Simulator.

The computers used in piloted, ground-based simulators may be digital, or analog, or a combination of both. When only digital computers are used, the simulator is called a digital simulator. When

20-4 Flying Quulities Testing

Flying Qualities Flight Test Simulators 2Q.1.2 Piloted, Ground-based Flying Qualities Simulators

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Figure 2 6 1 Rioted, ground-based simulators used (2f the Flight Test Center.


Flying Qualities Flight Test Simulators 20.1.3 Hardware-in-the-bp simulators

only analog computers are used, the simulator is called an analog simukztor. When both digital and . . analog computers are used, the simulator is called a hybrid simulator. Digital computers offer greater precision and repeatability than analog computers. But analog computers have a higher bandwidth than digital computers and do not suffer from computational time delay. The bandwidth of digital computers is limited by the highest frame rate that can be achieved. Hybrid simulators offer the best characteristics of both digital and analog computers.

Hybrid simulators are especially useful for simulating airplanes with digital flight control systems. An analog computer is used to simulate the aerodynamic response and the response of actuators, anti- aliasing filters, sensors, and other analog components with "life-like" bandwidth, all without introducing unwanted computational time delay. Simultaneously, a digital computer is used to simulate the digital part of the flight control system at the frame rate used in the airplane. The digital computer can also be used to simulate such low bandwidth functions as center of gravity movement and engine response.

Figure 20-2 A piloted, ground-based simulator at the Right LJynarniis Laboratory.

20.1.3 Hardware-in-the-Loop Simulators In hardware-in-the-loop simulators, real flight control hardware replaces all or selected parts of the simulated flight control system. For example, real flight


Flying Qualities Flight Test Simulators 20.1.4 Iron Bird Simulators

control computers are substituted for modeled control laws, real data busses are substitut& for simulated connections between computers, and so on. Sometimes, real actuators are substituted for the modeled actuators. In this way, designers get an early look at how well the real flight control system hardware works. In Chapter 26, you will learn that hardware-in-the-loop simulators play an important role in the process of verifying and validating a flight control system.

Hardware-in-the-loop simulators can take on a variety of forms. Sometimes, the piloted, ground- based simulators we described in section 20.1.2 also serve as hardware-in-the-loop simulators. This can be accomplished by making it possible to switch between the real flight control hardware and the flight control system model. A simpler but less flexible approach is to remove the flight control system model and substitute the real flight control system hardware.

Hardware-in-the-loop simulators are often involved in intensive, round-the-clock testing. This leaves little, if any, time for other work, such as handling qualities evaluation. As a result, dedicated simulators are sometimes built for hardware-in-the-loop testing. The aerodynamic model, equations of motion, atmospheric model, and other software used in these dedicated s@lators might be copied directly from existing piloted, ground-based simulators. Sometimes, dedicated hardware-in-the-loop simulators are also used for limited handling qualities evaluations. When this is the case, a cockpit and a visual display must be provided.

The flying qualities flight test simulators used at the Flight Test Center are occasionally used as hardware-in-the-loop simulators. This allows them to be used for limited verification and validation testing and for special purpose trouble-shooting.

20.1.4 Iron Bird Simulators In past chapters, we have often remarked on the importance of actuator rate limits, control system friction, deadband, and hysteresis, and other characteristics of mechanical systems. It is usually difficult to model these characteristics reliably. One way to determine the actual performance of the mechanical components of the control system is to build a special-purpose, hardware-in-the-loop simulator that is dedicated to testing them. Such a simulator is called an iron bird simularor.

An iron bird simulator gets its name from the fact that it is built on a large steel framework to which the mechanical components of the flight control system are attached. The hydraulic system pumps, accumulators, tubing, and actuators are laid out on the steel framework exactly as they are in the real airplane. The length of each hydraulic line and the geometry of every bend in the hydraulic lines is exactly duplicated. The control surface actuators are attached to specially made fittings on the steel framework that simulate the stiffness of the real airplane structure at the attachment points. And each control surface is simulated by a specially made block of material that closely matches the mass and moment of inertia of the real airplane control surface. The same care is taken in laying out the control stick and rudder pedals and associated cables, pushrods, pulleys, and so on. The electronic components of the flight control system, such as the flight control computers, are usually hardware, but might be software simulations in some cases. An aerodynamic model must also be provided.


Flying Qualities Flight Test Sinmlutom 20.1.5 Piloted Innight Simulators

Iron bird simulators are valuable assets for early model validation testing of the flight control system. . . Because real mechanical hardware is used, and because it is meticulously assembled to duplicate the real airplane, the performance of the real mechanical components may be tested and compared with the predicted performance. The fidelity of the iron bird simulator to the real airplane is good enough that rigid body limit cycle ground testing is sometimes conducted on the simulator rather than on the airplane.

Because iron bird simulators are typically devoted to flight control system testing rather than handliig qualities testing, pilots do not normally spend much time flying them. For this reason, if a cockpit and visual display are included at all, they are usually rudimentary. The aerodynamics, equations of motion, and so on are usually copied directly from the piloted, ground-based simulator.

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Figure 20-3 The USAFNeridian VISTA/F-I6.

20.1.5 Piloted Intlight Siulators When the flight control system design has been completed and handling qualities have been evaluated and improved as far as they can be with ground-based simulators, designers often turn to piloted inflight simulators for one more evaluation. An inflight simuiator is an airplane that has been specially modified so that the dynamics of other airplanes may be simulated in flight. Piloted inflight simulators offer better motion and visual fidelity than do their


Flying Qualities Flight Test Simulators 20.1.5 piloted Inflight Simulators

ground-based cousins, so they are commonly regarded as the "top of the line" in handling quditieS' simulators.

However, piloted inflight simulators are not entirely free of drawbacks. It is usually very expensive to conduct an inflight simulation program. Also, it is not always possible to exactly simulate the test airplane response. Sometimes, only relatively low bandwidth responses can be simulated with high fidelity, although this depends on the dynamics of the airplane bemg simulated.

Over the years, Test Pilot School students have flown a number of inflight simulators, including the AFFTC variable stability B-25, the Calspan variable stability B-26, the USAF/Calspan NT-33, the USAFNeridian TIFS (Total InFlight Simulator), the Veridian variable stability LearJets, and the USAFNeridian VISTA/F-16 (Variable Inflight Stability Training Aircraft). The USAFNeridian VISTAIF-16 is shown in Figure 20-3.

Figure 20-4 The AFFTC/HPE flight control system test stand and a ~ b g aerodym'c sinulkltor. connected to the VISTA/F-I6for ground testing by Test Pilot School students.


Flying Qualifies Flight Test Simularors 20.2.1 Motion Fidelity

20.1.6 Flight Control System Test Stand One more flight test simulator deserves mention. The Flight Test Center uses a special ground test stand that includes an analog aerodynamic simulator. This test stand and its aerodynamic simulator can be c o ~ e c t e d to a test airplane and used to conduct rigid body limit cycle testing, structural resonance testing, flight control system functional testing, and redundancy management system testing. In Figure 20-4 the USAF/HPE flight control system test stand is shown connected to the USAFNeridian VISTA/F-16 for verification and validation

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Figure 20-5 Schemoric showing connection ofAFnCflisht control system test stand to a test airplane.

ground testing, conducted by Test Pilot School students and Veridian, of a studenf project.

In Figure 20-5 we present a schematic diagram that shows how control surface deflections are transmitted to the test stand and simulated airplane responses are transmitted back to the flight control system in the airplane. This arrangement is similar to the hardware-in-the- loop and iron bird simulators,we described in sections 20.1.3 and 20.1.4. The only difference is that, instead of laying out hardware in a laboratory, the real airplane is connected to an aerodynamic simulator.

Despite its small size and somewhat innocuous appearance, this test stand, with its aerodynamic simulator, is a powerful piece of ground testing equipment.

20.2 Simulator Fidelity When we speak of simulator9delity we are referring to how closely a simulator matches the airplane it is simulating. For handling qualities evaluation, our interest in fidelity is directed mainly at dynamic response fidelity, or how well the simulator matches the dynamics of the real airplane. Aspects of dynamic response fidelity that are of particular interest include visual display response, motion response, the equations of motion, the control stick force-feel characteristics, the aerodynamic model, and the flight control system model. Of course, we are interested in other aspects of fidelity as well. For example, the placement of controls, switches, instruments, and displays in the simulator cockpit may affect the usefulness of the simulator in some ways.

In the following sections we will discuss several important aspects of simulator fidelity, including motion fidelity, visual display fidelity, risk fidelity, cockpit controls fidelity, aerodynamic and flight control system fidelity, equations of motion fidelity, and cockpit fidelity.

20.2.1 Motion Fidelity Let's begin hy acknowledging the importance of motion to handling qualities. A pilot's control inputs produce airplane rotational and translational accelerations, rates,

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Flying Qualities Flight Test Sirnuho& 20.2.1 Motion Fidelity

and displacements. These motion responses determine how easy it is for a pilot to land an air&&: track a target, perform aerial refueling, maintain formation, and so on. Because a pilot's assessment of handling qualities is closely tied to motion, we must approach motion fidelity carefully.

Motion is detected both visually and "physically." By "physically," we mean detection by the inner ear and by the "seat of the pants," or proprioceptively. For example, pitching and rolling motion can be detected visually by looking out of the cockpit or by looking at cockpit instruments. The same motion can also be detected by the inner ear and the seat of the pants. Wherwe refer to motion fidelity we are usually referring to motion that can be "physically" detected by the inner ear and the seat of the pants. In other words, motion fidelity refers to how closely the physical motion of the simulator cockpit matches the physical motion of the real airplane cockpit. This is to be distinguished from the appearance, or impression of motion produced by cockpit instruments or visual displays.

Inflight simulators provide the best opportunity for achieving a high level of motion fidelity, but even inflight simulators have limits. Special control surfaces are needed to produce the forces and moments required for high fidelity motion at the pilot station. These specid control surfaces are not available on all inflight simulators. Even when they are, they might not be sufficiently fast or effective to produce the desired motion.

For ground-based simulators, motion fidelity is a problematical issue. In fixed-base simulators there is no motion fidelity at all. Yet fixed-base simulators have proved to be very useful flight test tools.

In motion-based simulators, hydraulic or electric motion systems attached to a simulator cockpit can produce impressive rotational and translational accelerations and rates. But the available range of displacement is necessarily limited. As a result, accelerations and rates can be maintained for only a short length of time before the motion drive system exceeds the allowable range of displacement. To prevent the motion drive system from crashing into its limits, washout (or high-pass) filters are added to the motion system. Washout filters cause the motion system to attenuate low frequency motion (such as a turn or a loop) while responding more faithfully to higher frequency dynamics, such as the short period and dutch roll modes. This works well in preventing the motion system from exceeding its physical limits, but it has the unhappy sideeffect of changing the handling qualities of the simulated airplane. You may recall from section 12.2.4 in Chapter 12 that washout filters add low frequency phase lead. As a result, there may be less phase lag in the simulator motion than there is in the real airplane motion. According to the RSmith criteria, which we introduced in Chapter 16, if the simulator has less phase lag than the real airplane, the simulator handling qualities will be better than the airplane handing qualities.

The problem of restricted range of motion (and the necessity for washout filters) is one that cannot be avoided in ground-based simulators. This problem stimulates much discussion and disagreement within the flying qualities community. Is washed-out motion better or worse than no motion at all? Consider this question in terms of a simulator evaluation of pilot-in-the-loop oscillation (or PIO) susceptibility. It is widely accepted that some PIOs cannot occur without motion feedback to the pilot. Consequently, they cannot occur in a fixed-base simulator (unless they are artificially stimulated). But experience shows that they might not occur in a motion-base simulator either,


Flying Qualities Flight Test Sinurlators 20.2.2 Visual Display Fidelity

because the motion system washout filters artificially improve handling qualities enough to hide the tendency to PIO.

Another interesting aspect of motion fidelity is sometimes encountered in motion-based simulators. When the motion system is not carefully synchronized with the visual system, the resulting mismatch of motion and visual responses can be very disconcerting to the evaluation pilot, sometimes to the point of inducing nausea.

20.2.2 Visual Display Fidelity While much can be accomplished with a simulator that does not move, a piloted flying qualities simulator without a visual display of some kind would be worthless. Visual displays come in a variety of forms. Successful simulation programs have been conducted with visual displays as simple as the primary flight instnunents, and as sophisticated as a high resolution, all-aspect, "out-the-window'' visual scene. Out-the-window displays attempt to present the view a pilot sees when looking outside the cockpit. These displays are improving in quality as increasingly powerful computers make it possible to significantly improve resolution, clarity, and texture while reducing time delay.

Despite the importance of visual displays and the presumed importance of visual display fidelity, there is no definitive research and little agreement on how much and what kind of visual fidelity is necessary for a flying qualities simulator. Are primary flight instruments alone an adequate visual display? Is a television screen with a simple horizon bar, or a simple target, or a simple line drawing of a runway sufficient? Is a detailed, high resolution, high clarity, highly textured, "out-the-window" scene required? While we do not have definitive answers to these questions, experience suggests that the answers depend on the task the pilot is performing and on the objectives of the test. For example, there is little doubt that resolution, clarity, and texture are more important when performing handling qualities tasks that involve close proximity to the ground or to another airplane. Such tasks include approach and landing, terrain following, and aerial refueling.

Nor is there a consensus on how much visual system time delay is permissable. Time delay in the visual system adds phase lag to the simulator dynamics, which can result in degraded simulator handling qualities. According to the RSmith criteria, the degrading effect of visual system time delay depends on the phase lag of the modeled airplane dynamics. Suppose the RSmith criterion frequency for a test airplane were o, =4 radians/second and the predicted Cooper-Harper rating were 5. If the visual system time delay were 100 milliseconds, approximately 23 degrees of phase lag would be added to the augmented airplane transfer functions at the criterion frequency. This additional phase lag would degrade the predicted handling qualities from a Cooper-Harper rating of 5 to a Cooper- Harper rating of about 7.7. Clearly, it is important to strive for small visual system time delays.

Nor is there a consensus on how large the field of view must be. The role of peripheral vision in landing flare and touchdown, for example, is not completely understood.

Complete visual display fidelity is as difficult to achieve as complete motion fidelity. Inflight simulators offer the best opportunity to achieve high visual fidelity, because the pilot can look outside

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Flying QuaIMes Flight Test Sinurlators 20.2.4 Cockpit Controls Fidelity

and see the same clear, textured, undelayed real world that would be visible in the real airplane.. But c-

visual fidelity in an inflight simulator can be degraded by the same constraints that affect motion fidelity. When accurate motion cannot be produced at the pilot's location, visually sensed motion will be affected also.

20.2.3 Risk Fidelity An elusive but important (some might say critical) component of simulator fidelity is something we will call "risk fidelity." Riskfidelily refers to our ability to make pilots flying a simulator respond to hazards or surprises just as they would in a real airplane. Risk fidelity may be more important than you suppose. Flying qualities experience is replete with incidents and accidents that were triggered by a pilot's response to an imminent hazard. Unfortunately, risk fidelity is difficult to achieve for the simple reason that there is no penalty for "crashing" a simulator. The pilot simply presses the "Reset" button and starts over. Even in an inflight simulator, the evaluation pilot knows that if things get out of hand, the safety pilot will assume comrnand and return the simulator to a safe, baseline configuration. It has been sportingly proposed that risk fidelity might be impkved by administering memorable electrical shocks to evaluation pilots when they "crash." Or by poking them with needles driven by a special apparatus mounted in the simulator seat.

Another facet of risk fidelity is related to a high level of pilot excitement. Experience indicates that handling qualities deficiencies may be exposed not only by imminent danger, but also when a pilot's level of excitement is unusually high. Evidence of this has been observed during combat, when a pilot is tracking and shooting at a jinking target. The desire for a kill may increase the pilot's excitement to a very high level indeed. When the pilot's level of excitement exceeds a certain threshold, the pilot may begin to fly the airplane differently, exposing handling qualities which make it more difficult to score a hit. We discussed this phenomenon in section 23.1 in Chapter 21.

20.2.4 Cockpit Controls Fidelity Control stick, rudder pedal, and throttle fidelity are additional facets of simulator fidelity. Control stick fidelity is widely recognized as an important element of simulator fidelity. The rudder pedals and throttle are sometimes given shorter shrift. Let's discuss control stick fidelity first.

The control stick is the pilot's primary means of controlling the airplane. If the force-feel characteristics of the stick are not accurately modeled, the pilot's perception of handling qualities may be significantly affected. You may appreciate this by imagining that, in an airplane you fly regularly, the stick forces were suddenly halved or doubled, or the deadband or hysteresis were doubled. These changes would almost certainly affect your opinion of the airplane handling qualities. They might also make it more difficult, or perhaps easier, to land the airplane, or perform aerial refueling, or track a target, or maintain tight formation, and so on.

It is not always easy to model control stick force-feel characteristics accurately. This is particularly true when the force-feel characteristics include a nonlinear forcedeflection curve plus a deadband, complex hysteresis characteristics, and so on. Commercially available hardware, such as the widely

Flpng Qualities Testing 20-13

Flying Qualities Flight Test Simulators 20.2.4 Cockpit Controls Fidelity

known McFadden control stick simulators, offers impressive capability. Unfortunately, these control - . x

stick simulators tend to be complex and expensive.

Yet even when the measured simulator stick characteristics closely match the airplane, a frequent pilot comment is that the simulator stick doesn’t feel like the airplane stick. These comments may be traceable in part to evidence that a pilot’s perception of control stick fidelity is related to motion fidelity. One hypothesis is that when pilots do not feel the expected motion response to their stick inputs, they are naturally inclined to question the fidelity of the stick dynamics.

Control stick geometry, including location and pivot point, can also influence a pilot’s perception of control stick fidelity. For example, when the stick is further away in the simulator, pilots are likely to report that the stick forces are higher than in the airplane.

Rudder pedal fidelity is often regarded as being secondary in importance to control stick fidelity. There are two principal reasons for this. First, modem flight control systems often make it unnecessary (oi less necessary) for the pilot to use the rudder pedals to maneuver the airplane. This means that the rudder pedals are used less extensively than the control stick. Second: hands and arms are more sensitive than legs and feet, especially booted feet. Pilots are less likely to notice minor discrepancies between the simulated rudder pedals and the real airplane rudder pedals. So long as a reasonable level of rudder pedal fidelity is present, it is unlikely that pilots will complain.

The importance of throttle fidelity is sometimes underestimated. The force-feel characteristics of the throttle lever and the response of the engine model may significantly influence a pilot’s perception of handling qualities for certain tasks, such as close formation, aerial refueling, and approach and landing. Engine response characteristics are often modeled rather simply in flying qualities simulators. For example, a simple first order filter is often used to simulate engine spool-up and spool-down. In many cases this might be a perfectly satisfactory model. In others it might not. When a simulator will be used to evaluate aerial refueling, or close formation maneuvering, or powered lift landings, it may be important to model throttle characteristics and engine response with greater fidelity.

As in the case of the control stick, however, a pilot’s perception of throttle response fidelity might be affected by motion fidelity. Evidence suggests that when pilots do not feel the expected motion response to their throttle inputs, they are naturally inclined to question the fidelity of the throttle response.

We conclude by noting that the physical fidelity of the control stick and throttle may be important in a flying qualities simulator. In military airplanes, the stick and throttle grips have become important interfaces, or centers of activity, between the pilot and the airplane. Careful thought should be given to the consequences of mismodeling these interfaces. If the grips are different from the real airplane, or if switches are missing, or are in a different location, or work differently, the usefulness of the simulator may be compromised.

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Flying m e s Flighf Test Sirnuhorn 20.2.7 Cockpit Fidelity

20.2.5 Aerodynamic and Flight Control System Fidelity Time and again we have remark& on the importance to handling qualities of high fidelity aerodynamic and flight control system models. If either the aerodynamic or flight control system models are in error, the airplane response to a pilot input or a gust disturbance will be in error. In Chapter 7 we showed that an incorrect stability derivative value can have an important effect on the airplane response, and in Chapters 10 and 11 we showed that simplified actuator models can make an airplane appear to be more stable than it really is. Modeling errors such as these can affect the airplane response and hence the pilot’s

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perception of handling qualities. ~

Before ground testing and flight testing begin, the simulator aerodynamic and flight control system models are necessarily predicted models, with attendant levels of uncertainty. These levels of uncertainty may be significant. If these models are not validated and corrected during ground and flight testing, the lack of simulator dynamic response fidelity will quickly become apparent to the pilots. As a result, the usefulness of the simulator will decline steadily as the test program progresses. This would prove costly indeed, as you will learn in section 20.3. . 20.2.6 Equations of Motion Fidelity We have said nothing about the importance of high fidelity equations of motion since Chapter 4 in Part 11. Yet we devoted most of that chapter to developing a set of equations that would accurately describe the airplane motion you are most likely to experience. You may recall that we tailored these equations of motion to rigid body airplanes of constant or slowly changing mass, flying at speeds below 3000 to 5000 feet per second, during maneuvers lasting less than a minute or so. These equations of motion, which we presented as Equations (4-71) and (4-72) in section 4.6.9 in Chapter 4, are widely used in flying qualities simulators, including the simulators we use at the Flight Test Center.

But it is possible that you may one day test an airplane that violates the assumptions we made: a rocket powered hypersonic airplane perhaps. Equations (4-71) and (4-72) are unsuitable for such an airplane: they would produce airplane motion that is quite different from the real airplane motion. To simulate a rocket powered hypersonic airplane, it would be necessary to use higher fidelity equations of motion that accommodate rapid changes of mass, very high speeds, and perhaps lohger test maneuvers. A set of equations that satisfies these more exotic conditions is also available for use in Flight Test Center flying qualities simulators.

20.2.7 Cockpit Fidelity When we speak of cockpit fidelity we are referring to how closely the simulator cockpit duplicates the real airplane cockpit: the geometry; the seat; whether or not all cockpit instruments, control panels, warning lights, and circuit breakers are present and functional; and so on. Cockpit fidelity can be important. Imagine that a certain flying qualities test maneuver requires moving certain switches and using certain cockpit displays. If the switches and displays are missing, or in the wrong position, or don’t work, the usefulness of the simulator could be called into question. In cases such as this, cockpit fidelity is important.

Hying Qualities Testing 20-15

Flying eucJities Flight Test Simulators 20.3.2 Handling Qualities Evaluation

The level of cockpit fidelity you need depends on how you plan to use your simulator. For flying qualities testing, experience at the Flight Test Center indicates that cockpit fidelity is generally not as critical as aerodynamic, flight control system, or control stick fidelity. Much of the best simulator work done at the Flight Test Center involved relatively simple, general purpose cockpits. A rule of thumb is that primary flight instruments or multi-function displays should be present, functioning, and positioned as they are in the real airplane. Secondary instruments may not be necessary, and avionics control panels, warning light panels, and circuit breaker panels usually aren’t necessary. However, this may vary from test program to test program. -

20.3 Uses and Benefits of a Flight Test Sinlator Experience at the Flight Test Center shows that much may be accomplished with relatively simple, piloted, ground-based simulators. which we often refer to as flight test simulators. In this section we will enumerate some important uses and benefits of flight test simulators. These include education, handling qualities evaluation, development of new test maneuvers and analysis techniques, developing programmed test input signals, pilot proficiency, data reduction &heckout, test planning, safety, analyzing and exploring deficiencies, augmenting test data, hardware verification and (limited) validation, and dress rehearsals for specialhight tests. The list of uses and benefits we outline here is by no means complete. Simulators are so versatile that new uses and benefits are continually arising.

20.3.1 Education Chronologically, education is the first benefit provided by a flight test simulator. To build a simulator (or more accurately, to build the models that make up a simulator), test engineers must become intimately familiar with the details of the airplane aerodynamics and flight control system. As a result, there is no better way to prepare for a flight test program than to build a simulator. You will learn the details of the various flight control modes; where handling qualities are predicted to be satisfactory or less than satisfactory; at what test conditions the airplane is predicted to become directionally unstable; what the actuator rate limits are; which feedback parameters are most important; and so on.

20.3.2 Handling Qualities Evaluation Handling qualities evaluation using a simulator is probably most closely associated with the design process, but it is equally useful throughout the test program. During the design process, the primary use of a piloted ground-based simulator is to assist the designer in tailoring the flight control system to achieve good handling qualities. When the pilot is dissatisfied with the handling qualities, the designer adjusts the flight control system architecture or compensation until the problem is corrected.

During the flight test program, handling qualities evaluation using a simulator serves several purposes. One is to familiarize the pilots with the predicted handling qualities of the test airplane. This is important when the flight envelope is being expanded, when new test maneuvers are performed, or when new pilots are introduced to the airplane.


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Flying Qualities HigM Test Simuhtors 20.3.4 Creating Programmed Test Input Signals

Handling qualities evaluation using a simulator is also an important part of validating a simulator:' As test data become available, the simulator aerodynamic and flight control system models must be incrementally corrected and validated. An important step in this process is the evaluation of simulator handling qualities. Before a simulator can be regarded as validated, the pilots must judge that the simulator handling qualities are sufficiently similar to the real airplane. If the pilots judge that there are significant differences between the simulator and the airplane handling qualities, the source of the differences must be found and corrected.

Handling qualities evaluation using a simulator is also important when evaluating and correcting airplane deficiencies discovered during flight testing. The first step in this process is to validate the simulator aerodynamic and flight control system models, so the airplane deficiency can be duplicated in the simulator. Successive steps in the process are to identify and understand the cause of the deficiency (mispredicted aerodynamics, mismodeled flight control system, unreliable design guidance, and so on); to propose a solution, or perhaps several candidate solutions, for the deficiency; to evaluate the candidate solutions in the simulator and select the one that appears most promising; and to evaluate the selected solution in flight.

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. 203.3 Developing New Test Maneuvers and Analysis Techniques While building and using a flight test simulator, you may discover that certain features of the test airplane cannot be properly evaluated using conventional test or analysis methods. This may occur when the test airplane uses unusual control effectors (such as vortex control jets or thrust vectoring), or an unusual control function (such as inflight thrust reversing), or redundant control surfaces, or for other reasons. Similarly, an airplane designed to perform an unusual mission, or a mission performed to unusually exacting standards, may also require new or modified test or analysis methods. Simulators have proved to be an excellent tool for developing new test maneuvers and for obtaining data to validate new analysis techniques. And when unusual features of a new airplane require that the airplane be configured in a special way for testing, a simulator is almost indispensable to working out the details of implementation.

20.3.4 Creating Programmed Test Input Signals Simulators are an excellent tool for developing programmed test input signals for aerodynamic and flight control system model validation testing. At the Flight Test Center, many hours of simulator time have been devoted to creating test input signals that will produce satisfactory estimates of stability derivatives or frequency response functions. This is done by trying proposed test input signals on the simulator, collecting and analyzing simulator test results, and comparing the results with the model in the simulator. This procedure is repeated until satisfactory shapes and amplitudes have been developed for the test input signal. Many hours of expensive flight test time can be saved in this way, without risk to the airplane. In some cases this approach allows us to successfully conduct model validation testing that would otherwise prove impossible.


Flying Qualities Flight Test Sinwlators 20.3.8 Safety

20.3.5 Pilot Proficiency Pilots find that practicing test maneuvers in a simulator is an effective way - . I .

to improve or recover their proficiency. It is cheaper, safer, and more efficient to learn new test maneuvers and techniques, or polish familiar ones, in a simulator than in the real airplane. Increased pilot proficiency yields two important dividends: higher quality test data and more test maneuvers per flight hour.

20.3.6 Data Reduction Checkout At the Flight Test Center we find it helpful to use "test data" from a simulator to check out data reduction and analysis software. This is more important than it might sound. Data reduction and analysis software is complex, and must be tailored to each new test program. Experienced testers know that without a rigorous pre-first-flight checkout, several flights may be needed to expunge the bugs from sophisticated data reduction and analysis software. Using simulator "test data" to perform a pre-first-flight checkout can dramatically reduce lost flight time and test maneuvers.

20.3.7 Test Planning Using a simulator, we can learn before flight testing $hat kind of test maneuvers are needed to satisfy the test objectives, how many maneuvers must be flown, and how much time will be needed to fly them. We can also learn how much the test conditions are likely to change during the maneuver: for example, how much airspeed or altitude might be. lost. When flight test time is critical, a simulator can be used to work out the most efficient sequence of maneuvers.

20.3.8 Safety A flight test simulator enhances safety in at least three ways. First, it can be used to prepare pilots for a range of possible responses when they fly a new or modified airplane. Second, it can prepare the pilots for both planned and unplanned flight control system failures. And third, it can reduce the hazards associated with envelope expansion testing.

The first way a simulator can be used to enhance safety is by preparing pilots for a range of possible responses. As you know by now, the uncertainties in predicted aerodynamic and flight control system models can affect handling qualities in important ways. Using a procedure we call sensiriviry resting, a simulator can prepare pilots for the effects of these uncertainties. For example, varying the values of predicted stability derivatives (or combinations of stability derivatives) allows the pilot to develop a feel for how sensitive the handling qualities might be to errors in the aerodynamic model. Similarly, the effect of lower than expected actuator rate limits (induced, perhaps, by higher than anticipated hydraulic system demands) may be investigated. Sensitivity testing prepares the pilot to recognize some of the handing qualities surprises that are likely to be encountered during testing. Equally important, sensitivity testing prepares the pilot to respond correctly to those surprises.

The second way a flight test simulator can be used to enhance test safety is by preparing pilots for both planned and unplanned flight control system failures. Planned failures are intentionally induced (perhaps using an inflight fault simulation and clearing capability) so that failure state handling qualities may be evaluated. It is prudent to use a simulator to prepare for these tests so that the pilot knows what to expect in flight. Preparation should include an exploration of the effects of


Flying QuaWes Flight Test Simulcrtors 20.3.10 Augmenting Test Data

~ -, aerodynamic uncertainty. Unplanned failures are, of course, unexpected. Pilots should spendtime in a simulator learning how to recognize and respond to unexpected failures and the handling qualities they produce.

Occasionally, flight control system failure states produce handling qualities that are judged to be too hazardous for inflight evaluation. In these cases the only way to explore the failure. state handling qualities is to use a validated simulator.

The third way a flight test simulator can be used to enhance test safety is by reducing the hazards associated with envelope expansion testing. Envelope expansion is an incremental process of correcting and validating the predicted models of the airplane aerodynamics, flight control system, structure, and handling qualities. A cardinal principle of envelope expansion testing is that it begins in the least hazardous region of the flight envelope and progresses to the most hazardous regions. As envelope expansion progresses and flight test results become available, the simulator models can be coqected and validated. The validated simulator can in turn be used to predict the airplane response at succeeding (and more hazardous) test points, where the m$el validation process is repeated. This procedure can reduce the number of unpleasant surprises you encounter. By the time the envelope has been expanded to the most hazardous regions, the airplane models are reasonably well understood. As a result, the hazardous regions of the envelope may prove to be less hazardous than supposed when testing began.

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20.3.9 Analyzing and Correcting Deficiencies When deficiencies are discovered during testing, flight test simulators are an important tool for understanding and correcting them. The first step is to validate the simulator in that part of the flight envelope where the deficiency exists. Once the response of the simulator matches the response of the airplane, the deficiency may be explored in the simulator rapidly, inexpensively, and safely. The flight conditions at which the deficiency occurred can be easily controlled in a simulator, and the test maneuver may be repeated as often as desired without risk to the aircrew or airplane. When the problem is understood, candidate solutions can be proposed. These solutions may be evaluated in the simulator at length to determine which one, or more, should be evaluated in flight.

2Q3.10 Augmenting Test Data As a test program progresses and the simulator is incrementally validated, it can be used to augment flight test data. We can, for example, use the simulator to determine frequency, damping ratio, roll mode time constant, stability margins, and so on at selected flight conditions. This means that valuable flight test time may be devoted to more critical testing that can be accomplished only in the real airplane, such as handling qualities evaluation. Using a validated simulator to augment flight test data helps keep test programs on schedule and withii budget. Also, "Spec compliance" testing (demonstrating compliance with contractual flying qualities requirements) is more easily, more accurately, and less expensively accomplished using a validated simulator than a real airplane.


Flying Qualities Flight Test Simulators 20.4 Justifying a Flight Test Simulator

20.3.11 Hardware Verification and ( L i m i t e d ) Validation At the Flight Test Center, flying qualities flight test Simulators have sometimes been used for hardware-in-the-loop testing. This has proved valuable for verifying that control law changes have been correctly implemented in the flight control computers before the computers are replaced in the airplane for flight testing. Limited validation testing may also be performed. For example, the predicted handling qualities may be evaluated on the simulator to determine whether the control law changes are likely to produce the desired improvement. Full validation testing can only be conducted in flight.

20.3.12 Dress Rehearsals A flight test simulator may be used to conduct full dress rehearsals of an entire flight, or of portions of a flight. This can be very important for test programs that involve only a few short, high intensity flights, or unusual or especially hazardous test maneuvers. The X-15 test program, the lifting body test programs, and the space shuttle Enterprise approach and landing test program are examples of test programs made up of short, high intensity flights. High angle of attack testing includes examples of test maneuvers that are unusual and especially hazardous.

For test programs or test maneuvers such as these, pre-flight rehearsals offer segeral advantages. One is pilot proficiency. Timing and proficiency take on added importance when the duration of a flight may be no more than a few minutes, during which time many test maneuvers must be performed. Flight conditions may be changing rapidly, so each test maneuver must be flown at exactly the right moment, and correctly, because there are no second chances. Because these flights must go like clockwork, rehearsals are essential. In the past, pilots have reported that even with the help of rehearsals the flights seemed to go much faster than in the simulator. Success was achieved only because the rehearsals made it possible to step through the test maneuvers in an almost mechanical fashion. Otherwise, relatively little would have been accomplished.

Experience at the Flight Test Center indicates that, to be helpful, at least three rehearsals must be conducted. When fast-paced, high intensity flights are being rehearsed it may prove beneficial to run the simulator at a faster pace. For example, during the lifting body test programs, the pilots felt that running the simulator about 30 percent faster than real time made the rehearsal seem more realistic.

We should note that dress rehearsals are equally important to test engineers, who monitor the test data during the flight and who must be prepared to quickly interpret the data, diagnose anomalies, and if need be, recommend a course of action to the pilot. Rehearsals prepare the engineers to recognize and interpret test maneuver responses on the control room displays. Responses that differ significantly from simulator predictions should arouse a sense of caution. Rehearsals may also be used to validate minimum and maximum values for stripchart parameters, and "knock it off," or maneuver termination limits for key parameters.

20.4 Justifying a Flight Test Simulator Two of the most important components of a successful flying qualities test program are a properly configured test airplane and a flight test simulator. It is unlikely that a new or significantly modified airplane can be successfully tested without these two components. In Chapter 19 we discussed the importance of a properly configured test airplane and



in section 20.3 we outlined a few of the uses and benefits of a flight test simulator. In this &tion, you will learn why an independent flight test simulator is necessary at the flight test site, which in most cases is the Flight Test Center.

Air Force procuring agencies and contractors sometimes oppose building a simulator at the Flight Test Center. This is partly because they want to save money, partly because they believe one simulator (the contractor’s) is enough, and partly because they are unfamiliar with the uses of a flight test simulator. For these reasons they are inclined to regard a flight test simulator at the test site as an unnecessary expense.

It is understandable that the cost of building and supporting a simulator at the Flight Test Center is a matter of concern. Money doesn’t grow on trees, and to the inexperienced it may appear that a flight test simulator is a redundant expense. But return on investment must also be considered. Each of the uses of a simulator we outlined in the precediig section represents a return on investment: flight hours saved, improved test results, increased safety, new test maneuvers and analysis techni&es, increased efficiency, and so on. These add up to money the tegt program does not have to spend, and airplanes it might not have to repair or replace. To illustrate this point, consider the AFTVF-16 test program, which documented the return on investment in its flight test simulator during the first few years of testing. To the astonishment of everyone outside the test program, the cost of the sirnulaor w m repaid 120 times over. This return on investment represented the accumulated savings from all of the various uses we outlined in the preCeaig section. It did not include the potential savings of a damaged or lost test airplane.

A simulator pays for itself in another way, too. For a number of reasons, ranging from politics to operational requirements, it is important that a test program stay on schedule and withii budget. Nevertheless, schedules and budgets are routinely exceeded. But experience at the Flight Test Center indicates that test programs that have a flight test simulator and a properly configured test airplane fare better than those that don’t.

The procurement agency and the contractor sometimes argue that the contractor’s simulator is adequate to support flight testing. There are several reasons why this is not so. First, and perhaps surprisingly, contractors sometimes shut down their simulators soon after first flight. This is because their primary use for the simulator is flight control system design. After first flight they may feel that the simulator has served its purpose. When the contractor does maintain a simulator beyond first flight, it is often devoted to on-going design work, such as avionics integration, instead of flight test support.

Sometimes, the test team is required to use the contractor’s simulator for flight test support. In these cases, the test team might be given a few one or two week blocks of simulator time, arbitrarily sprinkled over the course of the program. This is completely inadequate. The uses we outlined in the previous section require almost daily access from months before first flight until the last flight is completed and the test reports are written. Envelope expansion alone requires daily use of a simulator for extended periods of time. Analysis of flight control system or handling qualities deficiencies requires that the simulator be available soon after the flight.



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Using the contractor’s simulator is inadequate for other reasons, too. The test team might not be allowed to modify the contractor’s simulator to serve flight test purposes. Without such modifications it may prove impractical to use the simulator productively. For example, it may prove difficult to conduct aerodynamic and flight control system sensitivity testing, or to develop test input signals, and so on. Moreover, data from the contractor’s simulator is rarely in a suitable format for flight test purposes.

Contractors do not always validate their simulators. This makes it difficult to use the s<mulator for envelope expansion, or to explore and correct deficiencies, or to augment flight test data.

Also, contractors may model the aerodynamics or the flight control system differently than would test team engineers. Here is an interesting, but not unique, example. Perhaps you have heard of the inadvertant first flight of the YF-16. This occurred when a high speed taxi test turned into a lateral pilot-in-the-loop oscillation and the pilot wisely elected to take off rather than run the airplane off the

Figure 204 Predicted and modekd aikron conuol t$eciiveness.

. This PI0 occurred because the lateral flight control system gain was based on mismodeled aileron control effectiveness. This is illustrated in Figure 20-6, which shows the predicted curve of C,

versus 6, together with the model of this curve used in the contractor’s simulator. The contractor’s model was a straight line connecting the two end points of the predicted curve. (The contractor chose this model for the sake of simplicity and to preserve the endpoints of the curve, so that full deflection roll rates could be reliably simulated.) Using this model, small aileron deflections were about half as effective in the simulator as they were in the real airplane. As a result, the contractor’s simulator was operating at about half the open-loop gain of the ..

real airplane. Consequently, the contractor’s simulator provided no indication of the roll sensitivity and PI0 experienced during the high speed taxi test.

In contrast to the contractor, the test team modeled the aileron effectiveness with greater fidelity in the Flight Test Center simulator. As a result, this simulator accurately predicted the behavior demonstrated during the high speed taxi test. Unfortunately, the contractor chose to be guided by the results from the contractor simulator.

Here is another example of a contractor modeling the aerodynamics differently than the test team might have. F-lll wind tunnel data indicated that the directional stability derivative, C”, , went to zero between 13 and 14 degrees angle of attack. The contractor regarded these results as suspect, and so discarded them. Consequently, the contractor’s aerodynamic model did not extend beyond 12 degrees angle of attack. During flight testing, two F-111s were lost when they exceeded 12 degrees angle of attack, departed, and entered unrecoverable spins.

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F l y i g Qualities Flight Test Simulators 20.5 Building a Flight Test Simulator

.. Another reason why Air Force procurement agencies and contractors resist building simulators at the Flight Test Center is their sense of optimism. Because they are "success-oriented" they do not anticipate problems. They believe everything will go smoothly, from design through flight testing. Consequently, they see no reason to spend money on a flight test simulator. At the Flight Test Center, however, we have learned through experience that problems are the norm.

20.5 Building a Flight Test Simulator Building a flight test simulator is a trig job. It would be dishonest to understate the time it takes, or the money. But, as we pointed out in the two prewediig sections, the uses and benefits of a flight test simulator outweigh the time and money required to build one.

It is important that the requirement for a flight test simulator at the AFFTC be acknowledged right from the start, before the contract for a new airplane is signed. Money must be allocated to the contraqtor to provide data on the aerodynamics, flight control system, cockpit layout, and so on. These data must be made available to the test engineers in a suitable format and as early as possible.

Work on the flight test simulator should begin early. Adequate lead time must be provided to purchase special computers (if needed), to fabricate hardware for the cockpit (if needed), and to build aerodynamic and flight control system models. The goal should be to have the simulator ready for use six months to a year before first flight.

Flight test simulators are built by simulation engineers and technicians working with flying qualities test engineers. Roughly speaking, the task is divided in the following way. Simulation engineers and technicians are responsible for writing and debugging software, fabricating hardware, and integrating the two. Test engineers are responsible for assembling aerodynamic data, flight control system diagrams, weight and balance data, propulsion system data, and so on. Test engineers are also responsible for outlining how the simulator will be used. Confirming that the simulator models, hardware, and software have been correctly implemented is the responsibility of both simulation and test engineers.

The availability of powerful desktop computers, together with generic cockpits and relatively simple but fast displays, makes it possible today to build reliable and useful simulators for a small fraction of the cost ordinarily associated with flight test simulators. The USAFMPE simulator depicted in Figure 20-1 in section 20.1.2 is an example of such a simulator, which could profitably be stationed next to the desks of flying qualities test engineers.

The first task in building a simulator is to decide how it will be used. The cost of a flight test simulator is determined primarily by the capabilities it must have. These capabilities are in turn dictated by the ways in which the simulator will be used. We discussed a number of important uses in section 20.3. Your test program may have others as well. Because the cost of a flight test simulator is related to the ways in which it will be used, you should not require capabilities that will not be used. For example, a medium fidelity, general purpose simulator cockpit is usually adequate for flight test purposes. Unless your test program has an unusual requirement for a high fidelity

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Flying Qualifies Flight Test Simulators 20.5.1 Defining Flight Test Simulator Requirements

-. cockpit, there is no good reason to spen6 extra money to exactly match the geometry, switches, lights, instruments, and displays in the real cockpit. That money can be spent more productively, or saved. In the next section we will show you how flight test simulator requirements are defmed.

20.5.1 Defining Flight Test Simulator Requirements Defining simulator requirements is a two step process. First, you must decide how the simulator will be used to support your test program. Second, you must decide how much fidelity is required to serve those uses.

The catalogue of uses we examined in section 20.3 and the discussion of fidelity we presented in section 20.2 are starting points for you to consider when you are determining simulator requirements. In Table 20-1 we have mapped fidelity requirements versus simulator use for a typical flight test simulator. Using this map, and tailoring it to your test program, may help you determine a set of cost effective simulator requirements. Consider, for example, that a high level of cockpit fidelity is not required for any of the uses listed in Table 20-1, whereas a medium level of fidelity is desired for a number of uses. Hence, money can be saved by specifying a medium level otcockpit fidelity, with no negative effect on usefulness. Or consider that a high level of motion fidelity is desirable for three of the flight test simulator uses listed in Table 20-1, whereas the remaining uses require a low level of motion fidelity. Motion systems for ground-based simulators are quite expensive, prohibitively so for most flight test programs. Also, motion systems for ground-based simulators may give misleading results, for the reasons we discussed in section 20.2.1. For these reasons, the AFFTC flight simulation laboratory no longer uses motion systems. The result is a simpler and less expensive simulator with little effect on most aspects of simulator usefulness. When motion fidelity is critically important to selected purposes, an inflight simulator should be considered. Adding or deleting uses from Table 20-1, or modifying fidelity requirements, may also be appropriate. For example, dress rehearsals may not benefit your test program. Or perhaps your airplane has a flight control system that augments directional control during landing roll-out. This might require augmenting equations of motion fidelity to improve landing gear, braking, and tire-runway interaction models, and augmenting visual fidelity to improve texture, resolution, and depth perception, while minimizing time delay.

In defining simulator requirements, each aspect of simulator fidelity must be addressed in terms of cost and intended use. Cost, of course, is the sum of the expenses incurred in buying or fabricating hardware, writing software, verifying and validating the simulator, writing documentation, and operating the simulator. When it is feasible to do so, you will find that it is much less expensive to use software that has already been written and tested, and hardware that is already available. The AFFTC simulation laboratory provides a good selection of hardware and maintains a library of software, including equations of motion, common elements of control systems, test related software such as a programmed test input capability, and so on. These are helpful in getting your simulator built, checked out, and operational as quickly and as inexpensively as possibly.

One aspect of building a simulator is crucial to success: assembling the aerodynamic model. Unfortunately, the aerodynamic model is also likely to be the single largest challenge. In the next section we will discuss the fundamentals of aerodynamic modeling.

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20-24 Flying Qualifies Testing

Y 8. z

Flying Quulities Flight Test Simulators 20.6 Aerodynamic Models for Flight Test Siulatocs

. -, 20.6 A e r o d y d c Models for Flight Test Simulators Two models are critically important in flying qualities simulators: the aerodynamic model and the flight control system model. In the next five subsections we will describe the general format of wind tunnel aerodynamic data and the three methods that are used to model those data. The first modeling method we will discuss uses force and moment coefficients; the second uses stability derivatives; and the third uses pseudo stability derivatives. In section 20.7 we will briefly discuss flight control system modeling.

When you embark on assembling an aerodynamic model for your flight test simulator you must make at least one important decision, and possibly a second. Your first decision is whether to use the contractor’s aerodynamic model or to build your own. If you decide to build your own model, your second decision is to determine the form of the model.

~

The contractor will build an aerodynamic model for the contractor simulator. This aerodynamic model is entered into computer memory as a database, or set of look-up tables. These tables are built from wind tunnel or computational fluid dynamics data. There are advantages to simply borrowing the contractor’s model, but there are also disadvantages. Among the advantages &e the saving of time, manpower, and money. Also, you may feel that you lack the experience needed to build a good aerodynamic model.

Among the disadvantages of using the contractor’s aerodynamic model are these: you won’t learn as much about the airplane aerodynamics; you will be forced to live with whatever assumptions the contractor made (recall the YF-16 and F-111 examples in section 20.4); and your flight test simulator may not have enough memory to store the contractor model. You will want to consult with flight test simulator engineers before deciding whether to borrow or build an aerodynamic model.

If you decide to build your own aerodynamic model, you must determine the form in which to cast it. (If you have chosen to use the contractor’s aerodynamic model, the form of the model has been selected for you.) There are three forms to choose from: the coefficient form; the stability derivative form; and the pseudo stability derivative form. It is possible to cast an entire aerodynamic model in either one of these forms. But it is more common to mix and match the forms, as the wind tunnel data, convenience, and computer resources dictate.

We should note, in passing, that a fourth form has been used in the past, but is only rarely used now. This fourth form might be called the equation form. It consists of equations that have been m e - fitted to the aerodynamics.

In the sections that follow, you will learn that each form has advantages and disadvantages. For example, you will learn that coefficient models of aerodynamics require the least amount of work to build, and use the processing power of computers more efficiently than either stability derivative or pseudo stability derivative models. However, coefficient models are not well suited to aerodynamic sensitivity testing and model validation testing, and stability derivatives cannot be easily extracted from a coefficient model.

Flying Qualities Testing

Flying Qualities Flight Test Simulators 20.6 Aerodynamic Models for Flight Test Simulators

. . .. Stability derivative models of aerodynamics are the most attractive from a flight test viewpoint. Stability derivative models are easily adapted to aerodynamic sensitivity testing; they are well suited to aerodynamic model validation testing; and stability derivatives may be readily extracted for analytical purposes. On the other hand, stability derivative models are time consuming to build, often require more computer memory, and use the processing power of computers less efficiently.

Pseudo stability derivative models usually require less computer memory than stability derivative models. But they are time consuming to build (though less so than stability dertvative models), use the processing power of computers inefficiently, are not well suited to aerodynamic sensitivity testing, and are difficult to work with during aerodynamic model validation testing. Also, it is difficult to extract stability derivatives for analytical work.

After we have discussed them in more detail, we will summarize the advantages and disadvantages of the three aerodynamic modeling forms in Table 20-16 in section 20.6.5.

To build a simulator aerodynamic model, force and moment coefficients, g stability derivatives, or pseudo stability derivatives, or a combination of the three, are stored in computer memory as multi- variable, or multidimensional look-up tables. Each time the simulator solves the equations of motion, the appropriate coefficients or derivatives are retrieved from the look-up tables and used to calculate the aerodynamic forces and moments.

Figure 243-7 A three dimensional h k - u p table of the static directional stabiIity derivative.

The variables, or arguments, of an aerodynamic look-up table usually include Mach number, angle of attack, angle of sideslip, control surface deflections, dynamic pressure, and other pertinent variables peculiar to the simulated airplane (such as thrust level in powered lift airplanes). The size of an aerodynamic model is determined by the number of look-up tables in the model, the number of variables in each look-up table, and the number of entries, or breakpoints, for each variable. The number of entries is determined by the range of the variable and the nonlinearity of the wind tunnel data. In Figure 20-7 we illustrate a three dimensional look-up table of C, . The variables in

this table are a, p , and 6,. Each value of these variables, such as p-0, 5, and 10 degrees, is called a breakpoint.

I

Of course, an actual look-up table of C,,, would likely have at least six dimensions (Mach number, a, p , a,, am, and 3, rather than three. But we can draw a picture of only three dimensions. There are 125 entries in the simple look-up table shown in Figure 20-7. If Mach number, 6,. and 4 also


Flying Qualities Flight Test Simulators 20.6.1 Wind Tunnel Aerodynamic Data

had four entries each, the six dimensional look-up table would contain 15,625 entries. As you can . . *

see, even simple aerodynamic models are not small.

The size of the model dictates how much computer memory will be needed for the look-up tables. A very simple aerodynamic model may easily contain 30,000 look-up table entries, displacing 120,000 bytes of memory. More complex aerodynamic models may contain millions of entries and occupy many gigabytes of memory.

Although memory is inexpensive today, the memory needed for a very complex model may exceed the memory available. When this happens, the aerodynamic model must be modified. In a few cases it might be possible to trim the size of the simulated flight envelope. In other cases it might prove necessary to break the aerodynamic model into smaller pieces that will fit, one piece at a time, into the available memory. For example, a large and complex model might be divided into four smaller, overlapping models: an approach and landing model, an up-and-away subsonic model, a transonic model, and a supersonic model. While this approach can dramatically reduce memory requirements, it also introduks a new set of problems. For example, it becomes difficult to conduct simulator evaluations which cross the boundaries of these smaller models.

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In the next section, we will briefly discuss wind tunnel testing and introduce the format in which wind tunnel data are typically presented. Computational fluid dynamics data are usually presented in a similar way. In the succeeding three subsections we will briefly discuss each of the three aerodynamic model forms.

20.6.1 Wind Tunnel Aerodynamic Data It is possible to build an aerodynamic model hy using computational fluid dynamics techniques, but it is more common at this time to rely on wind tunnels. To build an aerodynamic model using wind tunnels, physical, scale models of the airplane are built and tested over a matrix of test conditions. These airplane models are often referred to as "test articles." The matrix of test conditions, or test points, can be quite large, because it spans the range of Mach number, angle of attack, angle of sideslip, and control surface deflections the airplane is likely to encounter. It also includes landing gear position, speed brake position, and other pertinent variables.

The cost of conducting wind tunnel testing, which can be breathtakingly high, is related to the size of the test matrix. Frequently, the matrix spans subsonic, transonic, and supersonic Mach numbers, which means that more than one wind tunnel must be used. This is because wind tunnels are designed for testing across restricted ranges of Mach number. Testing at subsonic Mach numbers must be conducted in subsonic wind tunnels, testing at transonic Mach numbers must be conducted in transonic wind tunnels, and so on.

Interestingly, no two wind tunnels will produce the same test results, even when the same test airplane model is used and the test conditions are identical. Sometimes, the test results differ significantly.


Flying Qualities Right Test Sinurloors 20.6.1 Wind Tunnel Aerodynamic Data

We will use the pitch axis to illustrate our discussion of wind tunnel testing. In particular, we will use pitching moment aerodynamics. We begin by repeating the pitch acceleration equation of motion, which we presented as Equation (4-91e) in section 4.6.15 of Chapter 4.

The last term on the right hand side of Equation (20-1) is the aerodynamic component of pitch acceleration:

The aerodynamic pitching moment is

In this equation, the aerodynamic pitching moment, M, is constructed from stability derivatives. However, not all stability derivatives are determined from wind tunnel test data. Generally, only the "static" stability derivatives are determined from wind tunnel measurements. Static stability derivatives include Cm.. C,&,. C,,., Cnr, ~7,,~, and so on. We refer to them as static stability

derivatives because they are determined from wind tunnel testing conducted at static test conditions. Wind tunnel data, while not perfect in any case, is most reliable at static test conditions.

Rate derivatives, such as C-, Cmi, and C in the pitch acceleration equation (and C+, c , and so on in the lateral-directional equations) are difficult to measure reliably in wind tunnels. Instead, other methods are used to determine these derivatives.

". 'r

The speed derivative Cma can be handled in either of two ways: it can be combined with C%; or it can be calculated. In wind tunnel testing, Cn. is commonly accounted for by combining it with C%. Using this method, the effect of C, appears as a change in C% when Mach number changes. If testing is conducted at too few Mach numbers, this approach can make it difficult to accurately simulate the phugoid mode of motion, which is speed dependent.

For example, landing approach aerodynamics might be measured at a single Mach number in the wind tunnel. When this is the case, speed dependency cannot be measured and the effect of C, cannot be determined. As a result, the landing approach simulation will not exhibit a phugoid mode


Flying QuaUies Night Test Sirnuktors 20.6.1 Wind Tunnel Aerodynamic Data

. * of motion unless a calculated value of Cma is provided. Generally, a missing or inaccurate phugoid - mode of motion is not a significant problem, because phugoid dynamics are so slow that pilots control them subconsciously. Hence, phugoid dynamics are usually not of great interest during handling qualities evaluations. When the phugoid mode is important, we can resort to calculated values of Cm..

For a number of reasons (which we will not explore here), the derivatives Cmi and Cm are also difficult to measure reliably in a wind tunnel. They are also difficult to separate in flight test. For these reasons, they are usually combined into a single derivative C%+,,, which we abbreviate to C, . In practice, C is calculated rather than measured in a wind tunnel. Methods for calculating C and

a. 4 Cmi (as well as lateraldirectional angular rate derivatives) may be found in the USAF Stability and Control DATCOM. Although the calculated value is also somewhat unreliable, it has the advantage of being less expensive.

When we combine the effect of C,, with CI, and combine the angular rate effe'cts into a single

stability derivative C , we may rewrite the aerodynamic pitching moment equation as

,

.

-*

The pitching moment coefficient is

Cm=CI,+C a + - C C Q+Cm ae -. 2 5 -9 6,

(20-2)

(20-3)

Note that two of the pitching moment derivatives (Cm. and C ) are static derivatives. These two

derivatives, together with the bias term CI,, can be determined from wind tunnel test data. The third

derivative, C, , is a rate derivative that is usually calculated. Consequently, we may separate the pitching moment coefficient into two components: a static component that can be measured in a wind tunnel; and a calculated dynamic, or rotational rate, component. The static, or wind tunnel component is

ma.

*

The static, wind tunnel pitching moment is


Flying Qualities Flight Test Sirnulatots 20.6.1 Wind Tunnel Aerodynamic Data

A . .. To obtain the total pitching moment M, we must add the pitch rate tern -%", to the static, wind

tunnel pitching moment coefficient. This gives us 2Y,

Typically, the pitching moment measured during wind tunnel testing varies with Mach number, angle of attack, angle of sideslip, elevator deflection, and perhaps other variables pertinent to the airplane being tested (such as canard deflection, or thrust level in a powered lift airplane). The general form of the dependency is

Mrird = f ( M m h a, We) (m-a) wml =

This suggests that properly conducted wind tunnel testing must evaluate each of these variables. In the following paragraphs we will sketch out a commonly used procedure for accomplishing this. But first we pause to note that, in practice, static wind tunnel measurements of pitching moment are not distinguishednotationally from dynamic sources of pitching moment (such as speed changes and pitch rate). In the workaday world of flying qualities design and testing you are not likely to see the terms

or C- . From now on, we will observe this practice and omit the subscript mind tunnel Ms u unless a special purpose is served. c\ -1

Figure 20-8 wind funnel model being swept through a range for and the is again of angle of attack. swept incrementally through the angle of

attack range while the forces and moments are measured and recorded. Following these masurements, the elevator deflection angle is changed again and new measurements are made and recorded over the angle of attack range. This procedure is repeated until measurements have been made and recorded over the entire range of elevator deflection.

In Figure 20-8 we show a wind tunnel model being swept incremntally through a range of angle of attack at constant Mach number and zero sideslip angle. The elevator, ailerons, and rudder are locked in the trail position (zero degrees deflection). At each angle of attack in the test matrix the forces and moments acting on the model are measured and recorded.

Next, one control surface is deflected (the

Fly&! Qualities Tesiing 20-31

Flying Qualities Flight Test Sinurloors 20.6.1 Wind Tunnel Aerodynamic Data

When the effect of elevator deflection has been measured, the elevator is reset to the trail position - . and the effect of deflecting another control surface is measured and recorded. This procedure is repeated until the effect of deflecting each control surface has been measured and recorded over the entire angle of attack range.

Next, the effect of sideslip angle on the forces and moments is measured and recorded. The sequence of tests described in the preceding paragraphs is repeated for incremental sideslip angles over the specified range of sideslip angle. For example, at a sideslip angle of two degrees all control surfaces are locked in the trail position and the model is swept through the angle of attack range. Then the elevator is deflected and the model is swept through the angle of attack range again, while still at two degrees of sideslip. This is repeated at incremental elevator deflections until the effect of the elevator has been evaluated over its full deflection range. Next, the elevator is reset to the trail position and the effect of another control surface is evaluated over the angle of attack range when p =2 degrees. This procedure is repeated until the effect of each control surface has been measured and recorded over the angle of attack range when p =2 degrees.

The tests performed at p -2 degrees are then repeated at additional sideslip angles throughout the sideslip angle range. If the airplane is symmetrical about the X,z, plane, only positive (or negative) sideslip angles need be evaluated. The forces and moments associated with mirror image sideslip angles will be equal in magnitude but opposite in sign. In practice, a few mirror image test points are evaluated to confirm the symmetry of the model or to provide insight into the reliability of the wind tunnel measurements. If the airplane is not symmetrical, it will be necessary to measure the effect of both positive and negative sideslip angles at every test point.

The measurements we have just described must be repeated over a range of Mach numbers, and then they must be repeated once more with the landing gear extended (albeit over a smaller range of Mach number and, perhaps, a smaller angle of attack range).

The number of points in a wind tunnel test matrix depends on the flight envelope of the airplane and the number of control surfaces the airplane has. For simple, subsonic airplanes having only classical control surfaces and modest angle of attack and sideslip ranges, as few as 5,000 wind tunnel test points might be adequate. For more complex airplanes, several million test points or more might be necessary. Considering the cost of building a wind tunnel model, operating a wind tunnel, and reducing test data, it should come as no surprise that wind tunnel testing is expensive. To these costs we must add the inevitable cost of conducting additional testing as the shape of the airplane evolves over the course of the design program.

To reduce the cost of wind tunnel testing, the contractor and the Air Force procuring agency sometimes agree to reduce the number of test points. One way to accomplish this is to test at larger increments of angle of attack, angle of sideslip, or control surface deflection (for example, at 10 degree increments instead of five degree increments). Another way is to test over a smaller range (for example, over a range of 5 5 degrees of sideslip angle, rather than f 10 degrees). But reducing

. -,. -b


nyng Qualities nigh4 Test Sirnulatois 20.6.1 Wind Tunnel Aerodynamic Data

I Wind tunnel M, foot-powuis

the number of test points entails an element of risk. Important aerodynamic characteristics & be disguised or missed altogether.

The forces and moments that are measured and recorded during wind tunnel testing must be converted to force and moment coefficients, a form that is better suited to engineering use. These coefficients are tabulated and plotted versus Mach number, angle of attack, angle of sideslip, control surface deflection, and so on. Let’s walk through the process of converting the measured forces and moments to force and moment coefficients, and tabulating and plotting the results. We will use pitching moment as an example, but the procedure is equally applicable to other forces or moments.

In Table 20-2 we have presented the pitching moments, M, that were measured over a small but representative part of a wind tunnel test matrix. These measurements were made at a Mach number of 0.6, a sideslip angle of zero degrees, and with the ailerons and rudder fixed in the trail position. Only angle of attack and elevator deflection were varied over this part of the test matrix.

I

a, degrees . 0 5 I 10 1s

0

-5

-10

-15

a,, degrees

~. ._

-96000 -186Ooo -259200 -312000

-9600 -99600 -166800 - 2 1 m

64800 -19200 -70800 -102000

1 2 m 48000 0 -14400

Thepitching mmrmfs, M, that were measured at each test point in the wind tunnel may be converted to nondimensional pitching m m n r coe@cienrs, C,, using the following relationship, which we presented as Equation (4-83) in section 4.6.11 of Chapter 4:


Flying Qualities Flight Test Simulators 20.6.1 Wind Tunnel Aerodynamic Data

..

Table 20-3 Wnd tunnel predictedpitching moment coeflcient C, versus (I! and 8, when Mach=O.6 and j3=0 degrees.

For example, we see in Table 20-2 that when a =5 degrees and = -10 degrees, the wind tunnel pitching moment M is -19,200 foot-pounds. Converting to a pitching moment coefficient, we have

\ \ \

= -0.016

where the wing area is 300 feet2, the mean aerodynamic chord is 10 feet, and the dynamic pressure is 400 poundslfoot2. We have entered this value of C, in Table 20-3, where we have tabulated wind tunnel pitching moment coefficient versus angle of attack and elevator deflection. In a similar manner, we converted each of the measured pitching moments in Table 20-2 to the corresponding pitching moment coefficients in Table 20-3. We should pause here to remark on something you may already have noted. As a matter of

Figure 20-9 Surface plot of wind funnel predicted C , versus a and 6, convenience, we have presented when Mach=O.6 and j3=0 degrees. scale pitching moments in Table 20-2

and used the full scale wing area and mean aerodynamic chord to calculate the pitching moment coefficient, even though the wind tunnel test article may be a 10 percent scale model. When full scale values are desired, the wind tunnel data must be scaled up.


Flying Qualities Flight Test Simulator% 20.6.1 Wind Tunwl Aerodynamic Daw

"t

\ s, . -100

4 a

deg

-3 J Figure 20-10 Curves of wind funnel predicted C, versus 01 for c o n s m values of 8, when Mach=O.6 and p = O degrees.

Figure 20-11 Curves ofwind tunnel predicfed AC, versus 8, for consfam vahes ofu. when Mach=O.6 and p=O degrees.

In Figure 20-9 we present a surface plot of the wind tunnel pitching moment coefficients given in Table 20-3. The shape of the c, surface is defined by the lines of constant a and 6, projected onto it. That part of the surface that lies above the plane of a versus &e represents positive values of C,, and is denoted by solid lines of projected a and ae. Where the lines of constant a and ae are dashed, the surface lies below the a plane (negative Cm). A wind tunnel measurement of pitching moment was conducted at every point where the lines of constant a and intersect.

The plotted curves of wind tunnel test results that you will find useful as flying qualities test pilots and engineers are sections of the surface presented in Figure 20-9. For example, in Figure 20-10 we present curves of C, versus a for several constant values of ae. The small circles represent wind tunnel measurements, and the curves are hand-faired through these measurements. These curves show the effect that angle of attack and elevator deflection have on pitching moment coefficient.

A common way to present the effect of elevator deflection is shown in Figure 20-1 1. Each curve in this figure is also a section (when a is held constant) of the C, surface shown in Figure 20-9. However, the origin of these curves has been shifted to zero by plotting the c h g e in C, caused by deflecting the elevator from the trail position. We use the symbol AC, to denote this change in C, . For example, from Table 20- 3 we see that when a =5 degrees and =O

degrees, the pitching moment coefficent, C, ,

s


Flying Qualities Flight Test Sinurlotors 20.6.1 Wind Tunnel Aerodynamic Data

is -0.155. We also see that when 6e= -10 degrees at the same angle of attack, the pitching moment coefficient is -0.016. As a result, we have

= -0.016 - (-0.155)

= 0.139

The general formula for calculating the change in pitching moment coefficient, AC-, caused by elevator deflection is

where it is assumed that other test conditions (such as angle of attack, Mach number, and so on) are constant. The “_I’ in the subscript of C indicates a variable value of 6,. With this formula and

the values of dm in Table 20-3, we can construct the table of A C ~ shown in Table 204. When we plot AC, from Table 20-4 versus for constant values of a, we get the curves shown in Figure 20- 11.

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Table 20-4 Change in wind runnel predicted pitching mmnt coq7icient AC, caused by elevator dej&ction. versus (I and 6, when Mach=O.6. @=O degrees.

The effects on A C ~ of leading or trailing edge flap deflections, canard deflections, and so on can be determined in the same way.

Let’s urn now to the pitching moment created by pitch rate. As we noted earlier, the effect of pitch rate is usually not measured in a wind tunnel. Instead, it is calculated and presented as the stability derivative C, . The calculation is usually a function of primary variables only, such as Mach number

and angle of attack. An example curve of calculated C versus angle of attack, at a constant Mach number of 0.6, is presented in Figure 20-12.

A look-up table of Cm, versus a may be constructed from Figure 20-12 by reading values of Cm, at selected values of a. Such a table is presented in Table 20-5. The angles of attack selected for the

I -.

. -.


Flying Qualilies Flight Test SinuJaors ' 20.6.1 Wind Tunnel Aerodynamic Data'

Calculated

Ilradians cw

0.6 Mach number

(I, degrees

0 3 7 11 15

-13.0 -9.0 -6.7 -6.0 -6.9

0 .

6.

To find the total pitching moment coefficient C, of an airplane at any flight condition, we need only sum the pitching moment coefficient C, for a specified angle of attack and elevator deflection (which we can find in Figure 20-10 or Table 20-3) with the pitch rate contribution (which can be determined using Figure 20-12 or Table 20-5). For example, suppose we wanted to determine the total pitching

interpolated values of Ca, would lie reasonably 6 10 16 a close to the curve.

doe

When we need to determine the change in pitching moment coefficient caused by pitch rate,


Flying Qualities Flight Test Simulaiors 20.6.1 Wind Tunnel Aerodynamic Data

moment coefficient when the Mach number is 0.6, a = 10 degrees, = -10 degrees, and Q= 15 -. 4

degreeslsecond (0.26 radianslsecond). To do this, we would solve the equation

Mach-0.6 .=1v I 8,140.

Equation (20-7) is an aerodynamic model of pitching moment coefficient as a function of Mach number, angle of attack, elevator deflection, and pitch rate. To illustrate the use of this model, we will solve Equation (20-7) using Table 20-3 and Figure 20-12.

From Table 20-3 we see that the wind tunnel pitching moment coefficient, C, (which we denoted = -10 degrees. From Figure 20-12

we see that C =-6.0 per radian when a=lO degrees. (Note that elevator deflection does not influence the calculated value of Cm,.) Substituting these values into Equation (20-7). we obtain

in Equation (20-7)), is -0.059 when a = 10 degrees and C"-,

"r

= -0.059 + - lo (-6.0)(0.26) 2 (642)

= -0.071

where the true airspeed is 642 feet/second and the mean aerodynamic chord is 10 feet. At the specified conditions, the airplane has a nose-down pitching moment.

Although we have used pitching moment to illustrate our discussion in this section, the same principles are equally applicable to each aerodynamic force and moment.

In Parts I1 and IlI you learned that we rely on stability derivatives for most flying qualities analysis. Stability derivatives can also be used to build a simulator aerodynamic model. But force and moment coefficients and pseudo stability derivatives can also be used to build a simulator aerodynamic model. In fact, it is not unusual for a simulator aerodynamic model to be composed of all three of these forms.

In the next three subsections we will show you how coefficients, stability derivatives, and pseudo stability derivatives are determined from wind tunnel data.


Flying Qualities Flight Test Simulators 20.6.2 Coefficient Aerodynamic Modeb

20.6.2 Coefficient Aerodynamic Models Coefficient models of aerodynamics are the easiest to build from wind tunnel test data, often require less computer memory, and use the processing power of computers efficiently. But they are not well suited to such flight test uses as aerodynamic sensitivity testing and aerodynamic model validation testing. Moreover, when we need stability derivatives for analytical purposes, they cannot be easily extracted from a coefficient model. Despite these drawbacks, coefficient models are widely used.

Let's see how a coefficient model can be built, using pitching moment aerodynamics to illustrate. The aerodynamic pitching moment coefficient, C, , is

Cm=C++C a + - C E Q + C m &e -- ZV, '"r *.

The value of C, depends on Mach number, angle of attack, angle of sideslip, elevator deflection, and any other variables that might be pertinent to the test airplane (such as canard deflection, or thrust level in a powered lift airplane). A coefficient model of pitching moment aerodynamics can be built by storing these values of C, in a multi-variable look-up table. The variables of the look-up table are Mach number, angle of attack, angle of sideslip, elevator deflection, and so on.

Each time the simulator solves the equations of motion, the appropriate value of C, is retrieved from the look-up table and substituted into the pitch acceleration equation:

While this scheme is attractively simple, it does not use computer memory as efficiently as it might. For this reason, the coefficient form of aerodynamic modeling is rarely used alone. In practice, it is nearly always used in concert with the stability derivative form. When used in this combination, coefficients are used to model the "static" aerodynamic forces and moments measured in a wind tunnel, while stability derivatives are used to model the dynamic forces and moments produced by rotational rates.

The static component of the total pitching moment coefficient is C.=C,+C,.a I +C,,,,&,

where we use C: to denote the static wind tunnel component. Now the pitching moment coefficient is

C,=C,+C,.a + C &e+-Cm,Q C

ma* ZV,

I C =C,+-C Q zv,


Flying Qualities Flight Test Simulators 20.6.2 Caeffiaent Aerodynamic Models

As you can see, this model of pitching moment aerodynamics combines the coefficient and stability . ~

. - derivative forms.

That part of the aerodynamic model that is cast in coefficient form is built by storing the static pitching moment coefficients C: in computer memory, using a multi-variable look-up table. The look-up variables include Mach number, angle of attack, angle of sideslip, control surface deflection, dynamic pressure, and any other pertinent variables. (The effects of dynamic pressure are not measured in a wind tunnel, but are calculated, based on the predicted flexibility of the airplane.) The general form of the look-up table is

C: =f (Ma&a,B,i3,,i) (m-io) In practice, the coefficient part of an aerodynamic model might be composed of more than one look- up table. For example, there might be one table for landing approach and one for the remainder of the flight envelope.

That part of the aerodynamic mdel that is cast in stability derivative form is buat by storing the stability derivative C in a multi-variable look-up table. The look-up variables usually include Mach number and angle of attack. The general form is

a*

C., =f ( M a h a ) (20-11)

The stability derivative part of an aerodynamic model might also be divided into more than one look- up table.

Each time the simulator solves the equations of motion, the appropriate values of C: and C retrieved from the look-up tables and substituted into the pitch acceleration equation:

are "I

Perhaps you are wondering why it is more efficient to assign C: and C to separate look-up tables. As you can see by comparing Equations (20-10) and (20-11), there are fewer look-up variables for Cm,. As a result, separating the C: and C look-up tables can save a substantial amount of memory.

In the remainder of this section we will focus on the coefficient form of aerodynamic modeling. In section 20.6.3 we will discuss the stability derivative form.

Let's illustrate the construction of a coefficient model, using pitching moment aerodynamics. In Table 20-3 in section 20.6.1 we presented tabulated values of C, versus angle of attack and elevator deflection at 0.6 Mach number and zero degrees of sideslip angle. We repeat that table here as Table 20-6. Because these pitching moment coefficients were calculated from static wind tunnel measurements of pitching moment, we recognize that Table 20-6 is a table of C: . We see then, that

5

4


Flying Qualities Flight Test Sitnulatom 20.6.2 Cwffaent Aerodynamic Models

Tabk 20-6 Wind iunnel predicfedpifching mmenf cmficienr Cm’ versus a and 6, when Mach =0.6 and (3=0 degrees.

the wind tunnel data are already cast in coefficient form. Relatively little additional work is needed to build the multi-variable look-up tables that are loaded into the simulator computers. This is why Coefficient models are the easiest to build from wind tunnel test data.

We noted at the beginning of this section that in addition to being easy to build, coefficient models often require less computer memory and use the processing power of computers more efficiently. To illustrate this, consider Table 20-6. This table contains 16 entries, reflecting four angle of attack and four elevator deflection test points at a single Mach number. In the next section you will learn that a stability derivative model of the same aerodynamics requires three tables, each containing 16 entries, or three times the memory required by the coefficient model. Moreover, when a pitching moment coefficient is taken from Table 20-6, it is ready to be used immediately to determine the aerodynamic pitching moment. No intermediate mathematical operations are necessary. In this sense, coefficients are more efficient than stability derivatives, which must undergo multiplication and addition operations before they can be used.

.

Each time the simulator solves the 0 equation of motion, the appropriate value of C: is retrieved

from a look-up table similar to that shown in Table 20-6. When C: is needed for values of a and 6* that are not found in the table, we use linear interpolation between the nearest table entries. For

example, we can use Table 20-6 and linear interpolation to determine that C: = -0.062 when a -7

degrees and &e = -8 degrees. When values of C: are required beyond the boundaries of the table, extrapolation or some other scheme must be adopted. But it is important to understand that the validity of the simulation is questionable whenever a flight condition is attained that lies beyond the limits of the look-up table. In general, a simulator should not be used at test conditions lying outside the b0undarie.s of the aerodynamic model.

The use of interpolation to determine coefficients between table entries suggests that it is important to select the look-up table entry points carefully. These entry points are usually referred to as breukpoinrs. Breakpoints are the values of angle of attack, elevator deflection, Mach number, and

so on at which values of C: are entered into the table. In Table 20-6, the breakpoints are at five


Flying Qualities Flight Test Simulrrrors 20.6.2 Coeffiamt Aerodynamic Models

cm

t degree increments of a and a*. In .. - t

practice, however, the breakpoints are determined by the shape of the force and

I c 2 4 a a%

moment curves. 4 8 12 16 20

Consider, for example, the curve of C: versus a shown in Figure 20-13. In this figure, the wind tunnel teG data are represented by small circles and the curve is hand faired through the circles. It is evident that the curve is linear between zero and 12 degrees angle of attack. Hence we might use zero and 12 degrees as angle of attack breakpoints in the simulator look-

F i e 2@13 A curve of C,’ versus 01. up table. We have represented the look-up table breakpoints by small squares in

Figure 20-13. The test points at 4 and 8 degrees can be safely omitted from the model because linear interpolation may be used to determine C: between zero and 12 degrees. Beyond 12 degrees, it is evident that a breakpoint is needed at each wind tunnel test point to make linear interpolation work reasonably well.

Now consider another example, illustrated by the curve of C: versus a shown in Figure 20-14. In this figure, the wind tunnel test data are also represented by small circles and the curve is again hand faired through the circles. When the angle of attack is less than 15 degrees it is evident that reasonably accurate linear interpolation is possible when the look-up table breakpoints are at five degree increments. However, at higher angles of attack it appears that finer increments must be used. Adding a breakpoint at a = 18 degrees (denoted in the figure by the small square) would be helpful. But there is an element of risk involved in selecting the additional

msurc mi4 ~~~h~~ 0fc-3 versus breakpoint at 18 degrees. Relying on the hand faired curve introduces an extra dimension of uncertainty. If

the fairing (which is an estimate) is inaccurate, the added breakpoint might not improve the interpolated values. Additional wind tunnel testing would help to better define this part of the curve and reduce the risk of mismodeling the actual aerodynamics.

Cm

5 10 15 20 deg

From these two examples we see that the first step in selecting breakpoints is to plot the available wind tunnel data and fair curves through it. The second step is to examine the plotted data to determine whether the curves are reasonably well behaved. When the curves are well behaved, it


Flying Qualities Flight Tesi Sirnuhtom' 20.6.2 Coefficient Aerodynamic Models'

may be sufficient to select appropriate wind tunnel data points for your model breakpoints, as we did in Figure 20-13. If the curves are irregular in some sense, you might wish to select additional, eyeball interpolated, breakpoints for your model, as we did in Figure 20-14. Clearly, good engineering judgement and experience are helpful when breakpoints are selected.

As you learned in section 20.3.8, an important function of flight test simulators is aerodynamic sensitivity testing. Coefficient aerodynamic models are not well suited to this use. One method commonly used to perform aerodynamic sensitivity testing is to add a gain to each stability derivative in the equations of motion. For example, the pitching moment equation may be written

C, = Cs + klC,.a +&C ae + -k,C,,Q C "4 ZV,

Ordinarily, each of the gains kl through k, is set to one. But during aerodynamic sensitivity testing the gains may be varied to simulate the expected uncertainty in the stability derivatives. For example, & might be set to 1.2 to simulate the effect of C, being 20 percent more effective than the wind tunnel prediction.

When a coefficient model is used, gains cannot readily be applied to each stability derivative, because the stability derivatives are hidden within the coefficient. As a result, aerodynamic sensitivity testing becomes difficult and time consuming. This is an important drawback of coefficient models.

a. .

Another important function of flight test simulators is aerodynamic model validation, which we will discuss in Chapter 24. When aerodynamic models are designed for flight test simulators, provision must be made for correcting and validating the model. Validating the model consists of making necessary corrections to the wind tunnel predicted coefficients and demonstrating that the corrected model matches flight test results. The corrections to coefficient models are troublesome to d&ermine, because flight test results are presented in terms of stability derivatives. This is an important drawback of coefficient models.

One method of correcting an aerodynamic model is to replace the inaccurate wind tunnel data with flight test estimates of the real aerodynamics. For example, suppose we determined from flight

testing that the a = 5 degree and = -5 degree entry in Table 20-6 should be CL = -0.026 instead of

CL = -0.083. We could correct the model by simply replacing -0.083 in the table with -0.026. (As you might expect, this method is not so simple in practice. It requires interpolation, experience, and judgement.) This approach has the advantage of requiring no additional computer memory. But it also suffers from drawbacks. One of these is that, once a correction is made, the wind tunnel value is lost. This is more serious than it might seem. It is often desirable to switch back and forth between the wind tunnel model and the flight test validated model. This is useful, for example, when comparing predicted and actual airplane motion on the simulator. Another drawback of replacing the wind tunnel aerodynamics with flight test validated aerodynamics is that validating an aerodynamic model is not a one step procedure, but occurs over a period of time. Until validation testing is

Flying Qualities Testing 2043

Flying Qualities Flighf Test Sinurlotors 20.6.3 Stability Derivative Aerodynamic Models

completed, there may be discontinuities between the validated and unvalidated parts of the model. . . - . I

These discontinuities can prove troublesome.

A more convenient method of handling flight test corrections is to add special flight test correction terms to the wind tunnel model. We may visualize this method by modifying the coefficient model in the following way:

where C L is the wind tunnel value of the pitching moment coefficient and C:- is the correction II

that must be added to C L to make the aerodynamic model match the flight test results. For d

example, if the predicted wind tunnel value of C: at a specified test condition is 0.074, and flight

test results indicate that the true value is C: -0.051, the correction term is . = 0.051 - 0.M4 = -0.023

Unfortunately, this approach doubles the computer memory required for the simulator aerodynamic model. For example, the C L look-up table must be supplemented by a like-sized CL- look-up

table, and so on. This approach also requires more table look-ups and additional mathematical operations.

Y

In practice, the conflict between model validation requirements on the one hand and computer memory and processing efficiency on the other is resolved by a compromise. Two aerodynamic models are maintained: the original wind tunnel model and a flight test model. While this solution is not entirely convenient, it does make it possible to work on aerodynamic model validation without interfering with other uses of the simulator.

20.63 Stability Derivative Aerodynamic Models In Parts I1 and III we used the stability derivative model of aerodynamics exclusively. The stability derivative form lends itself naturally to flying qualities discussion and analysis. At trimmed flight conditions, much can be learned from stability derivatives that cannot be easily discerned from tables of force and moment coefficients. This is especially true near the boundaries of the flight envelope, where the natural aerodynamic forces and moments rival the capability of the flight control system to stabilize and control the airplane. You will learn more about this in Chapter 31, when we discuss high angle of attack testing. In this section you will learn how to build a stability derivative model of aerodynamics from wind tunnel data.

20-44 Flying Quolges Testing

Flying Qualities Flight Test Simulators 2Q.6.3 Stability Derivative Aerodynamic Modelg

If all things were equal, we would always use stability derivatives to model aerodynamics id flight test simulators. Stability derivatives make physical sense in a way that force and moment coefficients do not. When we need stability derivatives for analytical purposes, we may easily obtain them from a stability derivative aerodynamic model. Stability derivative models are the easiest to correct and validate, as you will learn in Chapter 24. And stability derivative models are tailor-made for aerodynamic sensitivity testing. These are attractive features.

But stability derivative models suffer from two important drawbacks as well. First, they often require more computer memory and use computer processing power less efficiently than coefficient models. Second, they require a great deal of work to build, as you will see.

Using pitching moment aerodynamics as an example, let's see how a stability derivative model is formed from wind tunnel data. When we use a stability derivative model, the pitching moment coefficient looks like this:

Cm=C*o+Cm.a+Cm 6,+-C C Q '. 2y -* . (20-12)

This is the form we grew accustomed to using in Parts II and 111. When there are additional control surfaces, such as a canard, we must augment Equation (20-12) accordingly. For example, to account

for the effect of canard deflection we would add C, 6,.

To build a stability derivative model we must convert wind tunnel pitching moment coefficients into several stability derivatives and a bias term,

C%. Let's begin by reviewing the geometry of stability derivatives, the bias term C%, and the pitching

' 0

a moment coefficient.

In Figure 20-15 we repeat the surface plot of wind tunnel pitching moment coefficient versus angle of attack and elevator deflection that we presented in Figure 20-9 in section 20.6.1. In Figure 20-16 we have isolated the curves of C, versus a when 6,=-5

degrees and of C, versus ae when as10 degrees. To aid in visualization, we have drawn these curves within their respective planes of

\

Figure 20-15 Surface plot of wind nutncl predzcted C, versus a and S, when Moch=0.6 ond B=O degrees.


Flying Qualities Flight Test Simu&ors 20.6.3 Stability Derivative Aerodynamic Models

- - a

pisure 20-16 Visualiuuion of wind runnel predicted C, and C, when Mach=O.6. a=lO degrees, &=-5 degrees, and @=O degrees.

t"

Figure 20-17 Detennimkm of C, ai a=IO degrees and &=-5 degrees.

20-46

C, versus ti,=-5 degrees and C, versus a=lO degrees. The pitching moment coefficient when a = 10 degrees and ti,=-5 degrees lies at the intersection of these two curves. At the point of intersection, we may draw tangent lines to each curve- within the plane of each curve. The slopes of these tangent lines are the stability derivatives Cm. and C, .

-

I'

Given these stability derivatives and C%, we show in Figure 20-17 how C, is determind at a=lO degrees and tie = -5 degrees. We begin at the C, axis intercept, C+, which is denoted by @ in the figure. Next, we proceed from a=O degrees at @ to a=10 degrees along a line having the slope c,.,

arriving at @. Finally, we proceed from tie =O degrees at @ to tie = -5 degrees along a line having the slope C, . This moves us to

8, which is the pitching moment coefficient C, we seek. This procedure corresponds to the equation

C, = C% + Cm.a + C tie (20-13)

Note the absence from Equation (20-13) of the

-C Q term, which is present in Equation 2v, (20-12). This term is missing because there is no pitch rate during wind tunnel testing. Hence, the effect of pitch rate is not reflected in wind tunnel test data. In other words, the wind tunnel pitching moment coefficients, C, , presented in Figure 20-15, are composed only of the terms shown in Equation (20-13).

8,

"%

C

Flying Qualities Testing

. -,

Flying QuaWes Flight Test Si&o+ 20.6.3 Stabiity Derivative Aerodynamic Models

Wind tunnel

lldegrees ~ U W .

0

. -, .. With this geometry in mind, let's see how C, , Cm8,, and C6 are determined from wind tunnel pitching moment coefficients. To illustrate the process, we will use the wind tunnel data presented in Figures 20-10, 20-11, and 20-12. These figures were presented in section 20.6.1.

ci, degrees

0 5 10 15

-0.0160 -0.0138 -0.0106 -0.00650 -

The first step is to convert the C, versus a curves in Figure 20-10 to a set of stability derivatives, Cas. We begin our illustration

-0.0158

-0.0152

-0.0134

4, degrees

Mach = 0.6 p = 0' &=-ti*

by repeating as Figure 20-18 the curve from Figure 20-10 that corresponds to 6,=-5 degrees. Recall that these data were obtained from a wind tunnel testing at 0.6 Mach number and zero degrees of sideslip.

Let's determine C.. when a=lO degrees. To do this, we drmv a line tangent to the curve of C, versus a at a = 10 degrees. The slope of this tangent line is -0.00910 per degree, so Cm.=-0.00910 per degree. We have entered this value of C,. in Table 20-7. The remaining entries in Table 20-7 were determined in a similar manner.

d%

.a &= -.OOSlQ'dq

Figure 20-18 A curve of wind nurnelpredined C, versus a, when 6.=-5 degrees, Mach=0.6, and @=O degrees.

-0.0134 -0.00910 -0.00540

-0.0118 -0.00690 -0.00280

-0.0104 -0.00580 0.00300

Table 20-7 Wnd nurnelpredicted C, versus a and 8 , when Mach=0.6 and 8=0 degrees.

Table 20-7 is a small slice of the multi-variable look-up table for C,. that will be stored in computer memory. The look-up variables for this table are Mach number, angle of attack, angle of sideslip, control surface deflection, dynamic pressure, and so on. (The variation of Cm. with 4 is calculated,

rather than measured in a wind tunnel.) Hence, the general form of a C, look-up table is no different from the form of a coefficient look-up table:

. Cm. = f ( M ~ h . a , P J , . ? )


Flying Qualities Flight Test Simulators 20.6.3 Stability Derivative Aerodynamic Models

Wind tunnel

lldegrees c*.

0

.. Each time the equations of motion are solved by the simulator computers, Cmm is retrieved from a look-up table such as Table 20-7, and other stability derivatives are retrieved from similar tables. When C, is needed for values of a and that are not found in the table, we use linear interpolation between the nearest table entries. For example, if Cm. were needed when a =7 degrees

and ae= -8 degrees, the simulator would enter the Cas table and use linear interpolation to obtain

Cm. = -0.0106 per degree.

m

a, degrees

0 5 10 15

-0.0144 -0,0144 -0.0154 -0.0174

The use of interpolation to determine stability derivatives between table entries suggests the importance of selecting the table breakpoints carefully. We illustrated this in section 20.6.2.

-0.0134

-0.0104 8.9

degrees

Now let's illustrate the procedure for converting curves of AC, versus to a table of C . As

you might imagine, this procedure is identical to the procedure we just used to convert curves of C, versus a to a table of Cam. We begin by repeating as Figure 20-19 the curve from Figure 20-1 1 that corresponds to a -0 degrees. Using this curve, we will determine C at an elevator

deflection of -10 degrees when a =O degrees.

At &,=-lo degrees we draw a line tangent to the curve of AC, versus The slope of this tangent line is -0.0104 per degree, so C =-0.0104 per degree. This result is

in Table 20-8. The other entries in Table 20-8 were determined in a similar manner.

"8.

lldach = 0.8 p=0* a=OO

ma.

Figure 2O-V *e of wind -lpredic@d W , versus 6 , when u=O degrees, Moch=O.6, and @=O degrees.

-0.0142 -0.0152 -0.0170

-0.0118 -0.0136 -0.0163

-15 -0.00800 -0.00970 -0.0107 -0.0151

Table 20-8 Wnd tunnel predicted C, versus 01 ond 6 , when Moch=O.6 ond @=O degrees.


Flying Qualities Flight Test Simdatok e

2Q.6.3 Stability Derivative Aerodynamic ModetQ'

Now that we have determined the stability derivatives C, and C, , we can turn our attention'io the

bias term C,,,. To determine C., we use Equation (20-13), recalling that wind tunnel measurements do not include the effects of rotational rates. We repeat Equation (20-13) here as Equation (20-14).

8.

C,=C.b+C,.a+C (20-14) "6.

To determine C.,, we need only rearrange Equation (20-14) in the following way:

C =C,-C a - C 6< '"0 I. "1.

To determine C., when a-10 degrees and 6,=-10 degrees we substitute into this equation C, = -0.059 from Table 20-3 in section 20.6.1, C,. = -0.00690 per degree from Table 20-7, and

C = -0.01% per degree from Table 20-8. The result is %

C =C,-C a - C , be "0 =. 4 .

= -0.059 - (-0.006W)(lO) - (-0.0136)(-10)

= -0.126

We have entered this value of C., in Table 20-9. calculated in the same way.

The remaining values in Table 20-9 were

Wind tunnel

Table 20-9 lyind tunnelpredicied C,,,, versus a! and 6, when Moch=0.60 and 8=0 &trees.

Finally, we hlrn our attention to C",. Recall from section 20.6.1 that the effects of rotational rates, such as pitch rate, on the aerodynamic forces and moments cannot be reliably measured in wind tunnels. Consequently, these effects are calculated and presented as curves or tabulated values of C, versus angle of attack and Mach number. In Figure 20-12 in section 20.6.2 we presented a curve of C versus a for 0.6 Mach number, and in Table 20-5 we tabulated selected values of C,, from this curve. We repeat Figure 20-12 and Table 20-5 here as Figure 20-20 and Table 20-10. This completes the task of building a look-up table of C, .

This completes the task of building a stability derivative model of the pitching moment aerodynamics.

#

*


Flying Qualities Flight Test Sirnubtors 20.6.3 Stabfity Derivative Aerodynamic Models

0.

6.

. -,

* 6 10 16 a aae

Calculated a, degrees

Ilradians 0 3 7 11 I5 Cw.

0.6 -13.0 -9.0 -6.7 -6.0 -6.9 Mach

number ~

C,,=C%+C a+C, &#+-C C Q -. '' 2v, -* (20-15)

Because the test conditions are 0.6 Mach number and p -0 degrees we may use Tables 20-7, 20-8, 20-9, and 20-10. From Table 20-7 we obtain Cm.= -0.0118 per degree; from Table 20-8 we obtain

C --0.0118 per degree; from Table 20-9 we obtain C%- -0.075; and from Table 20-10 we obtain -*

20-50 Fiying Qualities Testing

Flying Qualities Flight Test Simulators 20.6.3 Stability Derivative Aerodynamic Models

- -. .. the interpolated value Cm,= -7.85 per radian. When the mean aerodynamic chord, c , is 10 feet, we use Equation (20-15) to calculate

= -0.075 +(-0.0118)(5) +(-0.0118)(-10) +- lo (-7.85)(0.26)

= -0.0319 2 (642)

Although the procedure for building a stability derivative model is straightforward, it is evident that a great deal of work is involved. This is an important drawback of stability derivative models.

As you learned in section 20.3.8, an important function of flight test simulators is aerodynamic sensitivity testing. Stability derivative models are easily adapted to aerodynamic sensitivity testing by adding a gain to each stability derivative: .

C,=C,+klCm.a +&C 6,+-&Cm,Q C

-6. 2v,

Ordinarily, the value of each of the gains k, through k, is set to one. However, during aerodynamic sensitivity testing these gains may be adjusted to simulate the expected uncertainty in the wind tunnel data. For example, & might be set to 1.2 to simulate the effect of C, being 20 percent more

effective than the wind tunnel prediction. Suitability to aerodynamic sensitivity testing is an important advantage of stability derivative models.

4,

Another important function of flight test simulators is aerodynamic model validation, which we will discuss in Chapter 24. When aerodynamic models are designed for flight test simulators, provision must be made for correcting and validating the model. Validating the model consists of making necessary corrections to the wind tunnel predicted stability derivatives and demonstrating that the corrected model matches flight test results. Corrections to stability derivative models are the easiest to determine, because flight test results are presented as stability derivatives. This is an important advantage of stability derivative models.

One method of correcting the aerodynamic model is to replace the inaccurate wind tunnel data with flight test estimates of the real aerodynamics. For example, suppose we determined from flight testing that the a =5 degree and = -5 degree entry in Table 20-8 should be C = -0.020 per degree

instead of C, = -0.0142 per degree. We could correct the model by simply replacing -0.0142 in the

table with -0.0200. (As you can imagine, this method is not so simple in practice. It requires interpolation, experience, and judgement.) This approach has the advantage of requiring no additional computer memory. But it also suffers from drawbacks. One of these is that once a correction is made, the wind tunnel model is gone. This is more serious than it might seem. It is often desirable to switch back and forth between the wind tunnel model and the flight test validated model. This is useful, for example, when comparing predicted and actual airplane motion on the

"1.

8.


Flying Qualities Flight Test Sinuclators 20.6.3 Stability Derivative Aerodynamic Models

simulator. Another drawback of replacing wind tunnel aerodynamics with flight test validated aerodynamics is that validating an aerodynamic model is not a one step procedure. Until validation testing is completed, there may be discontinuities between the validated and unvalidated parts of the model. These discontinuities can prove troublesome.

A more convenient method of handling flight test corrections is to add special flight test correction terms to the wind tunnel model. We may visualize this method by modifying the stability derivative model in the following way:

where C, is the correction that must be added to the wind tunnel prediction of C, , and so on, to make the aerodynamic model match flight test results. For example, if the predicted wind tunnel value of c-. at a specified test condition is -0.009, and flight test results indicate that the true value

is c = -0.006,'the correction term is

.anb

-. . = -0.006 - (-0.009)

= 0.003

Unfortunately, this approach doubles the computer memory required for the simulator aerodynamic model. For example, the C, look-up table must be supplemented by a like-sized C Iook-Up, % -.- table, and so on. This approach also requires more table look-ups and additional mathematical operations.


At the outset of this section, we noted that stability derivative models often require more computer memory and use computer processing power less efficiently than coefficient models of comparable aerodynamics. This is evident from the following relationship:

Cm=C.lo+Cm.a+C I 6, "6.

where CL is the static pitching moment coefficient that is determined from wind tunnel test data. We see that look-up tables for two stability derivatives ( C-. and C ) and one bias term (C.,) are needed

to match a single pitching moment coefficient look-up table. This often means that stability derivative models require more memory and more time to perform the look-ups. For example, Tables 20-7

. -,


Flying QuaMes Flight Test Sitnuhators 20.6.4 Pseudo Stability Derivative Aerodynamic Modelk

(C".), 20-8 (C, ), and 20-9 (C,) each contain 16 entries, for a total of 48 entries. In section 20.6.2

you learned that a coefficient model needs only 16 entries (or one third the memory) to model the same aerodynamics. Moreover, stability derivative models make less efficient use of computer processing power than coefficient models. After the stability derivatives have been retrieved from memory, they must be multiplied by associated variables (for example, C, times a,) and the

products summed with the bias term to form a moment coefficient. In contrast, pitching moment coefficients are ready to use immediately after retrieval. These are important reasons why stability derivative models are not widely used in simulators, except within the flight test community.

a,

8.

20.6.4 Pseudo Stability Derivative Aerodynamic Models To distinguish pseudo stability derivatives from true stability derivatives we use a superscript + . Hence, Cni is a pseudo stability derivative. Pseudo stability derivatives are often used instead of true stability derivatives to reduce the s h of an aerodynamic model. A pseudo stability derivative model might require about one third less computer memory than a true stability derivatiye model.

Pseudo stability derivatives, which are not really stability derivatives at all, are sometimes called "simulator stability derivatives" because they are used only in simulators. Pseudo stability derivatives are of no use in flying qualities analysis and have no physical connection to airplane motion. In fact, they can be quite misleading to the unwary. Nevertheless, pseudo stability derivatives are commonly used to model airplane aerodynamics.

Pseudo stability derivatives can be used to model both longitudinal and lateraldirectional aerodynamics. But in practice they are most often used to model symmetrical lateraldirectional aerodynamics, and then only in conjunction with true stability derivatives.

Pseudo stability derivatives use the processing power of computers less efficiently than coefficient models. Also, pseudo stability derivative models are not well suited to either aerodynamic sensitivity testing or aerodynamic model validation. On the other hand, pseudo stability derivative models use less memory than true stability derivative models.

.

To illustrate the use of pseudo stability derivatives we will use wind tunnel measurements of yawing moment aerodynamics.

We begin by repeating the yaw acceleration equation of motion, which we presented as Equation (4- 910 in section 4.6.15 of Chapter 4.

The last term on the right hand side of Equation (20-16) is the aerodynamic component of yaw acceleration:


Flying Qualities Flight Test Simulators 20.6.4 Pseudo Stability Derivative Aerodynamic Models

. -,

In this formulation, the model of C, CBL rms of true sti ility atives. Recasting : model of C, in terms of pseudo stability derivatives we obtain

As you can see, this model is a combination of pseudo stability derivatives and true stability derivatives. As you can also see, the bias term C*, is missing. You will learn that this is because C%=O when pseudo stability derivatives are used, provided that the airplane is symmetrical about the

XbZb plane.

Let's see how pseudo stability derivatives are calculated and assembled into a model of lateraldirectional aerodynamics. We will begin with wind tunnel data.

~~~

Wind tunnel N,

Table Z M 1 wind n r n d measured yawing moment N versus B and 8, when Mach=O.6, a=5 &grees, and 6.=0 degrees.

In Table 20-1 1 we present wind tunnel measurements of yawing moment N versus sideslip angle and rudder deflection. These measurements were obtained at 0.6 Mach number, five degrees angle of attack, and zero degrees of aileron deflection. Note that only positive sideslip angles and positive rudder deflections were measured. When an airplane is symmetrical about the XbZb plane, positive and negative sideslip, rudder deflection, and aileron deflection will produce lateraldirectional forces and moments of equal magnitude, but opposite sign. Contractors take advantage of thii to reduce the number of points in the wind tunnel test matrix.


plying Qualities nighl Test Sirnulprors 20.6.4 Pseudo Stability Derivative Aerodynamic Model;

To keep our discussion of pseudo stability derivatives tractably simple, the wind tunnel measu-nts presented in Table 20-1 1 are restricted to variations in sideslip angle and 'rudder deflection. Also, the effects of roll and yaw rate are not included in Table 20-11. This is because wind tunnels cannot reliably measure the effects of rotational rates. Those effects are calculated (rather than measured) and are presented separately in the form of the true stability derivatives C", and C, .

For engineering purposes, wind tunnel test results are usually presented as nondimensional force and moment coefficients rather than forces and moments. To convert the yawing moments in Table 20-1 1 to yawing moment coefficients C, we use the relationship we presented in Equation (4-83) in section 4.6.11 of Chapter 4, which we repeat here.

N = i S b C ,

whe-re C,,=yawinpmommtoocfficient *

N-yawing foor-powrdr

i=dYnamicprrssllre, poundrlfoor~

s=wingarra, feet2

b = w i n g m fcn

For example, we see in Table 20-1 1 that when p =5 degrees and 6, = 10 degrees, the yawing momentN is -192,ooO foot-pounds. Converting this value of yawing moment to a yawing moment coefficient, we have

- 1!mW (4oo)(4oo)(40)

=

= -0.030

where the wing area is 400 feep, the wing span is 40 feet, and the dynamic pressure is 400 pounds/fooP. We have entered this value of C, in Table 20-12, where we present yawing moment coefficient C, versus sideslip angle and rudder deflection (for constant 0.6 Mach number,a=S degrees, and 6,=0 degrees). The remaining entries in Table 20-12 were calculated in a similar manner. We should pause here to remark on somethiig you may already have noted. As a matter of convenience, we have presented full scale yawing moments in Table 20-1 1 and used the full scale wing area and wing span to calculate the yawing moment coefficient, even though the wind tunnel test article may be a 10 percent scale model. When full scale values are desired, the wind tunnel data must be scaled up.

FTying QuQliiies Testing 20-55

Flying Qwlities Flight Test Simulutors 20.6.4 Pseudo Stability Derivative Aerodynamic Models

-. ~

Wind tunnel C

Table 20-12 Wnd tunnel predicted yawing mmeni coeflcient C,, versus @ and 6, when Moch=O.6, a=S &grees, and 8,=0 degrees.

In Figure 20-21 we present a surface plot of the yawing moment coefficients given in Table 20-12. The shape of the C,, surface is defined by the lines of constant p and 6, projected onto it. That part of the surface that lies above the plane of p versus 8, represents positive values of C,, and is denoted by solid lines of projected p and 6,. Where the lines of constant p and 6, are dashed, the surface

'4 lies below the pa, plane (negative C,,). Wind tunnel measurements of yawing moment were conducted at every point where the lines of constant p and 8, intersect.

Figure 20-21 Surface plot of wind runnel predicted C. versus B and 8, when Mach4.6, (r=S degrees, and 8.=0 degrees.

The plotted curves of wind tunnel test results you will find useful as flying qualities test aircrew and engineers are sections of the surface presented in Figure 20-21. For example, in Figure 20-22 we present curves of C,, versus p for several constant values of 6,. The small circles represent the actual wind tunnel measurements, and the curves are hand-faired through the measurements. Each of these curves is a section of the C, surface shown in Figure 20-21 for a constant value of 8,. These curves show the effect that sideslip angle and rudder deflection have on yawing moment coefficient.


Flying Qualities Flight Test Simulators 20.6.4 Pseudo Stabfity Derivative Aerodynamic Models

..

Figure 20-23 Curves of AC, caused by rudder deflection versus 6, at constant values of 8, when Mach=O.6. u=5 degrees, and 6.=0 degrees.

Fire 2622 Curves of wind huvtrlpredicred C, versus Bfor constant values of 6,, when Mach=O.6. a=5 degrees. and 6,=0 degrees.


Flying Qualities Flight Test Simulators 20.6.4 Pseudo Stability Derivative Aerodynamic Models

0

Another common way to show the effect of rudder deflection is shown in Figure 20-23. Each curve in this figure is also a section (when p is held constant) of the C, surface shown in Figure 20-18. However, the origin of these curves has been shifted to zero by plotting the change in C, caused by deflecting the rudder. We use the symbol AC, to denote the change in C,. For example, from Table 20-12 we see that when p =S degrees and 6,-0 degrees, the yawing moment coefficent, C,, is 0.070. At the same sideslip angle, the yawing moment coefficient is -0.030 when 6,=10 degrees. As a result, we have

5 I 10 I 15

9 -0.030 - (0.070)

= -0.100

0

5

10

15

6,. degrees

The general formula for calculating the change in yawing moment coefficient, AC, , caused by rudder deflection is e .

~~

0. 0. 0. 0.

-0.050 -0.060 -0.072 -0.082

-0.080 -0.100 -0.1% -0.144

-0.090 -0.120 -0.155 -0.190

where it is assumed that other test conditions (such as sideslip angle, Mach number, and so on) are constant. The "_'I notation in the subscript of C indicates a variable value of 6,. With this

formula, we may use the values of C,, in Table 20-12 to construct the table of AC, given in Table 20-13. When we plot AC, from Table 20-13 versus 6, for constant values of p , we get the curves shown in Figure 20-23.

TBP-7

The effects on AC" of aileron and other control surface deflections (such as rolling tail) can be determined in the same way.

Let's see how the yawing moment coefficient data presented in Figures 20-22 and 20-23 and in Tables 20-12 and 20-13 can be rearranged into a pseudo stability derivative model of yawing moment aerodynamics.

. ..


Flying QwWes FligJti Test Simulators 20.6.4 Reado Stability Derivative Aerodynamic Model4

@re 20-24 Use of pseudo stability &rivaiives to derermine C..

In Figure 20-24 we show how any -pint on the C, surface can be defined by two slopes. These two slopes are the pseudo

stability derivatives C,,, and C,,, . In the

case shown, we seek the yawing moment coefficient when B = 10 degrees and 6,=10 degrees: We begin at the origin of the axis system, denoted by @, and proceed from p -0 degrees to p =IO degrees along a line of slope C=, arriving at @. This line lies in

the plane defined by C, and 6,=0

degrees. Next, we proceed from 6,-0

degrees at @ to 6, = 10 degrees along a

line of slope Cm+ , which lies in the

plane defined by C,, and p = 10 degrees. This moves us to 0, which is the yawing moment coefficient, C,. that we

a,

seek. This graphical procedure corresponds to the equation:

c, = c:, B + c;,a, (20-18)

where, as we have already noted, the slopes and Cm;, are called psardo stability derivatives.

Compare Equation (20-18) with the combination pseudo stability derivative and true stability derivative model we presented in Equation (20-17), which we repeat here as Equation (20-19).

(20-19)

b We see that Equation (20-18) is missing two terms. The -(C P+C,,R) term is missing because

wind tunnel test data do not include the effects of rotational rates. These effects are calculated and

added separately. The C i term is missing from Equation (20-18) because the wind tunnel data

we are working with were collected when 6,=0 degrees. Hence we may delete the C' term,

because C* (O)=O. Recall that we intentionally selected test results for ae=0 degrees so that our

illustration would be tractably simple. Had we included aileron deflection as a third variable (with @ and 6,). we could not have presented C, as a three dimensional surface in Figure 20-21.

2v, 'i

8.

n*.

na.


Flying Qualities Flight Test Simulators a.6.4 Pseudo Stability Derivative Aerodynamic Models

Note too, that there is no bias term, c%, in Equations (20-18) or (20-19). As you can see from .

Figure 20-24, this is because the C, axis intercept is at the origin of the axis system, or C,,=O. In general, the bias term will be zero when we use pseudo stability derivatives to model lateraldirectional aerodynamics, provided the airplane is symmetrical about the XbZb plane. As a result, a cn, look-up table is unnecessary. This is one reason why pseudo stability derivative models of lateral-directional aerodynamics are smaller than true stability derivative models.

r

You might have noticed in Figure 20-24 that pseudo stability derivatives are not true stability derivatives. A pseudo stability derivative is simply the slope of a l i e connecting two points, rather than the slope of a line that is tangent to a curve. This distinction is illustrated in Figure 20-25.

Let's illustrate the procedure for Petermining c,,: and C":,.

Referring to Figure 20-24, we see that Cni is

calculated within the plane defined by the C,, and B axes. In this plane, 6,=0 degrees. In Figure 20- versus B when S,=S,=O degrees. Mach=O.6. a=5

degrees. 25 we have isolated from the C, surface shown in

Figure 20-21 the curve of C, versus p when 6,=0 degrees. This is the curve we use to calculate

C";. For example, suppose we wish to determine Cn: when p = 15 degrees. In Figure 20-25 we see

that Ci, is the slope of the line that connects C,, at p =O degrees to C, at p = 15 degrees. This means

that Ci, is

cn,

.1-

* 6 10 15 B

deg

~igure 20-25 Determining C,' from a a w e of C.

But C,=O when p =O degrees, so the calculation of Ci, at p =15 degrees reduces to

is merely a convenient way to denote the value of c, when p = 15 degrees. We find this

value in the 6,=0 degrees row of Table 20-12, where. we see that C,=O.lU). Consequently, we have c%.lp)


Flying Qualities Flignt Test SinuJcrors 20.6.4 Pseudo Stabfity Derivative Aerodynamic Mod&

Wind tunnel

lldegrees C,+,

@. degrees

0 5 10 15

0.0160 0.0140 0.0120 0.0080

= 0.00800 1 digree

We have entered this value of Cm, in Table 20-14, where we have tabulated C; versus p . Note from

Figure 20-25 that Ci, at p = 15 degrees is quite different from C”, at p = I5 degrees.

We can determine Ci, when fi =5 degrees in a similar manner:

- 0.070 5

--

= 0.0140 I digree

The p = 10 degree entry in Table 20-14 was calculated in the same way. But the p =O degree entry

is an exceptional case. The value of C,,, when p =O degrees is the slope of the tangent to the curve

at p =O degrees. In this case, the slope is 0.0160 per degree.

It is interesting to note that when the curve of C, versus p is a straight line, Cn, is equal to Cn, . When the curve is not a straight line, Ci, and Cn, are different, sometimes decidedly so. This is

evident in Figure 20-25 at p = 15 degrees, where both the signs and magnitudes of Cn; and C., are different.

We see in Table 20-14 that Ci, depends on sideslip angle only, rather than sideslip angle and rudder

deflection. Were we building a stability derivative model, C., would depend on both sideslip angle and rudder deflection. This is another reason why pseudo stability derivative models require less


Flying Qualities Flight Test Sirnuhators 20.6.4 Pseudo Stability Derivative Aerodynamic Models

computer memory than true stability derivative models. The only advantage of casting an aerodynamic model in pseudo stabiliry deriWve form. as opposed to true stability derivative form, is that it requires less computer memory.

Table 20-14 is a small slice of the fill, multi-variable look-up table that would be needed to model the effects of sideslip on yawing moment aerodynamics. Other variables, or dimensions, of the table include Mach number, angle of attack, and dynamic pressure. The general form of the look-up table is ~

C*; =f ( Mach a, B, 4)

where the effect of dynamic pressure, h, is not measured in a wind tunnel, but is calculated based on the predicted flexibility of the airplane.

..

Let's turn our attention now to C i . C' is determined in much the same way that we determined

Cn', . Referring to Figure 20-24, we see that Cn* is determined from curves of C,versus 6, when

sideslip angle is constant. For example, suppose we wish to calculate the value of C' when 6,- 10

degrees and p = 10 degrees. From Figure 20-24 we see that the equation for this calculation is

8, 5

8,

*b

We see that an easy way to calculate Cib is to use Table 20-13, in which we present AC, caused by

rudder deflection. When 6, = 10 degrees and p = 10 degrees, we find in Table 20-13 that AC, = -0.124.

Ci,, then, is given by

-0.124 lo

=-

= -0.0124 I

This value is entered in Table 20-15, where we present Cn;r versus sideslip angle and rudder

deflection. The remaining values in Table 20-15 are calculated in the same way, except when 6,=0

degrees. When 6,=0 degrees, C i is the slope of the tangent to the AC, versus 6, curve at 6,=0

degrees. In this case, the slope is -0.0172 per degree. 8,


Flying Qualities Flighi Test SimuIatori 20.6.4 Pseudo StaMily Derivative Aerodynamic Modelb

Wind tunnel

lldegrees c*+*

0

5

10

15

6,. degrees

@, degrees

0 5 10 15

-0.0120 -0.0130 -0.0172 -0.0175

-0.0100 -0.0120 -0.0144 -0.0164

-0.0080 -0.0100 -0.0124 - -0.0144

-0.o060 -0.0080 -0.0103 -0.0127

""t .-

Egure 20-26 Graphical comparison of and C,.

In Figure 20-26 we present a graphical interpretation of C; . The curve of c,, versus 6,

in Figure 20-26 was taken from Figure 20-23 for the case of p = 10 degree's. Note in Figure 20-26

that, in general, c"+ is not equal to c

Table 20-15 is a small slice of the full, multi- variable look-up table that would be needed to model the effects of rudder deflection on yawing moment aerodynamics. Other variables, or dimensions, of the table include Mach number, angle of attack, aileron deflection, and dynamic pressure. The general form of the look-up table is

%

'r "b.

c";. - f (Mocl2 a, B, a,, a'+?)

A look-up table of the pseudo stability derivative Cn'+ has as many variables as a look-up table of the

stability derivative C, . The same is true of C' and C, . Only the C": look-up table is smaller

than the corresponding stability derivative table. And of course, there is no table of C,, in a pseudo stability derivative model, because C., =O . This is why a pseudo stability derivative model of lateraldirectional aerodynamics may require about one third less memory than a true stability derivative model.

6, "*. 6.

Now let's illustrate how a combination pseudo stability derivative and true stability derivative model of yawing momnt aerodynamics can be used to determine C, . Suppose we want to determine the yawing moment coefficient of a simulated ailplane at the following test condition:


Flying Qualities Flight Test Simu&tom 20.6.4 Pseudo Stability Derivative Aerodynamic Models

. -. p = 5 &pees

a,= 10 degrees a = 5 &pees Mach mrmber = 0.6

R = 15 &grees/second V, = 642 feeflsecond

P-30 degrees/secd

=.26 radiam/second a , = O &pees

= 0.52 radkam/second

To determine C, we will use Equation (20-17), which we repeat here as Equation (20-20):

b C, = Cn;p + -(C,,P + C,,,R) + C' "a. + C* 5 6, (20-20)

Because the test conditions are 0.6 Mach number, a =5 degrees, and a,=o degrees we may use Tables 20-14 and 20-15. FromTable 20-14 we obtain Ca;=0.010140 per degree, and from Table 20-15

we obtain C' = -0.0100 per degree. From simulator look-up tables of C.,. C.,, and Ca:. (which we

have not shown) we obtain C,, = -0.3 per radian, C,=O.o4 per radian, and c* =0.00110 per degree.

When the wingspan, b , is 40 feet, we use Equation (20-20) to calculate

2K

. 5

"8.

C-=C,',p +2y,(C5P+Cn,R)+C' b 80+C' 6, "8. %

= (.0140)(5) + - [(.040)(.52) + (-.30)(.26)] + (.00110)(0) + (-.0100)(10)

= -.a18

2(642)

At the specified test condition the airplane will have a nose left yawing moment.

Although the procedure for calculating pseudo stability derivatives from wind tunnel data is less time consuming than that for determining true stability derivatives, a great deal of work is nevertheless involved. This is a drawback of pseudo stability derivative models.

As you learned in section 20.3.8, an important function of flight test simulators is aerodynamic sensitivity testing. However, pseudo stability derivative models are not easily adapted to sensitivity testing. Recall from section 20.6.3 that we adapted true stability derivative models to sensitivity testing by applying a gain to each derivative in the force or moment coefficient equation. If we pursue the same approach using pseudo stability derivatives we get


Flying Qualities Flight Test Sirnulato& 20.6.4 Pseudo Stability Derivative Aerodynamic Model$

But applying a gain to a pseudo stability derivative is not equivalent to applying the same gain-io the corresponding true stability derivative. For example, setting kl= 1.2 multiplies Ci, by 1.2, but this

is not equivalent to multiplying C*, by 1.2. Calculations must be undertaken to determine how much to change the pseudo derivatives in order to achieve the desired change in the true derivatives. This is inconvenient and time consuming. Hence we may conclude that pseudo stability derivatives are not well suited to aerodynamic sensitivity testing. This is a drawback of pseudo stability derivative models.

Another important function of flight test simulators is aerodynamic model validation, which we will discuss in Chapter 24. When aerodynamic models are designed for flight test simulators, provision must be made for correcting and validating the model. Validating the model consists of making necessary corrections to the wind tunnel predicted pseudo stability derivatives and demonstrating that the corrected model matches flight test results. When the aerodynamics are nonlinear the corrections to pseudo stability derivative models can be troublesome to determine, because flight test results are presenkd in terms of stability derivatives. This is an important drawback of pseudo stability derivative models. However, when the aerodynamics are linear, pseud; stability derivatives are indentical to true stability derivatives. In this case, there is no need to convert from the flight test to the model form.

One method of correcting the aerodynamic model is to replace the inaccurate wind tunnel data with flight test estimates of the real aerodynamics. For example, suppose we determined from flight

testing that the p =5 degree and &,= 15 degree entry in Table 20-15 should be C;,= -0.010 per degree

instead of -0.0080 per degree. We could correct the model by simply replacing -0.0080 in the table with -0.0100. (As you can imagine, this method is not so simple in practice. It requires interpolation, experience, and judgement.) This approach has the advantage of requiring no additional computer memory. But it also suffers from drawbacks. One of these is that once a correction is made, the wind tunnel model is gone. This is more serious than it might seem. It is often desirable to switch back and forth between the wind tunnel model and the flight test validated model. This is useful, for example, when comparing predicted and actual airplane motion on the simulator. Another drawback of replacing wind tunnel aerodynamics with flight test validated aerodynamics is that validating an aerodynamic model is not a one step procedure. Until validation testing is completed, there may be discontinuities between the validated and unvalidated parts of the model. These discontinuities can prove troublesome.

A more convenient method of handling flight test corrections is to add special flight test correction terms to the wind tunnel model. We may visualize this method by modifying the model in the following way:

Flying Q u a l ~ e s Testing 20-65

Flying Qualities Flight Test Simulators 20.6.5 Siunmarg of Advantages and Disadvantages

.. where C: is the correction that must be added to C";, and so on, to make the aerodynamic

model match flight test results. For example, if the predicted wind tunnel value of C,,, at a specified test condition is -0.0130 per degree, and flight test results indicate that the true value is -.0110 per degree, the correction term is

- e-

= - c.I,. cn*bW.. Cm+b-

= -0.0110 - (-0.0130)

= 0.oOu) I degree

Unfoaunately, this approach doubles the computer memory required for the simulator aerodynamic model. For example, the Clb, look-up table must be supplemented by a like-sized C' look-

up table, and so on. This approach also requires more table look-ups and additional mathematical operations. ,


At the outset of this section, we noted that pseudo stability derivative models use computer processing power less efficiently than coefficient models. This is evident from the following relationship:

%-

where C: is the static yawing moment coefficient that is determined from wind tunnel test data. We see that three pseudo stability derivative look-up tables are needed to match a single yawing moment coefficient look-up table. Hence the pseudo stability derivative model often requires more time to perform the lookups. Moreover, after the pseudo stability derivatives have been retrieved from

memory, they must be multiplied by associated variables (for example, C: times a,) and the

products summed to form a yawing moment coefficient. In contrast, in a coefficient model the yawing moment coefficient is ready to use immediately after retrieval. These are drawbacks of a pseudo stability derivative model.

a,

20.6.5 Summary of Advantages and Disadvantages In Table 20-16 we summarize the advantages and disadvantages of the coefficient, stability derivative, and pseudo stability derivative forms of aerodynamic modeling. Although the aerodynamics being modeled can have an affect, the assessment of advantages and disadvantages offered in Table 20-16 generally reflects Flight Test Center experience.


Flying Qualiiies Flight Test Simulators 20.7 Flight Control System Models for Flight Test Simulatok

Easily related to flying qualities

Pseudo Stability stability

Derivative Derivative Form

Coefficient Form

Form

I + -

+

Easy to build

Memory requirements

Efficient use of computer processing power

Adaptabdity to aerodynamic sensitivity testing

Adaptab~ty to aerodynamic model correction and validation

I extracted I + I - Ease with which stabfity derivatives may be

I + = advantage - = disadvantage 0 = neither a significant advantage nor disadvantaze 1 Tabk 20.16 Swunory ofadvwgesnnd disadvanrages of aeiodym’c modcl*rgfOrms.

20.7 Flight Control System Models for Flight Test Siulators We noted at the beginning of section 20.6 that two models are critically important to flying qualities simulators: the aerodynamic model and the flight control system model. In section 20.6 we introduced you to the large amount of work required to build an aerodynamic model from wind tunnel data. As you might imagine, the amount of work required to build a flight control system model depends on the size and complexity of the control system.

Today, most simulators use digital computers to model the flight control system, even when the real flight control system is analog. This means that the flight control system model will be cast in the form of difference equations. We showed you how to create difference equations when we outlined the rudiments of digital flight control system design in Chapter 15. The techniques you learned in that chapter are directly applicable to modeling a flight control system in a simulator.

When the flight control system is digital, it might be possible to transfer some of the code used in the airplane flight control computers to the simulator, although programming language or compiler differences might make this difficult.

In most cases, simulator flight control system models are created from flight control system block diagrams provided by the contractor. These block diagrams are quite similar to the block diagrams we introduced and used in Part III. Yon will find that gain schedules, filter time constants, and other

1


Flying Quulities Flight Test Simulators 20.9 Waypint: Flying Qualities Flight Test Simulators

important details are sometimes omitted from these block diagrams. You must be sure the contractor . =

provides these data.

20.8 Configuring a Flight Test Simulator In Chapter 19 we discussed the importance of configuring flying qualities test airplanes for testing. It is equally important to configure flight test simulators for testing. In sections 20.3 and 20.6 we discussed the use of simulators for aerodynamic sensitivity testing and aerodynamic model validation testing. Flight test simulators should be configured to support these uses. They should have the following capabilities as well:

programmed test inputs variable flight control system parameters flight test head-up display fault simulation and clearing data Pump

' data analysis

Given the power of computer hardware and software, it has become common to have a full suite of data analysis software resident on the simulator computers. This is an important advantage that increases the amount of work that may be accomplished and reduces the time required to accomplish it. Flight test simulators have always included a strip chart capability, but it is now possible to perform a full range of data processing immediately following a maneuver, including stability derivative estimation and fresuency response estimation.

As you learned in section 20.3, flight test simulators are used in many important ways during the course of a flying qualities test program. If the simulator is not properly configured, you will not realm its full potential. The simulation engineers you work with will help you configure your simulator properly.

It is important that the capabilities listed above be easy to use. For example, it should be possible to modify a programmed test input signal, or change a flight control system gain or time constant, or select a failure state quickly and easily. During a test program, the demands on your time will not allow you to spend a significant amount of time making each of the many changes you will want to make. This will be especially true once flight testing begins.

20.9 Waypoint: Hying Qualities Flight Test Simulators In this chapter we briefly described the types of simulators you are most likely to use in flying qualities flight testing. We also explored the meaning and importance of simulator fidelity; outlined a few of the many uses for a flight test simulator; showed why an independent simulator at the Flight Test Center is important; discussed the rudiments of building a simulator; showed how to convert wind tunnel data into a simulator aerodynamic model; and remarked briefly on flight control system models for a simulator.


Flying Qualities Flighi Test Simulators 20.9 Waypoink Flight Test Simulators

..

The types of simi tors we intro ce ;panned the gamut of those you are likely to encounter during a flying qualities test program. These include batch simulators; piloted, ground-based simulators; hardware-in-the-loop simulators; iron bird simulators; and piloted inflight simulators.

Simulator fidelity refers to how closely a simulator matches the airplane it is simulating. We discussed motion fidelity and the pitfalls attendant on trying to achieve motion fidelity, particularly in a ground-based simulator. We discussed other aspects of fidelity as well, sueh as visual fidelity; control stick, rudder pedal, and throttle fidelity; aerodynamic and flight control system fidelity; equations of motion fidelity; cockpit fidelity; and an elusive but important element of fidelity we called "risk fidelity. " Risk fidelity refers to our ability to make pilots flying a simulator respond to hazards or surprises just as they would in a real airplane.

The uses of a flight test simulator include educating the engineers and pilots; handling qualities prediction and evaluation; developing new or modified test maneuvers and analysis techniques; designhg programmed test inputs; test planning; sensitivity testing; performing tests that are too hazardous to conduct in flight; analyzing and correcting deficiencies; augmenting test data; conducting limited hardware-in-the-loop testing; and, in special cases, conducting preflight dress rehearsals.

It is important that an independent flight test simulator be available at the Flight Test Center. Unfortunately, a flight test simulator is often viewed by Air Force procuring agencies and contractors as an unnecessary expense. In fact, however, a flight test simulator and a properly configured test airplane are the two elements of a test program that have the greatest potential for minimizing cost and schedule over-runs. For example, in one test program it was estimated that the cost of the flight test simulator was repaid 120 times over.

Building a simulator is a very big job. We noted that work should begin in time to have the simulator operational six months to a year before first flight of the airplane. We also noted that the first task of the flying qualities engineers is to determine how the simulator will be used. These uses will determine the level of fidelity the simulator must meet.

Two critically important models used in a flight test simulator are the aerodynamic model and the flight control system model. Aerodynamics can be modeled using coefficients, stability derivatives, or pseudo stability derivatives. Often, an aerodynamic model is composed of two or more of these forms. We showed you how to transform wind tunnel test data into each of these modeling forms. We also remarked on the advantages and disadvantages of each form.

Flying Qualities Testing 2049

Flying Qualities Flight Test Sirnuhiom References

. -,

References

20-1. Engineering, Inc., PO Box 2718, hcaster, California, 93539-2718.

Nagy, Christopher J. , "Use of Simulation in Flight Testing" (course notes), Quartic

20-70

.

Flying Qdities Testing

Chapter 20

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Transcript of Chapter 20