Investigating the Effects of Altitude and Flap Setting on the Specific Excess Power of a PA-28-161 Piper Warrior

By Tjimon Meric Louisy

A thesis submitted to the College of Engineering and Science of Florida Institute of Technology In partial fulfillment of the requirements For the degree of

Master of Science in Flight Test Engineering

Melbourne, Florida December 2019

We the undersigned committee hereby approve the attached thesis, “Investigating the Effects of Altitude and Flap Setting on the Specific Excess Power of a PA-28-161 Piper Warrior”, by Tjimon Meric Louisy.

______Brian A. Kish, Ph.D. Assistant Professor Aerospace, Physics and Space Sciences Major Advisor

______Isaac Silver, Ph.D. Associate Professor College of Aeronautics

______Ralph Kimberlin, Dr. Ing Professor Aerospace, Physics and Space Sciences

______Daniel Batcheldor Professor and Department Head Aerospace, Physics and Space Sciences

Abstract

Investigating the Effects of Altitude and Flap Configuration on the Specific Excess Power of a PA-28-161 Piper Warrior Tjimon Meric Louisy Advisor: Brian A. Kish, Ph.D.

The high number of General Aviation (GA) accidents attributed to Loss of Control suggests that GA pilots are lacking low speed awareness and are unable to appropriately recognize when the aircraft is in a low energy state. There is, therefore, an urgent need for the development of an energy management system which is applicable to GA aircraft that can alert the pilot in situations of low energy conditions and recommends to the pilot the appropriate corrective action to restore conditions to a safe energy state. This will require the development of an algorithm that governs this energy management system that considers a comprehensive understanding of the performance capabilities of GA aircraft, particularly the ability of the aircraft to progress from one energy state to another. Given that low energy conditions are the primary concern, the aircraft’s ability to progress from a low energy state to a higher energy state, or the aircraft’s specific excess power (Ps), will be the parameter of most interest.

The focus of this research study was the testing of a PA-28-161 Piper Warrior to develop an understanding of the effects of altitude and flap configuration on the ability of the aircraft to change its energy state. Level accelerations and level decelerations

iii were performed and used to determine the Ps for the aircraft at various altitudes and configurations. The objectives of the test program were to generate Ps curves for each altitude and configuration, compare the curves obtained, and determine trends that could help model the Ps of the aircraft under any operating conditions.

The results of the test program showed that there was an inverse relationship between specific excess power and altitude for both the clean-flap and full flaps configurations.

The best climb speed for the aircraft was approximately 79 KIAS in the clean configuration and 62 KIAS in the full flaps configuration. Furthermore, extending the flaps resulted in a significant decrease in the maximum specific excess power of the aircraft, with the maximum specific excess power in the full flaps configuration being approximately 200 ft/min less than the maximum specific excess power in the clean configuration for all altitudes investigated. The best glide speed was observed to be 75

KIAS in the clean configuration.

The data collected and trends observed will be valuable in the development of an algorithm for a GA energy management system. Further investigation into the Ps with the flaps deployed and comparison between the trends observed on the PA-28-161 with other common GA aircraft parameters will also be required.

Table of Contents Abstract ...... iii

Table of Contents ...... v

List of Figures ...... vii

List of Tables ...... xi

List of Abbreviations and Symbols ...... xii

Acknowledgements...... xiv

Dedication ...... xvi

Section 1 Introduction...... 1

Section 2 Test Methods and Materials ...... 14

2.1 Test Aircraft ...... 14

2.2 Instrumentation ...... 15

2.3 Flight Log ...... 16

2.4 Flight Test Locations and Crew ...... 17

Section 3 Data Reduction Methods ...... 18

3.1 Data Requirements...... 18

3.2 Test Procedures...... 19

3.3 Data Reduction...... 21

Section 4 Results ...... 32

4.1 Ps Plots (풂풔풔풖풎풆 풅풉/풅풕 = ퟎ) ...... 32

4.1.1 Steady-Level Accelerations ...... 32

4.1.2 Steady-Level Decelerations ...... 51

4.2 Comparison to POH ...... 58

4.3 Ps Plots (풅풉/풅풕) component included ...... 59

4.3.1 Steady-Level Accelerations ...... 60

4.3.2 Steady-Level Decelerations ...... 64

Section 5 Conclusions and Future Work ...... 68

5.1 Conclusions ...... 68

5.2 Recommendations and Future Works ...... 73

References ...... 76

Appendix A: Flight Test Data ...... 78

Appendix B: Supplementary Graphs ...... 98

List of Figures

Figure 1: Loss of control in flight accidents and fatalities in GA 2011-2015 [2] ...... 2

Figure 2 Fatal accidents per aircraft upset event types 2011-2015 [2] ...... 3

Figure 3: Altitude-velocity diagram showing lines of constant specific Energy (Es) [5] ...... 7

Figure 4: Sample Ps Curves and Resulting Constant Ps Contours [9] ...... 10

Figure 5: Specific Total and Modified Total Energy Error Rate during approach [10] ...... 12

Figure 6 PA-28-161 Piper Warrior – N618FT ...... 14

Figure 7: Test Locations [12] ...... 17

Figure 8: CAS vs Time (First 15s) ...... 23

Figure 9: CAS vs Time (16s Onwards) ...... 24

Figure 10: Pressure Altitude vs Time ...... 25

Figure 11: Modeling Pressure Altitude vs Time ...... 27

Figure 12: Ps vs CAS Level-Acceleration ...... 30

Figure 13: Ps vs CAS Level-Acceleration (풅풉/풅풕 ≠ ퟎ) ...... 30

Figure 14: : Ps vs CAS Level-Deceleration ...... 31

Figure 15: Ps vs CAS for Clean Configuration Level-Accelerations ...... 32

Figure 16: : Ps vs CAS for Full Flaps Configuration Level-Accelerations ...... 34

Figure 17: : Relationships between Ps and Altitude ...... 35

Figure 18: Relationships between Vh and Altitude ...... 36

Figure 19: Relationships between Vy and Altitude ...... 37

Figure 20: Equation-derived Ps curves...... 39

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Figure 21: Ps curves for Level-Accelerations at 1300 feet ...... 41

Figure 22: Ps curves for Level-Accelerations at 3000 feet ...... 42

Figure 23: Ps curves for Level-Accelerations at 5000 feet ...... 43

Figure 24: Ps curves for Level-Accelerations at 7000 feet ...... 44

Figure 25: Equation-derived Ps curves for Full Flaps Configuration...... 49

Figure 26: Ps Curves for Clean Configuration Level-Decelerations ...... 51

Figure 27: Ps Curves for Full Flaps Configuration Level-Decelerations ...... 52

Figure 28: Ps Curves for Level-Decelerations at 1300 feet ...... 53

Figure 29: Ps Curves for Level-Decelerations at 3000 feet ...... 54

Figure 30: Ps Curves for Level-Decelerations at 5000 feet ...... 55

Figure 31: Ps Curves for Level-Decelerations at 7000 feet ...... 56

Figure 32: Ps Curves for Clean Configuration Level-Accelerations (풅풉/풅풕 ≠ ퟎ) ...... 60

Figure 33: Ps Curves for Full Flaps Configuration Level-Accelerations (풅풉풅풕 ≠ ퟎ) ...... 61

Figure 34: Ps Curves for Level-Accelerations at 1300 feet (풅풉/풅풕 ≠ ퟎ) ...... 61

Figure 35: Ps Curves for Level-Accelerations at 3000 feet (풅풉/풅풕 ≠ ퟎ) ...... 62

Figure 36: Ps Curves for Level-Accelerations at 5000 feet (풅풉/풅풕 ≠ ퟎ) ...... 62

Figure 37: Ps Curves for Level-Accelerations at 7000 feet (풅풉/풅풕 ≠ ퟎ) ...... 63

Figure 38: Ps Curves for Clean Configuration Level-Decelerations (풅풉/풅풕 ≠ ퟎ) ...... 64

Figure 39: Ps Curves for Full Flaps Configuration Level-Decelerations (풅풉풅풕 ≠ ퟎ) ...... 65

Figure 40: Ps Curves for Level-Decelerations at 1300 feet (풅풉/풅풕 ≠ ퟎ) ...... 65

Figure 41: Ps Curves for Level-Decelerations at 3000 feet (풅풉/풅풕 ≠ ퟎ) ...... 66

Figure 42: Ps Curves for Level-Decelerations at 5000 feet (풅풉/풅풕 ≠ ퟎ) ...... 66

Figure 43: Ps Curves for Level-Decelerations at 7000 feet (풅풉/풅풕 ≠ ퟎ) ...... 67

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Figure 44: CAS vs Time 1300 feet Clean Level-Acceleration (First 15s) ...... 78

Figure 45: CAS vs Time 1300 feet Clean Level-Acceleration (16s to end of run) ...... 78

Figure 46: Pressure Altitude vs Time 1300 feet Clean Level-Acceleration ...... 79

Figure 47: CAS vs Time 1300 feet Clean Level-Deceleration ...... 79

Figure 48: Pressure Altitude vs Time 1300 feet Clean Level-Deceleration ...... 80

Figure 49: CAS vs Time 1300 feet Full Flaps Level-Acceleration (First 20s)...... 80

Figure 50: CAS vs Time 1300 feet Full Flaps Level-Acceleration (21s to end of run) ...... 81

Figure 51: Pressure Altitude vs Time 1300 feet Full Flaps Level-Acceleration ...... 81

Figure 52: CAS vs Time 1300 feet Full Flaps Level-Deceleration ...... 82

Figure 53: Pressure Altitude vs Time 1300 feet Full Flaps Level-Deceleration...... 82

Figure 54: CAS vs Time 3000 feet Clean Level-Acceleration (First 15s) ...... 83

Figure 55: CAS vs Time 3000 feet Clean Level-Acceleration (16s to end of run) ...... 83

Figure 56: Pressure Altitude vs Time 3000 feet Clean Level-Acceleration ...... 84

Figure 57: CAS vs Time 3000 feet Clean Level-Deceleration ...... 84

Figure 58: Pressure Altitude vs Time 3000 feet Clean Level-Deceleration ...... 85

Figure 59: CAS vs Time 3000 feet Full Flaps Level-Acceleration (First 10s)...... 85

Figure 60: CAS vs Time 3000 feet Full Flaps Level-Acceleration (11s to end of run) ...... 86

Figure 61: Pressure Altitude vs Time 3000 feet Full Flaps Level-Acceleration ...... 86

Figure 62: CAS vs Time 3000 feet Full Flaps Level-Deceleration ...... 87

Figure 63: Pressure Altitude vs Time 3000 feet Full Flaps Level-Deceleration...... 87

Figure 64: CAS vs Time 5000 feet Clean Level-Acceleration (First 15s) ...... 88

Figure 65: CAS vs Time 5000 feet Clean Level-Acceleration (16s to end of run) ...... 88

Figure 66: Pressure Altitude vs Time 5000 feet Clean Level-Acceleration ...... 89

Figure 67: CAS vs Time 5000 feet Clean Level-Deceleration ...... 89

Figure 68: Pressure Altitude vs Time 5000 feet Clean Level-Deceleration ...... 90

Figure 69: CAS vs Time 5000 feet Full Flaps Level-Acceleration (First 10s)...... 90

Figure 70: CAS vs Time 5000 feet Full Flaps Level-Acceleration (11s to end of run) ...... 91

Figure 71: Pressure Altitude vs Time 5000 feet Full Flaps Level-Acceleration ...... 91

Figure 72: CAS vs Time 5000 feet Full Flaps Level-Deceleration ...... 92

Figure 73: Pressure Altitude vs Time 5000 feet Full Flaps Level-Deceleration...... 92

Figure 74: CAS vs Time 7000 feet Clean Level-Acceleration (First 15s) ...... 93

Figure 75: CAS vs Time 7000 feet Clean Level-Acceleration (16s to end of run) ...... 93

Figure 76: Pressure Altitude vs Time 7000 feet Clean Level-Acceleration ...... 94

Figure 77: CAS vs Time 7000 feet Clean Level-Deceleration ...... 94

Figure 78: Pressure Altitude vs Time 7000 feet Clean Level-Deceleration ...... 95

Figure 79: CAS vs Time 7000 feet Full Flaps Level-Acceleration (First 15s)...... 95

Figure 80: CAS vs Time 7000 feet Full Flaps Level-Acceleration (16s to end of run) ...... 96

Figure 81: Pressure Altitude vs Time 7000 feet Full Flaps Level-Acceleration ...... 96

Figure 82; CAS vs Time 7000 feet Full Flaps Level-Deceleration ...... 97

Figure 83: Pressure Altitude vs Time 7000 feet Full Flaps Level-Deceleration...... 97

Figure 84: Change in Vy due to Flap Extension [13] ...... 98

Figure 85: Altitude Effect on Vy [14] ...... 99

List of Tables

Table 1: Fatal LOC Accidents from 2011 to 2015 in GA and Commercial Operations [8] ...... 8

Table 2: Flight Log ...... 16

Table 3: Values to Produce Aircraft Specific Excess Power Curve in Clean Configuration .....38

Table 4: Max Ps Comparison between Clean Configuration and Full Flaps Configuration .....45

Table 5: VH Comparison between Clean Configuration and Full Flaps Configuration ...... 46

Table 6: Vy Comparison between Clean Configuration and Full Flaps Configuration ...... 46

Table 7: Values to Produce Aircraft Specific Excess Power Curve for Full Flaps ...... 49

Table 8: Comparison between POH Values and Measured Values ...... 58

List of Abbreviations and Symbols

AFM Airplane Flight Manual

ASEL Airplane Single Engine Land

CAS Calibrated Airspeed

CFIT Controlled Flight Into Terrain

CFR Code of Federal Regulations

EASA European Aviation Safety Agency

ESP Electronic Stability & Protection

Es Specific Energy

FAA Federal Aviation Administration

FTE Flight Test Engineer

GA General Aviation

HP Horsepower

Hp Pressure Altitude

IATA International Air Transportation Association

IAS Indicated Airspeed

KCAS Knots Calibrated Airspeed

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KIAS Knots Indicated Airspeed

LOC Loss of Control

LOC-I Loss of Control In-flight

NTSB National Transport Safety Board

OAT Outside Air Temperature

POH Pilot’s Operating Handbook

Ps Specific Excess Power

TAS True Airspeed

ROC Rate of Climb

SD Secure Digital

USP Underspeed Protection

VH Maximum Level Flight Speed

VY Best Rate of Climb Airspeed

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Acknowledgements

First, I would like to thank God for the endless blessings that He has bestowed upon me throughout my life, and especially during my academic career. Without His continued grace, none of my accomplishments, including this thesis, would have been possible. I am also particularly grateful to my entire family for their prayers, advice and encouragement throughout my academic career, especially during my pursuit of a college education.

I would like to extend my sincerest thanks to my thesis advisor, Dr. Brian Kish, for his continual support throughout my coursework and his excellent counsel towards the completion of my thesis research. His extensive experience and genius made performing this research a great learning and extremely fulfilling experience. I was given the liberty to perform most of the work on my own, but could always count on his cerebration whenever I ran into difficulty. Indeed, this thesis would not have been a possibility without him. Furthermore, I would like to express my gratitude for the profound impact he has had on my academic and career path. Following the completion of my undergraduate degree, I had a general idea of where I wanted to be career wise but was uncertain of the path that I would need to take to get there. His constant advice and willingness to work with me to define the most appropriate path was a service far beyond measure and what was required of him as an academic advisor and professor. As a result of this, I am now well poised to achieve the career goals that

I have set and look forward to an enjoyable journey in getting there.

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I would also like to thank Dr. Ralph Kimberlin for his constant impartment of knowledge and experience which has significantly accelerated my growth in the area of Flight Test. His extensive knowledge and his willingness to share has allowed me to develop a knowledge base far advanced of someone of similar experience.

I would like to acknowledge Dr. Isaac Silver, who performed the flight tests that provided the data for this thesis and graciously agreed to be a member of my thesis committee. Though my interaction with Dr. Silver throughout my academic career was limited, his willingness to share his vast wealth of knowledge and experience was quite evident from the fortunate occasions on which I interacted with him.

Dedication

This thesis is dedicated to my parents, Trevor and Luvette Louisy, who have continually supported me throughout my years of seeking a higher-level education and pursuing a career as an engineer in the aviation industry. Their constant support, both financial and prayerful encouragement and well-timed advice have spurred me along my journey prior to and at Florida Tech and will continue to motivate me as I continue along my life path.

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Section 1 Introduction

A Loss of Control (LOC) accident involves an unintended departure of an aircraft from controlled flight and is the major cause of aircraft fatalities in general aviation (GA) according to Federal Aviation Administration (FAA), with there being one fatal accident involving Loss of Control every four days [1]. Though Loss of control accidents in GA are currently on a downward trend, the number of accidents and fatalities due to LOC (or loss of control – in flight [LOC-I] as it is referred to in many

EASA documents) are still alarmingly high, as displayed in Figure 1 below. Over the five-year period analyzed, LOC accounted for an average of 39 fatal accidents and an average of 66 fatalities each year; therefore, being the root cause for more than 80% of the fatal accidents and fatalities recorded in Europe in that timeframe [2]. The numbers in North America, though slightly better, are still cause for great concern.

The National Transportation Safety Board indicated that LOC played a role in more than 40% of all single-engine, fixed-wing GA fatal accidents [3].

Figure 1: Loss of control in flight accidents and fatalities in GA 2011-2015 [2]

Though loss of control can occur during any phase of flight, statistics show that LOC incidents are more frequent during the takeoff, approach, and landing phases of flight.

Over the same five-year period (2011-2015) analyzed, the EASA found that over 70% of LOC accidents took place during those three aforementioned phases of flight, with takeoff accounting for a little less than one third (31 %) of those accidents (Figure 2).

Additionally, Figure 2 shows that spin and stall were the two most common type of aircraft upsets resulting from loss of control. Given that a spin must be preceded by an aerodynamic stall, the two types can be combined into one category, therefore accounting for more than 60% of aircraft upset events recorded in the five-year timeframe.

Figure 2 Fatal accidents per aircraft upset event types 2011-2015 [2]

The takeoff, approach and landing phases of flight are known slow speed operations, and pilots are trained to be extra diligent when monitoring airspeed during these phases of flight. However, the data points to the contrary, indicating that pilots are losing airspeed awareness, not recognizing the warning symbols of impending stall and ultimately stalling the airplane during these low speed operations. The primary goal of the pilot, especially during these low speed phases of flight, is to fly the aircraft. Yet the trends displayed in Figure 2 point to the pilot getting distracted by auxiliary tasks, losing low airspeed awareness and unable to recognize impending stall.

Stalling an aircraft is generally not “a nail in the coffin” moment as 14 CFR 23.2150 enforces aircraft to have controllable stall characteristics in all phases of flight and therefore, not have the tendency to inadvertently depart from controlled flight [4].

However, the takeoff, approach and landing phases of flight are also low altitude operations that take place within the traffic pattern (generally 1000 feet above ground

3 level), giving the pilot minimal time to correctly identify the upset and perform the appropriate recovery procedure.

Furthermore, the combination of slow speed (low kinetic energy) and low altitude (low potential energy) puts the aircraft at its lowest total energy during these phases of flight, making the aircraft most susceptible to LOC during these phases. Pilot awareness of the energy state of the airplane and proper energy management is, therefore, critical to safely operate the aircraft during these phases of flight.

The total energy of an aircraft is the sum of the aircraft’s potential energy, a function of the aircraft’s altitude in reference to the ground, and the aircraft’s kinetic energy, a function of the aircraft’s velocity. The total energy is depicted mathematically in the equation below:

퐸 = 퐸 + 퐸 = 푚푔ℎ + 1 푚푉2 [1] 푝표푡 푘𝑖푛 2

푊ℎ푒푟푒:

퐸 = 푎𝑖푟푐푟푎푓푡′푠 푡표푡푎푙 푚푒푐ℎ푎푛𝑖푐푎푙 푒푛푒푟푔푦

퐸푝표푡 = 푔푟푎푣𝑖푡푎푡𝑖표푛푎푙 푝표푡푒푛𝑖푎푙 푒푛푒푟푔푦 (푚푔ℎ)

1 퐸 = 푘𝑖푛푒푡𝑖푐 푒푛푒푟푔푦 ( 푚푉2) 푘𝑖푛 2

푔 = 푔푟푎푣𝑖푡푎푡𝑖표푛푎푙 푎푐푐푒푙푒푟푎푡표푛

ℎ = 푎𝑖푟푐푟푎푓푡′푠푎푙푡𝑖푡푢푑푒 푎푏표푣푒 푔푟표푢푛푑 푟푒푓푒푟푒푛푐푒

푉 = 푎𝑖푟푐푟푎푓푡′푠 푣푒푙표푐𝑖푡푦

The aircraft can be assumed to be a point-mass and the application of Newton’s second law results in the following equation for the forces acting on the aircraft along its flight path:

푇 − 퐷 = 푊푠𝑖푛(훾) + 푚푎 [2]

푤ℎ푒푟푒:

푇 = 푡ℎ푟푢푠푡

퐷 = 푑푟푎푔

푊 = 푎𝑖푟푐푟푎푓푡′푠 푤푒𝑖푔ℎ푡

훾 = 푓푙𝑖푔ℎ푡 푝푎푡ℎ 푎푛푔푙푒

푚 = 푎𝑖푟푐푟푎푓푡′푚푎푠푠

푎 = 푎𝑖푐푟푎푓푡′푠푎푐푐푒푙푒푟푎푡𝑖표푛

From equation 2 above, it can be seen that when 훾 = 0 푎푛푑 푎 = 0, (푇 − 퐷) = 0, representing the steady-state equation for level, unaccelerated flight.

The law of conservation of energy states that energy can neither be created nor destroyed – only converted from one form of energy to another [7]. In the case of level, unaccelerated flight, the aircraft’s total mechanical energy will be constant. From equation 1, the aircraft’s mass and gravitational acceleration are constant, indicating that energy can be transferred from potential to kinetic solely by descending in altitude in exchange for an increase in airspeed. This exchange of energy is depicted on Figure

3 as a move from point A to point B.

The transfer of energy, however, is not limited to within the system only, as the conservation law also states that energy can be added to or removed from the energy stored in an open system. In the case of an aircraft, energy is transferred to the system

(aircraft) via the engine thrust, while energy is transferred from the system (aircraft) via drag. However, the law of conservation of energy cannot be violated, indicating that there must be a balance between the net flow of energy transferred through the system (energy transferred in minus energy transferred out) and the resultant change in energy stored in the system illustrated by equation (3) below:

퐸푇 − 퐸퐷 = ∆퐸 [3]

푊ℎ푒푟푒:

퐸푇 = 푒푛푒푟푔푦 푔푎𝑖푛푒푑 푡ℎ푟표푢푔ℎ 푡ℎ푟푢푠푡

퐸퐷 = 푒푛푒푟푔푦 푙표푠푠 푡ℎ푟표푢푔ℎ 푑푟푎푔

∆퐸 = 푐ℎ푎푛푔푒 𝑖푛 푡표푡푎푙 푚푒푐ℎ푎푛𝑖푐푎푙 푒푛푒푟푔푦

From equation 3 above, it can be seen that ∆퐸 will be positive if 퐸푇 is greater than 퐸퐷, resulting in excess energy, or vice-versa, resulting in deficit energy. Excess energy is required for the aircraft to increase its total energy such as climbing to an altitude while maintaining airspeed, and is depicted on Figure 3 as a move from point B to C.

However, excess energy is not a very useful parameter, as it only indicates that a movement from point B to C is possible, but gives no indication how long it will take the aircraft to reach energy state C. Taking the derivative of equation of 3 with respect to time gives the rate of change of the airplane’s total mechanical energy (퐸̇ ), or as it is more commonly known as, the power as displayed in equation 4.

퐸̇ = 퐸̇ − 퐸̇ = 푚푔 (푑ℎ) + 푚푉(푑푣) [4] 푇 퐷 푑푡 푑푡

Similarly, if 퐸̇푇 is greater than 퐸̇퐷, the aircraft will possess excess power, not only indicating that a move from point B to C in Figure 3 is possible, but also indicating how long it would take the aircraft to reach that new energy state. Dividing equation

4 by weight (mg) gives the rate of change at which the airplane is able to change its total mechanical energy per unit weight, a term known as specific excess power which is presented in equation 5 below.

푃 = 푑ℎ + 푉 (푑푣) [5] 푠 푑푡 푔 푑푡

Figure 3: Altitude-velocity diagram showing lines of constant specific Energy (Es) [5]

The number of loss of control accidents, though still an area for concern, are significantly lower in commercial operations (Note: Commercial operations refer to regularly scheduled ticketed passenger flights or cargo flights) when compared to general aviation. The International Air Transport Association (IATA) indicated that over a ten-year period (January 2009 to December 2018), 777 total commercial aviation accidents were recorded, with 64 (approximately 8%) being classified as

LOC-I [8]. Table 1 below shows a comparison between the number of LOC accidents recorded in GA and commercial operations over the same five-year period.

Table 1: Fatal LOC Accidents from 2011 to 2015 in GA and Commercial Operations [8]

Number of 2011 2012 2013 2014 2015 Fatal LOC Accidents General 50 48 33 31 28 Aviation Commercial 8 5 8 6 3 Operations

It is clear from Table 1 above that LOC accidents are extremely more prevalent in GA operations when compared to commercial operations, almost 600% more frequent in

GA despite significantly more hours being flown in commercial operations.

Commercial operations owe their increased level of safety partly to better trained and more experienced pilots, as well as having two pilots in the cockpit. However, the increase in automation and implementation of systems such as autothrottles,

Underspeed Protection (USP) and Electronic Stability & Protection (ESP) contribute to the impeccable safety of commercial aviation. These systems not only increase the

8 pilot’s awareness of the aircraft’s energy state, but also reduce pilot workload and in emergency situations perform correct recovery procedures. The algorithms that govern these systems are developed from an understanding of the energy characteristics of the aircraft. Specific excess power is especially important to understand when designing recovery procedures and setting the margins for safety mechanisms as it defines the capability of the aircraft, indicating the limits at which the aircraft can safely operate and governing the recovery procedure that is most appropriate to the situation. Figure

4 below displays specific excess power for various altitudes and how they are combined to produce constant specific power contours.

Figure 4: Sample Ps Curves and Resulting Constant Ps Contours [9]

General aviation is still trying to catch up with the level of automation present in commercial operations, with higher-end aircraft incorporating advanced autopilots that include USP and ESP as well as autothrottles. However, most GA aircraft are old, built in the last century, and are difficult to retrofit with some of these systems.

Additionally, the cost of most of these systems far exceed the cost of most of the general aviation fleet, making these systems impractical. As a result, research has been conducted into creating an energy management system that takes principles from these

10 proven systems in an attempt to improve the safety in GA. The system must be relatively low cost, easily retrofitted onto aircraft and function off parameters already recorded on the aircraft.

Energy metrics studies have been conducted in an attempt to begin developing an algorithm that would govern this energy management system. Puranik et al (2017) conducted an analysis in energy-based metrics in order to develop a reference for what would define safe operation. Current operating conditions would then be compared to this reference and based on the level of deviation from the reference would determine the safety level of the current operation much like Figure 5 below. The top portion of the figure displays the specific total energy during approach for all flights investigated, and the shaded regions show the percentage of records within a certain region of specific energy during the approach. The dashed line represents the average specific total energy observed during the approach, and the solid line represents the individual record being compared against the entire sample. The bottom portion of the graph shows the modified total energy error rate, and essentially shows how far the current record deviates from the established norm. Based on the data, one is able to establish tolerance levels that ensures safe operation. Deviations beyond that tolerance (such as between 2.0 and 1.5 nautical miles left) will trigger the algorithm to provide appropriate corrective action to the pilot. However, the paucity of data available for

GA aircraft makes developing an accurate algorithm quite difficult. The research presented in this thesis is intended to assist in alleviating this issue by generating Ps curves that can be used in the development of this algorithm.

Figure 5: Specific Total and Modified Total Energy Error Rate during approach [10]

This research is unique as it investigates the effects of altitude and flap configuration on a Part 23 aircraft (PA-28-161). The PA-28-161 is a single-engine piston aircraft certified to fly in the United States under CFR 14 Part 23. Single- engine piston aircraft account for more than 80% of the GA fleet [11], making the results of this investigation applicable to most of the GA fleet. Much of the research conducted into specific excess power examines the aircraft in the flaps retracted configuration. As seen from FAA and EASA statistics, the most critical phases of flight for LOC (takeoff, approach and landing) almost always require flap operation. This investigation into the effects of

12 flap configuration will provide more operationally realistic data regarding specific excess power during those critical phases, therefore greatly increasing the accuracy of the algorithm. Additionally, this investigation examined relationships between altitude and specific excess power, in order to generate trends for comparison. The ultimate goal is to create a system that accurately models the energy of every aircraft it is installed on. The analysis of the trends observed was conducted in an attempt to develop a method that would generate an accurate algorithm, to avoid having to perform extensive flight testing of every aircraft that the system is intended to go on.

Continued research into Ps in GA aviation is integral to reducing the amount of accidents as a result of LOC, as shown by the “success” of commercial operations in this accident category. Increased knowledge of performance metrics will allow for the design of appropriate systems and measures that will help GA safety numbers eventually match those of commercial operations, as it pertains to LOC.

Section 2 Test Methods and Materials

2.1 Test Aircraft

Figure 6 PA-28-161 Piper Warrior – N618FT

The test aircraft depicted in Figure 6 is PA-28-161 Piper Warrior with FAA registration N618FT. The aircraft is owned and operated by the Flight Test

Engineering Department at Florida Institute of Technology. The Piper Warrior is a single-engine light trainer with a maximum gross takeoff weight of 2440 pounds. The aircraft is a low-wing, fixed landing gear, four-place aircraft powered by a normally aspirated Lycoming O-320 engine producing a maximum of 160 hp. The aircraft has a fixed pitch propeller and conventional flight controls, with full flaps setting corresponding to 40 degrees of flap deflection. This aircraft was manufactured in 1985 and is equipped with the Garmin G5.

2.2 Instrumentation

All data requirements for the level acceleration and level deceleration tests were parameters that are normally displayed to pilots; hence, no additional instrumentation was required aside from the instruments/avionics suite already installed in the aircraft.

The only supplementary instrumentation used for data collection was an SD card.

The primary form of data collection used was the data recorded by G5 and stored on the SD card installed inside it. Data displayed on the G5 were also collected on handwritten flight test cards in the rare case that the SD card data were unreadable.

2.3 Flight Log

Table 2: Flight Log

Date Aircraft Crew Flight Time (hours) 03/25/2019 PA-28-161 Isaac Silver, Brian Kish 1.5 03/26/2019 PA-28-161 Isaac Silver, Tjimon 1.6 Louisy, Brian Kish

Table 2 above shows the log of test flights that were performed as a part of this program. Instrument error resulted in no data being recorded on the flight performed on 03/25/2019, requiring the crew to re-fly the test points on 03/26/2019.

2.4 Flight Test Locations and Crew

Figure 7: Test Locations [12]

All test flights were launched from the FIT Aviation facility at the Orlando Melbourne

International Airport (KMLB) in Melbourne, Florida. The tests were conducted in areas to the east and southeast of the airport over the Atlantic Ocean.

The flight tests were conducted by a crew from the Florida Institute of Technology.

Isaac Silver was the pilot, and Tjimon Louisy and Brian Kish were the Flight Test

Engineers.

Section 3 Data Reduction Methods

3.1 Data Requirements

The test parameters required for the level acceleration and level deceleration tests were:

(i) time

(ii) indicated airspeed

(iii) pressure altitude

(iv) outside air temperature.

The indicated airspeed was converted to calibrated airspeed using the airspeed correction tables present in the PA-28-161 Warrior Pilot’s Operating Handbook

(POH). Additionally, the power-on stall speed and maximum level flight speed were utilized for data reduction of the steady level accelerations.

3.2 Test Procedures

All tests were conducted over the Atlantic Ocean, in areas east and southeast of the

Orlando Melbourne International Airport (KMLB). The tests were conducted at 1300 feet, 3000 feet, 5000 feet and 7000 feet. The original test plan called out testing at

1000, 3000, 5000 and 7000 feet. However, conditions below 1300 feet on the day of testing were deemed unfavorable for accurate data collection using the test procedures that were to be employed. The test pilot was responsible for operating the aircraft and performing the test point procedures, while the flight test engineer (FTE) recorded pertinent data.

The level acceleration tests commenced with the pilot slowing the aircraft down to a speed just above the power-on stall speed for the applicable configuration (clean or full flaps) at an altitude just below the target altitude. The mixture was set to the full rich position and the test pilot advanced the throttle to the full power position. The test pilot allowed the aircraft to climb to the target altitude at the designated minimum airspeed, and upon reaching the target altitude, the pilot levelled off and allowed the aircraft to accelerate. The FTE recorded the GPS time (for reference when retrieving data from the Garmin SD card) once the aircraft reached the target altitude and began filling in the handwritten flight test cards. The pilot maintained altitude (within ±50 feet of the target altitude) and configuration until the airspeed stabilized. Once the airspeed stabilized, the maximum level flight speed was recorded. The power-on stall speeds were recorded during stall characteristics testing of the PA-28-161. These were the lowest speeds achieved during testing in both configurations.

The level deceleration tests in the clean configuration commenced with the pilot achieving maximum level flight speed at the target altitude. Once airspeed stabilized, the FTE recorded the GPS time and the pilot retarded the throttle to idle power. For the level deceleration tests in the full-flaps configuration, the pilot achieved the lower of maximum flap extend speed or maximum level flight speed at the target altitude.

Once the airspeed stabilized, the FTE recorded the GPS time, and the pilot extended the flaps to its maximum deflection and retarded the throttle to idle power. For both the clean configuration and the full-flaps configuration, the pilot-maintained altitude

(within ±50 feet of the target altitude) and configuration until the plane decelerated to the power-off stall speed, while the FTE filled in the handwritten flight test cards.

(Note: The tests were terminated at 1.1 times the applicable stall speed for the configuration being tested at 1300 feet, to avoid stalling the aircraft at such a low altitude).

3.3 Data Reduction

Flight test data were recorded using an SD card placed inside the Garmin Primary

Flight Display. The Garmin display recorded data at a speed of 1 hertz. This allowed for the values for the necessary test parameters (altitude and airspeed) to be analyzed in one-second increments. Given that the temperature would remain relatively constant throughout the test run at the specified altitude, it was only recorded at the start of the run using the OAT probe. After tabulating a spreadsheet with time, airspeed, and altitude for each run, the following steps were performed to create Ps curves:

1. First, the airspeed corrections listed in the PA-28-161 Warrior Pilot’s

Operating Handbook (POH) were applied to the indicated airspeed (IAS)

values to obtain calibrated airspeed (CAS).

Example: 100 KIAS = 96 KCAS.

Note: The Garmin G5 was assumed to have zero instrument error.

2. The density ratio (σ) was then calculated using the equation 휎 =

−6 5.2561 (1−6.87535∗10 ∗ℎ푝) (푇푎+273.15) where Ta is the ambient temperature at altitude in 288.15

degrees Celsius.

Example:

(1 − 6.87535 ∗ 10−6 ∗ 3075푓푡)5.2561 휎 = = 0.88456 (18 + 273.15) 288.15

3. The calibrated airspeed values were then converted from knots to ft/s.

Example:

푓푡 6076.12 (푛푚) 100 푘푡푠 ∗ 푠 = 168.781 푓푡/푠 3600 (ℎ표푢푟)

4. Microsoft Excel software was then used to plot the values of CAS in ft/s against

time and the trend line function was used to derive an appropriate curve fit. For

the steady-level accelerations, a piecewise function was used to accurately

represent the trends observed at the low-speed end of the plot. This was

required because of the unique behavior experienced at the low-speed end, due

to propeller efficiency and the complexity of the thrust curve associated with

propeller driven aircraft.

Example: Figures 8 and 9 show the plot of calibrated airspeed against time for

the PA-28-161 aircraft in the clean configuration during the level acceleration

run at 1300 feet. The equation of the curve fit to six decimal places is shown

below Figures 8 and 9. Figure 8 was solved for t = 10s as this piece-wise

function accurately modeled velocity versus time for the first 15 seconds of the

run, while Figure 9 was solved for t = 30s, as this piece-wise function

accurately modeled velocity versus time for t = 16 seconds and onwards for

the run.

CAS vs Time for Steady-Level Acceleration in Clean Configuration 140

120

100

y = -0.017493x3 + 0.417240x2 - 0.563237x + 104.456023 80

60 CAS (ft/s) CAS

0 0 2 4 6 8 10 12 14 16 Time (s) Figure 8: CAS vs Time (First 15s)

3 2 푉푐 = −0.017493푡 + 0.417240푡 − 0.563237푡 + 104.456023 = −0.017493(103) + 0.417240(102) − 0.563237(10) + 104.456023 = 123.05 푓푡/푠

CAS vs Time for Steady-Level Acceleration in Clean Configuration 250

200

150

y = -0.012799x2 + 2.046088x + 110.742407

CAS (ft/s) CAS 100

0 0 10 20 30 40 50 60 70 80 90 Time (s)

Figure 9: CAS vs Time (16s Onwards)

2 푉푐 = −0.012799푡 + 2.046088푡 + 110.7742407 = −0.012799(302) + 2.046088(30) + 110.7742407 = 160.64 푓푡/푠

5. The derivative of the curve fit was obtained and used to calculate the rate of

change of velocity (푑푣) at each time step, or each fitted CAS value. 푑푡

Example:

푑푉 푓푡 푐 = −0.025598푡 + 2.046088 = −0.025598(30) + 2.046088 = 1.278 푑푡 푠2

Hp vs Time for Steady-Level Acceleration in Clean Configuration 3500 3400 3300 3200 3100 3000

Hp (ft) Hp 2900 2800 2700 2600 2500 0 20 40 60 80 100 120 Time (s)

Figure 10: Pressure Altitude vs Time 6. The pressure altitude was then plotted against time and the trend line function

was used to derive an appropriate curve fit. The nature of the test required the

pilot to maintain altitude within ±50ft of the test condition altitude, resulting

in constant corrections and a plot that shows continuous increases and

decreases in altitudes. Note: The pressure altitude referenced to conduct

the test was that displayed on the altimeter set to 29.92. The pressure

altitude used in the data reduction was that recorded on the Garmin

Display. The Garmin Display had a positive offset when compared with

the altimeter. A 35 foot offset was noted at 1300 feet, a 70 foot offset was

noted at 3000 feet, a 90 foot was noted at 5000 feet, and a 120 foot offset

was noted at 7000 feet. An initial plot was created to attempt to model each

change in altitude over the entire run (see Figure 10 above) but became

25 extremely complex due to the number of changes and the limited ability of

Excel for this type of analysis. Additionally, the plots resulted in inaccurately large rates of change due to the plot trying to encompass every single data point. Therefore, a more simplistic polynomial curve that modeled the general trend of the aircraft with reference to altitude (i.e. increasing, decreasing or maintaining) as time progressed was chosen (see Figure 11 below). This model tended to ignore the changes from point to point (one second increments) and focused on the larger trends (generally changes in altitude over 5 seconds or longer increments). This model appeared to be a better representation of what the actual aircraft was experiencing, and the derivative of this model was used to obtain more appropriate rates of change.

Hp vs Time for Steady-Level Acceleration in Clean Configuration 3500 3400 3300 3200 3100 3000 4 3 2

Hp (ft) Hp y = -0.000002x + 0.000638x - 0.063055x + 2.448068x + 2900 3,041.473979 2800 2700 2600 2500 0 20 40 60 80 100 120 Time (s)

Figure 11: Modeling Pressure Altitude vs Time

퐡 = −ퟎ. ퟎퟎퟎퟎퟎퟐ퐭ퟒ + ퟎ. ퟎퟎퟎퟔퟑퟖ풕ퟑ + ퟎ. ퟎퟔퟑퟎퟓퟓ풕ퟐ − ퟐ. ퟒퟒퟖퟎퟔퟖ퐭 + ퟑ, ퟎퟒퟏ. ퟒퟕퟑퟗퟕퟗ

푑ℎ = −0.000008푡3 + 0.001914푡2 − 0.12611푡 + 2.448068 푑푡 = −0.000008(0)3 + 0.001914(0)2 − 0.12611(0) + 2.448068 푓푡 = 2.448068 푠

푉푐 7. True airspeed values were calculated using the known equation, 푉푇 = . √휎

Example:

168.781 푓푡/푠 푉푇 = = 179.4568 푓푡/푠 √0.88456

8. The specific excess power values (Ps) were then calculated using values

obtained in previous steps. Two Ps values were calculated for each airspeed.

One using the conventional method that assumes the 푑ℎ component to be zero 푑푡

푑ℎ and the other that includes the calculated component. The Ps was calculated 푑푡

in the units of ft/minute. The Ps equation is derived from the energy

equation, 퐸 = 1 푊 푣2 + 푊ℎ. Dividing through by weight (W) gives 퐸 = 2 푔 푠

1 푣2 + ℎ. Taking the time derivative yields 푑 (퐸 ) = 푃 = 푣 푑푣 + 푑ℎ. The 2푔 푑푡 푠 푠 푔 푑푡 푑푡

푑ℎ 푉푇 푑푣 equation used to calculate Ps without the component was 푃 = ( ∗ ) ∗ 푑푡 푠 푔 푑푡

60. When the 푑ℎ component was included the equation became 푃 = 푑푡 푠

((푉푇 ∗ 푑푣) + 푑ℎ) ∗ 60. 푔 푑푡 푑푡

Examples:

푓푡 179.4568 푓푡 푠 푓푡 푃 = ( 푠 ∗ 0.4589 ) ∗ 60 = 153.452 푠 푓푡 2 32.2 푠 푚𝑖푛 푚𝑖푛 푠2

푓푡 179.4568 푓푡 푓푡 푠 푓푡 푃 = ( 푠 ∗ 0.4589 ) + 0.2761 ∗ 60 = 170.018 푠 푓푡 2 32.2 푠 푠 푚𝑖푛 푚𝑖푛 ( 푠2 )

9. Plots of Ps against KCAS were generated for every test run performed, with

and without the 푑ℎ components. The curves for the steady-level accelerations 푑푡

were anchored on the low speed end by the power-on stall speed and on the

high-speed end by the maximum level flight speed as the aircraft has zero

excess power at those airspeeds. The curves for the steady-level decelerations

were not anchored on either end (low speed nor high speed), and only the data

collected during the run was plotted. Outlying points were not used in

calculating the Ps curve to allow for the most accurate result.

dh Example: Figure 12 shows the Ps plot for the PA-28-161 Warrior aircraft with the dt component assumed to be zero for the clean configuration acceleration at 1300 feet.

The power-on stalling speed is 56 KCAS and the maximum level flight speed VH is

119 KCAS. Figure 13 shows the Ps plot for the PA-28-161 Warrior aircraft with the dh component incorporated for the clean configuration acceleration at 3000 feet. The dt power-on stalling speed is 56 KCAS and the maximum level flight speed VH is 114

dh KCAS. Figure 14 shows the Ps plot for the PA-28-161 Warrior aircraft with the dt component assumed to be zero for the clean configuration deceleration at 1300 feet.

The inclusion of the dh component will not change the overall shape of the graphs, nor dt the trends observed. However, the inclusion of the dh component is to try to make the dt absolute specific excess power values calculated for each airspeed more accurate. The steady-level deceleration plots will be below the airspeed axis (x-axis), as there will be a deficit in power (negative specific excess power).

Specific Excess Power vs CAS for Steady-Level Acceleration in Clean Configuration at 1300 Feet 600

500

400

300

Ps (ft/min) Ps 200

100

0 50.0 60.0 70.0 80.0 90.0 100.0 110.0 120.0 130.0 CAS (KTS)

Figure 12: Ps vs CAS Level-Acceleration

Specific Excess Power vs CAS for Steady-Level Acceleration in Clean Configuration at 3000 feet (with dh/dt component) 450 400 350 300 250 200

Ps (ft/min) Ps 150 100 50 0 50.0 60.0 70.0 80.0 90.0 100.0 110.0 120.0 130.0 CAS (kts)

풅풉 Figure 13: Ps vs CAS Level-Acceleration ( ≠ ퟎ) 풅풕

Specific Excess Power vs CAS for Steady-Level Deceleration in Clean Configuration at 1300 feet CAS (kts) 0 0.0 20.0 40.0 60.0 80.0 100.0 120.0 140.0 -200

-400

-600

-800

-1000 Ps (ft/min) Ps -1200

-1400

-1600

-1800

Figure 14: : Ps vs CAS Level-Deceleration

Section 4 Results 풅풉 4.1 Ps Plots (풂풔풔풖풎풆 = ퟎ) 풅풕

The Ps plots analyzed for the steady-level accelerations and steady-level decelerations are presented in Section 4.1.1 and Section 4.1.2 respectively.

4.1.1 Steady-Level Accelerations

Figure 15 below shows the specific excess power versus the calibrated airspeed in the clean configuration for the four altitudes investigated.

Specific Excess Power Vs CAS for Steady-Level Acceleration in Clean Configuration for Various Altitudes 1300 Feet 3000 Feet 5000 Feet 7000 Feet 600

500

400

300 Ps (ft/min) Ps 200

100

0 50.0 60.0 70.0 80.0 90.0 100.0 110.0 120.0 130.0 CAS (KTS)

Figure 15: Ps vs CAS for Clean Configuration Level-Accelerations

From the figure above it is observed that altitude had a negative effect on Ps, i.e. an increase in altitude resulted in a lower specific excess power for all speeds. The

32 reduction in specific excess power and the decrease in the maximum level flight speed observed can be attributed to a deterioration in engine performance with altitude, both in power and thrust available (via the propeller), for a normally aspirated piston engine. Stall speed (KCAS), in accordance with the known theory, remained unchanged with altitude. The slight variation noted was due to random error.

Additionally, Vy was approximately 79 KCAS for all altitudes, with a minor decrease noted in Vy as altitude increased. This is well in line with the principle that a slight decrease in Vy, in terms of CAS or IAS will occur as altitude increases, due to movement in both the power available and power required curves. Increasing altitude results in the power required curve moving upwards and shifting to the right. The power available curve on the other hand, comes straight down, due to the deterioration in engine performance with increased altitude. This results in Vy, in terms of TAS, increasing (moving to the right) as seen in Figure 85 in Appendix B. However, this increase in terms of TAS happens at a slower rate than the rate CAS or IAS fall behind

TAS as the aircraft climbs. The net result is a decrease in Vy, in terms of CAS or IAS.

Figure 16 below shows the specific excess power versus the calibrated airspeed in the full flaps configuration for the four altitudes investigated.

Specific Excess Power Vs CAS for Steady-Level Acceleration with Full Flaps for Various Altitudes 1300 Feet 3000 Feet 5000 Feet 7000 Feet 400

350

300

250

200

Ps (ft/min) Ps 150

100

0 40.0 50.0 60.0 70.0 80.0 90.0 100.0 CAS (KTS)

Figure 16: : Ps vs CAS for Full Flaps Configuration Level-Accelerations

From the figure above it is observed that an increase in altitude resulted in a reduction in specific excess power. Deterioration in engine performance with altitude, both in power and thrust available, for a normally aspirated piston engine is the main reason for the reduction in specific excess power, and also accounts for the decrease in the maximum level flight speed observed. Stall speed (KCAS), as expected from known theory, remained unchanged with altitude (slight variation noted due to random error).

Vy was approximately 62 KCAS for all altitudes, with a minor decrease noted in Vy as altitude increased. The minor decrease in Vy as altitude increased is also in line with known theory, as discussed previously for the clean configuration (Figure 15).

Figure 17 below shows the maximum specific excess power versus pressure altitude for the two configurations investigated.

Specific Excess Power Relationship with Altitude Clean Config Full Flaps 600

500

400 y = -0.047379x + 608.070344 R² = 0.942683

300 Ps (ft/min) Ps 200 y = -0.047044x + 402.954017 R² = 0.964446 100

0 0 1000 2000 3000 4000 5000 6000 7000 8000 Pressure Altitude (ft)

Figure 17: : Relationships between Ps and Altitude

The figure above shows that there is an inverse linear relationship between altitude and specific excess power for both configurations investigated. The figure also indicates that altitude has a similar effect on specific excess power for both clean and full flaps configuration, as displayed by the almost identical slopes of the graphs. The figure above also shows that the aircraft has a sea-level specific excess power of approximately 610 ft/min and 400 ft/min in the clean configuration and full flaps configurations, respectively. Additionally, it is observed that the aircraft has an absolute ceiling of approximately 12,800 feet and 8,500 feet in the clean configuration

35 and full flaps configurations, respectively. The above equation (clean config.) was used to obtain the specific excess power at altitude via the equation below:

( ) 푃푠푎푙푡 = −0.047379 ∗ 푎푙푡𝑖푡푢푑푒 + 608.070344 OR ( ) 푃푠푎푙푡 = 608.070344 − 0.047379 푎푙푡𝑖푡푢푑푒 [6]

Figure 18 below shows the maximum level flight speed versus pressure altitude for the two configurations investigated.

Maximum Level Flight Speed Relationship with Altitude

Clean Config Full Flaps 140 y = -0.002790x + 122.621185 120 R² = 0.969298 100

60 y = -0.002841x + 90.577528 Vh (KCAS) Vh R² = 0.957491 40

0 0 1000 2000 3000 4000 5000 6000 7000 8000 Pressure Altitude (ft)

Figure 18: Relationships between Vh and Altitude

The figure above shows an inverse linear relationship between altitude and maximum level flight speed for both configurations investigated. From the figure it can be inferred that altitude has a similar effect on the maximum level flight in both the clean configuration and the full flap configuration, as demonstrated by the nearly identical

36 slopes. Additionally, the maximum level flight speed at sea-level is observed to be approximately 123 KCAS and 91 KCAS in the clean configuration and full flaps configurations, respectively. The above equation (clean config.) was used to obtain the maximum level flight speed via the equation below:

( ) 푉퐻푎푙푡 = −0.002790 ∗ 푎푙푡𝑖푡푢푑푒 + 122.621185 OR

푉퐻푎푙푡 = 122.621185 − 0.002790(푎푙푡𝑖푡푢푑푒) [7]

Figure 19 below shows the best rate of climb speed (Vy) versus pressure altitude for the two configurations investigated.

Vy Relationship with Altitude Full Flaps Clean Config 85

80 y = -0.000314x + 80.178213 75 R² = 0.998522

65 y = -0.000325x + 62.476174 Vy (KCAS) Vy R² = 0.992179

50 0 1000 2000 3000 4000 5000 6000 7000 8000 Pressure Altitude (ft)

Figure 19: Relationships between Vy and Altitude

The figure shows an inverse linear relationship between altitude and Vy for both configurations investigated. However, the negative slope is quite negligible that Vy

37 can be assumed to be constant throughout all operating altitudes for the respective configurations. Most aircraft with a normally aspirated engine (like the PA-28-161) have an absolute ceiling of approximately 12,500 feet in the clean configuration, which would equate to an approximate 4 KCAS (based on the slopes above) decrease in Vy from the sea-level value, for both configurations.

A combination of these two linear relationships (and assuming a constant Vy), along with the constant stall speed, and assuming that specific excess power is zero at stall and maximum level flight speeds, can be used to manipulate the sea-level baseline specific excess power curve to depict the aircraft’s current specific excess power curve. Table 3 below outlines the process for the aircraft in the clean configuration, and Figure 20 below shows the resulting manipulated specific excess power curves.

Table 3: Values to Produce Aircraft Specific Excess Power Curve in Clean Configuration

Sea-level Baseline Altitude (Clean Config) 2000 6000 Airspeed Ps Airspeed Ps Airspeed Ps (KIAS) (ft/min) (KIAS) (ft/min) (KIAS) (ft/min) Stall 50[1] 0[2] 50[1] 0[2] 50[1] 0[2] [1] [1] [4] [3] [4] [3] Vy 79 644 79 549 79 360 Max 120[1] 0[2] 114[3] 0[2] 103[3] 0[2] [1] Value obtained from PA-28-161 Warrior POH [2] Assumption of zero excess power at stall speed and maximum level flight speed [3] Calculated from relationship obtained between altitude and respective variable [4] Assume constant Vy

Figure 20 below shows the sea-level baseline specific excess power curve and the derived specific power curves based on altitude.

Specific Excess Power vs KIAS for Clean Configuration

Sea-Level Baseline 2000 Feet 6000 Feet

700

600

500

400

300 Ps (ft/min) Ps 200

100

0 40 50 60 70 80 90 100 110 120 130 KIAS

Figure 20: Equation-derived Ps curves

The figure above shows the sea-level baseline, the 2000 feet altitude derived curve, and the 6000 feet altitude derived curve. It is observed that the shape of the curves obtained are not accurate representations of the specific excess power curve, as the backside of the curves depicted in Figure 20 are shallower in slope than the actual specific excess power curve. Additionally, the curves depicted in Figure 20 show maximum specific excess power being obtained at a speed which deviates slightly from Vy. These two incongruities can be attributed to having used only three data points to generate the curves, and the limitations of the graphing software (the software fits a smooth curve through the three data points, but is unable to decipher that the peak of the curve should occur at Vy). Overall, this does not adversely affect the

39 accuracy of the curves as the difference in the slope of the backside of the curves depicted and actual specific excess power curves are negligible, and the specific excess power is relatively constant (curve being relatively flat) at speeds around Vy.

The process can be repeated for the full flaps configuration. However, the sea-level baseline data would have to be obtained for the full flaps configuration before applying the linear equations derived above (Figures 17 to 19). Note: Given the identical slopes for both the clean configuration and full flaps configuration (minor variation attributed to random error), the slope values obtained in the clean configuration can be used to define the relationship between altitude and the pertinent parameters (Specific Excess Power, Maximum Level Flight Speed and

Vy) in the full flaps configuration.

Given that full flaps data for climb and cruise performance is not normally published in POHs and AFMs, additional flight testing would have to be performed to obtain the requisite sea-level baseline data. This method was deemed impractical, as it would be near impossible to flight test every aircraft that the Energy Management System is intended to be installed on. Therefore, an investigation was conducted to derive a set of equations that could calculate with a high degree of precision, the corresponding full flaps configuration performance based on the clean configuration data. This would allow the clean configuration data that are already posted in the POH or AFM to be manipulated to give an accurate representation of the aircraft’s energy state when the flaps are deployed.

Figure 21 below shows the specific excess power versus calibrated airspeed at 1300 feet for the two configurations investigated.

Specific Excess Power Vs CAS for Steady-Level Acceleration at 1300 Feet

Clean Config Full flaps

600

500

400

300

Ps (ft/min) Ps 200

100

0 40.0 50.0 60.0 70.0 80.0 90.0 100.0 110.0 120.0 130.0 CAS (kts)

Figure 21: Ps curves for Level-Accelerations at 1300 feet

The figure above shows a leftward shift and overall reduction in the Ps envelope when the flaps are fully deployed on the aircraft. From the clean configuration to full flap deployment, max Ps decreased from 530 ft/min to 330 ft/min, Vy decreased from 80

KCAS to 62 KCAS, and maximum level flight speed decreased for 118 KCAS to 86

KCAS.

Figure 22 below shows the specific excess power versus calibrated airspeed at 3000 feet for the two configurations investigated.

Specific Excess Power Vs CAS for Steady-Level Acceleration at 3000 feet

Clean Config Full Flaps

500 450 400 350 300 250

200 Ps (ft/min) Ps 150 100 50 0 40.0 50.0 60.0 70.0 80.0 90.0 100.0 110.0 120.0 130.0 CAS (kts)

Figure 22: Ps curves for Level-Accelerations at 3000 feet

KCAS to 62 KCAS, and maximum level flight speed decreased for 116 KCAS to 84

KCAS.

Figure 23 below shows the specific excess power versus calibrated airspeed at 5000 feet for the two configurations investigated.

Specific Excess Power Vs CAS for Steady-Level Acceleration at 5000 feet

Clean Config Full Flaps

450

400

350

300

250

200 Ps (ft/min) Ps 150

100

0 40.0 50.0 60.0 70.0 80.0 90.0 100.0 110.0 120.0 CAS (kts)

Figure 23: Ps curves for Level-Accelerations at 5000 feet

KCAS to 61 KCAS, and maximum level flight speed decreased for 108 KCAS to 75

KCAS.

Figure 24 below shows the specific excess power versus calibrated airspeed at 7000 feet for the two configurations investigated.

Specific Excess Power Vs CAS for Steady-Level Acceleration at 7000 feet

Full Flaps Clean Config

300

250

200

150

Ps (ft/min) Ps 100

0 40.0 50.0 60.0 70.0 80.0 90.0 100.0 110.0 120.0 CAS (kts)

Figure 24: Ps curves for Level-Accelerations at 7000 feet

KCAS to 60 KCAS, and maximum level flight speed decreased from 103 KCAS to 71

KCAS.

Figures 21-24 display a clear trend of reduction in specific excess power, maximum level flight speed, Vy, and lowering of stall speed with full flap deployment; all of which are in line with the known theory. Specific excess power decreases due to the increase in the power required, which results from an increase in the total drag of the aircraft due to flap deployment (both parasite and induced drag increase due to flap deployment). Maximum level flight speed decreases due to the increase in total drag resulting from flap deployment, for the same amount of thrust at the respective altitudes. Stall speed is lowered as flap deployment increases the camber of the airfoil and consequently increases the coefficient of lift at the respective angles of attack and the maximum lift coefficient. This allows for the aircraft to produce more lift for a given airspeed when compared to the clean configuration. The reduction in Vy is due to the shift in the power required curve, as a result of the deployment of the flaps causing an increase in the aircraft’s total drag (see Figure 84 in Appendix B).

Table 4 below displays the maximum specific excess power for the two configurations for all four altitudes investigated, as well as the decrease in maximum specific excess power, when comparing the full flaps configuration to the clean configuration.

Table 4: Max Ps Comparison between Clean Configuration and Full Flaps Configuration

Altitude Max Clean Ps Max Full Flaps Ps Reduction in Ps (ft) (ft/min) (ft/min) (ft/min) 1300 530 330 200 3000 470 290 180 5000 410 145 265 7000 250 80 170

Table 5 below displays the maximum level flight speed for the two configurations for all four altitudes investigated, as well as the decrease in maximum level flight speed, when comparing the full flaps configuration to the clean configuration.

Table 5: VH Comparison between Clean Configuration and Full Flaps Configuration

Altitude Clean VH Full Flaps VH Reduction in (ft) (KCAS) (KCAS) VH (KCAS) 1300 118 86 32 3000 116 84 32 5000 108 75 33 7000 103 71 32

Table 6 below displays the best rate of climb speed (Vy) for the two configurations for all four altitudes investigated, as well as the decrease in Vy, when comparing the full flaps configuration to the clean configuration.

Table 6: Vy Comparison between Clean Configuration and Full Flaps Configuration

Altitude Clean Vy Full Flaps Vy Reduction in (ft) (KCAS) (KCAS) Vy (KCAS) 1300 80 62 18 3000 80 62 18 5000 79 61 18 7000 78 60 18

Tables 4-6 all show a decrease in specific excess power, maximum level flight speed and Vy, when the full flaps configuration was compared to the clean configuration, for the respective altitudes. An attempt was made to obtain trend values that describe how flap deployment affects the previously mentioned variables, in order to develop a

46 system of equations that could be used to manipulate clean configuration data to determine with a high degree of precision, aircraft performance in the full flaps configuration. Given that the previous observations showed that altitude had a similar effect on the aircraft in both configurations, the effect of flap deployment could, therefore, be isolated from this comparison.

From Table 4 it can be seen that there is slight variation in the decrease in maximum specific excess power when comparing the clean configuration to the full flaps configuration. However, computing an average was determined to be a suitable method to address the variation observed. The average decrease in maximum specific excess power from the clean configuration to the full flaps configuration was approximately 200 ft/min. This indicates that the maximum specific power that the aircraft can attain in the full flaps configuration is 200 ft/min less than in the clean configuration at any altitude. This is illustrated by equation 8 shown below:

푓푡 푃 = 푃 − 200 ( ) [8] 푠푚푎푥푓푢푙푙 푓푙푎푝푠 푠푚푎푥푐푙푒푎푛 푐표푛푓푖푔 min

From Table 5 it can be seen that maximum level flight speed decreases by approximately 32.5 KCAS when comparing the clean configuration to the full flaps configuration. This indicates that the maximum level flight speed that the aircraft can obtain at any altitude in the full flaps configuration is 32 KCAS lower than in the clean configuration, and is illustrated by equation 9 shown below:

푉퐻푓푢푙푙 푓푙푎푝푠 = 푉퐻푐푙푒푎푛 푐표푛푓푖푔 − 32 (퐾퐶퐴푆) [9]

From Table 6 it can be seen that Vy decreases by approximately 18 KCAS when comparing the clean configuration to the full flaps configuration. This indicates that the best rate of climb speed at any altitude in the full flaps configuration is 18 KCAS lower than in the clean configuration, and is illustrated by equation 10 shown below:

( ) 푉푦푓푢푙푙 푓푙푎푝푠 = 푉푦푐푙푒푎푛 푐표푛푓푖푔 − 18 퐾퐶퐴푆 [10]

A combination of these three linear relationships presented in Equations 8, 9 and 10 above, were used to manipulate the clean configuration data to obtain the full flaps configuration data and produce the specific excess power curves. Given that the effect of altitude on both configurations was identical, the altitude and flap relationships were commutative (i.e. the order in which they were applied did not change the result). For curves at altitude, the sea-level baseline data was first manipulated using the altitude relationships (Equations 6 and 7) to obtain the clean configuration data for the specific altitude. The full flap relationships were then applied to the manipulated data for that altitude to obtain the full flaps configuration data for each specific altitude (Note: The full flap relationships could have been applied first, followed by the altitude relationships. This order of operations would have produced the same results).

Table 7 below outlines the process for obtaining the full flaps configuration specific excess power data, and Figure 25 below shows the resulting derived specific excess power curves.

Table 7: Values to Produce Aircraft Specific Excess Power Curve for Full Flaps

Altitude and Sea-level Baseline Sea-Level Full 2000 Clean Config (clean config) Flaps Config 2000 Full Flaps Airspeed Ps Airspeed Ps Airspeed Ps Airspeed Ps (KIAS) (ft/min) (KIAS) (ft/min) (KIAS) (ft/min) (KIAS) (ft/min) Stall 50[1] 0[2] 44[1] 0[2] 50[1] 0[2] 44[1] 0[2] [1] [1] [3] [3] [5] [4] [3] [3] Vy 79 644 61 444 79 555 61 355 Max 120[1] 0[2] 88[3] 0[2] 114[4] 0[2] 82[3] 0[2] [1] Value obtained from PA-28-161 Warrior POH [2] Assumption of zero excess power at stall speed and maximum level flight speed [3] Calculated from flap relationships established [4] Calculated from relationship obtained between altitude and respective variable [5] Assume constant Vy

Specific Excess Power vs KIAS

Sea-level Clean Config Sea-level Full Flaps 2000 feet Clean Config 2000 feet Full Flaps 700

600

500

400

300 Ps (ft/min) Ps 200

100

0 40 50 60 70 80 90 100 110 120 130 KIAS

Figure 25: Equation-derived Ps curves for Full Flaps Configuration

The figure above shows the sea-level baseline, the 2000 feet altitude derived curve and the corresponding full flaps derived curves for both the sea-level baseline and 2000 feet altitude derived curve. It is observed that the shape of the curves obtained are not

49 completely accurate representations of the specific excess power curve, as the backside of the curves depicted in Figure 25 are shallower in slope than the actual specific excess power curve. Additionally, the curves depicted in Figure 25 show maximum specific excess power being obtained at a speed which deviates slightly from Vy. These two incongruities can be attributed to having used only three data points to generate the curves, and the limitations of the graphing software (the software fits a smooth curve through the three data points but is unable to decipher that the peak of the curve should occur at Vy). These discrepancies however, do not adversely affect the accuracy of the curves due to the negligible difference between the slope of the backside of the curves depicted and actual specific excess power curves, and the specific excess power being relatively constant (curve being relatively flat) at speeds around Vy.

4.1.2 Steady-Level Decelerations

Figure 26 below shows the specific excess power versus the calibrated airspeed in the clean configuration for the four altitudes investigated.

Specific Excess vs CAS for Steady-Level Deceleration in Clean Configuration for Various Altitudes 1300 feet 5000 feet 7000 feet 3000 Feet CAS (kts) 0 40.0 60.0 80.0 100.0 120.0 140.0 -200

-400

-600

-800 Ps (ft/min) Ps -1000

-1200

-1400

-1600

-1800

Figure 26: Ps Curves for Clean Configuration Level-Decelerations

The figure above shows that decreases in Ps (become more negative) as the altitude increases when in the clean configuration. This is in line with the standard theory that power required increases with increasing altitude. For the same indicated airspeed, drag remains constant irrespective of a change in altitude, but at higher altitudes, that same indicated airspeed results in a greater true airspeed. Given that power required is the product of drag and true airspeed, the increase in power required with an increase in altitude for the same IAS or CAS is evident. Given also that the power available is

51 constant, effectively zero at idle power for all the altitudes, the increase in power required will result in a greater deficit in power (more negative excess power).

Figure 27 below shows the specific excess power versus the calibrated airspeed in the full flaps configuration for the four altitudes investigated.

Specific Excess Power vs CAS for Steady-Level Deceleration with Full Flaps for Various Altitudes 1300 feet 3000 feet 5000 feet 7000 feet CAS (kts) 0 40.0 50.0 60.0 70.0 80.0 90.0 100.0 110.0

-500

-1000

-1500 Ps (ft/min) Ps

-2000

-2500

Figure 27: Ps Curves for Full Flaps Configuration Level-Decelerations

The figure above shows that Ps is relatively equal for all the altitudes investigated in the full flaps configuration, except for the 1300 feet run. The 1300 feet run is considered an outlier due to the steepness of its slope when compared to the other three altitudes investigated. The trend observed in Figure 26 differs slightly from the known theory which states that the deficit in power should increase (specific excess power become more negative) with an increase in altitude, due to the increase in power required.

Figure 28 below shows the specific excess power versus calibrated airspeed at 1300 feet for the two flap configurations investigated.

Specific Excess Power vs CAS for Steady-Level Deceleration at 1300 feet Clean Config Full Flaps CAS (kts) 0 40.0 50.0 60.0 70.0 80.0 90.0 100.0 110.0 120.0 130.0

-500

-1000

-1500 Ps (ft/min) Ps

-2000

-2500

Figure 28: Ps Curves for Level-Decelerations at 1300 feet

The figure above shows that the specific excess power decreased (became more negative) when full flaps were deployed. It is noted that the steepness of the slope for

1300 full flaps run is very high when compared to other runs, which is a factor of concern for the accuracy of the data collected during this run.

Figure 29 below shows the specific excess power versus calibrated airspeed at 3000 feet for the two flap configurations investigated.

Specific Excess Power vs CAS for Steady-Level Deceleration at 3000 feet Clean Config Full Flaps

CAS (kts) 0 40.0 50.0 60.0 70.0 80.0 90.0 100.0 110.0 120.0 -200 -400 -600 -800 -1000

Ps (ft/min) Ps -1200 -1400 -1600 -1800

Figure 29: Ps Curves for Level-Decelerations at 3000 feet

The figure above shows that Ps decreased (became more negative) when the flaps were fully deployed at 3000 feet.

Figure 30 below shows the specific excess power versus calibrated airspeed at 5000 feet for the two flap configurations investigated.

Specific Excess Power vs CAS for Steady-Level Deceleration at 5000 feet Clean Config Full Flaps CAS (kts) 0 -20040.0 50.0 60.0 70.0 80.0 90.0 100.0 110.0 -400 -600 -800 -1000

-1200 Ps (ft/min) Ps -1400 -1600 -1800 -2000

Figure 30: Ps Curves for Level-Decelerations at 5000 feet

The figure above shows that Ps decreased (became more negative) when the flaps were fully deployed at 5000 feet.

Figure 31 below shows the specific excess power versus calibrated airspeed at 7000 feet for the two flap configurations investigated.

Specific Excess Power vs CAS for Steady-Level Deceleration at 7000 feet Clean Config Full Flaps CAS (kts) 0 40.0 50.0 60.0 70.0 80.0 90.0 100.0 110.0 -200 -400 -600 -800 -1000

Ps (ft/min) Ps -1200 -1400 -1600 -1800

Figure 31: Ps Curves for Level-Decelerations at 7000 feet

The figure above shows that Ps decreased (became more negative) when the flaps were fully deployed at 7000 feet.

All the four figures (Figures 28-31) show a decrease in Ps for the full flap configuration when compared with the clean configuration. This is quite in line with the known theory that flap deployment increases the zero-lift drag (parasite) and the induced drag, hence increasing the total drag of the aircraft and resulting in a subsequent upward movement in the power required curve. Given that the power available curve remains constant, approximately zero, the difference will be greater (larger negative) between the power available and power required curves for the full flap configuration.

For all the level deceleration test runs, the RPM slowly wound down throughout the test run from 2700 RPM to about 800 RPM as the aircraft approached stall, due to windmilling effects. The nature of the level deceleration procedure resulted in the backsides (low-speed end) of all the power curves presented in this section being non- existent, making it difficult to make any further inferences such as best glide speed. It was therefore determined that constant speed glides would be a more appropriate method to collect power deficit (negative specific excess power) data. Additionally, it appears that the docile nature of the backside of the power curve for the Piper Warrior contributed to its non-existence during the level deceleration runs.

4.2 Comparison to POH

Table 8: Comparison between POH Values and Measured Values

Pressure Ps (POH) Ps (Data) Vy (POH) Vy (Data) Altitude [feet] [ft/min] [ft/min] [IAS] [IAS] 1300 574[1] 530 79 80 3000 475 470 79 79 5000 376 410 79 79 7000 277 250 79 78 [1] POH value taken for 1000 feet.

There were some slight variations observed between the results obtained during the test program and the POH values. The maximum specific excess power values measured were lower than those values posted in the POH, except for the 5000-feet point. In addition, the Vy values measured were within 1 KIAS of the POH posted values for all the altitudes investigated.

These variations can be attributed to the differences in the test procedures used to obtain the POH values and those used in this test program. The POH procedures call for leaning the mixture per Lycoming instructions, while the mixture was set to full rich for all test points flown in this test program. The mixture being set at full rich results in less engine power and lower aircraft performance, particularly at higher altitudes. Additionally, this test program utilized level accelerations to determine climb performance data, while the POH climb performance data were generated from constant-speed climbs.

풅풉 4.3 Ps Plots ( ) component included 풅풕

푑ℎ The following section, Section 4.3, displays the Ps plots for all the runs with the 푑푡 component included. The purpose of including the 푑ℎ component was to try to 푑푡 increase the accuracy the of Ps values obtained for every run. However, while decent models of altitude versus time were created, the rate data obtained were merely approximations and subjected to significant error, especially when flying through unstable air masses. Additionally, the lag in the data collection, i.e. the time difference between the aircraft changing altitude and that altitude change actually being recorded on the Garmin display, also introduced significant uncertainty when calculating the 푑ℎ 푑푡 component. Lastly, analysis of all the test runs conducted revealed that the pilot maintained the aircraft within ±50 feet of the target, further increasing the confidence in the accuracy of the data that assumed the 푑ℎ component to be zero. Therefore, the 푑푡 following figures presented in this section were only analyzed for trend data for comparison with their counterparts that did not include 푑ℎ component, and as a result, 푑푡 do not include an elaborate description of any specific findings.

All the trends observed in section 4.1 were confirmed by the data presented in this section. The inclusion of the 푑ℎ component did not change the shape of the level 푑푡 acceleration graphs, but altered the absolute specific excess power value measured at each indicated airspeed. However, it must be noted that the inclusion of the

푑ℎ component made the backside (low-speed) end of some of the level deceleration 푑푡

59 test runs more visible, particularly in the case of the full flaps runs. Hence, from the test runs where the low-speed end was visible, it was possible to determine that the best glide speed in the clean configuration was around 75 KIAS, within 2 KIAS of the

POH posted value of 73 KIAS.

4.3.1 Steady-Level Accelerations

Specific Excess Power vs CAS for Steady-Level Acceleration in Clean Configuration for Various Altitudes [(푑ℎ/푑푡) component included]

1300 feet 3000 feet 5000 feet 7000 feet

600

500

400

300

Ps (ft/min) Ps 200

100

0 40.0 50.0 60.0 70.0 80.0 90.0 100.0 110.0 120.0 130.0 CAS (kts)

풅풉 Figure 32: Ps Curves for Clean Configuration Level-Accelerations ( ≠ ퟎ) 풅풕

Specfic Excess Power vs CAS for Steady-Level Acceleration with Full Flaps for Various Altitudes [(푑ℎ/푑푡) component included] 1300 feet 3000 feet 5000 feet 7000 feet 350

300

250

200

150 Ps (ft/min) Ps 100

0 40.0 50.0 60.0 70.0 80.0 90.0 100.0 CAS (kts)

풅풉 Figure 33: Ps Curves for Full Flaps Configuration Level-Accelerations ( ≠ ퟎ) 풅풕

Specific Excess Power vs CAS for Steady-Level Acceleration at 1300 feet [(푑ℎ/푑푡) component included]

Clean Config Full Flaps 600

500

400

300 Ps (ft/min) Ps 200

100

0 40.0 60.0 80.0 100.0 120.0 140.0 CAS (kts)

풅풉 Figure 34: Ps Curves for Level-Accelerations at 1300 feet ( ≠ ퟎ) 풅풕

Specific Excess Power vs CAS for Steady-Level Acceleration at 3000 feet [(푑ℎ/푑푡) component included] Clean Config Full Flaps 450 400 350 300 250 200 Ps (ft/min) Ps 150 100 50 0 40.0 60.0 80.0 100.0 120.0 140.0 CAS (kts)

풅풉 Figure 35: Ps Curves for Level-Accelerations at 3000 feet ( ≠ ퟎ) 풅풕

Specific Excess Power vs CAS for Steady-Level Acceleration at 5000 feet [(푑ℎ/푑푡) component included] Clean Config Full Flaps 400 350 300 250 200

Ps (ft/min) Ps 150 100 50 0 40.0 50.0 60.0 70.0 80.0 90.0 100.0 110.0 120.0 CAS (kts)

풅풉 Figure 36: Ps Curves for Level-Accelerations at 5000 feet ( ≠ ퟎ) 풅풕

Specific Excess Power vs CAS for Steady-Level Acceleration at 7000 feet

Clean Config Full Flaps

250

200

150

100 Ps (ft/min) Ps

0 40.0 50.0 60.0 70.0 80.0 90.0 100.0 110.0 120.0 CAS (kts)

풅풉 Figure 37: Ps Curves for Level-Accelerations at 7000 feet ( ≠ ퟎ) 풅풕

4.3.2 Steady-Level Decelerations

Specific Excess Power vs CAS for Steady-Level Deceleration in Clean Configuration for Various Altitudes [(푑ℎ/푑푡) component included] 1300 feet 3000 feet 5000 feet 7000 feet CAS (kts) 0 40.0 60.0 80.0 100.0 120.0 140.0

-500

-1000 Ps (ft/min) Ps

-1500

-2000

풅풉 Figure 38: Ps Curves for Clean Configuration Level-Decelerations ( ≠ ퟎ) 풅풕

Specific Excess Power vs CAS for Steady-Level Deceleration with Full Flaps for Various Altitudes [(푑ℎ/푑푡) component included]

1300 feet 3000 feet 5000 feet 7000 feet CAS (kts) 0 40.0 50.0 60.0 70.0 80.0 90.0 100.0 110.0 -500

-1000

-1500

Ps (ft/min) Ps -2000

-2500

-3000

풅풉 Figure 39: Ps Curves for Full Flaps Configuration Level-Decelerations ( ≠ ퟎ) 풅풕

Specific Excess Power vs CAS for Steady-Level Deceleration at 1300 Feet [(푑ℎ/푑푡) component included] Clean Config Full Flaps CAS (kts) 0 -20040.0 60.0 80.0 100.0 120.0 140.0 -400 -600 -800 -1000 -1200 -1400 Ps (ft/min) Ps -1600 -1800 -2000

풅풉 Figure 40: Ps Curves for Level-Decelerations at 1300 feet ( ≠ ퟎ) 풅풕

Specific Excess Power vs CAS for Steady-Level Deceleration at 3000 Feet

Clean Config Full Flaps

0 CAS (kts) 40.0 50.0 60.0 70.0 80.0 90.0 100.0 110.0 120.0

-500

-1000

-1500 Ps (ft/min) Ps

-2000

-2500

풅풉 Figure 41: Ps Curves for Level-Decelerations at 3000 feet ( ≠ ퟎ) 풅풕

Specific Excess Power vs CAS for Steady-Level Deceleration at 5000 Feet

Clean Config Full Flaps CAS (kts) 0 40.0 50.0 60.0 70.0 80.0 90.0 100.0 110.0 -500

-1000

-1500

Ps (ft/min) Ps -2000

-2500

-3000

풅풉 Figure 42: Ps Curves for Level-Decelerations at 5000 feet ( ≠ ퟎ) 풅풕

Specific Excess Power vs CAS for Steady-Level Deceleration at 7000 Feet Clean Config Full Flaps

0 CAS (kts) 40.0 50.0 60.0 70.0 80.0 90.0 100.0 110.0

-500

-1000

-1500 Ps (ft/min) Ps

-2000

-2500

풅풉 Figure 43: Ps Curves for Level-Decelerations at 7000 feet ( ≠ ퟎ) 풅풕

Section 5 Conclusions and Future Work

5.1 Conclusions

The purpose of this research was to investigate the effects of altitude and flap position on the specific excess power for Part 23 aircraft for implementation into an energy management system. The PA-28-161 was a fair representation of a typical Level 2 airplane under Part 23 classifications, given its single normally aspirated engine and fixed-gear.

The steady-level acceleration data showed that there was an inverse linear relationship between specific excess power and altitude for both configurations investigated, with altitude having an identical effect on the aircraft in both the clean configuration and full flaps configuration. The data also showed an inverse linear relationship between altitude and maximum level flight speed for both configurations investigated, with altitude also having an identical effect on the aircraft in both the clean configuration and full flaps configuration. Furthermore, an inverse linear relationship between altitude and best rate of climb speed (Vy) was observed for both configurations investigated. However, it was noted that the change in Vy with respect to altitude in both the configurations was quite negligible that Vy could be considered constant for the respective configurations from sea-level to service ceiling. Lastly, it was observed that altitude had no effect on the indicated/calibrated stall speed of the aircraft for both configurations investigated.

A combination of these three linear relationships, along with other basic assumptions, were used to successfully manipulate the sea-level baseline specific excess power curve (created from data posted in the POH) to derive altitude specific excess power curves. Though the linear relationships used in this derivation were obtained through flight tests, it was determined that similar relationships were easily obtained through reduction of data already posted in the POH or AFM. The effect of temperature was not considered in this study but is easily determined from temperature data already presented in POHs and AFMs and would further increase the accuracy of the model.

Given the impracticability of flight testing every aircraft that this energy management system is likely to be implemented on, the method of creating the basic energy model from data already available in the POH or AFM appears to be superior.

Flap configuration appeared to have no effect on the altitude relationships, i.e. the altitude relationships for the full flaps configuration and the altitude relationships for the clean configuration were identical (slight variation attributed to random error).

Hence, it was determined that computed altitude relationships from the clean configuration data already posted in the POH or AFM would also accurately represent the altitude relationships for the full flaps configuration. However, these relationships would only become useful if a sea-level baseline for the full flaps configuration curve was available; a curve that would have to be obtained through flight test, given that the data to produce such a curve is seldom posted in POHs or AFMs.

Therefore, an attempt was made to establish relationships between the clean configuration and full flaps configuration in order to be able to model the full flaps

69 specific excess power curve from the clean configuration curve. It was found that the full flaps configuration maximum specific excess power was 200 ft/min less than the clean configuration (maximum specific excess power was obtained when flying at Vy for the respective configurations). Additionally, it was found that the maximum level flight speed that the aircraft could attain was 32.5 KCAS less in the full flaps configuration than in the clean configuration. Furthermore, the best rate of climb speed

(Vy) in the full flaps configuration was 18 KCAS lower than the best rate of climb of speed in the clean configuration.

A combination of these three relationships (which are in fact constants, given that there are no variables in the respective equations), along with the power-on stall speed in the landing configuration obtained from the POH, were used to derive the full flaps configuration specific excess power curves from the clean configuration curves. Given that the altitude relationships for both the clean configuration and full flaps configuration were identical, and the full flaps from clean configuration relationships are independent of these altitude relationships, the two sets of relationships can be used in any order to obtain full flaps configuration specific excess power curves at a specific altitude. Though the resulting derived curves accurately represented the aircraft’s specific excess power in the full flaps configuration at the designated altitude, the relationships obtained may however, only be applicable to the PA-28-161.

Furthermore, parameters such as flap area, flap deflection and flap type will all influence the relationships between the clean configuration and the full flaps configuration. Again, noting the impracticability of flight testing every aircraft that the

70 energy management system is likely to be installed on, an analytical method using data that are readily available in the POH or AFM would be more ideal. This analytical method can then be substantiated by flight tests.

The steady-level acceleration specific excess power curves which included the 푑ℎ 푑푡 component, confirmed the trend values observed in the specific excess power curves which assumed the 푑ℎ component to be zero. Further analysis of the steady-level 푑푡 acceleration specific excess power curves that included the 푑ℎ component was not 푑푡 conducted, due to a lack of confidence in the accuracy of the 푑ℎ components calculated. 푑푡

The steady-level deceleration test runs did not generate useful data due to the RPM winding down throughout the test run because of windmilling effects, resulting in the low-speed end of the specific excess power curves being non-existent. The inclusion of the 푑ℎ component made the low-speed end of the specific excess power curve more 푑푡 visible for some test runs but was unable to rectify the issue to a point where the data became usable.

All the maximum specific excess power values measured through the steady-level accelerations in the clean configuration were within 10% of the POH posted values for the respective altitudes investigated. The measured best rate of climb speed was within

1 KIAS of the POH posted value for the respective altitudes investigated. The best glide speed was estimated from the clean configuration steady-level deceleration data with the 푑ℎ component included (3000-feet test run was not included, as the low-speed 푑푡

71 end was still not apparent) to be approximately 75 KIAS. This value was only 2 KIAS greater than the POH posted value of 73 KIAS.

It is envisaged that the data gathered in this flight test study will be a valuable addition to the body of knowledge towards the development of an accurate energy state management and warning system, which will hopefully contribute to increasing the safety in General Aviation.

5.2 Recommendations and Future Works

Though the steady-level accelerations were able to generate a body of useful data for determining the specific excess power envelope, data near the low-speed end (near stall) was a bit more dispersed. Furthermore, the steady-level decelerations did not produce as expected, usable data, particularly near the low-speed end. Performing constant speed climbs and constant speed idle power descents would alleviate both these issues and result in more accurate data being generated. Maintaining constant speed and RPM through the descent would also allow for the assumption of constant thrust to be more accurate. For aircraft with the capability, feathering the propeller would be most ideal. The increased accuracy of the data would directly affect the accuracy of the relationships developed for implementation into the energy management system. Important to note however, is that performing constant speed climbs and idle power descents would significantly increase the amount of flight test time required.

The flight tests will also need to be corrected for maximum gross weight, as this is most critical for performance, and will also be highly applicable to takeoff operations where the aircraft is operated very close to maximum gross weight. Though most other operations are not conducted at maximum gross weight, erring on the side of caution will only serve to increase the margin of safety.

Most general aviation aircraft do not have a binary flap system like what was assumed in this flight test program, but instead have an intermediate flap configuration between

73 fully retracted and fully extended. Furthermore, pilots often incrementally extend their flaps during the approach and landing phase and in certain conditions choose to land with flaps at an intermediate position as opposed to fully extended. Therefore, a further investigation into flap position that considers intermediate flap positions should be conducted to develop trends that can further increase the accuracy and applicability of the energy management system. Additionally, parameters such as flap area, flap deflection and flap type all differ for various aircraft types and will significantly affect the relationships between the full flaps configuration and the clean configuration.

Analysis of these parameters and their respective effects should be conducted to obtain accurate relationships for all aircraft that this energy management system may be applicable to.

The PA-28-161 Warrior is an aircraft equipped with a single normally aspirated engine and fixed-pitch two-bladed propeller. Though this aircraft is representative of most of the General Aviation aircraft population, there are certain subtle differences among aircraft that give rise to variations in the specific excess power curve. Investigations into the effects of turbocharging, multi-engine versus single engine, constant-speed propellers vs fixed pitch propellers and number of propeller blades (mainly three- bladed vs two-bladed, as very few general aviation aircraft have more than a three- bladed propeller) will be required to further develop an understanding of specific excess power as it pertains to GA aircraft.

The specific excess power data obtained revealed that most general aviation aircraft do not have enough performance to recover from low energy states. When on the

74 backside of the power curve, throttle advancement is very often not enough to return the aircraft to the region of normal control. The aircraft often needs to also trade altitude for airspeed to recover from the region of reversed control. Unfortunately, when in the traffic pattern, the aircraft has little to no altitude to trade with, making it impossible to safely recover from a low energy state. Given the difficulty associated with recovering from a low energy state, more attention should be paid to measures and methods that will assist the pilot in becoming more aware and avoiding situations in which the aircraft gets to a low energy state. The implementation of this energy management system is viewed as one way to increase pilot awareness. Other areas identified that will require further research or measures to address them include:

• The perception of many General Aviation pilots that stall recovery is of higher

importance than stall prevention, which is highly contrary to the thinking of

their Commercial counterparts who have a much better safety record as it

pertains to LOC incidents.

• The implementation of a Defined Minimum Maneuvering Speed for general

aviation aircraft. Maneuvering Speed is often a maximum airspeed limitation

that the aircraft designer selects to protect the aircraft from structural damage,

particularly when referring to GA aircraft. On the commercial side, there is a

maximum maneuvering speed for structural integrity, but there is also a

minimum maneuvering airspeed for stall/spin protection. Pilots are not allowed

to perform maneuvers unless above this designated airspeed, which gives them

enough margin for the effective increase in stall speed because of maneuvering.

References

[1] “Fly Safe: Prevent Loss of Control Accidents,” FAA seal Available: https://www.faa.gov/news/updates/?newsId=91285.

[2] “Loss of Control in General Aviation” Available: https://www.easa.europa.eu/sites/default/files/dfu/Loss of Control in General Aviation - update 17112016- sourcedoc-final_0.pdf.

[3] “NTSB News Release National Transportation Safety Board Office of Public Affairs,” National Transportation Safety Board (NTSB) Available: https://www.ntsb.gov/news/press-releases/Pages/nr20180419.aspx.

[4] “14 CFR § 23.2150 - Stall characteristics, stall warning, and spins.,” Legal Information Institute Available: https://www.law.cornell.edu/cfr/text/14/23.2150.

[5] Merkt, J. R., “Flight Energy Management Training: Promoting Safety and Efficiency,” Journal of Aviation Technology and Engineering, vol. 2, 2013, pp. 24–36. [6] Anderson, J. D. (2007). Introduction to flight (3rd ed.). New York: McGraw-Hill.

[7] “Law of conservation of energy,” Law of conservation of energy - Energy Education Available: https://energyeducation.ca/encyclopedia/Law_of_conservation_of_energy.

[8] Iata, “Loss of Control In-flight (LOC-I),” IATA Available: https://www.iata.org/whatwedo/safety/Pages/loss-of-control-inflight.aspx.

[9] Hermelin, S., “14 fixed wing fighter aircraft- flight performance - ii,” LinkedIn SlideShare Available: https://www.slideshare.net/solohermelin/14-fixed-wing-fighter- aircraft-flight-performance-ii.

[10] Tejas Puranik, Hernando Jimenez, and Dimitri Mavris. "Energy-Based Metrics for Safety Analysis of General Aviation Operations", Journal of Aircraft, Vol. 54, No. 6 (2017), pp. 2285-2297.

[11] “2016 General Aviation Statistical Databook & 2017 Industry Outlook,” 2016 General Aviation Statistical Databook & 2017 Industry Outlook.

[12] “KMLB - Melbourne International Airport,” AirNav Available: http://www.airnav.com/airport/KMLB.

[13] jezzc100 Epic Poster Join Date: May 2010 Posts: 161, and colin Bristol Instructor Join Date: Jul 2004 Posts: 2741, “Announcement,” Q845 - ATP Forum Available: http://www.atpforum.eu/forum/technical-subjects/-032-performance-a/13177-q845.

[14] “What Does Altitude Have To Do With Vx And Vy?,” Online Flight Training Courses and CFI Tools Available: https://www.boldmethod.com/learn-to-fly/performance/vx-vy- altitude-and-where-they-meet/.

[15] Piper Aircraft. (1982). Warrior II. PA-28-161 Pilot’s Operating Handbook. Vero Beach.

Appendix A: Flight Test Data

CAS vs Time for Steady-Level Acceleration in Clean Configuration 140

120

100

80 CAS (ft/s) y = -0.017493x3 + 0.417240x2 - 0.563237x + 104.456023 60

0 0 2 4 6 8 10 12 14 16 Time(s)

Figure 44: CAS vs Time 1300 feet Clean Level-Acceleration (First 15s)

CAS vs Time for Steady-Level Acceleration in Clean Configuration 250

200

150 CAS (ft/s) 100 y = -0.012799x2 + 2.046088x + 110.742407

0 0 20 40 60 80 100 Time (s)

Figure 45: CAS vs Time 1300 feet Clean Level-Acceleration (16s to end of run)

Hp vs Time for Steady-Level Acceleration in Clean Configuration 1390

1380

1370

1360

Hp (ft) 1350

1340

1330

1320

1310 0 20 40 60 80 100 Time (s)

Figure 46: Pressure Altitude vs Time 1300 feet Clean Level-Acceleration

CAS vs Time for Steady-Level Deceleration in Clean Configuration 250.0

200.0

150.0 CAS (ft/s) 100.0

y = 0.004483x3 - 0.209290x2 - 0.833868x + 200.249928 50.0

0.0 0 10 20 30 40 50 Time (s)

Figure 47: CAS vs Time 1300 feet Clean Level-Deceleration

Hp vs Time for Steady-Level Deceleration in Clean Configuration 1330 1320 1310 1300 1290 Hp (ft) 1280 1270 1260 1250 1240 1230 0 10 20 30 40 50 Time (s)

Figure 48: Pressure Altitude vs Time 1300 feet Clean Level-Deceleration

CAS vs Time for Steady-Level Acceleration with Full Flaps 140 120 100 80 CAS (ft/s) 60 y = -0.003011x2 + 1.642984x + 86.239804 40 20 0 0 5 10 15 20 25 Time(s)

Figure 49: CAS vs Time 1300 feet Full Flaps Level-Acceleration (First 20s)

CAS vs Time for Steady-Level Acceleration with Full Flaps 160 140 120 100 y = -0.008510x2 + 1.383397x + 93.674850 CAS (ft/s) 80 60 40 20 0 0 10 20 30 40 50 60 70 80 Time (s)

Figure 50: CAS vs Time 1300 feet Full Flaps Level-Acceleration (21s to end of run)

Hp vs Time for Steady-Level Acceleration with Full Flaps 1380 1375 1370 1365 1360 1355 Hp (ft) 1350 1345 1340 1335 1330 1325 0 10 20 30 40 50 60 70 80 Time (s)

Figure 51: Pressure Altitude vs Time 1300 feet Full Flaps Level-Acceleration

CAS vs Time for Steady-Level Deceleration with Full Flaps 200.0 180.0 160.0 140.0 120.0 CAS (ft/s) 100.0 80.0 y = -0.000310x3 + 0.103927x2 - 5.701329x + 174.884341 60.0 40.0 20.0 0.0 0 5 10 15 20 25 30 Time (s)

Figure 52: CAS vs Time 1300 feet Full Flaps Level-Deceleration

Hp vs Time for Steady-Level Deceleration with Full Flaps 1400 1390 1380 1370 1360 1350 Hp (ft) 1340 1330 1320 1310 1300 1290 0 5 10 15 20 25 30 Time (s)

Figure 53: Pressure Altitude vs Time 1300 feet Full Flaps Level-Deceleration

CAS vs Time for Steady-Level Acceleration in Clean Configuration 140 120 100 80 y = -0.015918x3 + 0.343597x2 - 0.040683x + 103.505812 60 CAS (ft/s) CAS 40 20 0 0 2 4 6 8 10 12 14 16 Time (s)

Figure 54: CAS vs Time 3000 feet Clean Level-Acceleration (First 15s)

CAS vs Time for Steady-Level Acceleration in Clean Configuration 200

150

100

y = -0.009799x2 + 1.828338x + 101.449748 CAS (ft/s) CAS 50

0 0 20 40 60 80 100 120 Time (s)

Figure 55: CAS vs Time 3000 feet Clean Level-Acceleration (16s to end of run)

Hp vs Time for Steady-Level Acceleration in Clean Configuration 3085 3080 3075 3070 3065 Hp (ft) 3060 3055 3050 3045 3040 3035 0 20 40 60 80 100 120 Time (s)

Figure 56: Pressure Altitude vs Time 3000 feet Clean Level-Acceleration

CAS vs Time for Steady-Level Deceleration in Clean Configuration 250.0

200.0

150.0 CAS (ft/s) 100.0 y = 0.001843x3 - 0.058100x2 - 2.994848x + 193.568149

50.0

0.0 0 5 10 15 20 25 30 35 Time (s)

Figure 57: CAS vs Time 3000 feet Clean Level-Deceleration

Hp vs Time for Steady-Level Deceleration in Clean Configuration 3040

3035

3030

3025 Hp (ft) 3020

3015

3010

3005 0 5 10 15 20 25 30 35 Time (s)

Figure 58: Pressure Altitude vs Time 3000 feet Clean Level-Deceleration

CAS vs Time for Steady-Level Acceleration with Full Flaps 98 96 y = -0.027297x3 + 0.525523x2 - 1.371995x + 84.420055 94 92 CAS (ft/s) 90 88 86 84 82 0 2 4 6 8 10 12 Time (s)

Figure 59: CAS vs Time 3000 feet Full Flaps Level-Acceleration (First 10s)

CAS vs Time for Steady-Level Acceleration with Full Flaps 160 140 120 100 CAS (ft/s) 80 60 y = -0.013559x2 + 1.782137x + 77.371168 40 20 0 0 10 20 30 40 50 60 70 Time (s)

Figure 60: CAS vs Time 3000 feet Full Flaps Level-Acceleration (11s to end of run)

Hp vs Time for Steady-Level Acceleration with Full Flaps 3100

3090

3080

Hp (ft) 3070

3060

3050

3040 0 10 20 30 40 50 60 70 Time (s)

Figure 61: Pressure Altitude vs Time 3000 feet Full Flaps Level-Acceleration

CAS vs Time for Steady-Level Deceleration with Full Flaps 200 180 160 140 120 CAS (ft/s) 100 80 60 y = 0.063029x2 - 5.723643x + 185.348937 40 20 0 0 5 10 15 20 25 Time (s)

Figure 62: CAS vs Time 3000 feet Full Flaps Level-Deceleration

Hp vs Time for Steady-Level Deceleration with Full Flaps 3130

3120

3110

3100 Hp (ft) 3090

3080

3070

3060 0 5 10 15 20 25 Time (s)

Figure 63: Pressure Altitude vs Time 3000 feet Full Flaps Level-Deceleration

CAS vs Time for Steady-Level Acceleration in Clean Configuration 118 116 y = -0.008796x3 + 0.276752x2 - 1.325591x + 103.710624 114 112 110 CAS (ft/s) 108 106 104 102 100 0 2 4 6 8 10 12 14 16 Time (s)

Figure 64: CAS vs Time 5000 feet Clean Level-Acceleration (First 15s)

CAS vs Time for Steady-Level Acceleration in Clean Configuration 200

150

CAS (ft/s) 100 y = -0.011001x2 + 2.000559x + 85.755057

0 0 20 40 60 80 100 Time (s)

Figure 65: CAS vs Time 5000 feet Clean Level-Acceleration (16s to end of run)

Hp vs Time for Steady-Level Acceleration in Clean Configuration 5115 5110 5105 5100 5095 5090 Hp (ft) 5085 5080 5075 5070 5065 5060 0 20 40 60 80 100 Time (s)

Figure 66: Pressure Altitude vs Time 5000 feet Clean Level-Acceleration

CAS vs Time for Steady-Level Deceleration in Clean Configuration 200.0 180.0 160.0 140.0 120.0 CAS (ft/s) 100.0 80.0 y = 0.006237x3 - 0.246603x2 - 0.858512x + 181.399473 60.0 40.0 20.0 0.0 0 5 10 15 20 25 30 Time (s)

Figure 67: CAS vs Time 5000 feet Clean Level-Deceleration

Hp vs Time for Steady-Level Deceleration in Clean Configuration 5055

5050

5045

5040 Hp (ft) 5035

5030

5025

5020 0 5 10 15 20 25 30 Time (s)

Figure 68: Pressure Altitude vs Time 5000 feet Clean Level-Deceleration

CAS vs Time for Steady-Level Acceleration with Full Flaps 98 96 94 92 CAS (ft/s) 90 88 86 y = -0.051555x3 + 0.778783x2 - 1.487541x + 85.170807 84 82 0 2 4 6 8 10 12 Time (s)

Figure 69: CAS vs Time 5000 feet Full Flaps Level-Acceleration (First 10s)

CAS vs Time for Steady-Level Acceleration with Full Flaps 140 120

100 80 y = -0.004741x2 + 0.844114x + 87.108259 CAS (ft/s) 60 40

20 0 0 10 20 30 40 50 60 70 80 Time (s)

Figure 70: CAS vs Time 5000 feet Full Flaps Level-Acceleration (11s to end of run)

Hp vs Time for Steady-Level Acceleration with Full Flaps 5140

5130

5120

5110 Hp (ft) 5100

5090

5080

5070 0 10 20 30 40 50 60 70 80 Time (s)

Figure 71: Pressure Altitude vs Time 5000 feet Full Flaps Level-Acceleration

CAS vs Time for Steady-Level Deceleration with Full Flaps 180.0 160.0 140.0 120.0 100.0 CAS (ft/s) 80.0 y = 0.005564x3 - 0.146537x2 - 3.112515x + 169.016219 60.0 40.0 20.0 0.0 0 5 10 15 20 25 Time (s)

Figure 72: CAS vs Time 5000 feet Full Flaps Level-Deceleration

Hp vs Time for Steady-Level Deceleration with Full Flaps 5130 5120 5110 5100 5090 Hp (ft) 5080 5070 5060 5050 5040 0 5 10 15 20 25 Time (s)

Figure 73: Pressure Altitude vs Time 5000 feet Full Flaps Level-Deceleration

CAS vs Time for Steady-Level Acceleration in Clean Configuration 112 111 y = -0.004921x3 + 0.144418x2 - 0.601938x + 104.286912 110 109 108 CAS (ft/s) 107 106 105 104 103 0 2 4 6 8 10 12 14 16 Time (s)

Figure 74: CAS vs Time 7000 feet Clean Level-Acceleration (First 15s)

CAS vs Time for Steady-Level Acceleration in Clean Configuration 180 160 140 120 100 y = -0.005535x2 + 1.327343x + 91.673797 CAS (ft/s) 80 60 40 20 0 0 20 40 60 80 100 Time (s)

Figure 75: CAS vs Time 7000 feet Clean Level-Acceleration (16s to end of run)

Hp vs Time for Steady-Leevel Acceleration in Clean Configuration 7130 7125 7120 7115 7110 7105 Hp (ft) 7100 7095 7090 7085 7080 7075 0 20 40 60 80 100 Time (s)

Figure 76: Pressure Altitude vs Time 7000 feet Clean Level-Acceleration

CAS vs Time for Steady-Level Deceleration in Clean Configuration 180.0 160.0 140.0 120.0 100.0 CAS (ft/s) 80.0 y = 0.004516x3 - 0.168619x2 - 1.120222x + 170.389097 60.0 40.0 20.0 0.0 0 5 10 15 20 25 30 Time (s)

Figure 77: CAS vs Time 7000 feet Clean Level-Deceleration

Hp vs Time for Steady-Level Deceleration in Clean Configuration 7130

7120

7110

7100 Hp (ft) 7090

7080

7070

7060 0 5 10 15 20 25 30 Time (s)

Figure 78: Pressure Altitude vs Time 7000 feet Clean Level-Deceleration

CAS vs Time for Steady-Level Acceleration with Full Flaps 92 y = -0.003352x3 + 0.079165x2 - 0.079427x + 85.347633 91 90 89 CAS (ft/s) 88 87 86 85 0 2 4 6 8 10 12 14 16 Time (s)

Figure 79: CAS vs Time 7000 feet Full Flaps Level-Acceleration (First 15s)

CAS vs Time for Steady-Level Acceleration with Full Flaps 120 100 80 y = -0.001828x2 + 0.545812x + 82.039767 CAS (ft/s) 60 40 20 0 0 20 40 60 80 100 Time (s)

Figure 80: CAS vs Time 7000 feet Full Flaps Level-Acceleration (16s to end of run)

Hp vs Time for Steady-Level Acceleration with Full Flaps 7120

7115

7110

7105 Hp (ft) 7100

7095

7090

7085 0 20 40 60 80 100 Time (s)

Figure 81: Pressure Altitude vs Time 7000 feet Full Flaps Level-Acceleration

CAS vs Time for Steady-Level Deceleration with Full Flaps 180.0 160.0 140.0 120.0 100.0 CAS (ft/s) 80.0

60.0 y = 0.012838x3 - 0.426130x2 - 0.388082x + 165.621163 40.0 20.0 0.0 0 5 10 15 20 25 30 Time (s)

Figure 82; CAS vs Time 7000 feet Full Flaps Level-Deceleration

Hp vs Time for Steady-level Deceleration with Full Flaps 7200 7180 7160 7140 7120 Hp (ft) 7100 7080 7060 7040 7020 0 5 10 15 20 25 30 Time (s)

Figure 83: Pressure Altitude vs Time 7000 feet Full Flaps Level-Deceleration

Appendix B: Supplementary Graphs

Figure 84: Change in Vy due to Flap Extension [13]

Note: The above figure displays data for a jet aircraft, as seen by the linear power available curve. A propeller-aircraft’s power available curve starts with power at zero velocity and is relatively flat, with a slight concave down shape due to propeller efficiency. However, the shift in the power required curve displayed in the figure above due to flap deployment is also applicable to propeller-driven aircraft. Hence, a similar decrease in Vy with flap deployment is observed for propeller-driven aircraft.

Figure 85: Altitude Effect on Vy [14]