# Introduction to Flight Testing

James W. Gregory, Tianshu Liu

Introduction to Flight Testing Introduction to Flight Testing Provides an introduction to the basic flight testing methods employed on general aviation aircraft and unmanned aerial vehicles Introduction to Flight Testing provides a concise introduction to the basic flight testing methods employed on general aviation aircraft and unmanned aerial vehicles for courses in aeronautical engineering. There is particular emphasis on the use of modern on-board instruments and inexpensive, off-the-shelf portable devices that make flight testing accessible to nearly any student. This text presents a clear articulation of standard methods for measuring aircraft performance characteristics. Topics covered include aircraft and instruments, digital data acquisition techniques, flight test planning, the standard atmosphere, uncertainty analysis, level flight performance, airspeed calibration, stall, climb and glide, take-off and landing, level turn, static and dynamic longitudinal stability, lateral-directional stability, and flight testing of unmanned aircraft systems. Unique to this book is a detailed discussion of digital data acquisition (DAQ) techniques, which are an integral part of modern flight test programs. This treatment includes discussion of the analog-to-digital conversion, sample rate, aliasing, and filtering. These critical details provide the flight test engineer with the insight needed to understand the capabilities and limitations of digital DAQ. Key features: Provides an introduction to the basic flight testing methods and instrumentation employed on general aviation aircraft and unmanned aerial vehicles. Includes examples of flight testing on general aviation aircraft such as Cirrus, Diamond, and Cessna aircraft, along with unmanned aircraft vehicles. Suitable for courses on Aircraft Flight Test Engineering. Introduction to Flight Testing provides resources and guidance for practitioners in the rapidly-developing field of drone performance flight test and the general aviation flight test community.

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Introduction to Flight Testing


James W. Gregory

The Ohio State University

Tianshu Liu

Western Michigan University


This edition first published 2021


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Names: Gregory, James W., author. | Liu, T. (Tianshu), author.

Title: Introduction to flight testing / James W. Gregory, The Ohio State University; Tianshu Liu, Western Michigan University.

Description: First edition. | Hoboken, NJ : Wiley, 2021. | Includes bibliographical references and index.

Identifiers: LCCN 2020048350 (print) | LCCN 2020048351 (ebook) | ISBN 9781118949825 (hardback) | ISBN 9781118949795 (adobe pdf) | ISBN 9781118949801 (epub)

Subjects: LCSH: Airplanes–Flight testing–Textbooks.

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> Dedicated to

> Deb, Alina, and Maggie – J. W. G.

> Ruomei and Ranya – T. L.


## About the Authors

James W. Gregory is professor and chair of the Department of Mechanical and Aerospace Engineering at The Ohio State University (OSU). He received his Bachelor of Aerospace Engineering from Georgia Tech in 1999 and his PhD in Aeronautics and Astronautics from Purdue University in 2005. He has been a faculty member at OSU since 2008 and served as Director of OSU's Aerospace Research Center from 2017 to 2020. In 2017, he led a team of research staff and students to set FAI/NAA‐sanctioned world records for speed and distance for an autonomous drone. He teaches classes at OSU on Flight Test Engineering and Introduction to Aerospace Engineering. Prof. Gregory also recorded a series of video lectures on the Science of Flight, produced by the Great Courses. He is an instrument‐rated commercial pilot and holds a remote pilot certificate.

Tianshu Liu is a professor in Department of Mechanical and Aerospace Engineering at Western Michigan University (WMU). He received a PhD in Aeronautics and Astronautics from Purdue University in 1996. He was a research scientist at NASA Langley Research Center from 1999 to 2004. His research focuses on experimental aerodynamics and fluid mechanics, particularly on global measurement techniques for various physical quantities such as pressure, temperature, heat flux, skin friction, velocity, aeroelastic deformation, and aerodynamic force. He teaches classes in aerodynamics and flight testing at WMU.


## Series Preface


The field of aerospace is multidisciplinary and wide‐ranging, covering a large variety of platforms, disciplines, and domains, not merely in engineering but in many related supporting activities. These combine to enable the aerospace industry to produce innovative and technologically advanced vehicles. The wealth of knowledge and experience that has been gained by expert practitioners in the various aerospace fields needs to be passed onto others working in the industry and also researchers, teachers, and the student body in universities.

The Aerospace Series aims to be a practical, topical, and relevant series of books aimed at people working in the aerospace industry, including engineering professionals and operators, engineers in academia, and allied professions such as commercial and legal executives. The range of topics is intended to be wide‐ranging, covering design and development, manufacture, operation and support of aircraft, as well as topics such as infrastructure operations and current advances in research and technology.

Flight testing is a vital part of the certification and validation phase of all new aircraft and is performed to determine or verify the performance and handling qualities. Although the flight characteristics are predicted in the design and development stages of new aircraft programs, the real‐world capabilities are not known until the aircraft is flown and tested. Most aircraft flight testing programs are focused on meeting airworthiness certification requirements and demonstrate all aspects of the flight vehicle's performance and handling characteristics to ensure flight safety.

This book, Introduction to Flight Testing, is aimed at advanced‐level undergraduate students, graduate students, and practicing engineers who are looking for an introduction to the field of flight testing. With a focus on light aircraft and UAVs, the book covers the engineering fundamentals of flight, including the flight environment, aircraft performance and stability and control, combined with the piloting, sensors, and digital data acquisition and analysis required to perform flight tests. This book is a very welcome addition to the Wiley Aerospace Series.

October 2020

> Peter Belobaba, Jonathan Cooper and Allan Seabridge


## Preface


The goal of this book is to provide an accessible introduction to the fascinating and intriguing world of aircraft flight testing. This unique discipline directly straddles the domains of engineering and piloting, requiring knowledge of both the theory and practice of flight. Our target audience is advanced‐level undergraduate students, beginning graduate students, and practicing engineers who are looking for an introduction to the field of flight testing. Flight testing professionals (engineers, pilots, managers, etc.) may also find this to be a helpful resource if they wish to solidify their understanding of the fundamentals beyond what is provided in most other flight testing resources. We have attempted to write this book in an engaging, conversational style that invites the reader into understanding the fundamental principles.

Both authors teach a senior‐year technical elective course at our home universities on the topic of flight test engineering. Within this context, we have found that students best learn the material when they actively engage with flight testing practice. Experiencing flight in an aircraft is the best way to develop a tacit understanding of the principles of flight, to augment and deepen the intellectual knowledge of engineering practice that students receive in the classroom. In working with our senior‐year engineering students, we have developed the following learning objectives for our courses, as well as for this book. Our aim is that readers of this book will:

• Have an appreciation for the purpose, scope, and magnitude of historical and modern flight test programs in the commercial and military aircraft sectors.

• Understand the theoretical foundations of the flight environment, aircraft performance, and stability and control as it applies to flight testing.

• Be familiar with aircraft cockpit instrumentation, supplemental sensors for flight testing, and digital data acquisition techniques.

• Be able to plan a flight test to evaluate the performance or handling qualities of a general aviation or unmanned aircraft.

• Have the ability to coordinate with an experienced pilot to successfully conduct the flight test.

• Have the knowledge and background needed to perform postflight analysis and data reduction.

• Be able to professionally and succinctly communicate the findings of a flight test program via oral and written communication.

• Have a general familiarity with piloting, aviation weather, and flight planning.

Thus, this book is best approached in conjunction with flight in an actual aircraft. No specially instrumented aircraft are needed in order to do most of the flight tests in this book. No exceptional training is needed in order to fly the basic maneuvers described in this book. In fact, all of the procedures described herein are routine maneuvers that are encountered often in piloting practice. An interested reader can simply head to their nearest airport and work with a qualified, professional pilot (e.g., a certified flight instructor) to conduct the flights described here. In our educational contexts, we collaborate with flight instructors in the aviation programs at The Ohio State University and Western Michigan University to conduct flight tests for our students, but any flight instructor would be capable of performing these basic maneuvers.

We must be sure to emphasize that flying an aircraft involves elevated risk compared to other routine activities in daily life. It is critical for the pilot in command to always maintain positive control of the aircraft and to maintain flight within the performance envelope of the aircraft. All operating limitations of the Pilot's Operating Handbook, as well as all regulatory limitations and best practices for safety of flight, must be observed. Flights should be conducted with a minimum crew of two, where the pilot is solely focused on safe operation of the aircraft. Since precise flying is important for acquiring quality data, the pilot should be experienced – a pilot with a commercial license is likely a safe minimum standard for piloting credentials. The second crew member – the flight test engineer – should be dedicated to acquiring flight data and not have any responsibilities related to ensuring safe operation of flight. The flight test engineer is essentially a passenger for these flights, and all piloting authority and responsibility for the flight rest with the pilot in command. Chapter 6 of this book describes the principles of flight test safety and risk management, which form an essential foundation for the flight test profession. Fly safely!

While there are several other resources on flight testing already available, we saw a specific need for this textbook. Some of the existing resources are targeted toward flight testing professionals and may not be as accessible to the general student. Other resources have become dated, with the relatively recent rewrite of airworthiness certification standards for normal category airplanes (Title 14 of the U.S. Code of Federal Regulations, Part 23). In writing this book, we have sought to provide a modern and accessible resource for flight test educators and students, with several unique features that we hope will set it apart as a helpful and leading resource. Our primary audience is engineering students, with the goal of drawing connections between engineering practice and flight testing experience. We have provided guidelines on how to conduct each flight test, which will guide the reader in the flight test planning process. We have also included unique chapters on digital data acquisition and analysis techniques, uncertainty analysis, and unmanned aircraft flight testing. These are all modern topics that are not covered in the flight testing literature, but are now critical topics. And, with the proliferation of smartphones (repurposed as digital data acquisition devices in manned flight testing) and drones, the modern principles of flight testing are more accessible than ever.

The focus of our book is predominantly on light aircraft (small general aviation airplanes) and small unmanned aircraft. We have homed in on this subset of aviation since these aircraft are generally accessible to the public. While our focus is on light aircraft, the principles described here are equally applicable to all regimes of flight testing. This book provides an introduction, while other resources can be consulted for more advanced topics. The discussion here has been tailored to academic classroom instruction to convey the main principles of flight testing, rather than as a “field manual” for definitive best practices in all situations for flight testing. Having said that, we have made a reasonable effort to align the guidance provided here with accepted best practices. Also, we have decided to omit discussions of spin flight testing and flutter flight testing. These are significant and important topics in flight testing practice, but these are hazardous flight tests. We wish to encourage the reader to engage only with the safer dimensions of flight testing as an entry point.

Throughout this book, we'll predominantly use English units. This is primarily because aviation practice in North America has mostly converged on English units. For example, most air traffic control organizations around the world assign altitude in units of feet and airspeed in units of knots. While SI units are generally preferable in science and engineering environments, we'll generally work with the aviation standard. We view this choice as an educational opportunity for the reader to become acquainted with and proficient in multiple unit systems. There is clear pedagogical value in learning how to quickly convert between and track various units – we hope that students and professional engineers alike will become comfortable with all units and how to convert between them. Appendix B includes a range of unit conversion factors and discussion on best practices for handling units in aviation and engineering practice.

Furthermore, we have avoided embedding implied units into equations. This practice can be convenient for some cases when input and output units for a formula are well established and clearly documented – this can facilitate situations where rapid computations are needed without encumbering the analysis with unit conversions. However, in many cases this practice leads to confusion or ambiguity since the input and output units are seldom clearly documented or agreed upon. Another disadvantage of embedded units is that constants must be embedded in the formula, which have no basis on the physics. This can be confusing to a student who is exposed to theory for the first time. Finally, embedded units force the reader into one specific unit system. Our approach with equations that are unit‐agnostic will allow the reader to use either English or SI consistent units as desired. Thus, the assumption throughout this text (unless otherwise specified) is that equations are based on standard, consistent units.

To the reader – thank you for picking up this book. We are passionate about flight testing and are eager to share our deep interest in this domain with you. We hope that this book will be rewarding, enriching, and fascinating.


September 6, 2020

> James W. Gregory

> Columbus, Ohio

> Tianshu Liu

> Kalamazoo, Michigan

## Acknowledgements


The authors are grateful for a wide array of colleagues, collaborators, and students who have shaped our thinking and provided input and feedback on this book.

JG would like to thank Profs. Stacy Weislogel and Gerald M. Gregorek, who as pioneers of educational flight testing in the 1970s were inspirations for this work. Prof. Hubert C. “Skip” Smith was also generous with ideas and resources along the way. The flight education department and colleagues in Aviation at The Ohio State University have been extremely helpful in providing tactical support over the years – D. Gelter, D. Hammon, B. Mann, S. Morgan, S. Pruchnicki, C. Roby, B. Strzempkowski, and S. Young. Special thanks go to Profs. Jeffrey Bons and Cliff Whitfield, who helped review significant portions of a near‐final version of the manuscript. (Any remaining errors or inaccuracies are solely the responsibility of the authors). Portions of this book were written in 2014–15 while JG was on sabbatical at the Technion in Israel; the support of Ohio State University and the Fulbright foundation is gratefully acknowledged.

JG also wishes to extend special thanks to Dr. Matt McCrink, who assisted with many of the flight tests presented in this book and coauthored the final chapter on UAV flight testing. He has been an instrumental sounding board and key partner throughout this project.

TL would like to thank M. Schulte, M. Mandziuk, S. Yurk, M. Grashik, S. Woodiga, P. Wewengkang, D. M. Salazar, and WMU's College of Aviation.

Numerous colleagues, including M. Abdulrahim, J. Baughn, K. Colvin, C. Cotting, K. Garman, B. Gray, C. Hall, J. Jacob, J. Kidd, K. Kolsti, J. Langelaan, B. Martos, N. Sarigul‐Klijn, R. Smith, J.P. Stewart, A. Suplisson, A. Tucker, J. Valasek, C. Walker, O. Yakimenko, and M. Yukish, helped influence the presentation of ideas in this book. The Flight Test Education Workshop, hosted by the USAF Test Pilot School, was a particularly helpful resource for materials and connections. A. Bertagnolli of Continental Aerospace Technologies (Continental Motors) and J. J. Frigge of Hartzell Propeller generously provided data and resources for the text. C. Daniloff, K. King, R. Heidersbach, H. Henley, K. King, N. Lachendro, H. Rice, H. Sakaue, B. Stirm, and R. Winiecki gracefully allowed their images or likenesses to be published in this book.

JG and TL also wish to thank their doctoral advisor, Prof. J. P. Sullivan of Purdue University, for his encouragement for us to pursue and finish this project.

Finally, JG and TL especially thank their families for their patience and support over the many years it took to complete this project.


## About the Companion Website


The companion website for this book is at

https://www.wiley.com/go/flighttesting


Scan this QR code to visit the companion website.


## 1. Introduction

Flight testing is seemingly the stuff of legends, with tales of derring‐do and bravery, spearheaded by great pilots such as Yeager, Armstrong, Glenn, and others. But what exactly is flight testing all about? What is being tested, and why? What's the difference between a test pilot and a flight test engineer? Is flight testing an inherently dangerous or risky activity?

With this book, we hope to show that flight testing is both exciting and accessible – we hope to make flight testing understandable and achievable by the typical undergraduate aerospace engineering student. The basic principles of flight testing can be explored in any aircraft, all the while remaining safely well within the standard operating envelope of an aircraft. This book will introduce students to the principles that experienced flight test engineers work with as they evaluate new aircraft systems.

Flight testing is all about determining or verifying the performance and handling qualities of an aircraft. These flight characteristics may be predicted in the design and development stages of a new aircraft program, but we never really know the exact capabilities until the full system is flown and tested. Most aircraft flight testing programs are focused on airworthiness certification, which is the rigorous demonstration of all facets of the flight vehicle's performance and handling characteristics in order to ensure safety of flight.

We also wish to highlight that most flight testing should not incur the levels of risk and danger that we associate with the great test pilots of the 20th century. Their bravery was indeed laudable, since they ventured into flight that no human had done before, such as breaking the “sound barrier” or being the first person to walk on the Moon. But, if done correctly, flight testing should be a methodical process where risks are managed at an acceptable level, where human life and property are not exposed to undue risk. Even more hazardous flight testing such as flutter boundary determination or spin recovery should be done in a methodical, well‐controlled manner that mitigates risk. In fact, most flight testing, at least to an experienced professional, can be almost mundane (Corda 2017).

Nor is flight testing an individualistic activity where an intrepid pilot relies solely on their superlative piloting skills to push the aircraft to its limits, as suggested by the caricature in Figure 1.1. Quite the contrary, flight testing is a team effort with many individuals carefully contributing to the overall success of a flight testing program (see Figure 1.2). There is, of course, a pilot involved whose job it is to fly the aircraft as precisely and accurately as possible to put the aircraft through the necessary maneuvers to extract the needed performance or handling data. If an aircraft can carry more than just the pilot, then there is almost always a flight test engineer on board. The flight test engineer is responsible for preparing the plan for the flight test and for acquiring the data in flight while the pilot puts the aircraft through the required maneuvers. Beyond the role of the flight test engineer, there are many others involved – including those who monitor systems and downlinked data on the ground, data analysts who post‐process and interpret the data after the test is complete, and program managers who set the strategic direction for the program and make budgetary decisions.


Figure 1.1 The caricature view of flight test is of an individualistic, cowboy‐like, rugged test pilot who single‐handedly defies danger. Here, Joe Walker playfully boards the Bell X‐1A in a moment of levity.

Source: NASA.


Figure 1.2 A more realistic view of the people behind flight testing – a team effort is required to promote safety and professionalism of flight. Depicted here is the team of NACA scientists and engineers who supported the XS‐1 flight test program.

Source: NASA.


Flight testing is a critical endeavor in the overall design cycle of a new aircraft system. The main objective is to prove out the assumptions that are inherent to every design process and to discover any hidden anomalies in the performance of the aircraft system. Aircraft design typically proceeds by drawing upon historical data to estimate the performance of a new aircraft concept, but there is always uncertainty in those design estimates. The initial stages of design have very crude estimates made for a wide range of parameters and theories applied to the design. Over time, the design team reduces the uncertainty in the design by refining the analysis with improved design tools and higher‐fidelity (more expensive!) analysis, wind tunnel testing, and ground testing of functional systems and even the entire aircraft. But, then the moment of truth always comes, where it is time for first flight of the aircraft. It is at this point that the flight test team documents the true performance of the airplane. If differences arise between actual and predicted performance, minor tweaks to the design may be needed (e.g., the addition of vortex generators on the wings). Also, the insight gleaned from flight testing is documented and fed back into the design process for future aircraft.

This chapter will provide a brief overview of the flight testing endeavor through a historical anecdote that illustrates the key outcomes of flight testing, how flight testing is actually done, and the roles of all involved. Following this, we'll take a look at the various kinds of flight testing that are done, with a particular emphasis on airworthiness certification of an aircraft, which is the main objective of many flight testing programs. We'll then conclude this chapter with an overview of the rest of the book, including our objectives in writing this book and what we hope the reader will glean from this text.

### 1.1 Case Study: Supersonic Flight in the Bell XS‐1

A great way to learn about the essential elements of a successful flight test program is to look at a historical case study. We'll consider the push by the Army Air Forces (AAF) in 1947 to fly an aircraft faster than the speed of sound. Along the way, we'll pick up some insight into how flight testing is done and some of the values and principles of the flight test community.

At the time, many scientists and engineers did not think that supersonic flight could be achieved. They observed significant increases in drag as the flight speed increased. On top of that, there were significant loss‐of‐control incidents where pilots found that their aircraft could not be pulled out of a high‐speed dive. These highly publicized incidents led some to conclude that the so‐called “sound barrier” could not be broken. We now know, however, that this barrier only amounted to a lack of insight into the physics of shock–boundary layer interaction, shock‐induced separation, and the transonic drag rise, along with a lack of high‐thrust propulsion sources to power through the high drag. Scientific advancements in theoretical analysis, experimental testing, and flight testing, along with engineering advancements in propulsion and airframe design, ultimately opened the door to supersonic flight.

In a program kept out of public sight, the U.S. Army Air Forces, the National Advisory Committee for Aeronautics (NACA, the predecessor to NASA), and the Bell aircraft company collaborated on a program to develop the Bell XS‐1 with the specific intent of “breaking the sound barrier” to supersonic flight. (Note that the “S” in XS‐1 stands for “supersonic”; this letter was dropped early in the flight testing program, leaving us with the commonly known X‐1 notation.) The XS‐1 (see Figure 1.3) was a fixed‐wing aircraft with a gross weight of 12,250 lb, measured 30‐ft 11‐in. long, had a straight (unswept) wing with an aspect ratio of 6.0 and a span of 28 ft, and an all‐moving horizontal tail (a detail that we'll soon see was important!). The XS‐1 was powered by a four‐chamber liquid‐fueled rocket engine producing 6000 lb of thrust. The overarching narrative of the program is well documented in numerous historical and popular sources (e.g., see Young 1997; Gorn 2001; Peebles 2014; Hallion 1972; Hallion and Gorn 2003; or Wolfe 1979), but we'll pick up the story in the latter stages of the flight test program at Muroc Army Airfield, positioned on the expansive Rogers Dry Lake bed that is today the home of Edwards Air Force Base and NASA Armstrong Flight Research Center.


Figure 1.3 Three‐view drawing of the Bell XS‐1.

Source: NASA, X‐1/XS‐1 3‐View line art. Available at http://www.dfrc.nasa.gov/Gallery/Graphics/X‐1/index.html.


The XS‐1 had an aggressive flight test schedule, with not too many check‐out flights before going for the performance goal of supersonic flight. The extent of the test program was actually a matter of contentious debate between the AAF, the NACA, and Bell. In the end, Bell dropped out of the mix for contractual and financial reasons, and the NACA and AAF proceeded to collaborate on the flight test program. But the continued collaboration was not without tension. The AAF leaders and pilots continually pushed for an aggressive flight test program, making significant steps with each flight. The NACA, on the other hand, advocated for a much slower, methodical pace where substantial data would be recorded with each flight and carefully analyzed before proceeding on to the next boundary. In the end, the AAF vision predominantly prevailed, although there was a reasonable suite of instrumentation on board the aircraft. The XS‐1 was outfitted with a six‐channel telemeter, where NACA downlinked data on airspeed, altitude, elevator position, normal acceleration, stabilizer position, aileron position, and elevator stick force, along with strain gauges to record airloads and vibrations (Gorn 2001, p. 195). On the ground, the NACA crew had five trucks to support the data acquisition system – one to supply power, one for telemetry data, and three for radar. The radar system was manually directed through an optical sight, but if visual of the aircraft was lost, the radar system could be switched to automatic direction finding (Gorn 2001, pp. 187–188).

To lead the flying of the aircraft toward the perceived “sound barrier,” the AAF needed a pilot with precision flying capabilities, someone who was unflappable under pressure, and someone with scientific understanding of the principles involved. The Army turned to Captain Charles E. “Chuck” Yeager – a young, 24‐year‐old P‐51 ace from World War II – for the honor and responsibility of being primary pilot. According to Colonel Albert Boyd who selected him, Yeager had impeccable instinctive piloting skills and could work through the nuance of the aircraft's response to figure out exactly how it was performing (Young 1997, p. 41). Not only could he fly with amazing skill, but the engineering team on the ground loved him for his postflight debriefs. Yeager was able to return from a flight and relate in uncanny detail exactly how the aircraft responded to his precise control inputs, all in a vernacular that the engineering staff could immediately appreciate (Peebles 2014, p. 29). But it wasn't just Yeager doing all of the work – he had a team around him. Backing him up and flying an FP‐80 chase plane was First Lieutenant Robert A. “Bob” Hoover, who was also well known as an exceptional pilot. Captain Jackie L. “Jack” Ridley, an AAF test pilot and engineer with an MS degree from Caltech, was the engineer in charge of the project. Others involved included Major Robert L. “Bob” Cardenas, pilot of the B‐29 Superfortress carrier aircraft and officer in charge, and Lieutenant Edward L. “Ed” Swindell, flight engineer for the B‐29. Backing up these AAF officers was Richard “Dick” Frost, a Bell engineer and test pilot who already had flight experience in the XS‐1 and got Yeager up to speed on the intricacies of the aircraft. This cast of characters is depicted in Figure 1.4.

Beyond this core group of military professionals was a team of NACA scientists and engineers led by Walt Williams (see Figure 1.2). This team was focused predominantly on understanding the flight physics in this exploratory program, providing deep technical insight and support to the Air Force crew. Yet, this objective was inherently at odds with the AAF's stated desire to push to supersonic flight as quickly and safely as possible. This tension was aptly described by Williams: “We were enthusiastic, there is little question. The Air Force group – Yeager, Ridley – were very, very enthusiastic. We were just beginning to know each other, just beginning to work together. There had to be a balance between complete enthusiasm and the hard, cold facts. We knew that if this program should fail, the whole research airplane program would be set back. So, our problem became one of maintaining the necessary balance between enthusiasm and eagerness to get the job completed with a scientific approach that would assure success of the program. That was accomplished” (Gorn 2001, pp. 194–195).


Figure 1.4 The Air Materiel Command XS‐1 flight test team, composed of (from left to right): Ed Swindell (B‐29 Flight Engineer), Bob Hoover (XS‐1 Backup and Chase Pilot), Bob Cardenas (Officer‐in‐charge and B‐29 Pilot), Chuck Yeager (XS‐1 Pilot), Dick Frost (Bell Engineer), and Jack Ridley (Project Engineer).

Source: U.S. Air Force.


In the run‐up to the first supersonic flight, the team carefully pushed forward. On Yeager's first powered flight on August 29, 1947, he accelerated up to Mach 0.85, exceeding the planned test point of Mach 0.8. This negated NACA's need to acquire telemetered data in the Mach 0.8–0.85 range, leading to further tension between Yeager and Williams. In Yeager's words, “They [the NACA engineers and technicians] were there as advisers, with high‐speed wind tunnel experience, and were performing the data reduction collected on the X[S]‐1 flights, so they tried to dictate the speed in our flight plans. Ridley, Frost, and I always wanted to go faster than they did. They would recommend a Mach number, then the three of us would sit down and decide whether or not we wanted to stick with their recommendation. They were so conservative that it would've taken me six months to get to the [sound] barrier” (Young 1997, p. 51 – quoted from Yeager and Janos (1985), p. 122).

Yeager was admonished by Colonel Boyd to cooperate more carefully with the NACA technical specialists and to follow the test plan. This led to careful preflight briefings that, while Yeager considered to be tedious, were essential to flight safety and accomplishment of the test objectives. At each briefing, Williams would review the lessons learned from the previous flight and detail the objectives of the upcoming mission (Gorn 2001, pp. 195–196).

As Yeager flew at progressively higher flight speeds, he noticed significant changes in the trim condition of the aircraft. At certain Mach numbers, the trim condition would change nose‐up, and at other Mach numbers it would trend toward nose‐down, all accompanied by buffeting at various flight conditions. For example, on one flight at Mach 0.88 and 40,000 ft, Yeager was unable to put the aircraft into a light stall (even with the stick full aft), due to the lack of control authority. Then, on October 10, 1947, Yeager piloted another mission in a series of powered flights to ever‐higher Mach numbers to test the response of the aircraft in this untested regime. After accelerating up to an indicated Mach number of 0.94 at an altitude of 40,000 ft, Yeager found that he had lost virtually all pitch control! He moved the control stick full fore and aft, yet obtained very little pitch response. Fortunately, the XS‐1 was still stable at this flight condition, if not controllable. At this point, Yeager cut off the engines and came back for a landing on the expansive Rogers lakebed (Young 1997).

All of these various anomalies were due to compressibility effects, which were only poorly understood at the time. As the aircraft exceeded the critical Mach number, shock waves would form at various locations on the aircraft body. Furthermore, these shock waves could move substantially, with only a minor adjustment in freestream Mach number. Since there is a significant pressure gradient across a shock wave, this could result in dramatic changes in the forces and moments produced on control surfaces, and the strong pressure gradient across the shock would often lead to boundary layer separation. Thus, if a shock happened to be present at a hinge line for the elevator, the shock‐induced boundary layer separation would create a thick unsteady wake flow over the elevator, causing the dynamic pressure on this control surface to drop dramatically and the elevator to lose effectiveness. With some foresight, researchers at NACA and designers at Bell anticipated this eventuality and designed the XS‐1 to enable pitch control by moving the incidence angle of the entire horizontal tail (rather than inducing pitch changes using the elevator alone). So, as Yeager and Ridley discussed the phenomena occurring on October 10 and earlier, Ridley encouraged Yeager to adjust the horizontal tail angle of incidence to achieve pitch control, instead of using the elevator.

The plan for the next flight was to go for it – Yeager's intent was to fly supersonic. However, with the technical uncertainty associated with loss of elevator control and shock‐induced buffeting, the NACA engineering team admonished Yeager to not exceed Mach 0.96 unless he was completely certain that he could do so safely. Beyond the NACA team, however, Jack Ridley was the one whom Yeager trusted the most. Ridley thought Yeager would be just fine controlling pitch with the moving horizontal tail, actuating it in increments of a quarter or a third of a degree to achieve pitch control without using the elevator. Ridley explained, “It may not be much, and it may feel ragged to you up there, but it will keep you flying” (Young 1997, p. 56). Yeager trusted Ridley implicitly – much more so than the NACA team. He later recounted, “I trusted Jack with my life. He was the only person on earth who could have kept me from flying the X [S]‐1” (Young 1997, p. 56).

So, on the morning of October 14, 1947, Yeager set out with his team to fly faster than Mach 1. With Cardenas at the controls of the B‐29, the Superfortress carried the Bell XS‐1 up to altitude. On the way up, Bob Hoover and Dick Frost joined up in formation in their FP‐80s. Hoover positioned himself in the “high chase” position: 10 mi ahead of the B‐29 at an altitude of 40,000 ft, to give Yeager an aiming point as he climbed and accelerated in the XS‐1. Frost joined up slightly to the right of and behind the B‐29 in order to observe the rocket firing and drop of the XS‐1.

When everyone was ready, Cardenas put the B‐29 in a slight dive and started a countdown: “10‐9‐8‐7‐6‐5‐3‐2‐1” (yes, he skipped “4”!, as he often skipped a number on these flights) and pulled the release mechanism at 10:26 a.m. an altitude of 20,000 ft and an airspeed of 250 knots. This airspeed was slightly lower than planned, causing the XS‐1 to nearly stall. Yeager pitched the nose down to regain airspeed and then lit all four burners to rapidly accelerate upward. As he breezed past the high‐chase FP‐80, Hoover was able to snap the world‐famous photo of Yeager's flight (Figure 1.5) as the XS‐1 continued going faster and higher. Yeager then shut down two of the rocket chambers in order to keep the vehicle's acceleration in check. Accelerating through Mach 0.83, 0.88, and 0.92, he tested the aircraft's response to horizontal stabilizer control. With the small increments of a quarter or a third of a degree that Ridley recommended, Yeager was able to maintain effective control of the aircraft. Then, as Yeager recounted in his postflight report: “At 42,000' in approximately level flight, a third cylinder was turned on. Acceleration was rapid and speed increased to .98 Machi. The needle of the machmeter fluctuated at this reading momentarily, then passed off the scale. Assuming that the off‐scale reading remained linear, it is estimated that 1.05 Machi was attained at this time. Approximately 30% of fuel and lox remained when this speed was reached and the motor was turned off” (Young 1997, p. 75).


Figure 1.5 Yeager accelerates in the Bell XS‐1 on his way to breaking the “sound barrier” on October 14 1947.

Source: NASA.


Yeager had done it! As mentioned in his postflight report, his Machmeter indications were a bit unusual. In fact, during the flight he radioed: “Ridley! Make another note. There's something wrong with this Machmeter. It's gone screwey!” (Young 1997, p. 73). That radio transmission heralded the dawn of a new era in aviation to supersonic speeds and well beyond. After maintaining supersonic flight for about 15 seconds, he shut down the rocket motors, performed a 1‐g stall, and descended for a landing on Rogers dry lakebed.

Postflight analysis of the data, including corrections of the Machmeter reading for installation error, revealed that Yeager had reached a maximum flight Mach number of 1.06. A reproduction of this data is shown in Figure 1.6, where the initial jump in total and static pressures heralded the formation of a shock wave in front of the probe tip, causing a loss of total pressure. This is the characteristic “Mach jump” experienced by every Machmeter as the aircraft accelerates to supersonic speeds.

There are a number of interesting and revealing features of this story that can tell us something about flight testing. First, we see that this endeavor was anything but an individual effort. There was a large team with many players involved – pilots, engineers, managers, analysts, range safety officers, and so on. In this particular case, the flight test program was a collaboration between two separate organizations – the AAF was leading the program execution, and were supported by NACA's technical experts. Even though there was tension between these two groups, they were able to rise above those difficulties to work together in an effective manner to achieve the test objectives.

The source of the tension was inherently due to different test objectives – the AAF crew was tasked with breaking the sound barrier as quickly and safely as possible, while the NACA team was focused on developing a scientific understanding of transonic and supersonic flight, requiring a slower and more methodical approach. Flight test programs sometimes have such competing objectives in mind, which requires deft coordination and program management in order to ensure safety of flight and accomplishment of the test objectives. There is always a tension between programmatic needs, budget, and safety.


Figure 1.6 Plot of the total and static pressure for the first supersonic flight of the XS‐1 on October 14 1947.

Source: Data from NASA.


Another hallmark of successful flight testing is the careful probing of the edges of the flight envelope. Notice how the team approached the uncertain conditions associated with loss of control and buffeting. They gingerly pushed the Mach limits higher and higher, with the hope that any loss‐of‐control situation could be quickly recovered from. Despite the accelerated nature of the test program, the team took the time to carefully analyze the data and debrief after each flight. This was essential for gleaning insight from each test condition and informing the next step in the flight test program. They took an incremental buildup approach – starting from low‐risk flights with known characteristics and carefully advancing to higher‐risk flights, where the flight characteristics were unknown and potentially hazardous.

Also note how the aircraft was instrumented beyond what a normal production aircraft would have been. In fact, the record‐setting XS‐1 (the first airframe built) was only lightly instrumented compared to its sister ship, the second airframe off the production line, which was targeted for a much more detailed exploration of supersonic flight by the NACA team. This instrumentation is critical for understanding exactly what is happening during flight and preserving a record for postflight analysis. The analytical work was done by a large team of engineers, technicians, and, in that day, human “computers” who did many of the detailed computations of the data (see Figure 1.2).

After some initial renegade flying by Yeager, the flight test team settled into a rhythm of carefully planned and executed flights. Before each flight they carefully planned the objectives and specific maneuvers to fly on the next mission. The injunction was that the flight must proceed exactly as planned, with specific plans for various contingencies and anomalies. This culture of flight testing is absolutely essential for the safety and professionalism of the process. One common phrase captures this mentality of flight testing: “plan the flight, and fly the plan.”

This initial foray into exploring the flight testing program of the XS‐1 illustrates many of the hallmarks of flight test programs. We'll next discuss some of the different kinds of flight testing being done today. Clearly, not every flight test program is as ambitious or adventurous as the XS‐1 program, but a common objective is to answer the remaining unknown questions that are always present in an aircraft development program, even after rigorous design work backed up by wind tunnel testing and computational studies.

### 1.2 Types of Flight Testing

There are several different kinds of flight testing, driven by the objective of a particular program. These motivations include scientific research, development of new technologies or experimental capabilities, evaluation of operational performance, or airworthiness certification of new aircraft for commercial use. Other kinds of flight tests include production flight test (first flight of a new airframe of an already certified type, to verify compliance with design performance standards), systems flight test (new systems installed, new external stores on a fighter aircraft that must be tested for separation, new avionics systems), and post‐maintenance test flight. Here, we'll focus our attention on flight testing for scientific research, assessment of experimental technologies, developmental test and evaluation, operational test and evaluation, and airworthiness certification programs. Other perspectives on the different kinds of flight testing are provided by Kimberlin (2003), Ward et al. (2006), or Corda (2017).

#### 1.2.1 Scientific Research

In many instances, the highest‐quality scientific research can only be done in actual flight. Even though wind tunnels are commonly available, results from these facilities are always limited in some way – facility effects such as streamwise pressure gradients in the test section, wall boundary layer effects, test section blockage, turbulence intensity level, constraints on model size, lack of Mach and/or Reynolds scaling, etc. are always present (see Tavoularis 2005 or Barlow et al. 1999 for a discussion of wind tunnels and their limitations). Similarly, computational fluid dynamics simulations are inherently limited in their ability to model viscous, unsteady separated flows, particularly when the model – such as a full aircraft – is large (see Cummings et al. 2015 for the limitations on computational aerodynamics). Grid resolution, turbulence modeling strategies, and time‐accurate solutions will always need validation of some kind. Thus, the ultimate proof of scientific principles associated with flight is to actually conduct experiments in flight.

The range of scientific experiments that can be studied via flight testing can be very broad and conducted by government labs, universities, and industry. University flight test efforts have included Purdue University's development of pressure‐sensitive paint (PSP) for in‐flight measurements of chordwise surface pressure distribution on an aircraft wing (Figure 1.7). The advantage of PSP is that there is minimal flow intrusiveness, compared to the traditional pressure belts mounted on top of the wing, which are banded and flexible tubes. Furthermore, it is much simpler to instrument the aircraft with PSP, since no tubing has to be run into the fuselage and connected to pressure transducers. In fact, the production Beechjet 400 shown in Figure 1.7 was returned to normal flight under its regular airworthiness certification immediately following flight testing (Lachendro 2000).

Another leading flight test program for scientific research is the University of Notre Dame's Airborne Aero‐optics flight research program (Jumper et al. 2015). Researchers at Notre Dame, led by Prof. Eric Jumper and Prof. Stanislav Gordeyev, study approaches for correcting optical aberrations to laser beams propagating through unsteady shear flows and turbulence. Their active correction schemes allow them to focus a laser beam emitted from one aircraft on the fuselage of a target aircraft such as the Dassault Falcon 10 shown in Figure 1.8. These concepts are used for applications ranging from optical air‐to‐air communications to directed energy for military applications.

The US government is also active with scientific research enabled by flight testing programs. One notable example is NASA's F‐18 high alpha research vehicle (HARV). The goal of the first phase of this program was to understand vortex formation, trajectory, and breakdown on the F‐18 operated at high angle of attack. The specially instrumented F‐18 had tufts (short pieces of yarn) taped to the top of the wing, smoke tracer particles released from orifices near the nose, dye flow visualization, and hundreds of pressure taps. These various techniques were used to study local flow separation and vortex trajectories. In‐flight measurements, shown in Figure 1.9, clearly documented the formation of vortices on the leading‐edge extension (LEX) of the F‐18 at high angle of attack, the trajectory of these vortices, and the specific location of vortex breakdown. The vortex breakdown phenomenon, when occurring in the vicinity of the aft tail, led to significant tail buffeting and issues with fatigue (see Fisher et al. 1990).


Figure 1.7 Inspection of pressure‐sensitive paint on Purdue University's Beechjet 400 following a flight test in 1999 (depicted left to right are Hirotaka Sakaue, Brian Stirm, and Jim Gregory).

Source: Photo courtesy of Nate Lachendro.


Figure 1.8 Notre Dame's Dassault Falcon 10.

Source: U.S. Air Force.


Figure 1.9 Smoke and tuft flow visualization on the NASA F‐18 High Alpha Research Vehicle at an angle of attack of 20°.

Source: NASA.

#### 1.2.2 Experimental Flight Test

Now, we turn our attention from basic scientific and engineering studies to development and test of new vehicle concepts. NASA Armstrong Flight Research Center (formerly known as NASA Dryden) has led the way over the years with this type of flight research (for a good historical overview of NASA's many flight research programs, see Gorn 2001 or Hallion and Gorn 2003). This type of flight testing is all about pushing the boundaries of what is possible, through development and demonstration of new flight technologies. Beyond the Bell XS‐1 discussed earlier, there are numerous flight research programs that the US Government has conducted (Miller 2001; Jenkins et al. 2003). These cutting‐edge aircraft are generally classified as X‐planes, with the goal of proving out new technologies or advanced concepts (see Figure 1.10). The Bell XS‐1 was the first aircraft in this distinguished lineup, which includes over 60 aircraft (and counting!). Many of these X‐planes led to successful production flight vehicles after a period of focused flight testing (see Miller 2001; Jenkins et al. 2003; Corda 2017).

One interesting example is the X‐wing project, which had the goal of improving the forward flight speed of helicopters. This interesting vehicle, the Sikorsky S‐72 shown in Figure 1.11, is a hybrid between a fixed wing aircraft and a traditional rotorcraft. It could take off vertically like a traditional helicopter, but then its rigid rotors could be stopped mid‐flight as the aircraft transitioned from vertical flight to forward flight. Instead of articulating the rotor blades as a traditional helicopter does, the S‐72 used compressed air blown from the edges of the blades to achieve lift control (called circulation control – see Reader and Wilkerson 1977 for details). This innovative aircraft from the early 1980s has paved the way for high‐speed helicopters today, such as the Sikorsky S‐97 Raider or the Airbus RACER program.


Figure 1.10 Early X‐planes, including the Douglas X‐3 Stiletto (center) and (clockwise, from lower left) Bell X‐1A, Douglas D‐558‐1 Skystreak, Convair XF‐92A, Bell X‐5, Douglas D‐558‐2 Skyrocket, and the Northrop X‐4 Bantam.

Source: NASA.


Figure 1.11 Sikorsky S‐72 X‐wing testbed aircraft.

Source: NASA.


Vehicle flight testing programs are also pushing into the domain of unmanned aircraft systems (UAS), commonly known as drones. For example, The Ohio State University developed and flight tested the Avanti UAS, which is a 70‐lb jet capable of autonomous, unmanned, high‐speed flight (Figure 1.12). This flight vehicle featured dual‐redundant radio control links and a third independent satellite communications link, to provide robust beyond‐line‐of‐sight flight. Flight research with this vehicle assessed the robustness of the control links, along with adaptive control laws for real‐time in‐flight system identification (see Warwick 2017; McCrink and Gregory 2021; or Chapter 16 for details). In the midst of the flight testing program, the Ohio State team set official world records for speed (147 mph) and out‐and‐back distance (28 mi) of an autonomous unmanned aerial vehicle (UAV), as certified by the Fédération Aéronautique Internationale (FAI) and the National Aeronautic Association (NAA).


Figure 1.12 The Ohio State University's Avanti jet unmanned aircraft system.

Source: Photo courtesy of Kamilah King.

#### 1.2.3 Developmental Test and Evaluation

Within the US military, a significant amount of time and energy are invested in development test and evaluation (DT&E) flight testing. This aspect of flight testing involves a careful assessment of how an aircraft flies, including evaluation of aircraft performance, stability, and handling qualities. DT&E also includes performance assessment of new weapons, new software, and new airframes. These tests are centered on assessment of compliance with performance standards and focus on identifying anomalies in new systems. Test pilots (see Figure 1.13) push the performance limits of the system and are often involved in test planning very early in the design cycle. For example, if a new weapon system is designed for an aircraft, the developmental test pilot will evaluate the separation characteristics, compatibility of the new weapon with the aircraft system across a wide range of flight conditions, and evaluation of flutter flight characteristics. This testing and evaluation are done through a gradual build‐up approach that minimizes (but does not eliminate) risk.

#### 1.2.4 Operational Test and Evaluation

Operational test and evaluation (OT&E) involves assessment of an air vehicle's performance under representative operational conditions. This often includes operation on different runways under different conditions (e.g., rain, sleet, snow, etc.) or at high‐density altitude (high elevation, hot day). Operational testing also involves determination of crosswind limits on landing and taxiing operations. Aircraft manufacturers will also assess aircraft system robustness and reliability under a wide range of extreme weather conditions, including heat, cold, and icing.


Figure 1.13 Maj Rachael Winiecki, a developmental test pilot with the 461st Flight Test Squadron at Edwards Air Force Base, and the first F‐35 female test pilot. Also shown is Airman 1st Class Heather Rice, a crew chief with the 412th Aircraft Maintenance Squadron.

Source: U.S. Air Force.

#### 1.2.5 Airworthiness Certification

Airworthiness certification is the process by which an aircraft is demonstrated to conform to approved design principles and that it is in a condition for safe operation. But what constitutes safe flight? This generally involves an insignificant hazard to people or property on the ground and minimal hazard to the occupants of the aircraft. Typically, a government's civil aviation authority, such as the Federal Aviation Administration (FAA) in the United States, grants an airworthiness certificate to an applicant submitting reports that document airworthiness for a new aircraft type. This process can be lengthy, involving flight testing to document aircraft performance and demonstrate compliance with safety standards.

In the United States, the regulatory authority for the FAA to certify the airworthiness of light aircraft is Title 14 of the Code of Federal Regulations (“Aeronautics and Space”), Chapter I (“Federal Aviation Administration, Department of Transportation”), Subchapter C (“Aircraft”), Part 23 (“Airworthiness Standards: Normal Category Airplanes”) – we'll refer to this as 14 CFR §23 or simply part 23 (U.S. Code of Federal Regulations 2021). Part 23 covers the certification standards for general aviation aircraft, which have a maximum takeoff weight of 19,000 lb or less and carry 19 or fewer passengers. Since the scope of this book focuses on light aircraft, Part 23 is most relevant for our purposes. The subpart that is most relevant for flight testing is Subpart B (14 CFR §23.2100 through §23.2165), which defines the requirements for flight testing of aircraft for airworthiness certification.

Aircraft certified under Part 23 are grouped into different certification and performance levels based on number of passengers that can be carried and flight speed (14 CFR §23.2005), which are summarized in Table 1.1. Each level indicates a higher hazard, and a correspondingly higher bar is set to mitigate the risks associated with those hazards. Aircraft at the higher certification levels and higher performance levels will have higher standards to meet for certification.

Part 23 details the standards of safe flight that must be met for an aircraft to be certified as airworthy by the FAA, organized into broad categories of performance metrics and flight characteristics. Performance metrics include defining limits on the aircraft weight and center of gravity position, the stall speed of the aircraft under various operating conditions, takeoff performance, climb performance, glide performance, and landing distance required. The flight characteristics for certification include demonstration that the airplane is controllable and maneuverable; that the airplane can be trimmed in flight; that it has static and dynamic longitudinal, lateral, and directional stability; that the aircraft has controllable stall characteristics in all maneuvers and that sufficient stall warning is provided; that spins are recoverable; that the airplane has controllable ground handling characteristics; and that vibration and buffeting do not interfere with control of the airplane or cause excessive fatigue. If certification is requested for flight into known icing conditions, then the aircraft performance and handling characteristics must be shown to the same level of safety even in icing conditions. This textbook provides an introduction to the underlying principles for some of these flight tests; more detailed information is available from Kimberlin (2003) or FAA Advisory Circulars (2003, 2011).


Table 1.1 Airworthiness certification levels defined by part 23.

Source: Based on FAA (2011).

VNO = maximum structural cruising speed, VMO = maximum operating limit speed, MMO = maximum operating Mach number, and KCAS represents the units for knots calibrated airspeed.


While the regulatory framework and overall safety criteria are defined in Part 23, the regulations are intentionally sparse on details on how to actually demonstrate compliance for certification. Instead, means of compliance (§23.2010) can be determined by the applicant, subject to approval by the FAA. Typically, the means of compliance is established by a consensus standard. A type certificate applicant for a new light aircraft could demonstrate compliance with a consensus‐based industry standard, which has been approved by the FAA. This compliance mechanism is a dynamic and flexible approach (compared to explicitly defining the compliance mechanisms in part 23), since consensus‐forming bodies can quickly respond to new technologies and develop consensus standards. One key example of such a body is ASTM International. The ASTM convenes a number of committees, which are populated by representatives from various industry groups, and also includes government (FAA) representatives. The key ASTM committee that covers certification standards for light aircraft is the F44 committee on General Aviation Aircraft and specifically the F44.20 subcommittee on Flight. At the time of writing this book, ASTM F44.20 had published standard specifications for flight test demonstration of aircraft weight and center of gravity, operating limitations, aircraft handling characteristics, performance, and low‐speed flight characteristics (ASTM 2017, 2018a, 2018b, 2019a, 2019b). Historical guidance from the FAA is also available for means of compliance with 14 CFR part 23 through nonregulatory advisory circulars (FAA 2003, 2011).

It's important to also be familiar with the historical approaches to airworthiness certification, since there are many aircraft flying today that were certified under older versions of the regulations. Predating certification of general aviation aircraft under part 23, certification was granted under the Civil Air Regulations (from the late 1930s until 1965). Kimberlin (2003, chapter 1) provides a good synopsis of these older regulations and how antique aircraft are still flying under airworthiness certificates granted under the older regulations.

For decades, certification of light general aviation aircraft followed regimented flight testing protocols that were explicitly defined in part 23. Over the years, the part grew more complex as additional safety measures and compliance protocols were codified. The resulting regulation was a rigid document that could not easily accommodate new technologies. For example, part 23 was strictly written to document how a type applicant must demonstrate the performance of internal combustion engines and the associated fuel system. This strict delineation of a compliance pathway was fine when all general aviation aircraft were powered by internal combustion engines running off Avgas. However, there are new propulsion system concepts emerging such as electric motors driven by fuel cells, batteries, or hybrid battery‐generator systems, but these could not be certified under the former regimented structure of part 23. Type certificate applicants would have had to demonstrate an equivalent level of safety and obtain waivers, but there was no established and agreed‐upon process for doing so. Thus, certification of new technologies such as electric propulsion would have been costly, with an uncertain outcome.

The current certification framework was developed in response to these challenges, leading to a complete rewrite of part 23 in 2016. With the rewrite of part 23, the FAA removed historical designations of various certification categories for airplanes. While these categories no longer exist for new aircraft certifications, any aircraft certified under the old part 23 will retain its category designation. These categories are normal, utility, acrobatic, and commuter. The commuter category is the designation for the largest general aviation aircraft, with a maximum takeoff weight of 19,000 lb, a passenger seating capacity of up to 19, and multiple engines. The normal, utility, and acrobatic categories all have a much lower weight limit of 12,500 lb and a seating capacity of up to 9. Normal category airplanes are approved for normal (routine) flying, stalls (but not “whip stalls”), and routine commercial maneuvers (less than 60° bank). Airplanes certified for utility category are approved for limited aerobatic maneuvers, which may include spins and commercial maneuvers at higher bank angles (up to 90°). Acrobatic category airplanes are approved for acrobatic maneuvers, which is basically any maneuver that a pilot can fly, and found to be safe in the flight testing program. For the normal, utility, and acrobatic categories, a given airplane could be certified for one, two, or all three, with varying operating limitations corresponding to each. Given that there are many aircraft routinely flying today that are well over 60 years old, one can anticipate that these legacy certification categories will persist for quite some time as historical and current aircraft continue flying.

### 1.3 Objectives and Organization of this Book

Our objective for this book is to provide the reader with an introduction to the exciting world of flight testing of light aircraft and UAS. Within the broad theme of that overarching objective, we specifically seek to:

(1) Provide a solid foundation for the reasons why flight testing is done the way it is. This involves a clear and concise establishment of the theoretical principles. Each equation that is presented here is backed up by physical explanations of the phenomena involved.

(2) Offer aerospace engineering students the context for connecting engineering theory with practice through guided flights in an aircraft. This provides the student with a visceral, empirical way of connecting their theoretical knowledge of flight with practical knowledge. The goal is for the student to develop a tacit understanding of flight beyond the explicit knowledge gleaned in traditional classrooms.

(3) Introduce the concepts and practice of digital data acquisition and signal processing, which is the underpinning of complex industrial and governmental flight test programs. These concepts are typically not taught in the undergraduate aerospace curriculum, but are important for knowing how to acquire and analyze flight test data using advanced, micro‐scale sensors and digital data acquisition systems.

(4) Provide an overview of many of the foundational flight test topics encountered in performance flight testing. Individual chapters address each topic in turn, starting with the theoretical basis for that aspect of aircraft performance and moving on to flight test methods for acquiring and analyzing data for each performance metric.

This text is partitioned into two main segments – the first half of the book (Chapters 1–6) deals with preliminary content and fundamental principles, while the second half (Chapters 7–16) covers a series of flight test topics in detail. The flight tests covered here focus predominantly on the performance and stability characteristics of an aircraft. We predominantly focus on light general aviation aircraft and UAVs, since these are accessible to most students, and optimal learning takes place when a student can experience flight testing firsthand. The material is designed to be accessible such that a student can go with a qualified pilot in nearly any general aviation aircraft and acquire meaningful flight test data. Dedicated flight test instrumentation, modifications to the aircraft, or expensive hardware is not required. Thus, many of the flight test methods presented here may be simplified relative to what is done in industry.


Figure 1.14 Ohio State University students Greg Rhodes and Jennifer Haines following turn performance flight testing in a Piper PA‐28R at the Ohio State University Airport.

Source: Courtesy of Greg Rhodes and Jennifer Haines.


This textbook should not be regarded as a definitive or even advisory source on how to conduct flight testing. Instead, this book should be considered a general introduction to the ideas, scientific principles, theoretical foundations, and some of the best practices associated with flight testing. We provide a mix of aircraft performance theory with flight testing methods. Our goal is to invite the student or practitioner into understanding the physical fundamentals underlying flight testing – this will enable the reader to more fully appreciate why flight testing is done the way it is, to spot errors or problems in theory or procedures, and to know how to adapt established practices to unanticipated circumstances or new vehicle concepts. So, our aim is to provide a general overview and introduction to flight testing: a general idea of the nature of the field and a sound theoretical basis for what is done. We hope that this book will be a good first step as preparation for entry into the flight testing domain, where more detailed methods can be picked up on the way.

Official publications, standards, and advisory documents from the relevant civil aviation authority must be regarded as the definitive source for guidance on how to safely conduct flight testing and how to provide sufficient information to comply with the certification requirements. In the United States, this documentation is primarily found in 14 CFR 23, FAA Advisory Circular 23‐8C, and any consensus standards accepted by the FAA (such as standards produced by ASTM International's F44 committee on General Aviation Aircraft). Other helpful sources of procedural and practical information are found in Hamlin (1946), Smith (1981), Stoliker et al. (1996), Stinton (1998), Kimberlin (2003), Ward et al. (2006, 2007), McCormick (2011), Mondt (2014), Corda (2017), and the publicly available flight test guides from the governmental flight test organizations (Herrington et al. 1966; USAF TPS 1986; USN TPS 1977, 1997; Gallagher et al. 1992; Stoliker 1995; Olson 2003). More advanced details on system identification for aircraft are available from Klein and Morelli (2006), Tischler and Remple (2012), or Jategaonkar (2015).

Flight testing is a fascinating, exhilarating field of aerospace engineering. It's incredibly rewarding to connect theory with practice, and we hope that the thoughts we provide here will draw students into a deeper understanding of flight through the intertwined approaches of theory and flying in flight test. And we hope to inspire the next generation of flight test professionals (Figure 1.14) to pursue this fascinating line of work. Hang on for a wild ride!

Nomenclature

MMO

maximum operating Mach number

VMO

maximum operating limit speed

VNO

maximum structural cruising speed


Acronyms and Abbreviations

AAF

Army Air Forces

CFR

Code of Federal Regulations

CG

center of gravity

DT&E

developmental test and evaluation

FAA

Federal Aviation Administration

HARV

high alpha research vehicle

LEX

leading‐edge extension

NACA

National Advisory Committee for Aeronautics

NASA

National Aeronautics and Space Administration

OT&E

operational test and evaluation

PSP

pressure‐sensitive paint

UAV

unmanned aerial vehicle


References

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ASTM Committee F44 on General Aviation Aircraft, Subcommittee F44.20 on Flight. (2018a). Standard Specification for Performance of Aircraft. F3179/F3179M‐18, approved 1 May 2018, West Conshohocken, PA: ASTM International. doi: https://doi.org/10.1520/F3179_F3179M-18.

ASTM Committee F44 on General Aviation Aircraft, Subcommittee F44.20 on Flight. (2018b). Standard Specification for Aircraft Handling Characteristics. F3173/F3173M‐18, approved 1 December 2018, West Conshohocken, PA: ASTM International. doi: https://doi.org/10.1520/F3173_F3173M-18.

ASTM Committee F44 on General Aviation Aircraft, Subcommittee F44.20 on Flight. (2019a). Standard Specification for Establishing Operating Limitations and Information for Aeroplanes. F3174/F3174M‐19, approved 1 May 2019, West Conshohocken, PA: ASTM International. doi: https://doi.org/10.1520/F3174_F3174M-19.

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Gallagher, G.L., Higgins, L.B., Khinoo, L.A., and Pierce, P.W. (1992). Fixed Wing Performance. USNTPS‐FTM‐No. 108,. Patuxent River, MD: Naval Air Warfare Center.

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Hamlin, B. (1946). Flight Testing Conventional and Jet‐Propelled Airplanes. New York: Macmillan Company.

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Jategaonkar, R.V. (2015). Chapter 2. In: Flight Vehicle System Identification: A Time‐Domain Methodology, 2e. Reston, VA: American Institute of Aeronautics and Astronautics.

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## 2. The Flight Environment: Standard Atmosphere

In this chapter, we will discuss the properties of the environment for flight testing – Earth's atmosphere. It is critical to understand the nature of the atmosphere, since aircraft performance depends significantly on the properties of air. For example, the lift produced by the aircraft is proportional to the air density, and the amount of power produced by an internal combustion engine also varies with density. For these two reasons, aircraft performance decreases as density decreases. We will see in this chapter that density decreases with altitude, so key aircraft performance metrics such as takeoff distance, rate of climb, acceleration, etc. all degrade with altitude. Since aircraft performance depends significantly on the local properties of air, we need some way to factor out altitude effects. We also need to be able to predict the performance of an aircraft as a function of altitude, once its baseline performance is known. Thus, we need an agreed‐upon standard definition of the properties of the atmosphere – this is the standard atmosphere. Definition of the standard atmosphere allows us to evaluate and compare aircraft performance in a consistent manner, no matter what the altitude is.

The important atmospheric parameters are the atmospheric temperature, pressure, density, and viscosity, which depend on the distance from the earth surface, geographic location, and time. In order to describe the atmosphere in a universal way, a standard atmosphere model has been developed, where the atmospheric parameters are determined as the univariate functions of altitude from sea level. Temperature exhibits strong variations with time of year, geographic location, and altitude. And, on a daily basis, temperature depends on current weather conditions in a stochastic manner. It is impossible to develop a first‐principles model that will capture all of these parameters that influence the temperature profile; thus, the standard temperature profile is determined from an average of a large ensemble of atmospheric measurements. The variation of pressure with altitude, however, is rigorously described by some basic physical principles – we will derive these here. In fact, pressure is so intricately and reliably linked to altitude that aircraft altimeters measure pressure and convert the measurement to an indicated altitude through the definition of the standard atmosphere. Density is related to the estimated value of temperature and the derived value of pressure via the ideal gas law. Finally, we will provide a relationship that determines the viscosity of air as a function of temperature. Based on these developments, we will define a standard atmosphere that can be expressed in tabular form, or equations coded for computational analysis. This chapter will start with a physical description of the atmosphere and then present a detailed development of the standard atmosphere. Most of the development of the standard atmosphere presented in this chapter will rely on SI units, since this was the unit system used to define the standard atmosphere and the boundaries of atmospheric regions. The input and output of the standard atmosphere can be easily converted from SI units to English units as needed.

### 2.1 Earth's Atmosphere

Earth's atmosphere is an envelope of air surrounding the planet Earth, where dry air consists of 78.08% nitrogen, 20.95% oxygen, 0.93% argon, 0.031% carbon dioxide, and small amounts of other gases (NOAA et al. 1976). In addition, air contains a small amount of water vapor (about 1%). The entire atmosphere has an air mass of about 5.15 × 1018 kg (1.13 × 1019 lb), and three quarters of the total air mass are contained within a layer of about 11 km (∼36,000 ft) from the Earth's surface.

There is a general stratification of Earth's atmosphere, which leads to the definition of distinct regions of the atmosphere: the troposphere (0–11 km), stratosphere (11–50 km), mesosphere (50–85 km), and thermosphere (85–600 km). The atmosphere becomes thinner as the altitude increases, and there is no clear boundary between the atmosphere and outer space. However, the Kármán line has been defined at 100 km and is often used as the border between the atmosphere and outer space. Atmospheric effects become noticeable during atmospheric reentry of spacecraft at an altitude of around 120 km. Aircraft propelled by internal combustion engines and propellers are generally limited to operating in the troposphere, while jet‐propelled aircraft routinely operate in the stratosphere.

Figure 2.1 illustrates the bottom three layers of Earth's atmosphere, which is where all atmospheric flight vehicles conduct flight. The delineation between the various regions of the atmosphere is based on historical measurements of temperature profiles, which lead to distinct regions with different temperature lapse rates. In the troposphere (the layer of the atmosphere nearest the surface), the air temperature generally decreases linearly with the altitude. This temperature reduction with altitude is due to the increasing distance from Earth and a concomitant reduction in heating from Earth's surface. Weather phenomena are directly dependent on this temperature reduction with altitude, causing most storms and other weather phenomena to develop and reside within the troposphere. The dividing boundary between the troposphere and the next layer (the stratosphere) is called the tropopause, at 11 km. Within the lower portion of the stratosphere (11–20 km), the air temperature remains constant; it then increases with altitude in the upper stratosphere (20–50 km), due to absorption of the sun's ultraviolet radiation by ozone in this region of the atmosphere.


Figure 2.1 The layers of Earth's atmosphere.


In contrast with the temperature–altitude profile, the variation of pressure with altitude is highly repeatable and deterministic. Air pressure continually decreases with altitude from Earth's surface all the way to the edge of the atmosphere. The primary reason for this is the action of Earth's gravitational acceleration on air, causing a given mass of air to exert a force on the air below it. Air at a given altitude must support the weight of all of the air mass above it, and it balances this force by pressure. As altitude increases, there is less air mass above that altitude, so there is less force (weight) acting on the air at that point and the pressure decreases. Thus, pressure decreases as altitude increases. We will discuss this physical mechanism in greater detail in Section 2.2, when we derive an expression for the variation of pressure with altitude.

### 2.2 Standard Atmosphere Model

A standardized model of the atmosphere allows scientists, engineers, and pilots in the flight testing community to have a commonly agreed‐upon definition of the properties of the atmosphere. The definition of the standard atmosphere includes the variation of gravitational acceleration, temperature, pressure, density, and viscosity as a function of altitude. There is actually more than one definition of the standard atmosphere: the U.S. Standard Atmosphere (NOAA et al. 1976) and the International Civil Aviation Organization (ICAO) Standard Atmosphere (ICAO 1993). Thankfully, the two definitions are identical at lower altitudes where aircraft fly – the only differences are in the upper stratosphere and beyond. Our discussion here will generally follow the development of the U.S. Standard Atmosphere (NOAA et al. 1976).[1]

#### 2.2.1 Hydrostatics

The development of the standard atmosphere directly results from the hydrostatic equation, which is derived here based on a control volume analysis. Figure 2.2 illustrates an arbitrary control volume, measuring dx × dy × dhG, and the forces acting upon it (here, hG is the geometric altitude, or height above mean sea level (MSL)). The forces due to pressure acting on all of the side walls balance one another out in this static equilibrium condition, and we will consider only the forces acting in the vertical direction. The force acting upward on the bottom surface of the control volume is the pressure, p, times the cross‐sectional area dx dy. Similarly, on the top surface, we have a force of (p + dp)dx dy acting downward. (Here, the differential pressure dp accounts for pressure changes in the vertical direction.) Finally, we have the weight of the air inside the control volume acting downward, W = mg, where g is the local gravitational acceleration and the mass of the air inside the control volume can be found from the product of density and the volume,


(2.1)


Figure 2.2 Forces acting on a hydrostatic control volume.


Summing all the forces in the vertical direction and setting equal to zero (from Newton's second law applied to a stationary control volume), we obtain


(2.2)


Canceling terms leads to


(2.3)


which is the hydrostatic equation as a function of geometric altitude. This expression mathematically expresses the physical explanation that we presented earlier for the variation of pressure with altitude. As altitude increases (positive dhG), the minus sign indicates that the pressure decreases (negative dp). The ρg term is an expression of the weight of the air inside the control volume, which is the reason for the pressure difference.

#### 2.2.2 Gravitational Acceleration and Altitude Definitions

As we proceed with the development of the standard atmosphere, we must consider how gravitational acceleration varies with altitude. From Newton's law of universal gravitation, we know that gravitational acceleration varies inversely with the square of the distance to the center of the earth. Thus, we have


(2.4)


where g is the local gravitational acceleration (varies with altitude), g0 is the gravitational acceleration at sea level (9.806 65 m/s2 or 32.174 ft/s2), hA is the distance from the center of the earth (defined here as the absolute altitude[2]), and rEarth is Earth's mean radius, which is 6356.766 km (NOAA et al. 1976).

Despite the fact that gravity varies with altitude, it is convenient to derive the standard atmosphere based on the assumption of constant gravitational acceleration. In order to do so, we must define a new altitude, the geopotential altitude, h, which we will use in the hydrostatic equation with the assumption of constant gravity. Referring to Eq. (2.3), we can also write the hydrostatic equation as a function of geopotential altitude and constant gravitational acceleration,


(2.5)


Taking the ratio of (2.5) and (2.3), we have


(2.6)


since the differential pressure and density terms cancel out for a given change of pressure. The small difference between g0 and g then leads to a small difference between the geopotential and geometric altitudes. Combining Eqs. (2.4) and (2.6) produces


(2.7)


which can be integrated between sea level and an arbitrary altitude to find


(2.8)


This expression defines the relationship between geopotential altitude, h, and geometric altitude, hG, which can also be solved for geometric altitude,


(2.9)


In our derivation of the standard atmosphere, we will use geopotential altitude, h, and assume constant g0. Properties of the standard atmosphere such as temperature, pressure, and density, i.e., (T, p, ρ), will be found as a function of geopotential altitude, h, and then mapped back to geometric altitude, hG, by Eq. (2.9). In this work, we are focused on the lower portions of the atmosphere where most aircraft fly (h ≤ 20 km or 65, 617 ft). At that upper altitude limit, Eq. (2.9) predicts a maximum difference of 0.31% between the geometric and geopotential altitude. Thus, in many cases related to flight testing, this difference between geopotential and geometric altitudes can be neglected.

#### 2.2.3 Temperature

Temperature at any given point in the Earth's atmosphere will depend not only on the altitude but also on time of year, latitude, and local weather conditions. Since the variation of temperature has spatial, temporal, and stochastic input, the development of the standard atmosphere as a function of only altitude inherently involves many approximations. Thus, we might anticipate that the actual temperature at a given location can deviate significantly from the standard value.

The standard temperature profile has been determined through an average of significant amounts of data from sounding balloons launched multiple times a day over a period of many years, at locations around the globe. The resulting temperature profile is a function of geopotential altitude, with the lapse rate, a = dT/dh, representing the linear variation of temperature with altitude for each region (see Table 2.1 and Figure 2.3). In the troposphere (0 ≤ h ≤ 11 km), the standard temperature lapse rate is defined as −6.5 K/km, starting at TSL = 288.15 K. In the lower portion of the stratosphere (11 < h ≤ 20 km), the temperature is presumed to be constant at 216.65 K. Starting at 20 km, the temperature then increases at a rate of 1 K/km due to ozone heating of the upper stratosphere. Based on the data in Table 2.1, we can write expressions for the temperature profile throughout the standard atmosphere as


(2.10)


where “ref” refers to the base of the layer (defined by either sea level conditions, or the top of the prior atmospheric layer, working upwards). Output from Eq. (2.10) can be stacked for each altitude layer, one on top of another, to define the entire standard temperature profile. Since most flight testing, especially for light aircraft and drones, occurs at altitudes below 20 km, we will focus our attention on the troposphere and lower portion of the stratosphere.


Table 2.1 Definition of temperature lapse rates in various regions of the atmosphere.

Source: Data from NOAA et al. 1976.

h1 and h2 are the beginning and ending altitudes of each region, respectively.


Figure 2.3 Standard temperature profile.

#### 2.2.4 Viscosity

We also need to define an expression for dynamic viscosity, μ, which depends on temperature. The most significant impact of viscosity is in the definition of Reynolds number,


(2.11)


which is an expression of the ratio of inertial to viscous forces (here, U∞ is the freestream velocity or airspeed, and c is the mean aerodynamic chord of the wing). Reynolds number has a significant impact on boundary layer development and aerodynamic stall, as we will see in Chapter 12.

The viscosity of air is related to the rate of molecular diffusion, which is a function of temperature (Sutherland 1893). This relationship has been distilled down to Sutherland's Law,


(2.12)


where T is the temperature in absolute units, and β and Svisc are empirical constants, provided in Table 2.2 for both English and SI units (NOAA et al. 1976). Based on Eq. (2.12), the viscosity of a gas increases with increasing temperature. Thus, the dynamic viscosity decreases gradually through the troposphere, starting with the standard sea level value of μSL = 1.7894 × 10−5 kg/(s m) = 3.7372 × 10−7 slug/(s ft) at a temperature of TSL = 288.15 K = 518.67 ° R. If kinematic viscosity (ν) is desired instead of dynamic viscosity, it can be found based on its definition,


(2.13)


Table 2.2 Constants used in Sutherland's Law.

Source: Based on NOAA et al. 1976.


#### 2.2.5 Pressure and Density

To derive an expression for the variation of pressure with altitude, we need to integrate the hydrostatic equation. Since density and gravitational acceleration also vary with altitude, we need to cast the hydrostatic equation in terms of only pressure and altitude, with all other variables being constant. We will work with the hydrostatic equation shown in Eq. (2.5), based on geopotential altitude and constant gravity. Density can be expressed as a function of pressure and temperature via the equation of state for a perfect gas,


(2.14)


where R = 287.05 J/(kg K) is the gas constant for air. Taking a ratio of Eqs. (2.5) and (2.14), we have


(2.15)


We will work with Eq. (2.15) for two different cases: first, where the temperature is constant with altitude, and then when temperature varies linearly with altitude.

Equation (2.15) can be directly integrated to find pressure as a function of altitude for the isothermal regions of the atmosphere (11 < h ≤ 20 km and 47 < h ≤ 51 km) since all terms in the equation are constant except pressure and altitude. Performing this integration between the base (href) and an arbitrary altitude within that region (h) yields


(2.16)


where “ref” indicates the base of that particular region of the atmosphere. When the ideal gas law, Eq. (2.14), is applied to isothermal regions of the atmosphere, we see that density is directly proportional to pressure. Thus, we can also write an expression for density in the isothermal regions as


(2.17)


Equations  then form a complete definition of temperature, viscosity, pressure, and density in the isothermal regions of the standard atmosphere.

Portions of the atmosphere with a linear lapse rate, however, require a different approach to integrating Eq. (2.15). In this case, T is no longer constant with respect to altitude, so we must substitute it in the temperature lapse rate. Combining a = dT/dh with Eq. (2.15) yields


(2.18)


Integration of Eq. (2.18) gives the pressure ratio as a function of the temperature ratio, i.e.,


(2.19)


where pref and Tref are the pressure and temperature at a reference altitude, respectively. Again applying the ideal gas law, Eq. (2.14), the density ratio is given by


(2.20)


Thus, for regions of the atmosphere with linear temperature lapse rates, Eqs. (2.10), (2.12), (2.19), and (2.20) form a complete description of the temperature, viscosity, pressure, and density variation with altitude. The reference condition for the base of each region is simply the values corresponding to the top of the previous (lower) region.

In the flight testing community and elsewhere, we often express the above ratios as specific variables referenced to sea level conditions. Temperature ratio, pressure ratio, and density ratio are defined as


(2.21)


In the standard atmosphere, sea level conditions are defined as TSL = 288.15 K, pSL = 101.325 kPa, and ρSL = 1.225 kg/m3, where the subscript “SL” denotes sea level. The ratios defined in Eq. (2.21) still satisfy the ideal gas law, giving


(2.22)


It is important to bear in mind that these equations are a function of geopotential altitude, which presumes constant gravitational acceleration. If properties are desired as a function of geometric altitude, then the corresponding geometric altitudes can be found by solving for hG in Eq. (2.9).

#### 2.2.6 Operationalizing the Standard Atmosphere

Applying the equations developed above, we can take one of several approaches to implementing the standard atmosphere for flight testing work. Most simply, these equations form the basis for tabulated values of the standard atmosphere, which are tabulated by NOAA et al. (1976) or ICAO (1993). In addition, a limited subset of the U.S. Standard Atmosphere (NOAA et al. 1976) is reproduced in Appendix A. Alternatively, pre‐written standard atmosphere computer codes may be downloaded and used in a straightforward manner. Popular examples include the MATLAB code by Sartorius (2018) or the Fortran code by Carmichael (2018). If these are not suitable for a particular purpose, then custom code can be written, as described below in a form that simplifies the coding.

In the troposphere where the temperature gradient is a = dT/dh =  − 6.5 K/km, the temperature distribution in Eq. (2.10) can be expressed as a linear function


(2.23)


where h is the geopotential altitude and k = 2.256 × 10−5 m−1 = 6.876 × 10−6 ft−1 is a decaying rate. According to Eqs. (2.19) and (2.20), the pressure ratio and density ratio in the troposphere (0 ≤ h ≤ 11 km) are given by


(2.24)


and


(2.25)


where n =  − g0/aR = 5.2559.


Figure 2.4 The normalized temperature, pressure, and density distributions in the standard atmosphere.


In the lower stratosphere (11 km < h ≤ 20 km), the atmospheric temperature is constant at 216.65 K. If we define the critical altitude at the tropopause to be htrop = 11 km, then the temperature and pressure ratios at the tropopause are θtrop = 0.7518 and δtrop = 0.2233, respectively. Recasting (2.16) in terms of these ratios, we obtain


(2.26)


for the pressure ratio in the lower stratosphere. Finally, the density ratio in the lower stratosphere is simply found by the ideal gas law,


(2.27)


Figure 2.4 shows the pressure, density, and temperature distributions normalized by the sea level conditions in the standard atmosphere.

#### 2.2.7 Comparison with Experimental Data

The above equations describe the idealized atmosphere where the parameters are considered as the mean values of the measured quantities. However, as indicated in The U.S. Standard Atmosphere (NOAA et al. 1976), measurement data show considerable variations of the atmospheric parameters depending on time (day and season) and geographic location, which should be considered in flight testing.

Experimental measurements may be compared with the theoretical variation of pressure and temperature derived from the standard atmosphere. Atmospheric data can be collected by a weather balloon (Figure 2.5), which ascends through the atmosphere and measures pressure and temperature throughout the flight. For the case presented here, the balloon ascended to an altitude of 30.161 km (98,953 ft) before bursting and descending via parachute back to Earth. Data throughout the ascent and descent were collected and are presented in Figures 2.6 and 2.7. The temperature data shown in Figure 2.6 show similar trends to the standard temperature profile, but the agreement is not very good. This is not surprising, since the details of the temperature profile are strongly dependent on local weather, time of year, latitude, etc. However, some of the similarities are noteworthy: the experimental temperature lapse rate is approximately the same as the standard lapse rate, particularly at low altitudes. Also, the location of the tropopause, corresponding to a change to an isothermal temperature profile, is in good agreement. Finally, the slope of the high‐altitude lapse rate is also in fairly good agreement with the standard temperature profile. Pressure data, in Figure 2.7, show excellent agreement with the standard atmosphere. This is also expected since the hydrostatic equation is a good descriptor of the physics of pressure variation with altitude. The good agreement shown here underscores the utility of using pressure measurement for measuring altitude on aircraft (see Chapter 3 for further details on how altimeters operate).


Figure 2.5 Launch of a high‐altitude weather balloon from the oval of The Ohio State University.


Figure 2.6 Comparison of the standard atmosphere with temperature data measured by a weather balloon.


Figure 2.7 Comparison of the standard atmosphere with pressure data measured by a weather balloon.

### 2.3 Altitudes Used in Aviation

We will now conclude this chapter with a discussion of different altitude definitions used in aviation. We have already introduced several definitions of altitude for the preceding discussion on the standard atmosphere. To recap, these include absolute altitude, geometric altitude, and geopotential altitude. Absolute altitude, hA, is measured from the center of the Earth and is only relevant when determining the value of gravitational acceleration at a particular altitude. Geometric altitude, hG, is the height of an aircraft above mean sea level. And, geopotential altitude, h, is the height above sea level with the assumption of constant gravitational acceleration. Geopotential altitude is only relevant in the context of deriving the standard atmosphere, so should not be used elsewhere. For the remainder of this book, we will presume that the differences between geometric altitude and geopotential altitude are small and will simply refer to the geometric altitude as h.

However, these altitude definitions are limited to an engineering context. To make things interesting, we also have a set of altitudes that are defined for the aviation community. And, to make things more interesting, some of the aviation altitudes use the same terms but different definitions! The aviation set of altitudes include true altitude, indicated altitude, pressure altitude, density altitude, and absolute altitude. We will discuss each of these as follows.

True altitude is the height above mean sea level. In the aviation community, this altitude is often abbreviated as MSL. When an aircraft altimeter is referenced to the local barometric pressure reading, it indicates true altitude. (Details on altimeter operation are provided in Chapter 3.) Pilots around the world often refer to this setting of the altimeter as QNH. Note that the aviation definition of true altitude is identical to the engineering definition of geometric altitude.

Similarly, indicated altitude is a direct reading from the altimeter, no matter how the altimeter is set. This may or may not be the same as true altitude, depending on the reference pressure used on the altimeter. (The reference pressure essentially shifts the calibration of the altimeter to match local barometric pressure, instead of standard sea level pressure.)

Pressure altitude, in the aviation realm, is defined as the altitude read from the altimeter when it is set to a reference pressure of 29.92 inHg, which is the standard sea level pressure. In many locations around the world, barometric pressure readings are reported in millibars or hPa, where 1013 mbar (=1013 hPa) is equal to 29.92 inHg (both being standard sea level pressure). Pilots refer to this setting of the altimeter – to provide pressure altitude – as QNE. In engineering terms, pressure altitude has essentially the same meaning. An engineer would express pressure altitude as the altitude corresponding to a given pressure in the standard atmosphere. Both the engineering and aviation definitions for pressure altitude are equivalent, since the altimeter referenced to 29.92 inHg (1013 mbar) is calibrated based on the standard atmosphere.

Density altitude is defined, in aviation terms, as the pressure altitude corrected for non‐standard temperature. If the temperature on a given day at a particular altitude is hotter than the standard temperature, then the density altitude will be higher. In engineering terms, density altitude is defined as the altitude corresponding to a given density in the standard atmosphere. Aircraft performance depends significantly on local air density, so density altitude is a direct indication of aircraft performance. Higher density altitude (corresponding to lower density) will lead to longer takeoff ground roll, slower rates of climb, higher true airspeed for stall, etc.

Finally, pilots are also concerned with the height of the aircraft above the local terrain, which is termed absolute altitude. In the aviation realm, absolute altitude is often also termed height above ground level, so the acronym AGL is often used. On aviation charts, both true altitude (MSL) and absolute altitude (AGL) are reported for various obstacles. For example, the top of a 500‐ft tall radio tower mounted on ground that is 1500 ft above sea level will have a maximum height of 2000 ft MSL or 500 ft AGL. Thus, pilots pay close attention to the absolute altitude (also referred to as QFE) as well as the true altitude (QNH). Note that absolute altitude (AGL) in an aviation context is not the same as absolute altitude (hA) in an engineering context. The engineering definition of absolute altitude is seldom used in aerospace or aviation, outside of discussions of the standard atmosphere.

A selection of the most significant of these altitudes is illustrated in Figure 2.8. The aircraft depicted in this figure is cruising at a true altitude of 5000 ft (MSL), but because its flight is over mountains rising 2000 ft above sea level, the aircraft is at an absolute altitude of only 3000 ft AGL. On this given day, the local barometric pressure reading is lower than standard, causing the pressure altitude to be higher than the true altitude. And, if the temperature on this day is higher than standard, then the density altitude will be even higher than pressure altitude or true altitude. Thus, we could easily have a situation where absolute altitude, true altitude, pressure altitude, and density altitude are all different. In Chapter 3, as we move into instrumentation used for flight testing, we will discuss the operation of the altimeter in greater detail.


Figure 2.8 Illustration of different altitudes used in aviation.


Nomenclature

a

temperature lapse rate,

dT

/

dh

c

chord

g

gravitational acceleration

g0

gravitational acceleration at sea level

h

geopotential altitude

hA

absolute altitude (height relative to the center of the Earth)

hG

geometric altitude (height above mean sea level)

k

constant,

a

/

T

SL

m

mass of air in the control volume

n

constant, −

g

0

/

aR

p

pressure

R

gas constant for air

rEarth

Earth's mean radius

Rec

Reynolds number based on chord

Svisc

Sutherland's constant

T

temperature

U∞

freestream velocity

W

weight of air in the control volume

x

length of control volume element

y

width of control volume element

β

constant used in Sutherland's Law

δ

pressure ratio,

p

/

p

SL

μ

dynamic viscosity

ν

kinematic viscosity

ρ

density

σ

density ratio,

ρ

/

ρ

SL

θ

temperature ratio,

T

/

T

SL


Subscripts

ref

reference conditions at the base of a given atmospheric layer

SL

sea level

trop

tropopause

1

beginning of an atmospheric layer

2

end of an atmospheric layer


Acronyms and Abbreviations

AGL

height above ground level

ICAO

International Civil Aviation Organization

MSL

height above mean sea level

NOAA

National Oceanic and Atmospheric Administration


References

Anderson, J.D. Jr. (2016). Introduction to Flight, 8e. New York: McGraw‐Hill.

Carmichael, R. (2018). Public domain aeronautical software for the aeronautical engineer. http://www.pdas.com/atmos.html (accessed 28 December 2020).

ICAO (1993). Manual of the ICAO Standard Atmosphere (Extended to 80 Kilometres (262 500 Feet)), 3e, ICAO Document 7488. Montréal, QC: International Civil Aviation Organization.

NOAA, NASA, and USAF (1976). U.S. Standard Atmosphere, 1976, NOAA‐S/T‐76‐1562, NASA‐TM‐X‐74335. Washington, DC: U.S. Government Printing Office. http://hdl.handle.net/2060/19770009539.

Sartorius, S. (2018). Standard Atmosphere Functions, v. 2.1.0.0. MathWorks File Exchange. https://www.mathworks.com/matlabcentral/fileexchange/28135-standard-atmosphere-functions.

Sutherland, W. (1893). LII. The viscosity of gases and molecular force. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, Series 5 36 (223): 507–531. https://doi.org/10.1080/14786449308620508.

## 3. Aircraft and Flight Test Instrumentation

This chapter fundamentally deals with how we will measure the various aircraft performance characteristics. We will cover common instruments used in the aircraft cockpit (both traditional and modern avionics systems), as well as instrumentation found in external data acquisition (DAQ) systems. This fundamental understanding is important for developing an appreciation of the capabilities and limitations of each instrument and sensor system. We will begin with a discussion of various sensors and instrumentation hardware used in flight testing (these instruments can be either the standard cockpit instrumentation or supplemental instrumentation dedicated for flight testing purposes).

A discussion of instrumentation and DAQ must begin by detailing what we wish to measure and how we will measure it. For aircraft flight testing, we essentially need to know the vehicle's state – we need to know the aircraft's position and orientation as a function of time. Practically speaking, this requires measurements of the vehicle's velocity, acceleration, orientation (pitch, roll, and yaw angle relative to a defined set of coordinate axes), altitude, and magnetic heading.

Aircraft instruments are generally calibrated to report quantities in the English unit system, sometimes using nonstandard units. Speed is most often reported in knots (nautical miles per hour), altitude is in feet, vertical speed is in feet per minute, distance is in nautical miles, angles are in degrees, and angular rates are in degrees per second. When analyzing flight test data from these measurements, it is critical to convert to standard consistent units before further analysis. All analysis must be done in a single, consistent unit system with standard units (e.g., English: ft/s, ft, deg, and deg/s, or SI: m/s, m, deg, and deg/s). After completion of the analysis, the results may be converted to any desired units for reporting. This section provides an orientation to the instruments installed in general aviation (GA) aircraft cockpits, including both classical “steam gauge” instruments and more modern glass panel instrument displays. We will first discuss the traditional instruments, followed by glass panel avionics systems.

### 3.1 Traditional Cockpit Instruments

In traditional flight testing methods at the university level, many of the desired parameters are hand‐recorded from cockpit indicators such as the airspeed indicator (ASI), attitude indicator, heading indicator, and altimeter, which are illustrated in Figures 3.1 and 3.2 for a traditional “steam gauge” cockpit. The traditional instruments are arranged in a “six pack” configuration (Figure 3.2): starting at the upper left and moving clockwise, the instruments are the ASI, attitude indicator, altimeter, vertical speed indicator (VSI), heading indicator (also known as the directional gyro), and turn/slip indicator (also known as the turn coordinator). We will group these instruments into two types. The first group, consisting of the attitude indicator, heading indicator, and the turn/slip indicator, is based on gyroscopes. The second group, consisting of the ASI, altimeter, and VSI, is based on physical measurements of pressure. We will discuss each group of instruments in more detail as follows. Interested readers can also consult various publications such as Chapter 7 of the Pilot's Handbook of Aeronautical Knowledge (2008), Chapter 5 of the Instrument Flying Handbook (2012), and the Advanced Avionics Handbook (2009) for more details.


Figure 3.1 Overview of aircraft cockpit instrumentation for traditional “steam gauge” instruments.

Source: https://upload.wikimedia.org/wikipedia/commons/thumb/e/e7/Slingsby.t67c.panel.g-bocm.arp.jpg/1200px-Slingsby.t67c.panel.g-bocm.arp.jpg.


Figure 3.2 Detailed view of the six pack of key instruments in a traditional cockpit.

Source: Modified from photo by Mael Balland on Unsplash, https://unsplash.com/photos/V5hAryReZzo.

#### 3.1.1 Gyroscopic‐Based Instruments

Before discussing the first group of instruments, it is helpful to briefly review the ideas behind gyroscopes. The operation of a gyroscope is based on the Newtonian principle of conservation of angular momentum. Due to conservation of angular momentum, the axis of rotation of a spinning object with a given angular momentum (L = Iω, where I is the moment of inertia and ω is the angular speed) will remain fixed unless acted upon by an external applied torque. (Think of how the axis of a child's spinning top remains upright as long as the top is spinning.) Over time, small external forces and moments that are present in any practical implementation of a physical gyro will lead to gyroscopic precession, which results in small changes in the axis of rotation that can grow over time.

The three gyroscopic instruments in a traditional six pack of instruments – the attitude indicator, heading indicator, and turn coordinator – all depend on gyroscopic principles. The rotational speed of the gyros in the attitude and heading indicators are traditionally powered by a vacuum system that flows air over a small turbine connected to the spinning disks in order to maintain rotation. The turn coordinator, on the other hand, is typically powered by the aircraft's electrical system. The attitude indicator provides an artificial horizon that provides an indication of the amount of bank and pitch that the aircraft has at a given moment. Essentially, the internal gyroscope (to which the artificial horizon is mounted) maintains its rigidity in space and the aircraft pitches and rolls about the internal gyro. Arcing along the top of the indicator, the first three white lines on either side of the centerline indicate increments of 10° bank angle (up to 30° bank). The next two lines on either side represent a 45° and 60° bank angles, respectively. The heading indicator is based on a geared gyro and simply indicates the magnetic heading of the aircraft (as long as the gyro has been set to match the magnetic compass). Both the attitude indicator and the heading indicator experience errors due to gyroscopic precession that must be occasionally corrected. For example, periodically in straight and level flight, the pilot may need to reset the heading indicator to match the indication on the magnetic compass. The turn coordinator, also based on a gyro, indicates the instantaneous rate of turn. The two white lines below the level lines each indicate a standard rate of turn of 3°/s to the right or left, which would require two minutes for the aircraft to complete a 360° turn.

#### 3.1.2 Pressure‐Based Instruments

The second group of instruments is based on measurement of total pressure and static pressure on the aircraft. Total pressure is measured by a pitot probe, which is often mounted under the wing on GA aircraft (see Figure 3.3(a)). Static pressure is measured by flush‐mounted static pressure ports on the side of the aircraft fuselage (see Figure 3.3(b)). The pitot probe and static port are connected via tubing to the ASI, altimeter, and VSI mounted on the instrument panel (Figure 3.4).

Total pressure from the pitot tube and static pressure from the static port are fed into the ASI. The ASI is calibrated based on the assumption of standard sea‐level conditions with the isentropic Mach relation to convert a measured “impact pressure” (difference between total and static pressure) into indicated airspeed. For low‐speed, low‐altitude flight this is equivalent to converting a measured dynamic pressure to velocity by the Bernoulli equation. Further details on the functioning of the ASI are provided in Chapter 8 on calibration of the ASI.


Figure 3.3 Examples of the pitot tube (a) and static pressure port (b) on an aircraft.


The VSI, connected to the static pressure port, measures the time rate of change of pressure and converts this to a vertical speed. It is based on a mechanical comparison of the rate of change of static pressure with a known rate of change coming from a calibrated leak. Indications of vertical speed on the VSI tend to fluctuate so it is not as useful for measuring rate of climb or descent in a precise manner. Instead, for measurement of vertical speed in flight test, it is best to establish a steady rate and directly measure altitude from the altimeter and time with a stopwatch.

The altimeter (Figure 3.5) is based on a measurement of static pressure, which is converted into an indicated altitude. Altitude is displayed on the traditional altimeter by three hands, much like an analog clock displays time. The long, thin pointer with a triangle at the end indicates ten thousands of feet; the short, thick hand displays thousands of feet; and the medium length, slender hand displays hundreds of feet. So, the medium, slender hand makes a full revolution of the dial every 1000 ft; the short, thick pointer makes a complete revolution every 10,000 ft; and the long, slender pointer makes a full revolution every 100,000 ft. For example, the altimeter depicted in Figure 3.5 indicates an altitude of 10,180 ft.


Figure 3.4 Schematic of the pitot‐static system.

Source: Flight Instruments, Federal Aviation Administration.


Figure 3.5 Diagram of an aircraft altimeter. The reference pressure is set by the knob on the lower left side and indicated in the Kollsman window on the right side of the instrument.

Source: Bsayusd, A 3‐pointer pressure altimeter. Originally from en.wikipedia.


The calibration of the altimeter is based on the pressure lapse rate of the standard atmosphere (assuming standard temperature). As discussed in Chapter 2, the pressure lapse rate is extremely consistent, which enables the altimeter to provide a highly accurate measurement. However, the local barometric pressure can change significantly, which would have a first‐order impact on the indicated altitude provided by an altimeter. Thus, an altimeter must account for variations in local barometric pressure reading, which is done by setting a reference pressure. This reference pressure appears in a small window on the right side of the altimeter and is set by a knob on the lower left side of the instrument (see Figure 3.5). It is important to note that the reference pressure is not related in any way to the actual pressure at some arbitrary altitude. Instead, the reference pressure simply shifts the base of the calibration curve, providing an offset above or below standard sea level pressure in order to accommodate the actual local barometric pressure reading and providing a more accurate reading of altitude.

This type of altimeter – the so‐called sensitive altimeter – was first invented by Paul Kollsman, leading to the naming of the Kollsman window where the reference pressure is read on the altimeter (e.g., the reference pressure shown in Figure 3.5 is 29.92 inHg). The Kollsman setting essentially shifts the altimeter's calibration curve in order to account for local variations in sea level pressure, which is routinely encountered due to weather variations (e.g., low or high pressure regions moving through a geographical area). Since accurate measurement of altitude is critical in most flight testing work, we will devote some attention to the calibration and correct setting of the altimeter.

The most typical use of the altimeter under routine flight is to set the Kollsman reference pressure to the local barometric pressure, such that the indicated altitude is the aircraft's height above mean sea level (MSL). A pilot can easily obtain up‐to‐date readings of the local barometric pressure by listening to broadcasts from local weather stations (such as the Automated Weather Observing System, or AWOS, found at many airports). Alternatively, air traffic control (ATC) will often report the local barometric pressure setting, especially when aircraft are transitioning from one controller to another with responsibility for different geographical areas. Reporting of the local barometric pressure is an important function for ATC, since they aim to maintain consistent vertical separation between all aircraft. Thus, for a pilot to ensure an accurate reading of MSL altitude, the altimeter must be set to the correct local barometric pressure reading (viewed in the Kollsman window) by adjusting the Kollsman knob.

However, in flight testing, we often wish to know the pressure altitude, or the pressure at our flight altitude. This can be accomplished by setting the altimeter to a reference pressure of 29.92 inHg (1013 hPa) instead of the local barometric pressure reading. Under this situation, the altimeter will not provide an accurate indication of height above sea level; rather, it will indicate pressure altitude. A flight test engineer can readily take the measured pressure altitude and convert this to a value of the local freestream static pressure via the standard atmosphere, using the theory described in Chapter 2[3].

#### 3.1.3 Outside Air Temperature

Knowledge of ambient (freestream) temperature of the flight environment is important for calculating the freestream density from the ideal gas law and for determination of true airspeed. The challenge of measuring outside air temperature (OAT) from a moving aircraft is related to the frame of reference of the air (the desired temperature) versus the aircraft reference frame (where temperature is measured). Since the air is moving relative to the aircraft, the temperature measured in the aircraft frame of reference will be higher. If a temperature probe completely stagnates the flow (i.e., with no loss of energy), the isentropic Mach relation,


(3.1)


may be used to find the freestream temperature (T∞) from measurements of the stagnation temperature (T0) and the freestream Mach number (M∞), where γ = 1.4 is the ratio of specific heats for air. However, most temperature probes do not fully recover the full stagnation temperature, so a recovery factor (k) must be introduced. Furthermore, there may be differences between the local Mach number (Mℓ) and the freestream Mach number, due to local acceleration or deceleration of the flow around the aircraft body. Thus, we can modify Eq. (3.1) to accommodate these two factors,


(3.2)


where Mℓ and k can be found by calibration (Gracey 1980).

#### 3.1.4 Other Instrumentation

Other relevant instruments on a traditional cockpit panel include a clock (for timing various events), the engine tachometer (for measuring engine speed in RPM), manifold pressure for the engine air intake, fuel flow rate, and total fuel burned. In traditional flight testing at the university level, readings from the “steam gauge” instruments must be manually recorded via pen and paper. These manual data recording techniques can be effective, as long as the time scale of any transient characteristic of the flight maneuver is long relative to the speed at which data can be manually recorded. For example, the rate of climb in a sustained, steady climb can be easily recorded by hand with a stopwatch and the altimeter, while the level acceleration of an aircraft would be much more difficult to manually record since velocity is changing quickly over time.

### 3.2 Glass Cockpit Instruments

Glass panel avionics displays (Figures 3.6–3.8) are becoming increasingly common on small GA aircraft. Glass panels measure and display the same data as traditional instruments, but the organization and display of data is greatly improved for better scanning and interpretation by the pilot. The glass panel display is usually physically segmented into a primary flight display (PFD), where critical data such as airspeed, altitude, heading, and attitude are displayed (left screen in Figures 3.6 and 3.7), and a multifunction display (MFD) where secondary data such as engine performance, navigation, terrain, traffic, etc. are displayed (right screen in Figures 3.6 and 3.8). We will discuss the glass panel display of the same data streams that are found on a traditional six pack of instruments, followed by a few notes on recording data from glass panel avionics systems. The following discussion refers to Figures 3.7 and 3.8.


Figure 3.6 Overview of aircraft cockpit instrumentation for a glass panel avionics display in a Cirrus SR20.


Figure 3.7 Detailed view of the primary flight display (PFD) on a Cirrus SR20, with key indications identified.


Measurements such as airspeed and altitude continue to be made in the same manner, where total pressure and static pressure are used to calculate the indicated airspeed. Since the calibration of airspeed is known, and real‐time measurements of pressure and OAT are available, the flight computer can calculate the true airspeed in real time. Since global positioning system (GPS) data are also available for measuring ground speed, the flight computer can also calculate the winds aloft, which represent the difference between true airspeed and ground speed. (See Chapter 8 for detailed definitions of these speeds, and details on how they are computed.) Indicated airspeed is prominently displayed on the left side of the glass panel on a linear, sliding scale along with a digital readout in the center of the scale. Altitude is also displayed on a linear sliding scale, but on the right side of the screen. The Kollsman setting (reference pressure) is displayed immediately beneath the altitude scale. On the right side of the altitude ticker is a display of the rate of climb in numerical and graphical form.

The attitude indicator is displayed in much the same way as it is on a traditional attitude indicator; one critical difference is that the artificial horizon completely spans the width of the display for better situational awareness for the pilot. The heading indicator is in the bottom center of the PFD, with heading information displayed in much the same way as on the analog instrument. Both the attitude indicator and the heading indicator are based on microelectromechanical systems (MEMS)‐based gyroscopes, magnetometers, and accelerometers. The details of these sensor schemes will be discussed in the following subsections. OAT is typically displayed on the lower left side of the PFD. Engine parameters such as engine speed, percent power, manifold pressure, fuel flow rate, fuel burned, exhaust gas temperature, oil pressure, oil temperature, etc. are displayed on the MFD (see Figure 3.8).


Figure 3.8 Detailed view of the multifunction display (MFD) on a Cirrus SR20, with key engine parameters identified.


The airspeed and altitude tickers, along with the heading indicator, have accompanying magenta trend bars (on the inside edge of each ticker or along the circumference of the heading indicator) that indicate the projected value that will be true 6 seconds in the future, based on current rates of change. Rate of turn can be inferred from the length of the magenta bar on the heading indicator (e.g., a standard rate turn would have a magenta bar extending 18° from the center).

Data from glass cockpit displays may also be recorded manually (pen and paper), or in some cases, limited data streams are available in digital form from the avionics suite itself. For example, the Avidyne FlightMax Entegra avionics suite records aircraft data including latitude, longitude, pressure altitude, density altitude, exhaust gas temperatures and cylinder head temperatures for all cylinders, oil temperature, oil pressure, engine RPM, OAT, and manifold pressure. While this data stream is predominantly focused on engine parameters (for engine health monitoring), it can be a useful supplement to other data streams used in flight testing. The avionics suite records the data at a rate of one sample per 6 seconds (0.167 Hz) and stores it in internal data storage. The data can be retrieved after the flight via the USB port on the front of the avionics panel.

The fundamental principles for the sensors at the heart of an aircraft's glass panel avionics are the same as those underlying traditional cockpit instruments. Glass cockpit sensors are based on gyroscopic principles and measurement of physical quantities such as pressure and temperature, but there are critical differences. Sensors such as magnetometers, accelerometers, and rate gyroscopes are grouped together into an inertial measurement unit (IMU), known as the attitude and heading reference system (AHRS), that fuses the sensor data streams to provide real‐time computations of an aircraft's heading and orientation in space. A second major subsystem is the air data computer (ADC), which computes aircraft speed, altitude, and rate of change of altitude based on measurements of total pressure, static pressure, and OAT. The third major subsystem used in glass panel avionics is the navigation instruments. In modern avionics, this primarily relies upon a global navigation satellite system (GNSS) receiver (i.e., a GPS receiver) but also includes radio receivers for radio‐based navigation aids. A significant advantage of glass panel avionics is that derived quantities such as winds aloft, density altitude, true airspeed, etc. can be determined real time in flight via the onboard computer at the heart of the avionics system.

### 3.3 Flight Test Instrumentation

Recent developments in MEMS have revolutionized sensor design and fabrication, making these sensors available at low cost and in small packages. Complex sensors such as gyroscopes and magnetometers can be fabricated with an extremely small form factor, allowing for them to be installed in very compact devices (see Figure 3.9). Most notably, the rapid development of MEMS has been driven by the proliferation of smartphones, which have many of the same sensors as those found on aircraft. MEMS developments have also enabled integration of these instruments into the cockpit – the modern avionics glass cockpit systems discussed in the previous section rely upon MEMS sensors for determining aircraft state. Alternatively, small external sensor packages such as smartphones, or the custom‐built unit, illustrated in Figure 3.9, can be mounted in any convenient location within the aircraft cockpit for simple installation and reasonably accurate DAQ. These comprehensive sensor suites are roughly equivalent to the AHRS that supports glass panel avionics.


Figure 3.9 Modern flight testing board with built‐in GPS, accelerometers, gyroscopes, magnetometers, and pressure transducer.

Source: Photo courtesy of Matthew H. McCrink.


The most significant deficiency of these instrumentation packages is the lack of air data measurements such as total pressure, static pressure, and OAT. Measurement of these properties requires direct access to dedicated instrumentation on the aircraft (the pitot‐static system), which is not normally possible on GA aircraft commonly accessible to students in an aircraft flight testing course. However, there are techniques (“work‐arounds”) for inferring these missing flight data. OAT changes very slowly at a given altitude, allowing it to be manually read and recorded at sparse intervals at a particular flight condition. Freestream static pressure can be measured to fairly good approximation by measuring cockpit pressure using a MEMS barometer on the DAQ device (see Gregory and McCrink 2016 for details). Total pressure (and, thus true airspeed) cannot be measured in flight without access to a pitot probe. However, using the techniques described in Chapter 8, true airspeed may be found by measuring ground speed during flight at a single test condition along three separate headings.

Key sensors in a typical external DAQ unit are a satellite navigation receiver and antenna (e.g., the GPS), 3‐axis gyroscopes, 3‐axis accelerometers, 3‐axis magnetometers, and a pressure transducer (barometer). A brief overview of each of these sensors is discussed as follows, but a much more detailed discussion is available in Titterton and Weston (2004).

#### 3.3.1 Global Navigation Satellite System

One example of a global navigation satellite system used for determining position in 3D space (latitude, longitude, and altitude) is the GPS (for the remainder of this book, GPS will be considered synonymous with GNSS, although there are other satellite‐based navigation systems in use such as the Russian GLONASS, the European Galileo, or the Chinese BeiDou systems.). GPS signals offer very high positioning accuracy, typically resolving location to within a few meters or less. The basis for the measurement is transmission of a modulated carrier signal with a known pseudorandom code, a time stamp based on a highly stable atomic clock on board the satellite, and the precise location of the satellite in space. The GPS receiver infers the distance to each satellite being received based on the time required for the signal to traverse the distance from the satellite to the receiver (based on the ultrastable clock on each satellite). Since the position of each satellite in space is known with high accuracy and precision, and the speed of light is well known, the receiver can infer the distance to each satellite by phase aligning the pseudorandom code. The receiver then uses multilateration techniques to infer its own location in space based on these distances – the calculated distance from a particular satellite restricts the receiver location to being somewhere on a spherical shell centered on the satellite. The intersection of at least three spherical shells results in position being defined as a single point in space. Note that the clock on the receiver itself generally does not have a high degree of accuracy, so this represents an unknown in the calculation of position. Therefore, there are four unknowns in the computation: latitude, longitude, altitude, and instantaneous time, so the GPS receiver must have at least four satellites in view simultaneously in order to determine an accurate position estimate. GPS receivers can reliably report latitude and longitude with high accuracy, but altitude indications typically have much more error. In particular, smartphone‐based GPS receivers lack an external antenna and rely upon algorithms that are optimized for terrestrial applications. Thus, altitude reported by smartphone‐based GPS sensors is generally unreliable and should not be used for measurement of altitude in aircraft flight testing (see Gregory and McCrink 2016 for details). General overviews of satellite‐based navigation schemes are provided by Misra and Enge (2010) and Kaplan and Hegarty (2017).

Several key error sources limit the accuracy of GPS position estimates. These errors include propagation delays due to dispersion of the signal by the ionosphere (termed ionospheric delay), uncertainty in the time due to drift of the atomic clocks on board the satellites, and uncertainty in the location of the satellites (ephemeris error). Advanced signal processing algorithms have been introduced to correct for these errors, but the most basic correction scheme is to introduce a real‐time error correction term from a receiver at a fixed, accurately known position. These correction schemes include differential GPS (DGPS), real‐time kinematic (RTK) GPS, and the FAA's Wide Area Augmentation System (WAAS). We will provide a brief overview of each of these as follows.

Differential GPS can provide refined position and velocity histories for flight test applications (Sabatini and Palmerini 2008). A typical DGPS architecture for flight testing is shown in Figure 3.10. The system consists of a reference receiver located at a known location that has been previously surveyed, and one or more DGPS user (mobile) receivers mounted on a test aircraft. The reference receiver antenna, differential correction processing system, and datalink equipment are collectively called the reference station. Both the user receiver and the reference receiver data can be collected and stored for later processing, or sent to the desired location in real time via the datalink. DGPS is based on the principle that receivers in the same vicinity will simultaneously experience common errors on a particular satellite ranging signal. In general, mobile receivers use measurements from the reference receiver to remove the common errors. The limiting factor for DGPS is that the mobile and fixed receivers need to be in proximity to one another such that they experience the error sources in the same way and to facilitate radio communication from the fixed reference receiver to the mobile receiver on board the aircraft. Thus, DGPS is most applicable to local‐area flight operations such as takeoff and landing flight tests.


Figure 3.10 Typical differential GPS architecture.


RTK GPS is a technique similar to DGPS, but offers higher accuracy. Similar to DGPS, RTK provides a correction to the position estimate, which can be transmitted in real time to the mobile GPS receiver or stored for subsequent analysis. The correction factor is determined by measuring the distance to the satellite using a different technique from traditional GPS. Instead of relying solely on the pseudorandom code transmitted by the satellites, RTK GPS uses statistical methods to estimate the number of cycles present in the waveform between the receiver and the satellite and then multiplies the number of cycles by the wavelength (19 cm for the L1 signal) to infer range. There is some resulting error in the estimated distance, due to ambiguity in determining the correct integer number of cycles due to phase differences. The RTK technique can provide remarkable positioning accuracy, improving the position estimate to 1 cm accuracy. However, RTK GPS also requires that the mobile receiver be in the same vicinity as a fixed reference station, which limits its applicability to downrange flight tests.

In the aviation realm, an augmentation system has been recently developed in order to improve upon the baseline accuracy of the satellite‐based position measurement system and enable precision instrument approaches without requiring nearby ground‐based reference stations. The Wide Area Augmentation System is a satellite‐based augmentation system developed by the US Federal Aviation Administration that covers the majority of North America. It is based on a system of ground‐based reference stations that calculate the local difference between the GPS‐indicated position and the station's actual position (surveyed to very high accuracy). This error data, expressed as a deviation correction, is uplinked in real time to geostationary WAAS satellites at least once every five seconds, which then broadcast the correction to aircraft throughout the national airspace. WAAS GPS corrects for positioning errors predominantly resulting from ionospheric disturbances, which add phase distortion to received GPS signals. The WAAS correction is broadcast over the same frequency bands used for the baseline GPS signal, which reduces system cost and complexity. The resulting accuracy of a WAAS GPS receiver is improved to approximately 2‐m in the horizontal and vertical directions, which is an order of magnitude improvement relative to the baseline accuracy of standard GPS.

An important point to recognize when using GPS data for flight test is that the position from a GPS receiver is reported as decimal degrees for latitude and longitude, with a sign convention for positive being North of the equator and East of the prime meridian (e.g., the latitude/longitude coordinates 40.074199 ° , – 83.07968° are in North America). If relative distance is desired (say, in units of ft, m, or nautical miles), then some type of transformation is needed to convert the difference between latitude/longitude coordinate pairs into distance. This transformation is commonly done in the fields of geodesy and navigation, where a model of the Earth's shape must be assumed. Generally speaking, Earth is in the shape of an ellipsoid that bulges near the equator (relative to a perfect sphere) due to the rotation of the planet. One of the most common Earth models is the World Geodetic System 1984 ellipsoid (WGS84), which is periodically refined and revised (National Imagery and Mapping Agency 2000; Pavlis et al. 2012). WGS84 forms the basis of GPS position reporting, with latitude and longitude forming a measure of distance within the WGS84 coordinate system. However, these coordinates must be transformed to local Cartesian coordinates before distance calculations can be made for flight testing. This transformation can be done via the Universal Transverse Mercator conformal projection. This system involves the segmentation of Earth's surface into 60 zones, each measuring 6° of longitude wide. Bands of latitude measuring 8° high are sometimes used to further subdivide the zones. The transformation for each zone from WGS84 to Cartesian coordinates can be performed by methods described by Snyder (1987), and a wide array of MATLAB toolboxes are available for this purpose (e.g., see Wasmeier 2015).

#### 3.3.2 Accelerometers

A three‐axis accelerometer provides a direct measurement of acceleration in all three directions, with the acceleration being relative to the local inertial frame of reference. Thus, an aircraft in steady level flight will have an acceleration of 9.81 m/s2 in the vertical direction (+1g), and zero acceleration in the other directions, since the local inertial frame corresponds with a freely falling object and the aircraft is accelerating upwards relative to the inertial frame. Accelerometers essentially operate as a spring‐mass‐damper system, where the applied acceleration along a particular axis will cause a displacement of the mass by an amount that depends on the properties of the system. The displacement is then measured by converting it to a voltage, and calibrating this voltage to acceleration. In MEMS devices, the spring‐mass‐damper system is often a cantilevered beam with a proof mass, where transduction of the displacement to voltage is most often done through capacitive or piezoresisitve schemes. Capacitive transduction involves a gap between the cantilevered beam and a fixed beam, which varies the capacitance of a circuit which can then modulate a measured voltage. The piezoresistive scheme involves a piezoelectric material as the spring in the system, where the voltage drop across the piezoresistor changes with the applied strain due to acceleration.

Accelerometers can be used in flight testing to detect events with sudden changes in acceleration (such as stall), measure the orientation of the aircraft relative to the ground in steady flight, indicate the bank angle in a steady turn by measuring g's in the aircraft's frame of reference, determine the period of dynamic stability phenomena such as the long‐period phugoid mode, and other applications. In principle, the measured acceleration can be integrated in order to infer a change in velocity, although the noise in the signal often precludes this in practice. Further, the measured accelerations are integrated into the flight data computer for determining vehicle state in modern avionics systems.

#### 3.3.3 Gyroscopes

Building upon our earlier discussion of gyroscopic principles for traditional flight instruments, we will now consider how they are used for modern avionics systems and instrumentation. Rate gyros used in modern glass panel avionics and DAQ systems are based on MEMS‐fabricated gyros. These gyros sense the rate of angular motion, rather than directly measuring the angle itself. A three‐axis gyro will have three independent rate gyros mounted along mutually perpendicular planes. One example of a MEMS rate gyro is based on the principle of sensing Coriolis acceleration. In this configuration, a proof mass is mounted on springs and oscillated in a direction perpendicular to the measured axis of rotation. As the proof mass oscillates, its radial distance from the aircraft's center of rotation also changes, leading to time‐varying tangential velocity that subjects the mass to varying amounts of Coriolis acceleration while the body rotates. This leads to a time‐varying reaction force in a direction perpendicular to the axis of rotation and the direction of oscillation of the proof mass. This reaction force is applied across springs in the lateral direction, which translate the reaction force into a linear motion that is sensed by capacitive elements (interdigitated fingers).

Since rate gyros measure the angular speed – pitch rate, roll rate, or yaw rate – rather than directly measuring the respective angles, the rotation rates must be integrated with respect to time in order to determine the pitch, roll, or yaw angles. Through the integration process, any noise present in the signals accumulates and leads to growing error in time.

#### 3.3.4 Magnetometers

A three‐axis magnetometer can be used to sense the aircraft's magnetic heading, much in the same way that a compass provides magnetic heading by always pointing toward magnetic north. On a MEMS‐based device, each of the three magnetometers is mounted mutually perpendicular with a reasonably high degree of precision. Each magnetometer senses the local magnetic field via the Hall effect, whereby a voltage difference is induced across an electrical conductor in a direction transverse to both an applied magnetic field and an electric current flowing through the device. For sensing the aircraft's heading, each axis of the magnetometer responds to Earth's magnetic field lines, which are aligned between the magnetic North and South poles. Since the North and South poles are not aligned with the physical poles, there is a difference between magnetic north and true north (referred to as magnetic declination, or variation). The amount of magnetic variation depends on geographic location and time, with a time scale of years (National Centers for Environmental Information 2019).

When using a magnetometer in an aircraft, the sensing of the Earth's magnetic field can be strongly influenced by nearby magnetic fields and ferromagnetic materials, through an effect known as magnetic deviation. Thus, an aircraft's compass must be calibrated to account for these error sources – this is typically done by positioning the aircraft along various points of the compass (typically referenced to a so‐called “compass rose” painted on the ramp with 30° heading intervals) and noting the difference between the compass reading and the actual magnetic bearing. The two error sources are referred to as hard and soft iron distortions. Hard iron distortions are due to the presence of nearby magnetic fields, which could be from magnets or electronic circuits, and result in a constant bias offset on the measured magnetic field. Soft iron distortions are due to the presence of nearby ferromagnetic materials (such as the engine block), and result in skewing of the measurement or an offset whose magnitude is heading‐dependent. These error sources can be nontrivial when using a three‐axis magnetometer on board an aircraft. Thus, a magnetometer that is part of an external DAQ system should be calibrated before flight to remove these effects (the magnetometers built into the aircraft's built‐in avionics have already been calibrated).

Fortunately, a compass rose is not required for calibration of a MEMS magnetometer, and the required calibration process is fairly straightforward. Before takeoff, with all electronics operating, the DAQ unit in place, and the magnetometer acquiring data, the aircraft should be swung through two complete 360° circles (a total heading change of 720°). When plotted in time, data from the x‐ and y ‐ axes of the magnetometer from this maneuver will form an ellipse. If the magnetometer was not subject to any error sources, the acquired data should form a constant radius circle centered on the origin. However, the error sources result in an elliptical pattern, where the offset of the ellipse from the origin (0, 0) depends on the error from hard iron distortions, and the eccentricity of the ellipse depends on the magnitude of error from soft iron distortions. A mapping can be determined to take the acquired data and transform it to a circle. This can be done by the following equation,


(3.3)


where xnc, ync, and znc are the noncalibrated data straight from the magnetometer; the B vector contains the bias errors due to hard iron distortions, the M matrix corrects for the soft iron distortions; and xc, yc, and zc are the calibrated data. Values of M and B are determined from a least‐squares fit to the data and subsequently applied to all magnetometer data acquired during the flight test.

#### 3.3.5 Barometer

A MEMS pressure transducer can be used as a barometer for an indication of pressure altitude. MEMS barometers are typically piezoresistive devices, where the deformation of a thin silicon diaphragm is measured through piezoresitive principles. The silicon diaphragm is doped at certain locations, thus locally altering the electrical conductivity and imparting resistor‐like properties. As the diaphragm deflects in response to an imposed pressure, the resistances of the doped regions change. If these piezoresistors are connected to a Wheatsone bridge, the change in resistance is converted to a change in voltage that can be easily measured. The calibration of these sensors is typically temperature dependent, so MEMS barometers often include an integrated temperature sensor for compensation.

The pressure reading of a MEMS barometer can be converted to altitude via hydrostatics. Necessary input values are the local barometric pressure reading and/or field elevation, along with OAT. All of the necessary theory for this conversion is detailed in Chapter 2 on the definition of the standard atmosphere. The pressure reading (and indicated altitude) of MEMS barometers used in some external DAQ devices can have a nonnegligible bias error (offset) in the reading. This is a minor concern, however, since it is a straightforward matter to determine the offset when the aircraft is on the ground, where a pressure measurement is made and field elevation and/or local barometric pressure are known. For flight testing, the other predominant source of error is a difference between cabin pressure (where the DAQ unit is typically mounted for student flight testing) and freestream static pressure. Gregory and McCrink (2016) evaluated the magnitude of this error for flight in a Diamond DA40 and found that cabin pressure was approximately 140 Pa higher than freestream static pressure at cruise conditions. For this particular aircraft, ram air effects that slightly pressurize the aircraft cabin in flight are the likely cause of the discrepancy. Despite these error sources, altitude indication from cabin pressure tends to be more accurate than GPS‐reported altitude.

#### 3.3.6 Fusion of Sensor Data Streams

As noted in the previous subsections, each individual sensor has some limitations to its utility due to various sources of noise or other errors such as temperature drift. This makes direct inference of vehicle state from one set of sensors problematic (e.g., integrating the signals from the rate gyros alone to determine vehicle orientation would introduce substantial errors). Optimal performance, however, is obtained when different data streams can be fused together in a manner such that the collected set provides a much more accurate and reliable estimate of vehicle state. One very common method for fusing together data streams is Kalman filtering. The Kalman filter is an algorithm that takes multiple time records of sensor data and produces estimates of vehicle state with improved accuracy compared to the estimate if only a single data stream were available. In essence, it gives a solution or prediction of vehicle state with an accuracy that is much improved over the estimate provided by any subset of sensors. The basis of the Kalman filter is described as follows.

First, we need a precise definition of the vehicle's state. It is the set of data that completely describes the vehicle's position and orientation, along with the rates of change of position and orientation. Thus, the position estimate and its derivatives would be the spatial location of the vehicle, its velocity, and its acceleration in some frame of reference. The orientation estimate is the vehicle's pitch, yaw, and roll angles, along with rates and accelerations of those same angles. These estimates of position and orientation have some uncertainty associated with them, which the Kalman filter assumes to be random and Gaussian distributed.

At each time step, a prediction of the vehicle's state at the next time step is formulated based on knowledge of the current state, an estimate of the uncertainty of the knowledge of that state, and a model based on the vehicle dynamics. When that next time step arrives, the prediction of the vehicle state is compared with measured data of the vehicle's state (along with the associated uncertainty in both the prediction and the measurements of the state). A refined estimate of the vehicle's state is generated by a weighted sum of the predicted state and measured state. Since the Kalman filter relies on both measurements of the vehicle state and model predictions of the vehicle state, the accuracy of the resulting state estimate is dramatically improved.

This is just a very brief overview of data fusion using Kalman filtering, for the purposes of providing perspective. These filters are routinely used in cockpit avionics systems, unmanned aerial vehicle (UAV) flight control systems, and in DAQ systems to improve the reliability and accuracy of vehicle state estimation. A much more detailed discussion of Kalman filtering is available in the literature (e.g., Rogers 2007; Zarchan and Musoff 2015).

### 3.4 Summary

We have covered a broad range of content related to instrumentation in this chapter. The central theme of this chapter is a description of how various aspects of aircraft performance can be measured in flight, and the key operating principles of standard aircraft instrumentation and avionics, as well as dedicated flight test instrumentation.

Standard aircraft instruments that are commonly used in flight testing include the airspeed indicator, altimeter, vertical speed indicator, engine tachometer and manifold pressure, and the heading indicator. MEMS‐based sensors include GPS, magnetometers, accelerometers, gyroscopes, and barometer. The general utility of these sensors across the range of flight tests presented in this text is mapped out in Table 3.1, assuming that raw data from each sensor are used individually (rather than the robust estimation of vehicle state via Kalman filtering, which may likely be beyond the scope of an undergraduate course on flight testing). Table 3.1 clearly shows that GPS, accelerometers, and the barometer are the most broadly useful sensors. Each particular sensor has strengths and weaknesses, as discussed earlier in this chapter, making them more or less useful for acquiring flight test data. This concise summary of the relevancy of each sensor provides an overview of the relative importance of each sensor and a quick reference for test planning for a given flight test. Specific details for various performance flight tests are covered in detail in Chapters 7–16.


Table 3.1 DAQ sensor utility matrix.


GPS provides ground speed, heading, and location at a maximum sample rate of about 1 Hz. Altimetry provided by GPS can have substantial errors: the vertical dimension is the least accurate for GPS positioning due to the geometry of the position estimation problem, the fact that antenna reception may be poor from within an aircraft (particularly for a smartphone‐based GPS receiver), and because the position estimation algorithms are optimized for terrestrial applications. Also, measurements of distance with GPS must involve transformation of latitude/longitude coordinates into an appropriate local Cartesian plane before further analysis can be done. Location, ground speed, and heading information are useful for nearly every flight test described in this text.

The magnetometer, in practice, is of marginal utility for aircraft performance flight testing. This is primarily because heading information is also available from the GPS receiver, the fact that the magnetometer signal is relatively noisy, and calibration is required. The magnetometer indication must be calibrated for hard and soft iron sources via a quick pre‐flight maneuver consisting of two complete turns on the ground. Postprocessing of this calibration and application to the magnetometer data for derivation of heading are more involved. However, the magnetometer provides heading information at a more rapid rate than GPS, and it is highly advantageous to incorporate magnetometer data into a state estimation algorithm such as the Kalman filter.

Three‐axis gyroscopes are also of marginal utility as a stand‐alone sensor, since MEMS gyros measure angular rates instead of the absolute angles that are more relevant for determination of aircraft attitude. Further, significant noise can be introduced when integrating these signals in order to determine aircraft attitude.

Accelerometers provide a good indicator of any transient event found in flight testing, making it straightforward to find that event in a long data record. Features in the flight such as the stall event, takeoff point, measurement of load factor in a turn, and identification of the characteristic frequency in dynamic longitudinal stability are relatively straightforward to find and measure in accelerometer data. The accelerometers are also useful for measuring the frequency of engine vibrations, which is an indicator of engine speed (rpm), as long as the sampling rate is high enough to avoid aliasing (discussed in the next chapter). Accelerometer signals also facilitate identification of dynamic stability characteristics of the aircraft, such as the phugoid or Dutch roll modes. One key limitation of a 3‐axis accelerometer is that the DAQ device axes may not be coaligned with the aircraft body axes, but this can be calibrated by comparing accelerometer signals during steady (1 g) flight.

A barometer can provide a measurement of cabin pressure, which serves as a reasonable proxy for freestream static pressure in most situations. Both altitude and vertical speed can be reliably estimated from barometry data. Pressure altitude can be inferred using the local barometric pressure reading and refined with a measurement of outside static temperature.

Finally, we will conclude with a note of caution about comparing data from different sensors to infer flight test results. Some sensors can have inherent temporal delays, which could lead to timing or phase mismatch between sensor streams. For example, the computation of GPS position estimates requires processing time on board the receiver, so it is important to make sure the correct time base is used for comparison of GPS data with other sensor data streams. Similarly, different sensors (even those installed on the same DAQ device) can have different sample rates. For example, GPS data are often sampled at a rate on the order of 4 Hz, while accelerometers may be sampled at 100 Hz. Again, it is important to use the correct time base for comparing data streams. The next chapter will discuss in detail how data streams are digitized, along with analysis techniques such as filtering and spectral analysis.


Nomenclature

B

magnetometer calibration, bias error vector

g

gravitational acceleration

I

moment of inertia

k

recovery factor

L

angular momentum vector

M

magnetometer calibration matrix

Mℓ

local Mach number

M∞

freestream Mach number

t

time

T∞

freestream static temperature

T0

stagnation temperature

yc

calibrated magnetometer data,

y

‐component

zc

calibrated magnetometer data,

z

‐component

xnc

uncalibrated magnetometer data,

x

‐component

ync

uncalibrated magnetometer data,

y

‐component

znc

uncalibrated magnetometer data,

z

‐component

γ

ratio of specific heats

ω

angular velocity vector


Subscripts

c

calibrated

nc

uncalibrated


Acronyms and Abbreviations

ADC

air data computer

AHRS

attitude and heading reference system

ATC

air traffic control

AWOS

automated weather observing system

GLONASS

Globalnaya Navigazionnaya Sputnikovaya Sistema (Russian GNSS)

GNSS

global navigation satellite system

GPS

Global Positioning System

IMU

inertial measurement unit

MEMS

microelectromechanical systems

MFD

multifunction flight display

MSL

mean sea level

OAT

outside air temperature

PFD

primary flight display

RTK

real‐time kinematic

UAV

unmanned aerial vehicle

WAAS

Wide Area Augmentation System

WGS84

World Geodetic System 1984 ellipsoid model


References

Gracey, W. (1980). Measurement of Aircraft Speed and Altitude. NASA‐RP‐1046, https://ntrs.nasa.gov/citations/19800015804.

Gregory, J.W. and McCrink, M.H. (2016). Accuracy of smartphone‐based barometry for altitude determination in aircraft flight testing. AIAA 2016‐0270, Proceedings of the 54th AIAA Aerospace Sciences Meeting, San Diego, CA.

Kaplan, E.D. and Hegarty, C. (2017). Understanding GPS/GNSS: Principles and Applications, 3e. Boston, MA: Artech House.

Misra, P. and Enge, P. (2010). Global Positioning System: Signals, Measurements, and Performance, 2e. Lincoln, MA: Ganga–Jamuna Press.

National Centers for Environmental Information, and British Geological Survey (2019). World magnetic model. In: National Ocean and Atmospheric Administration. http://ngdc.noaa.gov/geomag/WMM/.

National Imagery and Mapping Agency. (2000). Department of Defense World Geodetic System 1984, Its Definition and Relationships With Local Geodetic Systems. NIMA Technical Report TR8350.2, 3e, Amendment 1, http://earth-info.nga.mil/GandG/publications/tr8350.2/wgs84fin.pdf.

Pavlis, N.K., Holmes, S.A., Kenyon, S.C., and Factor, J.K. (2012). The development and evaluation of the Earth Gravitational Model 2008 (EGM2008). Journal of Geophysical Research, vol. 117 (B04406): 1–38. https://doi.org/10.1029/2011JB008916.

Rogers, R.M. (2007). Applied Mathematics in Integrated Navigation Systems, 3e. Reston, VA: American Institute of Aeronautics and Astronautics.

Sabatini, R. and Palmerini, G.B. (2008). Differential global positioning system (DGPS) for flight testing. In: RTO AGARDograph 160, Flight Test Instrumentation Series, vol. 21.

Snyder, J. P. (1987). Map Projections – A Working Manual. U.S. Geological Survey Professional Paper 1532, http://pubs.er.usgs.gov/publication/pp1395.

Titterton, D.H. and Weston, J.L. (2004). Strapdown Inertial Navigation Technology, 2e. Stevenage, Hertfordshire, UK: The Institution of Electrical Engineers https://doi.org/10.1049/PBRA017E.

Wasmeier, P. (2015). Geodetic Transformations Toolbox. Matlab Central, http://www.mathworks.com/matlabcentral/fileexchange/9696-geodetic-transformations-toolbox.

Zarchan, P. and Musoff, H. (2015). Fundamentals of Kalman Filtering: A Practical Approach, 4e. Reston, VA: American Institute of Aeronautics and Astronautics.


## 4. Data Acquisition and Analysis

This chapter fundamentally deals with how we'll digitally represent the various aircraft performance characteristics for further analysis. A critical element of this chapter is a detailed discussion of how digital data acquisition (DAQ) systems work. Our discussion of DAQ techniques is motivated by industry and military flight test programs, which rely on complex data acquisition systems. Instrumentation on board the aircraft can involve hundreds or thousands of sensors of various kinds, and an equivalent number of channels to digitize and record this data. Data can be sampled at high rates in order to effectively capture transient phenomena, leading to vast quantities of data which require high bandwidth and storage. Furthermore, these data are often streamed in real time to ground stations via radio telemetry link, such that flight test engineers can monitor the data as the test is being conducted. Live telemetry of data and real‐time analysis adds to the safety and efficiency of the flight test program, enabling the flight test team to avoid hazardous test conditions or to adapt to test events as they develop.

While the typical student will not be able to work with such high‐end systems in the university environment, the basic principles of DAQ are still relevant in low‐cost, small‐scale data acquisition systems. With the continued evolution and miniaturization of digital electronics, these systems are now readily accessible even to students. Simple data acquisition systems in contemporary flight testing use include smartphones (Gregory and Jensen 2012; Gregory and McCrink 2016), LabVIEW‐ or MATLAB‐based digital DAQ systems (Muratore 2012), Arduino microprocessors (Koeberle et al. 2019), commercially available systems, and even the standard avionics onboard the aircraft (see Chapter 3). Thus, students can readily get exposure to the basic principles of DAQ systems, methods, and data analysis employed in flight testing.

This chapter provides an overview of the foundations related to DAQ and processing, such that the capabilities and limitations of DAQ methods can be appreciated. Our discussion of DAQ will begin with defining how signals may be represented as a function of time or frequency. This will directly lead to a discussion of filtering, whereby unwanted frequency content can be attenuated in a signal. Following this, we'll focus on the essential characteristics of DAQ, with an overview of the methods used to digitally represent an analog signal. We'll then conclude with an example of how DAQ techniques are applied to flight testing.

### 4.1 Temporal and Spectral Analysis

We'll start our discussion of DAQ by considering how signals can be represented in either the time domain or the frequency domain. Both representations of a signal are of use in the flight testing environment. The time domain representation is the most intuitive, where the signal is plotted as a function of time. The frequency domain representation is less intuitive, but no less powerful. This form of presenting a signal shows the relative significance of different frequency components found in the signal, facilitating visual separation of different frequency peaks in the spectrum. We'll examine both approaches of data representation as follows, and establish the link between the two.


Figure 4.1 Sample signal in the time domain.


A time‐domain representation of a signal is our intuitive view of signal waveforms, which is a plot of voltage as a function of time. For example, Figure 4.1 shows a plot of the function


(4.1)


in the time domain, where c0 = 2, c1 = 1, c2 = 0.5, c3 = 0.5, ω1 = 50.3 rad/s (f1 = ω1/2π = 8 Hz), ω2 = 5ω1, and ω3 = 10ω1. A representation of the same signal in the frequency domain, however, will plot the amplitude of each frequency component of the signal versus the corresponding frequency. Inspection of Eq. (4.1) reveals that the signal has three non‐zero frequency components: a dominant, low‐frequency component with amplitude of c1 at a frequency of ω1; and two smaller, higher‐frequency components with amplitudes c2 and c3 at frequencies ω2 and ω3. We can take these three amplitudes (c1, c2, and c3), along with the time‐averaged amplitude of the signal (c0, which has a frequency of ω0 = 0) and plot them versus the corresponding frequencies, resulting in the frequency domain plot shown in Figure 4.2.

Plotting the signal represented in Figure 4.1 in the frequency domain is straightforward in this case since we know the amplitude and frequency of each component from Eq. (4.1). But what if we don't know the frequency content of a signal? How would we generate a frequency domain representation of some arbitrary signal that we have acquired? The answer lies in a computational technique known as the fast Fourier transform (FFT), which is a straightforward and fast algorithm for computing spectral content of digitized signals. This section will provide only a very abbreviated overview of spectral analysis, which is the process of representing a time‐based signal in the frequency domain. The interested reader is encouraged to consult other sources such as Wheeler and Ganji (2003) or Bendat and Piersol (2010) for further details.

The concept behind Fourier analysis is that an arbitrary, periodic signal may be represented by a summation of a constant with an arbitrary number of sine and cosine functions (Powers 1999). The mathematical representation of a Fourier series is given as


(4.2)


Figure 4.2 Sample signal in the frequency domain.


Note that our example function defined earlier (Eq. (4.1)) is of the same form as Eq. (4.2), which made it straightforward for us to pick out the coefficients of the Fourier series by inspection and plot the signal in the frequency domain (Figure 4.2). For an arbitrary periodic waveform, the coefficients in Eq. (4.2) may be determined from


(4.3)


which is the time‐average of the signal over one period of the waveform, T = 1/f = 2π/ω. The other coefficients are given by


(4.4)


Note that Eq. (4.2) is an infinite series, implying that an infinite number of coefficients may be required to fully represent an arbitrary periodic waveform. In practice, the number of coefficients used to represent a signal is truncated to some reasonable number of computationally determined coefficients. If Eqs. (4.2)–(4.4) are evaluated for the sample function given by Eq. (4.1), with T = 2π/ω1 = 0.125 seconds, we could directly compute the integrals and find that the coefficients of the Fourier series are a0 = c0, b1 = c1, b5 = c2, and b10 = c3, with all other coefficients being zero.

Figure 4.3 shows another example of the application of a Fourier series representation to a triangle waveform,


(4.5)


Figure 4.3 Fourier series approximation of a triangle waveform.


with frequency ω = 314.2 rad/s (f = 50 Hz). Note that the function represented in Eq. (4.5) is odd, meaning that f(t) =  − f(−t). The implication of this for the Fourier series is that the an coefficients are zero and the function can be represented entirely by the sine terms in Eq. (4.2), making it a Fourier sine series. The coefficients of this sine series are b1 =  − 0.8106, b3 = 0.09006, b5 =  − 0.03242, b7 = 0.01654, …. Inclusion of each successive term in the sine series improves the fidelity of the Fourier approximation to the original waveform (Figure 4.3), with higher frequency coefficients improving the fit at the peaks of the triangle waveform. This is because the amplitude of the higher order terms decays rapidly with frequency, as shown in Figure 4.4.


Figure 4.4 Fourier components of the sine series approximation to a triangle waveform.


While the definition of the Fourier series is useful for illustrating the representation of signals in the frequency domain, the development thus far is not yet useful for frequency representation of an arbitrary waveform that we might encounter in flight testing. Actual analysis of signals via Fourier techniques is done through the Fourier transform, which relaxes the constraint on periodicity. The steps in frequency (ωn = nω) in Eq. (4.2) are reduced until ω becomes a continuous function of frequency and we have


(4.6)


which is the Fourier transform of a function f(t). Here the exponential function is another way of representing the sine and cosine terms, and such that F(ω) is a complex‐valued function (see Wheeler and Ganji 2003 or Bendat and Piersol 2010 for further details). Similarly, if one has a defined Fourier transform, F(ω), the original signal f(t) can be determined from the inverse Fourier transform,


(4.7)


In applying the Fourier transform to a digital representation of a signal (sampled at discrete time intervals) the discrete Fourier transform (DFT) is used. The DFT is represented by


(4.8)


where N is the total number of samples in the data record, Δt is the time interval between samples, Δf is the increment in frequency (equal to the inverse of the period), and there are k frequency components in the transform. (Note that only values up to k = N/2 are unique). In the same way that we defined an inverse Fourier transform, we can also define an inverse DFT,


(4.9)


for recovering the original signal.

The DFT and inverse DFT can be determined numerically, but this process tends to be computationally expensive since the number of computations is on the order of N2 real‐valued multiply‐add operations. Due to this computational expense, the FFT technique has been developed, which requires on the order of Nlog2N computations. (For a record length of N = 216, the FFT requires 212 fewer computations compared to the DFT). Bendat and Piersol (2010) may be consulted for complete details on the derivation and implementation of the FFT algorithm. Returning to our analysis of a triangle waveform (Eq. (4.5)), spectral analysis based on the FFT algorithm results in the power spectrum shown in Figure 4.5. The dominant frequency and higher harmonics are faithfully captured by the FFT algorithm, as is evident when we compare Figure 4.5 with Figure 4.4.

Note that the power spectral density is often represented on a logarithmic scale, which helps the higher‐frequency components of the signal appear more prominently on the plot (this is in contrast to the linear scaling employed in Figures 4.2 and 4.4). Power spectra often have broader frequency peaks along with lower‐amplitude ripple between the peaks, which are characteristic of the DFT and FFT algorithms. This phenomenon, referred to as spectral leakage, results from a non‐integer number of waveforms being present within the data record analyzed by the FFT, with the end effects being the primary culprit. Leakage may be reduced through windowing, where the window is a tapering function (high in the center region, with low values at the ends) multiplied with a subset of the data. Since the window size is a subset of the full data record, the full FFT is then the average of the computed FFTs of the windowed portions of the signal. An amount of overlap may be specified, which determines how much the window is shifted along the length of the record. Welch's modified periodogram method (Welch 1967) is one common approach to implementing a windowing function with overlap (see the function in MATLAB). Welch's method reduces the noise in the power spectrum, at the expense of reduced frequency resolution.


Figure 4.5 Power spectrum based on the FFT of the triangle waveform.

### 4.2 Filtering

We'll now discuss filtering techniques, and how they can be used to improve the interpretation of the signal by removing unwanted frequency content. When considering a signal represented in the frequency domain, filtering suppresses the amplitude of signal content over a select range of frequencies. This is done by defining and applying a transfer function, which is a frequency‐dependent weighting value that is multiplied with the signal in the frequency domain.

Common types of filters include low pass, high pass, band pass, and band stop schemes, which are illustrated in Figure 4.6. A low pass filter will attenuate signal content at frequencies above a specified cutoff frequency, and preserve signal content below that cutoff frequency. Low pass filtering is useful for removing high‐frequency noise in a signal, which may obscure the desired low frequency data. High pass filtering does just the opposite – it attenuates signal content at frequencies below the cutoff, and preserves signal content at higher frequencies. High pass filtering is particularly useful for removing the steady‐state voltage (a DC mean value) from a signal. The band pass filter is essentially a combination of the two, where the high‐pass cutoff frequency is at a lower frequency than the cutoff for the low‐pass filter. The region between the two cutoff frequencies is the passband. Finally, a band stop filter is designed to selectively remove a range of frequencies – it is the logical inverse of a band pass filter, where the low‐pass cutoff frequency is below the high‐pass cutoff frequency.

Figure 4.6 illustrates the effect of each of these filters on a signal (Eq. (4.1)) in both the time domain (left column) and in the frequency domain (center column). The right‐most column represents the transfer function for each filter. A filter can be applied to a given signal by transforming that signal into the frequency domain (via FFT), linearly multiplying the signal's power spectrum with the filter's frequency response function in the frequency domain, and then transforming the signal back into the time domain (via the inverse FFT). In Figure 4.6, the baseline signal is the same waveform that we considered in an earlier example (see Eq. (4.1)). The effects of the low pass filter are to suppress the higher frequency components at 40 and 80 Hz, leaving only the DC level and the sinusoidal component at 8 Hz. In contrast, the high pass filter removes the DC level and the lowest frequency component (8 Hz), leaving both high frequency components unattenuated. The band pass and band stop filters have equivalent performance, where the filter suppresses signal content in portions of the spectrum where the filter's transfer function has a high level of attenuation.


Figure 4.6 Examples of various filtering schemes applied to signals in the time domain (left column) and frequency domain (center column). The right column shows the transfer function associated with each defined filter: low pass, high pass, band pass, and band stop.


Beyond the definition of the various filter types, there are other filter characteristics that are important to consider. Common filter classes include Butterworth, Bessel, Chebyshev, and elliptical – each of which has varying characteristics. One important parameter is the filter order, which governs the stopband attenuation rate – a description of how much increase in attenuation can be achieved over a given frequency interval. Attenuation rates are typically specified as dB/octave or dB/decade, where an octave is a factor of two change in frequency and a decade is an order of magnitude change in frequency. Filter order is related to attenuation rate for the Butterworth filter by 6m dB/octave, where m is the filter order. A third important parameter is the amount of ripple allowed in the passband or the stopband. Figure 4.6 illustrates ripple throughout the stopband, where the transfer function is not flat across a range of frequencies. There is typically a tradeoff between ripple and attenuation rate, where high attenuation rate is achieved at the expense of increased ripple, and the filter class has a significant impact on the attenuation rate.

One final, critical characteristic of filters is the phase lag induced by the filter. In the same way that a filter exhibits attenuation as a function of frequency, there will be induced phase delay that is also frequency‐dependent. In most data processing applications this is an undesirable feature of the filter, but can be worked around through careful filter design or creative application of the filter (e.g., the function in MATLAB's Signal Processing Toolbox, which feeds a signal forward and then backward through the filter in order to cancel the phase effect). Phase delay in processed flight test data can be important when comparing a filtered signal with an unfiltered signal. A detailed discussion of filter design is beyond the scope of this text, but appropriate resources may be consulted for further details (Wheeler and Ganji 2003; Bendat and Piersol 2010).

Filtering can be applied before digitization or afterwards. Typically pre‐DAQ analog filtering is used to prevent aliasing, which will be discussed in Section 4.4. Analog filtering involves the use of dedicated circuitry, and once the signal has been digitized there is no longer any flexibility to change the filter cutoff frequency or characteristics. Digital filtering, on the other hand, can be changed at will during post‐processing, allowing an interactive and adaptive approach to data analysis.

### 4.3 Digital Sampling: Bit Depth Resolution and Sample Rate

Let's now consider the details of how a signal is actually captured in digital form. The fundamental principle of DAQ is creating a digital representation of an analog signal. An analog signal is defined as one where the signal level (e.g., voltage) is a continuous function of time. Digital signals, however, are always a discretized representation of that continuous function, with the fidelity of that representation depending on how many discretization levels are used across amplitude and time. Resolution of the signal amplitude depends on the bit‐depth resolution of the data acquisition device, and the defined input range. The input range essentially determines the minimum and maximum voltages that can be recorded for a given measurement, where any input values exceeding those limits will be clipped. Typical data acquisition ranges can be unipolar, where all of the input voltages are of the same sign (e.g., 0–5 V, or 0–10 V), or bipolar, where positive or negative voltages can be measured (e.g., −5 to 5 V, or −10 to 10 V). Bit depth resolution is a measure of how many discretization levels are used to subdivide the input range. This resolution is typically expressed as a power of 2, due to the architecture of the data acquisition hardware. For example, a 12‐bit data acquisition device will have 212 (4096) discretization levels spanning the input range.

A combination of input range and the bit depth resolution defines the minimum change in voltage that can be resolved in a digital waveform. The maximum error between a given analog voltage and its digital representation is the quantization error,


(4.10)


where R is the input range, and B is the number of bits of the DAQ device. Digitization of a desired signal should use an input range that is as close to the limits of the anticipated signal as possible (with little risk of the signal exceeding that input range) and a bit depth resolution as high as possible. The downsides of increased bit depth resolution are increased cost of the data acquisition hardware, and larger file sizes required to store the digitized signals. In practice, the bit depth resolution should be sufficiently high such that the discretization error is small relative to the smallest voltage change in the desired signal.

Figures 4.7 and 4.8 illustrate the effects of bit depth resolution on the digital representation of an analog signal. For this example, a simple sine wave with frequency of 1000 Hz (628 rad/s) is defined as


(4.11)


A digital representation of that signal with an input range of 0–5 V and a 4‐bit converter (24, or 16 steps) is shown in Figure 4.7, compared to the original analog function. The step‐stair appearance of the signal is due to quantization error, where the digital representation of the continuous waveform is rounded off to the nearest quantization level. If the bit depth resolution is increased to 212, as shown in the zoomed‐in waveform in Figure 4.8, the signal representation is much more faithful to the original analog signal. The increase in bit depth resolution from 24 to 212 provides a factor of 256 more levels to represent the analog waveform than the 4‐bit case shown in Figure 4.7.

Sample rate, defined as the number of digital samples acquired per second, is the other predominant factor that dictates the fidelity of the digital representation of the analog waveform. Sampling rate is determined by the time required to perform the analog‐to‐digital conversion process, limiting how many samples can be digitized in a given amount of time. If the sample rate is low – i.e., there is a long period of time between each sample of the analog signal – the acquisition process could miss important changes in the analog signal in the intervening time. Not only is important information missed by an insufficient sample rate, but the resulting digital representation can be misleading.


Figure 4.7 Digital representation of an analog waveform with input range of 0–5 V, a 4‐bit converter, and very high sample rate.


Figure 4.8 Digital representation of the analog waveform with input range of 0–5 V, a 12‐bit converter, and very high sample rate.


The sample rate must be sufficiently high relative to the highest frequency present in the signal. Note that signals can be a superposition of many constituent frequencies. As a general rule of thumb, a sample rate of at least 10 to 20 times the highest frequency present in the signal will provide a reasonable representation of the analog signal in the time domain. For example, Figure 4.9 shows a generally insufficient representation of the analog signal, where the sample rate of 4400 Hz is only 4.4 times higher than the 1000 Hz frequency being measured. In contrast, Figure 4.10 shows a fairly good representation of the signal, with a sample rate of 22 000 Hz (22 times the frequency of the sampled waveform), with only minor residual error in capturing the magnitude of the waveform peaks (approximately 80 mV error).


Figure 4.9 Digital representation of the analog waveform with a sample rate of 4400 Hz (4.4 samples per cycle of the 1000 Hz analog waveform), with very high bit depth resolution.


Figure 4.10 Digital representation of the analog waveform with a sample rate of 22 000 Hz (22 samples per cycle of the 1000 Hz analog waveform), with very high bit depth resolution.

### 4.4 Aliasing

A theoretical minimum sampling rate needed to capture all frequency content is given by the Nyquist criterion (Nyquist 1928). This limit states that the sampling rate (fs) must be greater than twice the maximum expected frequency component (fmax),


(4.12)


Notice that the criterion dictates that the sample rate must be greater than, not greater than or equal to, the maximum frequency. If a sample rate equal to twice the maximum frequency were employed, the digital representation of that frequency (if the signal were a single‐frequency waveform) could be a straight line, a situation illustrated by Figure 4.11. Based on this understanding of the Nyquist criterion, it is clear that the scenario illustrated in Figure 4.9, while not capturing the magnitude of the waveform peaks very well, is sufficiently high to identify the frequency of the signal being measured.

The consequences of not meeting the Nyquist criterion can be significant. If the Nyquist limit is not met, then frequencies in the signal beyond fs/2 cannot be resolved. This situation alone would be somewhat benign if the high frequencies were simply omitted. However, these high frequencies beyond the cutoff are actually represented as lower frequency content in the digital misrepresentation of the waveform. This can be insidious if the flight test engineer is unaware of the presence of this high‐frequency content and misinterprets these false low‐frequency representations as being real. This phenomenon of false representation of high frequency content (beyond the Nyquist cutoff) as low frequency content is referred to as aliasing.

The effects of aliasing can be represented in the time and frequency domain, as shown in Figure 4.12. The top row of the figure illustrates the actual waveform to be represented in digital form (the analog signal). The frequency of this signal is 20 Hz (left column), 80 Hz (center column), or 120 Hz (right column). Below this, the second row shows the digital representation of each signal when sampled at 100 Hz. Note that only the left‐most column satisfies the Nyquist criterion. Even though the indicated sample rate (100 Hz) is higher than the signal's fundamental frequency of the center column (80 Hz), the Nyquist criterion in this case (f

# Notes

1

There have been many iterations of the U.S. Standard Atmosphere over the years. The original version was published in 1958, and as scientific understanding of the atmosphere advanced, was updated in 1962, 1966, and finally 1976. Some older versions of the standard atmosphere persist today – for example, Anderson (2016) continues to refer to a 1959 definition of the standard atmosphere from the U.S. Air Force. However, the 1976 U.S. Standard Atmosphere and the 1993 ICAO standard atmosphere are widely accepted as the appropriate standards to use today.

2

There are two different definitions of absolute altitude that we will use in this chapter. The first one, considered here, is for development of the standard atmosphere. The second definition is widely used in aviation as the height above ground level. We will clarify these distinctions at the end of this chapter.

3

Additional details are available in an online supplement, “Effects of Kollsman Setting on Altimeter Reading.”