flight testing of the piper j4a cub coupe

Flight Testing

of the

Piper J4A Cub Coupe

by

Kenneth Burton Connick

A thesis submitted to the

College of Engineering and Science

Florida Institute of Technology

in partial fulfillment of the requirements

for the degree of

Master of Science

in

Flight Test Engineering

Melbourne, Florida

May, 2020

We the undersigned committee hereby recommend

That the attached document be accepted as fulfilling in

Part the requirements for the degree of

Master of Science of Flight Test Engineering

“Flight Testing of the Piper J4A Cub Coupe,”

A thesis by Kenneth Burton Connick

______________________________

Brian Kish, Ph.D.

Assistant Professor, Aerospace Engineering

Thesis Advisor

______________________________

Ralph Kimberlin, Ph.D.

Professor, Aerospace Engineering

______________________________

Isaac Silver, Ph.D.

Associate Professor, College of Aeronautics

______________________________

Daniel Batcheldor, Ph.D.

Professor and Head

Department of Aerospace, Physics and Space Sciences

iii

Abstract

Title

Flight Testing of the Piper J4A Cub Coupe

Author

Kenneth Burton Connick

Principal Advisor

Brian Kish, Ph.D.

Flight testing is an important part of in the airplane design process. This

testing is performed to ensure that the airplane complies with the established

requirements and regulations for flight safety, as well as to ensure it meets its mission

objectives. The Federal Aviation Administration (FAA) currently governs these

requirements and regulations for civilian aircraft and provides airworthiness

certifications. The FAA regulations were introduced in 1965. Prior to that, civilian

aircraft were certified through the Civil Aeronautics Administration using Civil Air

Regulations (CARs).

iv

The Piper J4A Cub Coupe was originally certified under CAR 3 – Airplane

Worthiness. This CAR was used to evaluate the airplane for its current level of both

performance, and stability and control.

To evaluate the airplane per CAR 3 requirements, it was put through a series of

nine flight tests, 5 for performance, and 4 for stability and control. The results of the

performance tests are described first. These tests showed that the position error fell

within the 5mph error maximum as required by regulations. The stalling speed for the

airplane was calculated to be 35.5 mph, which was below the allowable 70mph

maximum. Level flight performance is not a requirement per CAR 3, but the test was

performed in order to produce a chart of true airspeed vs density altitude, which is

useful to the pilot. This chart was successfully produced, except for the full throttle

line, which was due to a data collection error. The climb rate of the airplane was

calculated to be 322 ft/min, which was above the 300 ft/min specified in CAR 3.

Finally, the best rate of climb and aircraft ceiling were calculated to be 43.4mph and

4510 feet, respectively. Both of these numbers seem to be on the low side, because

the best rate of climb is just above stall speed, and the ceiling obtained in the climb

performance flight test was 11,485 ft. Parasitic drag may have played a part in the low

numbers, as it is not accounted for in the calculations.

v

The results from the stability and control flights showed that most of the

maneuver points were forward of the aft C.G. limit, which indicates that the aircraft is

unstable. The data used to generate the maneuver points is suspect, as we know that

the aircraft is stable. The main cause of this is likely due to an insufficient spread in

the center of gravity between the test flights. The lower C.G. was 16.06 inches, and

the upper C.G. was 16.70 inches for the longitudinal static stability flight. The

differences in the collected data from these two C.G. points was not great enough to

show meaningful plots upon data reduction. The results of the longitudinal

maneuvering stability flight produced better results, because the C.G. spread was

greater. The maneuver points were still forward of the aft C.G. limit, which leads to a

possible conclusion that the published C.G. range needs to be adjusted. Also, based

on conversations with Dr. Isaac Silver, who piloted this aircraft on many occasions, a

C.G. of more than 17 inches reduces the handling of the airplane, and is not

recommended. By simply moving the aft C.G. limit closer to 17 inches, it would

move most of the maneuver points aft of the upper C.G. limit, and indicate that the

airplane is stable. Meaningful results were obtained for longitudinal dynamic stability,

and showed that the phugoid motion was sufficiently damped. Finally, a partial test

for static and dynamic lateral-directional stability was performed and showed that the

Dutch Roll oscillation was heavily damped as required.

vi

Table of Contents

Abstract ......................................................................................................................... iii

List of Figures ................................................................................................................. x

List of Tables ............................................................................................................... xii

Acknowledgement ........................................................................................................ xv

Chapter 1 Introduction .................................................................................................... 1

1.1 Background ...................................................................................................... 1

1.2 Objectives ......................................................................................................... 1

Chapter 2 Test Information ............................................................................................. 2

2.1 Test Aircraft ..................................................................................................... 2

2.2 Test Location .................................................................................................... 3

2.3 Test Equipment ................................................................................................ 5

2.4 Scope of Flight Tests ........................................................................................ 5

2.5 Test Exceptions ................................................................................................ 6

Chapter 3 Performance Flight Tests ............................................................................... 7

3.1 Flight Test 1: Position Correction Using GPS Method .................................... 7

Background .............................................................................................................. 7

Description of Flight Test ........................................................................................ 9

Test Results.............................................................................................................. 9

Conclusions ........................................................................................................... 10

3.2 Flight Test 2 - Determination of Stall Speeds ................................................ 11

Background ............................................................................................................ 11

Description of Flight Test ...................................................................................... 11

Test Results............................................................................................................ 13

Conclusions ........................................................................................................... 13

3.3 Flight Test 3: Level Flight Performance ........................................................ 14

Background ............................................................................................................ 14


vii

Test Results............................................................................................................ 15

Conclusions ........................................................................................................... 17

3.4 Flight Test 4: Determination of Climb Performance ..................................... 18

Background ............................................................................................................ 18


Test Results............................................................................................................ 19

Conclusions ........................................................................................................... 22

3.5 Flight Test 5: Level Acceleration Test ........................................................... 23

Background ............................................................................................................ 23


Test Results............................................................................................................ 24

Conclusions ........................................................................................................... 27

Chapter 4 Stability and Control Flight Tests ................................................................ 29

4.1 Flight Test 6: Longitudinal Static Stability ................................................... 29

Background ............................................................................................................ 29


Test Results............................................................................................................ 32

Conclusions ........................................................................................................... 35

4.2 Flight Test 7: Longitudinal Dynamic Stability ............................................. 37

Background ............................................................................................................ 37


Test Results............................................................................................................ 38

Conclusions ........................................................................................................... 40

4.3 Flight Test 8: Longitudinal Maneuvering Stability ....................................... 41

Background ............................................................................................................ 41


Test Results............................................................................................................ 42

Conclusions ........................................................................................................... 45

4.3 Flight Test 9: Static and Dynamic Lateral-Directional Stability................... 47

Background ............................................................................................................ 47

viii


Test Results............................................................................................................ 49

Conclusions ........................................................................................................... 49

References ..................................................................................................................... 50

Appendix A ................................................................................................................... 51

Weight and Balance ...................................................................................................... 51

Performance .............................................................................................................. 51

Stability and Control ................................................................................................. 52

Appendix B ................................................................................................................... 54

Flight Test Procedures .................................................................................................. 54

1. Position Correction Using GPS Method ............................................................ 54

2. Determination of Stall Speeds ........................................................................... 54

3. Determination of Level Flight Performance ...................................................... 55

4. Determination of Climb Performance ................................................................ 55

5. Level Acceleration Test ..................................................................................... 56

6. Longitudinal Static Stability .............................................................................. 56

7. Longitudinal Dynamic Stability ......................................................................... 57

8. Longitudinal Maneuvering Stability .................................................................. 58

9. Dynamic Lateral-Directional Stability ............................................................... 59

Appendix C ................................................................................................................... 60

Collected Data ............................................................................................................... 60










ix

Appendix D ................................................................................................................... 72

Data Reduction Techniques .......................................................................................... 72








b. DETERMINE THE DAMPING FACTOR ....................................................... 91



Appendix E ................................................................................................................... 96

Reduced Data ................................................................................................................ 96




4. Determination of Climb Performance .............................................................. 101

5. Level Acceleration Test ................................................................................... 105

6. Longitudinal Static Stability ............................................................................ 109

7. Longitudinal Dynamic Stability ....................................................................... 110

8. Longitudinal Maneuvering Stability ................................................................ 110

9. Dynamic Lateral-Directional Stability ............................................................. 111

x

List of Figures

Figure 1: Test Aircraft ................................................................................................... 2

Figure 2: Test Location ................................................................................................... 4

Figure 3: Static pressure variation around airplane ........................................................ 8

Figure 4: Average indicated airspeed vs position correction .......................................... 9

Figure 5: PIW vs VIW .................................................................................................. 15

Figure 6: NIW vs PIW .................................................................................................. 16

Figure 7: NIW vs VIW ................................................................................................. 16

Figure 8: Density Altitude vs True Airspeed ................................................................ 17

Figure 9: Time vs altitude – Higher altitude ................................................................. 19

Figure 10: Time vs altitude – Lower altitude ................................................................ 20

Figure 11: PIW vs CIW ................................................................................................ 20

Figure 12: Rate of climb vs pressure altitude ............................................................... 21

Figure 13: Time vs Calibrated Airspeed – High Altitude ............................................. 24

Figure 14: Time vs Calibrated Airspeed – Low Altitude ............................................. 25

Figure 15: Calibrated Airspeed vs Rate of Climb ......................................................... 25

Figure 16: Best angle of climb and best rate of climb .................................................. 26

xi

Figure 17: Calibrated Airspeed vs Weight Corrected Thrust HP in Excess ................. 26

Figure 18: Calibrated Airspeed vs Elevator Position – Stick-Fixed Climb .................. 32

Figure 19: Coefficient of Lift vs Elevator Position – Stick-Fixed Climb ..................... 32

Figure 20: C.G. vs Slope – Stick-Fixed Climb ............................................................. 33

Figure 21: Calibrated Airspeed vs Elevator Position – Stick-Free Climb .................... 33

Figure 22: Coefficient of Lift vs Elevator Position – Stick-Free Climb ....................... 34

Figure 23: C.G. vs Slope – Stick-Free Climb ............................................................... 34

Figure 24: Phugoid oscillatory motion ......................................................................... 37

Figure 25: Time vs Indicated Airspeed – Climb ........................................................... 38

Figure 26: Time vs Indicated Airspeed – Power Approach .......................................... 39

Figure 27: Acceleration vs Elevator Position – Stick Fixed ......................................... 42

Figure 28: Acceleration vs Elevator Position – Stick Free ........................................... 43

Figure 29: C.G. vs slope – Stick Fixed ......................................................................... 43

Figure 30: C.G. vs slope – Stick Free ........................................................................... 44

Figure 31: Acceleration vs Maneuvering Points – Stick Fixed .................................... 44

Figure 32: Acceleration vs Maneuvering Points – Stick Free ...................................... 45

Figure 33: Half Cycle Amplitude vs Damping Factor .................................................. 91

Figure 34: Brake HP vs Propeller Load ........................................................................ 98

xii

List of Tables

Table 1: Aircraft Specifications ...................................................................................... 3

Table 2: Damped and Natural Frequency Data Reduction ........................................... 39

Table 3: Weight and Balance - Flight Tests 1-5 ........................................................... 51

Table 4: Weight and Balance - Flight Test 6-7 (No Ballast) ........................................ 52

Table 5: Weight and Balance - Flight Tests 6-7 (Aft Ballast) ...................................... 52

Table 6: Weight and Balance - Flight Test 8-9 (No Ballast) ........................................ 53

Table 7: Weight and Balance - Flight Tests 8-9 (Aft Ballast) ...................................... 53

Table 8: Flight Information – Flight Tests 1-3 ............................................................. 60

Table 9: Collected Data – Flight 1 ................................................................................ 61

Table 10: Collected Data – Flight 2 .............................................................................. 61

Table 11: Collected Data – Flight 3 .............................................................................. 62

Table 12: Flight Information – Flight Tests 4-5 ........................................................... 62

Table 13: Collected Data – Flight Test 4 – Higher Altitude Heading 200 ................... 63

Table 14: Collected Data – Flight Test 4 – Higher Altitude Heading 20 ..................... 63

Table 15: Collected Data – Flight Test 4 – Lower Altitude Heading 200 .................... 64

Table 16: Collected Data – Flight Test 4 – Lower Altitude Heading 20 ...................... 64

xiii

Table 17: Collected Data – Flight Test 5 – Higher Altitude ......................................... 65

Table 18: Collected Data – Flight Test 5 – Lower Altitude ......................................... 65

Table 19: Collected Data – Flight Test 6 – Climb - Forward C.G................................ 66

Table 20: Collected Data – Flight Test 6 – Climb - Aft C.G. ....................................... 66

Table 21: Collected Data – Flight Test 6 – Power Approach - Forward C.G. .............. 67

Table 22: Collected Data – Flight Test 6 – Power Approach - Aft C.G. ...................... 67

Table 23: Collected Data – Flight Test 7 – Forward C.G. ............................................ 68

Table 24: Collected Data – Flight Test 7 – Aft C.G. .................................................... 69





Table 29: Reduced Data - Position Correction Using GPS Method ............................ 96

Table 30: Reduced Data – Determination of Stall Speeds ............................................ 97

Table 31: Reduced Data – Determination of Level Flight Performance ...................... 99

Table 32: Density Altitude vs True Airspeed ............................................................. 100

Table 33: Reduced Data - Climb Performance Higher Altitude 200 Degree Head .... 101

Table 34: Reduced Data - Climb Performance Higher Altitude 20 Degree Heading . 102

xiv

Table 35: Reduced Data – Climb Performance Lower Altitude 200 Degree Head .... 103

Table 36: Reduced Data - Climb Performance Lower Altitude 20 Degree Heading . 104

Table 37: Reduced Data – Level Acceleration Higher Altitude ................................. 105

Table 38: Reduced Data – Level Acceleration Higher Altitude (Continued) ............. 106

Table 39: Reduced Data – Level Acceleration Lower Altitude .................................. 107

Table 40: Reduced Data – Level Acceleration Lower Altitude (Continued) ............. 108

Table 41: Reduced Data - Stick Fixed Longitudinal Static Stability – C.G. 16.06 .... 109

Table 42: Reduced Data – Stick Fixed Longitudinal Static Stability – C.G. 16.70.... 109

Table 43: Reduced Data – Longitudinal Dynamic Stability ....................................... 110

Table 44: Derivatives of Equations – Stick Fixed ...................................................... 110

Table 45: Derivatives of Equations – Stick Free ........................................................ 110

xv

Acknowledgement

I would like to thank Dr. Brian Kish, who was my advisor for this thesis, as

well as an instructor for course work. His flight test data reduction videos were an

important part of my initial learning, as well as a great reference during the production

of this thesis. His enthusiasm and guidance played a critical role on my journey

through graduate school, and this thesis would not have been possible without his

guidance.

I would also like to thank Dr. Ralph Kimberlin, who played a crucial role in

my understanding of the flight test methods used in this thesis. He laid the foundation

of my knowledge on flight testing methods, for which I am forever grateful. This

thesis would not have been possible without his teaching and assistance.

Finally, I would like to thank Dr. Isaac Silver, who agreed to be a member of

my thesis committee. I also flew with Dr. Silver during my coursework, and it was an

enjoyable occasion.

1

Chapter 1

Introduction

1.1 Background

One purpose of flight testing is to ensure that an aircraft complies with the

established requirements and regulations for flight safety. The Federal Aviation

Administration (FAA) currently governs these requirements and regulations for

civilian aircraft and provides airworthiness certifications. The FAA regulations were

introduced in 1965. Prior to that, civilian aircraft were certified through the Civil

Aeronautics Administration using Civil Air Regulations (CARs). The airplane used in

the test flights was originally certified under CAR 3 – Airplane Worthiness, and this

CAR was used in analysis of test results.

1.2 Objectives

The objective of this thesis is to test the performance, stability, and control of the

Piper J4A Cub Coupe, and to compare the test results to the requirements of 14 CFR

Part 23 and show that the airplane meets airworthiness standards.

2

Chapter 2

Test Information

2.1 Test Aircraft

The test aircraft was the Piper J4A Cub Coupe, tail number NC 26735. This

aircraft is a two-seat high wing airplane, with a Continental A-65-1 engine, fixed pitch

propeller, and fixed tail wheel landing gear.

Figure 1: Test Aircraft

3

Table 1: Aircraft Specifications

Manufacturer Piper Aircraft, Inc.

Model J4A Cub Coupe

Serial Number 4-878

Registration Number NC26735

“Empty” Weight (full oil and fuel) 941 lbs

Max Takeoff Weight 1301 lbs

Engine Continental A-65-8

Max Power 65 H.P.

Wing Area 183 ft2

Length 22 ft 6 in

Height 6 ft 10 in

2.2 Test Location

All flight tests originated and ended at the Melbourne International Airport

(ICAO: KMLB), in Melbourne, Florida. All flight tests and measurements were taken

south of the airport, in the area shown in Figure 2.

4

Figure 2: Test location

5

2.3 Test Equipment

Production Instrumentation

• Airspeed indicator (mph)

• Altimeter (ft)

• Magnetic heading indicator (degrees)

• Engine RPM indicator

Miscellaneous Equipment

• iPhone 6 Gauges app and compass

• Stratus ADSB receiver

• iPad running ForeFlight software

• GoPro Hero 3 digital camera

2.4 Scope of Flight Tests

A total of four flights were performed to collect data on the performance, and

stability and control of the airplane. Multiple distinct flight tests were performed

during each flight to save time and fuel. Each flight was completed within the flight

area as shown in Figure 2.

6

2.5 Test Exceptions

Instrument correction graphs are normally generated for the airspeed and

altitude gauges, and these graphs are used to produce instrument corrected airspeed

and altitude for all test flights during data reduction. This requires scale error

information from the instrument manufactures. Because of the manufacture date of

the test aircraft (1940), this information was unavailable, and no instrument

corrections were performed. The data read from the airspeed indicator and altimeter

were used uncorrected during data reduction.

A thermometer was not present in the airplane to record outside air

temperature. Temperature values for the flight tests were interpolated using METAR

ground temperature data and the known temperature lapse rate in the troposphere. A

fuel gauge was also not present in the airplane. Fuel usage was interpolated using the

amount of fuel spent between engine start and engine shutoff, and the time the data

point was collected, referenced from engine start time.

7

Chapter 3

Performance Flight Tests

3.1 Flight Test 1: Position Correction Using GPS Method

Background

In flight testing, there is always a level of error in the collected data. This error

is the difference between the measured value and the true value. There are many

sources of error in flight testing, one of which is position error, and this was the

subject of this flight test.

Position error is the error in airspeed and altitude caused by the static and total

pressure pickups inability to accurately sense the free stream pressures. Most position

errors are caused by the location of the static pickup on the aircraft. Static pressure

varies around the airplane in flight and resembles that of Figure 3. The figure shows a

static pressure variation of zero along the Ps line, and positive and negative variations

in the direction of +P and -P respectively. Based on the figure, static pressure is most

accurate somewhere along the wing, and at about the middle of the aft fuselage. The

location of the static pickup on the test airplane was under the wing on the pilot side.

8

Figure 3: Static pressure variation around an airplane

CAR 3.663 regulates the allowable error in the airspeed indicating system and

it states the following:

§ 3.663 Air-speed indicating system.

This system shall be so installed that the air-speed indicator shall indicate true

air speed at sea level under standard conditions to within an allowable

installational error of not more than plus or minus 3 percent of the calibrated

air speed or 5 miles per hour, whichever is greater, throughout the operating

range of the airplane with flaps up from Vc to 1.3 Vs1 and with flaps at 1.3

Vs1. The calibration shall be made in flight.

9

Description of Flight Test

This flight test used the Global Positioning System (GPS) Method to determine

position error. This method uses the groundspeed and track obtained from a GPS

receiver, along with the heading obtained from the onboard compass to determine the

position error. The flight test procedures, collected data, and data reduction

techniques are detailed in Appendix B, C, and D respectively.

Test Results

The result of the data reduction, yielded the graph shown in Figure 4.

Figure 4: Average Indicated Airspeed vs Position Correction

y = -0.113x + 5.024

-10

-8

-6

-4

-2

0

2

4

6

8

10

40 60 80 100

Del

ta V

pc

(mp

h)

Vi average (mph)

Position Correction vs. Indicated Airspeed

Lower Acceptable Limit

Upper Acceptable Limit

10

Conclusions

The results show that the aircraft meets the regulation as defined in CAR

3.663, which is a maximum of 5 mph error.

11

3.2 Flight Test 2 - Determination of Stall Speeds

Background

A stall is an aerodynamic condition where the airplane is no longer able to

produce enough lift to keep the airplane flying. The determination of an airplane’s

stalling speed is very important because many other aspects of airplane performance

are based on a multiple of this value.

CAR 3.82, 3.83, and 3.120 describe and define the regulations for stall speed.

CAR 3.83 defines the allowable maximum stalling speed as follows:

§ 3.83 Stalling speed

Vso at maximum weight shall not exceed 70 miles per hour for (1) single-

engine airplanes and (2) multiengine airplanes which do not have the rate of

climb with critical engine inoperative specified in §3.85 (b).


The purpose of this flight test was to determine the stall speeds of the airplane.

The flight test procedures, collected data, and data reduction techniques are detailed in

Appendix B, C, and D respectively.

12

There were multiple deviations from normal stall speed flight tests that

occurred during this flight test, as noted below:

1. Flight testing for stall speeds is normally performed in both no-flap and

full-flap configurations. Because the test airplane does not have flaps, only

the no-flap configuration was tested.

2. Most aircraft have a stall warning system to alert the pilot of an impending

stall. The pilot operating handbook for the airplane defines a velocity delta

between the stall warning and the actual stall, which can be confirmed

during the flight test. This aircraft had no stall warning system, so the stall

warning to stall velocity delta could not be determined.

3. The stall speed is usually provided by the manufacturer of the airplane, and

the initial speed of the aircraft during the flight test is about 1.5 times this

speed. Because no stall speed data was available from the manufacturer,

and initial speed of 60 mph was used in the flight test.

The flight test procedures, collected data, and data reduction techniques are

detailed in the appendix.

13

Test Results

The average weight corrected stall speed was 35.5 mph.

Conclusions

The objective of this flight test was to determine the airplane stall speed and

compare it to the requirements found in CAR 3. The average stall speed 35.5 mph,

which was well within the allowable maximum of 70 mph as started in CAR 3.83.

Normally, the altitude loss during stall recovery and the calculated coefficient

of lift is compared to that of the manufacturers pilot operating handbook. Because this

manual was unavailable, the determination of the average stall speed was the only

result obtained for the flight test.

14

3.3 Flight Test 3: Level Flight Performance

Background

Level flight performance is steady state performance where the forces acting

on the airplane are balanced. For small angles of attack, lift equals drag, and thrust

equals weight, so level flight performance is essentially the measure of airplane drag

as a function of velocity. There are two components of drag: parasitic and induced.

Induced drag is drag due to creating lift. Parasitic drag is all other types drag, such as

profile, skin friction, interference, and varies as a function of true airspeed.

Most methods for determining level flight performance have problems with

determining full throttle performance under standard conditions and cannot be used for

determining drag. The PIW-VIW-NIW method solves these problems, and was the

method used in this flight test. This method makes the assumption that for at a given

angle of attack, the lift coefficient and drag coefficient are constant. Using this

assumption, we can equate a sea level standard day condition to a non-standard test

condition, and derive an equation for VIW.

There are no CAR requirements for level flight performance. However, a chart

relating true airspeed vs density altitude for a given power setting can be developed

from the collected data, which is useful to a pilot.

15


The purpose of this flight test was to determine level flight performance. The

flight test procedures, collected data, and data reduction techniques are detailed in

Appendix B, C, and D respectively.

Test Results

The result of the data reduction yielded charts for PIW vs VIW, PIW vs NIW, NIW

vs VIW, and density altitude vs true airspeed, as shown below.

Figure 5: PIW vs VIW

y = 0.02x2 - 1.578x + 63.224

40

45

50

55

60

65

70

75

80

50 60 70 80 90 100

Piw

(H

p)

Viw (mph)

Piw vs Viw

16

Figure 6: NIW vs PIW

Figure 7: NIW vs VIW

y = 13.792x + 1321.7

1,500

1,600

1,700

1,800

1,900

2,000

2,100

2,200

2,300

2,400

2,500

20 30 40 50 60 70 80

Niw

(R

PM

)

Piw (HP)

Niw vs Piw

y = -0.000129x2 + 0.588150x - 592.232767

30

40

50

60

70

80

90

100

1500 1600 1700 1800 1900 2000 2100 2200 2300 2400 2500

Viw

(m

ph

)

Niw (RPM)

Niw vs Viw

17

Figure 8: Density Altitude vs True Airspeed

Conclusions

There is no CAR requirement for level flight testing. However, data collected

during the flight test was reduced to generate a graph relating true airspeed vs density

altitude for a given power setting. This information is more useful to a pilot than the

PIW-VIW-NIW charts.

Due to insufficient collection of data during the flight test, the full power line

on the density altitude vs true airspeed chart was not able to be produced.

0

2000

4000

6000

8000

10000

12000

14000

40.0 45.0 50.0 55.0 60.0 65.0 70.0 75.0 80.0

Den

sity

Alt

itu

de

(ft)

True Airspeed (mph)

Density Altitude vs True Airspeed

75% Power

65% Power

55% Power

18

3.4 Flight Test 4: Determination of Climb Performance

Background

Climb performance is a basic requirement of flight testing, and is required by

the FAA, and likewise, was required by the Civil Aeronautics Administration. There

are two methods of determining climb performance, steady climb and level

acceleration. Because the steady climb method is generally used for low-speed

aircraft, this was the method used in this flight test. The method to reduce the

collected data was the CIW/PIW method, which involved making corrections for a

non-standard day.

CAR 3.85 defines the climb requirements for the airplane used in this test, and

is listed below:

§ 3.85a

Climb requirements - airplane of 6,000 lbs. or less. Airplanes having a

maximum certificated take-off weight of 6,000 lbs. or less shall comply with

the requirements of this section.

(a) Climb - take-off climb condition. The steady rate of climb as sea level shall

not be less than 10 Vs1 or 300 feet per minute, whichever is the greater, with:

(1) Take-off power,

(2) Landing gear extended,

(3) Wing flaps in take-off position,

(4) Cowl flaps in the position used in cooling tests specified in §§ 3.581

through 3.596.

19


The purpose of this flight test was to determine climb performance at various

altitudes. The flight test procedures, collected data, and data reduction techniques are

detailed in Appendix B, C, and D respectively.

Test Results

Figure 9: Time vs altitude – Higher Altitude

h = -0.0044t2 + 4.7976t + 3510.7

h= -0.0015t2 + 3.4881t + 3513.1

3000

3200

3400

3600

3800

4000

4200

4400

4600

4800

5000

0 30 60 90 120 150 180

Alt

itu

de

(ft

)

Time (s)

Climb PerformanceTime vs Altitude

Higher Altitude

200 Heading

20 Heading

20

Figure 10: Time vs Altitude – Lower Altitude

Figure 11: PIW vs CIW

y = -0.0036x2 + 5.25x + 1019.3

y = -0.002x2 + 5.369x + 998.57

0

500

1000

1500

2000

2500

0 30 60 90 120 150 180

Alt

itu

de

(ft

)

Time (s)

Climb PerformanceTime vs Altitude

Lower Altitude

200 Heading

20 Heading

y = 0.0367x + 55.371

50

55

60

65

70

75

80

0 50 100 150 200 250 300 350 400 450 500

Piw

(h

ors

ep

ow

er)

CIW (ft/min)

PIW vs CIW

21

Figure 12: Rate of Climb vs Pressure Altitude

The derivatives of the curve equations in Figure 8 and Figure 9 were used

generate the rate of climb for each data set, and later, a temperature corrected rate of

climb. Figure 10 shows the PIW vs CIW chart, which can be used to determine

maximum rate of climb at horse powers. Figure 11 shows the rate of climb vs

pressure altitude can be used by a pilot to determine the rate of climb at different

altitudes.

y = -34.638x + 11485

0

2000

4000

6000

8000

10000

12000

0 100 200 300 400 500

Pre

ssu

re A

ltit

ud

e (f

t)

ROC (ft/min)

Climb PerformanceRate of Climb vs Pressure Altitude

22

Conclusions

This aircraft was originally certified under the Civil Air Regulations. For an

airplane with a gross takeoff weight of less than 6000 feet, the CAR 3.85 requirement

for steady rate of climb at sea level shall not be less than 10 VS1 or 300 ft/min,

whichever is greater, under the following conditions:

(1) Take-off power.

(2) Landing gear extended.

(3) Wing flaps in take-off position.

(4) Cowl flaps in the position used in cooling tests.

The aircraft under test did not have wing or cowl flaps, but based on the chart

in Figure 11, it had a rate of climb of about 322 ft/min at sea level. This is above the

required minimum of 300 ft/min per CAR 3.85, so the airplane met the requirements.

23

3.5 Flight Test 5: Level Acceleration Test

Background

An alternate method to perform some of the performance flight tests is to use

what is known as the Rutowski energy method. This method allows the energy state

of an aircraft to be determined. If we determine an aircraft’s ability to change its

energy level at a given time, we can use this information to determine an aircraft’s

performance abilities.

The rate of climb performance capabilities of an airplane can be determined by

using this method. By performing a level acceleration test and plotting the reduced

data, the best rate of climb, best angle of climb, and aircraft ceiling can be determined.

The FAA currently has not accepted Rutowski energy method for determining

compliance with regulations, so there are no regulations to compare the test results

with.

24


The purpose of this flight test is to determine specific excess power and to use

that information in determining climb performance. The flight test procedures,

collected data, and data reduction techniques are detailed in Appendix B, C, and D

respectively.

Test Results

Figure 13: Time vs Calibrated Airspeed – High Altitude

y = -0.0005x3 + 0.0339x2 + 0.8254x + 54.905

0.0

20.0

40.0

60.0

80.0

100.0

120.0

140.0

160.0

0 10 20 30 40 50 60

Cal

ibta

red

Air

spe

ed

(ft

/se

c)

Time (sec)

Level Accelerated Flight PerformanceTime vs Calibrated Airspeed - High Altitude

25

Figure 14: Time vs Calibrated Airspeed – Low Altitude

Figure 15: Calibrated Airspeed vs Rate of Climb

y = 0.0005x3 - 0.0672x2 + 3.4026x + 55.866

0.0

20.0

40.0

60.0

80.0

100.0

120.0

140.0

160.0

0 10 20 30 40 50

Cal

ibta

red

Air

spe

ed

(ft

/se

c)

Time (sec)

Level Accelerated Flight PerformanceTime vs Calibrated Airspeed - Low Altitude

y = -0.4594x2 + 55.281x - 1358.4

y = -0.2432x2 + 22.29x - 120.54

0

100

200

300

400

500

600

0 20 40 60 80 100 120

Rat

e o

f C

limb

(ft

/min

)

Calibrated Airspeed (mph)

Level Accelerated Flight PerformanceCalibrated Airspeed vs Rate of Climb

Hic 3500 ft

Hic 500 ft

max points

tangent points

26

Figure 16: Best Angle of Climb and Best Rate of Climb

Figure 17: Calibrated Airspeed vs Weight Corrected Thrust HP in Excess

0

1000

2000

3000

4000

5000

0 20 40 60 80 100

Pre

ssu

re A

ltit

ud

e (

ft)


Level Accelerated Flight PerformanceBest Angle (Vx) and Best Rate (Vy) of Climb vs Vc

Vy

Vx

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

18.0

0 20 40 60 80 100

(FH

Pxc

)wc


Level Accelerated Flight PerformanceCalibrated Airspeed vs (FHPxc)wc

Hic 3500 Ft

Hic 500 ft

27

Taking the derivatives of the equations in Figure 12 and Figure 13,

acceleration can was determined for both the higher and lower altitude tests. This data

was used later in the data reduction, and ultimately used to produce the remaining

graphs for this flight test.

The max and tangent data points in Figure 14 were used to produce the best

angle of climb, best rate of climb, and aircraft ceiling in Figure 15. The best rate of

climb was 43.4 mph. The ceiling of the aircraft was determined to be 4510 feet.

Figure 16 shows the correlation between calibrated airspeed and weight

corrected thrust HP in excess. This information is helpful in determining the overall

performance capabilities of an airplane.

Conclusions

The reduced data showed that the best rate of climb was 43.4 mph, and the

ceiling of the aircraft was 4510 feet. Both of these numbers seem to be on the low

side, because the best rate of climb is just above stall speed, and the ceiling obtained in

the climb performance flight test was 11,485 ft. Parasitic drag may have played a part

in the low numbers, as it is not accounted for in the calculations.

28

Parasitic drag is any form of drag other than induced drag. This type of drag

can be produced by any object that protrudes from the airplane, such as landing gear,

struts, or antennas. The piper J4A Cub Couple has large tires, and struts for the high

wings, which is a major contributor to parasitic drag. Misaligned doors and control

surfaces can also contribute to parasitic drag Any gaps present between the doors and

fuselage can increase the drag. Misaligned control surfaces, i.e. rudders, elevators,

and ailerons, can cause the aircraft to fight itself during flight, resulting in an increase

of parasitic drag. Both misaligned doors and control surfaces may have been present

during this test flight, and contributed to the reduced performance.

29

Chapter 4

Stability and Control Flight Tests

4.1 Flight Test 6: Longitudinal Static Stability

Background

Longitudinal stability is concerned with stability about the lateral axis and can

be broken down into two conditions: stick-fixed and stick-free. Stick-fixed refers to

the elevator being in a fixed position and not free to float with the relative wind.

Stick-free refers to the condition where the elevator is free to float.

The aerodynamic center of an airplane is the point where the pitching moments

remain constant with a changing lift coefficient. As long as the center of gravity stays

ahead of the aerodynamic center of the airplane, the pitching moment will be down, or

stable for both the stick-fixed and stick-free conditions.

30

CAR 3.114 and 3.115 detail the requirements for static longitudinal stability.

For the purposes of this test flight, we were concerned with only climb and landing

stability.

§ 3.114

Static longitudinal stability. In the configurations outlined in § 3.115 and with the

airplane trimmed as indicated, the characteristics of the elevator control forces and

the friction within the control system shall be such that:

(a) A pull shall be required to obtain and maintain speeds below the specified trim

speed and a push to obtain and maintain speeds above the specified trim speed.

This shall be so at any speed which can be obtained without excessive control

force, except that such speeds need not be greater than the appropriate

maximum permissible speed or less than the minimum speed in steady un-

stalled flight.

(b) The air speed shall return to within 10 percent of the original trim speed when

the control force is slowly released from any speed within the limits defined in

paragraph (a) of this section.

§ 3.115

Specific conditions. In conditions set forth in this section, within the speeds

specified, the stable slope of stick force versus speed curve shall be such that nay

substantial change in speed is clearly perceptible to the pilot through a resulting

change in stick force.

(a) Landing. The stick force curve shall have a stable slope and the stick force

shall not exceed 40 lbs. at any speed between 1.1 Vs1 and 1.3 Vs1 with:

(1) Wing flaps in the landing position,

(2) The landing gear extended,

(3) Maximum weight,

(4) Throttles closed on all engines,

(5) Airplanes of more than 6,000 pounds maximum weight trimmed at 1.4

Vs1, and airplanes of 6,000 pounds or less maximum weight trimmed at 1.5

Vs1.

(b) Climb. The stick force curve shall have a stable slope at all speeds between 1.2

Vs1 and 1.6 Vs1 with:

(1) Wing flaps retracted,

(2) Landing gear retracted,

(3) Maximum weight,

(4) 75 percent of maximum continuous power,

(5) The airplane trimmed at 1.4 Vs1.

31

(c) Cruising.

(1) Between 1.3 Vs1 and the maximum permissible speed, the stick force

curve shall have a stable slope at all speeds obtainable with a stick force

not in excess of 40 pounds with:

(i) Landing gear retracted,

(ii) Wing flaps retracted,

(iii) Maximum weight,

(iv) 75 percent of maximum continuous power,

(v) The airplane trimmed for level flight with 75 percent of the

maximum continuous power.

(2) Same as subparagraph (1) of this paragraph, except that the landing gear

shall be extended and the level flight trim speed need not be exceeded.




32

Test Results

Figure 18: Calibrated Airspeed vs Elevator Position – Stick-Fixed Climb

Figure 19: Coefficient of Lift vs Elevator Position – Stick-Fixed Climb

y = 0.0037x2 - 0.7056x + 32.073

y = 0.0007x2 - 0.2944x + 17.298

0

1

2

3

4

5

6

7

40 50 60 70 80 90 100

Elev

ato

r P

osi

tio

n (

deg

)

Vc (mph)

STICK-FIXED STATIC LONGITUDINAL STABILITYCLIMB

C.G = 16.06

C.G. = 16.70

y = -8.9899x2 + 22.793x - 9.6716

y = -3.7626x2 + 15.706x - 6.6336

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

0.0000 0.2000 0.4000 0.6000 0.8000 1.0000 1.2000 1.4000

Elev

ato

r P

osi

tio

n (

deg

)

CL


C.G = 16.70

C.G. = 16.06

33

Figure 20: C.G. vs Slope – Stick-Fixed Climb

Figure 21: Calibrated Airspeed vs Elevator Position – Stick-Free Climb

0

2

4

6

8

10

12

14

16

18

20

15 17 19 21 23 25

Slo

pe

((𝑑𝐹𝑠/𝑞

)/𝑑𝐶𝐿

)

C.G (in)


CL - 0.4

CL = 0.6

CL = 0.8

CL = 1.0Aft

C.G

. Lim

it

Stick-FixedNeutral Points

y = 0.0121x2 - 1.6435x + 57.923

y = 0.0144x2 - 1.967x + 69.367

0

1

2

3

4

5

6

7

8

9

40 50 60 70 80 90 100

Stic

k Fo

rce

(lb

s)

Vc (mph)

STICK-FREE STATIC LONGITUDINAL STABILITYCLIMB

C.G. = 16.06

C.G. = 16.70

34

Figure 22: Coefficient of Lift vs Elevator Position – Stick-Free Climb

Figure 23: C.G. vs Slope – Stick-Free Climb

y = 16.42x2 - 22.495x + 10.489

y = 19.929x2 - 26.522x + 11.943

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40

Fs /

q

CL

STICK-FREE STATIC LONGITUDINAL STABILITYCLIMB

C.G. = 16.06

C.G. = 16.70

-20

-15

-10

-5

0

5

10

15

20

15 17 19 21 23 25

Slo

pe

((𝑑𝐹𝑠/𝑞

)/𝑑𝐶𝐿

)

C.G (in)


CL - 0.4

CL = 0.6

CL = 0.8

CL = 1.0

Aft

C.G

. Lim

it

35

Conclusions

An analysis of the data plots indicates that most of the maneuver points are

forward of the aft C.G. limit, which indicates that the aircraft is un-stable. The data

used to generate the maneuver points is suspect, as we know that the aircraft is stable.

The main cause of this is likely due to an insufficient spread in the center of

gravity between the test flights. The lower C.G. was 16.06 inches, and the upper C.G.

was 16.70 inches. The differences in the collected data from these two C.G. points is

not great enough to show meaningful plots upon data reduction. The aft C.G. could be

moved farther aft with an increase in ballast to increase the spread, but based on

conversations with Dr. Isaac Silver, who piloted this aircraft on many occasions, a

C.G. of more than 17 inches reduces the handling of the airplane, and is not

recommended. The published CG range for this airplane is 12.9 inches to 21 inches

aft of datum. Due to the handling characteristics noted from an experience pilot, a

revision to the aft C.G. limit for this airplane should seriously be considered.

Another alternative to increase the spread of the C.G.s during flight testing

would be to move the initial C.G. forward for the first flight, and add additional

weight in the baggage compartment for the second flight. For the first flight, this

could be accomplished by adding ballast farther up near the engine compartment, or

36

only performing the flight test with a pilot and no flight test engineer. For the second

flight, simply adding additional ballast in the baggage compartment would accomplish

the goal.

37

4.2 Flight Test 7: Longitudinal Dynamic Stability

Background

Dynamic longitudinal stability is concerned with how an airplane responds to a

disturbance over time. For the aircraft to be dynamically stable, the amplitude of the

displacement caused by a disturbance should decrease over time. There are three

modes of longitudinal motion: the short period, the long period or phugoid, and the

elevator short period. This flight test is concerned only with the long period phugoid

mode.

The phugoid mode is characterized by an oscillatory motion about the lateral

axis, where airspeed and altitude above and below the trim is experienced. Graphing

the airspeed during the phugoid motion at regular intervals for a dynamically stable

airplane would resemble the graph in Figure 23 below. This figure shows that the

amplitude of the displacement is decreasing over time, resulting in positive dynamic

stability.

Figure 24: Phugoid oscillatory motion

38

CAR 1.117 contains the requirements for dynamic longitudinal stability. The

requirement only applies to the short period oscillation. The long period oscillation is

not included because the pilot can usually recognize the long period oscillation and

easily damp it as long as a visual reference is available.




Test Results

Figure 25: Time vs Indicated Airspeed – Climb

6062646668707274767880

0 5 10 15 20 25 30 35 40 45 50 55 60 65

Vi (

mp

h)

Time (sec)

DYNAMIC LONGITUDINAL STABILITYCLIMB

24 sec

X2 = 3

X3 = 2X1 = 5

X4 = 1.5

39

Figure 26: Time vs Indicated Airspeed – Power Approach

The damped frequency and natural frequency were calculated, and are

displayed in Table 2. This data was not needed to show that the airplane exhibited

positive dynamic stability, but was included as a reference.

Table 2: Damped and Natural Frequency Data Reduction

Damping Factor ωd ωn

Climb 0.125 0.262 rads/sec 0.264 rads/sec

Power Approach 0.163 0.262 rads/sec 0.265 rads/sec

60

62

64

66

68

70

72

74

76

78

80

0 5 10 15 20 25 30 35 40 45 50 55 60 65

Vi (

mp

h)

Time (sec)

DYNAMIC LONGITUDINAL STABILITYPOWER APPROACH

24 sec

X1 = 4

X2 = 2.25

X3 = 2

X4 = 1

40

Conclusions

The graphs of the collected data show that the amplitude of the displacement of

the airplane caused by the initial disturbance decreases over time. This shows that

oscillation is sufficiently damped and that the airplane has dynamic longitudinal

stability.

41

4.3 Flight Test 8: Longitudinal Maneuvering Stability

Background

All airplanes must be maneuverable in order to perform their mission. The

pilot can maneuver the airplane longitudinally in multiple ways, such as pull-ups,

push-overs, or banking turns. All of these maneuvers cause an increase or decrease in

the angle of attack and lift coefficient, and the rate of rotation about the airplane’s

center of gravity. This in turn causes a change in the relative wind across the elevator,

which contributes to the stability of the airplane in maneuvering flight, and is directly

dependent on the pitch rate of the airplane. If airspeed is held constant, then the pitch

rate is a function of normal acceleration. Normal acceleration can be used as an

independent variable for maneuvering stability. Elevator position per normal

acceleration and stick for per normal acceleration are used in evaluating maneuvering

stability.

Elevator maneuvering stability is referred to as “stick-fixed” maneuvering

stability, and stick force maneuvering stability is referred to as “stick-free”

maneuvering stability. CAR 3 does not specify requirements for maneuvering

stability, but for an aircraft to have “stick-fixed” and “stick-free” maneuvering

stability, it must have its maneuver points aft of the aft center of gravity limit.

42




Test Results

Figure 27: Acceleration vs Elevator Position – Stick Fixed

y = -44.287x2 + 137.01x - 92.476

y = -18.986x2 + 66.347x - 47.192

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80

Elev

ato

Po

siti

on

(d

eg)

Normal Acceleration (g)

STICK-FIXED MANEUVERING STABILITY

C.G. = 16.06

C.G. = 17.26

43

Figure 28: Acceleration vs Elevator Position – Stick Free

Figure 29: C.G. vs slope – Stick Fixed

y = -38.07x2 + 131.12x - 92.724

y = -51.02x2 + 148.47x - 86.949

0.0

5.0

10.0

15.0

20.0

25.0

1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50 1.55 1.60 1.65 1.70 1.75 1.80

Stic

k Fo

rce

(Fs)

(lb

s)

Normal Acceleration (g)

STICK-FREE MANEUVERING STABILITY

C.G. =16.06

0.00

10.00

20.00

30.00

40.00

50.00

60.00

12 14 16 18 20 22 24 26 28 30

(ele

vato

r) /

d (

Nz)

C.G. (in)


Nz = 1.0

Nz = 1.2

Nz = 1.4

Aft

C.G

. Lim

it

Maneuver Points

44

Figure 30: C.G. vs slope – Stick Free

Figure 31: Acceleration vs Maneuvering Points – Stick Fixed

0.00

10.00

20.00

30.00

40.00

50.00

60.00

12 17 22 27

(ele

vato

r) /

d (

Nz)

C.G. (in)


Nz = 1.0

Nz = 1.2

Nz = 1.4Aft

C.G

. Lim

it

Maneuver Points

12

14

16

18

20

22

24

26

28

30

0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1

Man

uev

er P

oin

t (i

n)

Normal Acceleration (Nz) (g)


Aft C.G. Limit

45

Figure 32: Acceleration vs Maneuvering Points – Stick Free

Conclusions

An analysis of the data plots indicates that all of the stick-fixed, and most of

the stick-free maneuver points are forward of the aft C.G. limit, which indicates that

the aircraft is un-stable. We know that the airplane is stable, so either the collected

data is suspect, and/or the criteria for determining acceptable maneuver points in

relation to the aft C.G. limit may need to be revised.

12

14

16

18

20

22

24

26

28

30

0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1

Man

uev

er P

oin

t (i

n)

Normal Acceleration (Nz) (g)


Aft C.G. Limit

46

As was discussed in the conclusion of flight test 6, increasing the spread of the

C.G. between flights would probably help. However, the calculated maneuver points

for the test flights look much better than that of flight test 6, because the C.G. spread is

already larger: forward C.G. is 16.06 inches, and aft C.G. is 17.26 inches. By simply

moving the aft C.G. limit closer to 17 inches, as was also discussed for flight test 6, it

would move most of the maneuver points aft of the upper C.G. limit, and indicate that

the airplane is stable. Once again, serious consideration should be given to adjusting

the recommended aft C.G. limit to a value closer to 17 inches aft of datum.

47

4.3 Flight Test 9: Static and Dynamic Lateral-Directional

Stability

Background

Lateral-directional stability refers to an airplane’s reaction when its flight path

deviates from the plane of symmetry. The sideslip angle is the angle of the plane of

symmetry with the relative wind, and the yaw angle is the angle of the plane of

symmetry about a fixed reference. The sideslip angle can be equated to angle of

attack, and the yaw angle can be equated to the pitch angle.

CAR 3.118 details the requirements for lateral-directional stability:

48

§ 3.118 Directional and lateral stability

(a) Three-control airplanes.

(1) The static directional stability, as shown by the tendency to recover from a

skid with rudder free, shall be positive for all flap positions and symmetrical

power conditions, and for all speeds from 1.2 Vs1 up to the maximum

permissible speed.

(2) The static lateral stability as shown by the tendency to raise the low wing in

a sideslip, for all flap positions and symmetrical power conditions, shall:

(i) Be positive at the maximum permissible speed.

(ii) Not be negative at a speed equal to 1.2 Vs1.

(3) In straight steady sideslips (unaccelerated forward slips), the aileron and

rudder control movements and forces shall increase steadily, but not

necessarily in constant proportion, as the angle of sideslip is increased; the rate

of increase of the movements and forces shall lie between satisfactory limits up

to sideslip angles considered appropriate to the operation of the type. At

greater angles, up to that at which the full rudder control is employed or a

rudder pedal force of 150 pounds is obtained, the rudder pedal forces shall not

reverse and increased rudder deflection shall produce increased angles of

sideslip. Sufficient bank shall accompany side-slipping to indicate adequately

any departure from steady un-yawed flight. (4) Any short-period oscillation occurring between stalling speed and maximum

permissible speed shall be heavily damped with the primary controls (i) free and

(ii) in a fixed position.

Due to the lack of an automatic data collection device for this flight test, only

item 4 was evaluated. This flight condition is known as the Dutch Roll. The Dutch

Roll can be described as the concurrent rolling and yawing of the airplane.

49


The procedure for this test flight was to have the pilot induce a Dutch Roll

using a rudder doublet then released all controls. The time for the Dutch Roll to be

damped was then recorded.

Test Results

The damping of the Dutch Roll occurred in about 15 seconds for both the

forward and aft C.G. positions.

Conclusions

Based on the damping time of the Dutch Roll in both forward and aft C.G.

positions, it shows that the oscillation is heavily damped as required by CAR 3.118.4

50

References

[1] R. D. Kimberlin, Flight Testing of Fixed Wing Aircraft, Reston, Virginia:

American Institute of Aeronautics and Astronautics, 2003.

[2] R. D. Kimberlin, Laboratory Manual - Performance Flight Test Engineering,

Melbourne, Florida: Florida Institute of Technology, 2017.

[3] B. Kish, ‘Various Flight Test Data Reduction Videos, Available:

https://www.youtube.com/. [Accessed January-March 2020].

[4] Stephen Corda, Introduction to Aerospace Engineering with a Flight Test

Perspective, Chichester, West Sussex, United Kingdom: John Wiley and Sons

Ltd., 2017.

[5] Joe Christy & Greg Erikson, Engines for Homebuilt Planes, New York, New

York, Sports Car Press Ltd., 1977.

[6] ‘Plymouth State Weather Center’,

http://vortex.plymouth.edu/cgi-bin/sfc/gen-textobs-

a.cgi?ident=FL&if=sfc_dat&yy=17&mm=09&dd=30&hh=09&pg=web

[7] Federal Aviation Administration, Civil Air Regulations,

http://rgl.faa.gov/Regulatory_and_Guidance_Library/rgccab.nsf/MainFrame?Op

enFrameSet.

[8] Federal Aviation Administration, Aircraft Specification No. A-703 Revision 4,

July 31 1995.

[9] ‘FlugzeugInfo.net’,

http://www.flugzeuginfo.net/acdata_php/acdata_piper_j4_en.php

https://www.youtube.com/

http://vortex.plymouth.edu/cgi-bin/sfc/gen-textobs-a.cgi?ident=FL&if=sfc_dat&yy=17&mm=09&dd=30&hh=09&pg=web

http://vortex.plymouth.edu/cgi-bin/sfc/gen-textobs-a.cgi?ident=FL&if=sfc_dat&yy=17&mm=09&dd=30&hh=09&pg=web

http://rgl.faa.gov/Regulatory_and_Guidance_Library/rgccab.nsf/MainFrame?OpenFrameSet

http://rgl.faa.gov/Regulatory_and_Guidance_Library/rgccab.nsf/MainFrame?OpenFrameSet

http://www.flugzeuginfo.net/acdata_php/acdata_piper_j4_en.php

51

Appendix A

Weight and Balance

Performance

Table 3: Weight and Balance - Flight Tests 1-5

Flight Tests 1-5

Weight (lbs) Arm (in) Moment (in-lbs)

Empty Aircraft - Front Wheels (full fuel and oil) 885 3.25 2876.3

Empty Aircraft - Tail Wheel (full fuel and oil) 56 182.50 10220.0

Pilot 115 23.00 2645.0

Passenger 175 23.00 4025.0

Baggage 0 43.00 0.0

Total Loaded Airplane 1231 16.06 19766.3

52

Stability and Control

Table 4: Weight and Balance - Flight Test 6-7 (No Ballast)

Flight Tests 6-7




Pilot 115 23.00 2645.0

Passenger 175 23.00 4025.0

Baggage 0 43.00 1075.0


Table 5: Weight and Balance - Flight Tests 6-7 (Aft Ballast)

Flight Tests 6-7




Pilot 115 23.00 2645.0

Passenger 175 23.00 4025.0

Baggage 25 43.00 1075.0

Delta Fuel Weight -19.7 10.00 -197.0


53

Table 6: Weight and Balance - Flight Test 8-9 (No Ballast)

Flight Tests 18-9




Pilot 115 23.00 2645.0

Passenger 175 23.00 4025.0

Baggage 0 43.00 0.0


Table 7: Weight and Balance - Flight Tests 8-9 (Aft Ballast)

Flight Tests 8-9




Pilot 115 23.00 2645.0

Passenger 175 23.00 4025.0

Baggage 50 43.00 2150.0

Delta Fuel Weight -26.2 10.00 -262.0


54

Appendix B

Flight Test Procedures

1. Position Correction Using GPS Method

a. Prior to flight, the airplane was fully fueled. The date, time, and engine start

time were recorded on the flight card.

b. Once in the air, with smooth conditions, the pilot maintained a constant

airspeed and altitude, and required data was collected per the flight card.

c. The pilot changed the airplane heading by 180°, while maintaining the same

airspeed as in step 2. Required data was then collected per the flight card.

d. Steps 2 and 3 above were repeated at different speeds until a total of five sets

of data were collected

2. Determination of Stall Speeds

a. At appropriate altitude listed in the flight card, the pilot trimmed the aircraft to

a speed of about 60 mph.

b. Speed was then reduced by about 1 mph/sec until the stall occurred.

c. Data was collected per the flight card.

d. This process above was repeated multiple times at different altitudes.

55

3. Determination of Level Flight Performance

a. At appropriate altitude, the airplane was stabilized and maximum continuous

power was applied for level flight.

b. Airspeed and altitude were recorded on the flight card.

c. The RPM was adjusted down by about 100, then airspeed and altitude were

recorded on the flight card.

d. Step 3 was repeated until a total of six measurements were taken.

4. Determination of Climb Performance

a. At a higher altitude, the airplane was stabilized and a climb was initiated while

maintaining constant airspeed and RPM.

b. The following data was recorded on the flight card: airspeed, altitude, outside

air temp, and engine RPM,

c. The climb was continued while maintaining constant airspeed and RPM, and

the data mentioned in step 2 was recorded every 30 seconds for a 3-minute

duration.

d. Steps 2 and 3 were repeated at the same higher altitude, but in the opposite

heading.

56

5. Level Acceleration Test

a. Prior to flight, the airplane was fully fueled. The date and engine start time

were recorded on the flight card.

b. The airplane was stabilized at 3500 feet.

c. RPM and heading were recorded on the flight card.

d. Power was steadily increased while altitude and RPMs were maintained. The

airspeed was then recorded every 5 seconds.

e. This process was continued until the maximum speed was reached.

f. The airplane was then stabilized a 500 ft, and steps 3 through 5 were repeated.

6. Longitudinal Static Stability

a. Prior to flight, the airplane was fully fueled. The date and engine start time

were recorded on the flight card.

b. The airplane was trimmed to the airspeed and power setting required by

regulation for the flight condition, i.e. climb or power approach. Data was

collected per the flight card.

c. Airspeed was increased or decreased by using longitudinal control, without re-

trimming the aircraft. The new airspeed was held constant by exerting force

upon the longitudinal control. For climb configuration, the first point was

above trim, and for power approach, the first point was below trim. Data was

collected per the flight card.

57

d. Step (b) was repeated at an airspeed on the opposite side of trim.

e. Airspeed was alternated above and below trim 5 to 10 knots apart until the

required stable range was covered. Data was collected per the flight card.

f. After the last point, longitudinal control force was gradually released until the

pilot’s hand could be removed without any further airspeed change. This

airspeed was recorded as the “free return” airspeed.

7. Longitudinal Dynamic Stability

a. Trim airplane.

b. Using only elevator control, reduce airspeed 10 to 15 mph.

c. Let go and observe.

d. Record airspeed and pressure altitude over time (every 5 seconds).

58

8. Longitudinal Maneuvering Stability

a. Trim the aircraft to a specified airspeed and power setting. Record the

following data prior to either the steady pull-up, steady push-over, or wind-up

turn:

• Airspeed

• Stick force (should be 0)

• Elevator position

• Fuel quantity

• Altitude

• Outside air temperature

b. Steady Pull-up: from the trim condition. Zoom climb the airplane (without

changing trim or power settings). Perform a push-over to enter a shallow dive

toward the trim altitude. When the airspeed approaches the trim airspeed,

perform a steady pull-up to establish a pitch rate that will place the airplane

back on the trim airspeed at the desired normal acceleration (load factor). At

each point, record the following data:

• Stick force


• Normal acceleration (NZ)

c. Steady Push-over: this is essentially the reverse of the steady pull-up

maneuver above. It provides data at less than 1g. At each point (up to the

desired negative load factor limit or down elevator limit), record the following

data:

• Stick force



59

d. Wind-up Turn: without changing longitudinal trim, set climb power and climb

500-1000 feet above the trim altitude. Reset trim power and obtain trim

airspeed. Smoothly and slowly begin rolling the airplane into a wind-up turn

while maintaining trim airspeed. The pilot will call out the stick force readings

throughout the maneuver until the airplane reaches maximum normal

acceleration (load factor) or begins to stall. At each point, record the following

data:

• Stick force



9. Dynamic Lateral-Directional Stability

a. The pilot trimmed the airplane in level flight.

b. The pilot excited the Dutch Roll mode using a rudder doublet then released all

controls

c. The wingtip response was observed.

d. The time period of the damped oscillation was estimated.

60

Appendix C

Collected Data


Table 8: Flight Information – Flight Tests 1-3

Date 11/19/2019

Engine Start Time 12:09Z

Engine Shutoff Time 13:41Z

Flight Location Melbourne International Airport (KMLB)

Aircraft Piper J4A Cub Coupe - Tail NC26735

Purpose Multiple performance flights

METAR KMLB 191153Z 00000KT 10SM CLR 12/12 A2986 RMK AO2 SLP111 T01220117 10133 20111 53000

61

Table 9: Collected Data – Flight 1

Test Pt Time of

Day

Alt

(ft)

Airspeed

(mph)

Heading

(deg)

GPS

Track

(deg)

GPS

Ground

Speed

(kts)

OAT

(°C)

1 7:34am 1540 82 200 185 74 10.5

2 7:35am 1540 82 10 34 72 10.5

3 7:38am 1520 76 200 181 72 10.5

4 7:39am 1560 76 10 35 67 10.5

5 7:42am 1560 70 200 183 68 10.5

6 7:43am 1560 70 10 38 62 10.5

7 7:44am 1550 63 10 36 58 10.5

8 7:45am 1550 63 200 175 62 10.5

9 7:47am 1530 55 200 179 57 10.5

10 7:48am 1530 55 10 45 51 10.5



Test Pt Time of Day

Initial Altitude

(ft)

Stall Airspeed

(mph)

Stall Altitude

(ft)

Recovery Altitude

(ft)

OAT (°C)

1 7:50am 2540 35 2540 2400 9

2 7:54am 2000 35 2000 1900 10

3 7:58am 1500 34 1500 1380 11

4 8:02am 2740 38 2740 2640 8.5

5 8:06am 3000 38 3000 2920 8

6 8:10am 3300 39 3300 3240 7.4

62



Test Pt Altitude (ft)

Airspeed (mph)

RPM

1 3500 83 2270

2 3500 75 2200

3 3500 71 2100

4 3500 67 2000

5 3500 58 1900 6 3500 43 1800


Table 12: Flight Information – Flight Tests 4-5

Date 11/26/2019

Engine Start Time 12:40Z

Engine Shutoff Time 14:10Z

Flight Location Melbourne International Airport (KMLB)

Aircraft Piper J4A Cub Coupe - Tail NC26735

Purpose Multiple performance flights

METAR KMLB 261253Z 28003KT 10SM CLR 09/09 A3005 RMK AO2 SLP173 T00940089

63

Table 13: Collected Data – Flight Test 4 – Higher Altitude Heading 200

Test Pt Time (sec)

Altitude (ft)

Airspeed (mph)

Heading (deg)

OAT (°C)

RPM

1 0 3500 60 200 8.0 2000

2 30 3660 60 200 7.7 2100

3 60 3800 60 200 7.4 2100

4 90 3900 60 200 7.2 2100

5 120 4010 60 200 7.0 2100

6 150 4130 60 200 6.7 2100

7 180 4240 60 200 6.5 2100

Table 14: Collected Data – Flight Test 4 – Higher Altitude Heading 20

Test Pt Time (sec)

Altitude (ft)

Airspeed (mph)

Heading (deg)

OAT (°C)

RPM

1 0 3500 60 20 8.0 2100

2 30 3640 60 20 7.7 2100

3 60 3710 60 20 7.6 2100

4 90 3820 60 20 7.4 2100

5 120 3900 60 20 7.2 2100

6 150 4000 60 20 7.0 2100

7 180 4100 60 20 6.8 2100

64

Table 15: Collected Data – Flight Test 4 – Lower Altitude Heading 200

Test Pt Time (sec)

Altitude (ft)

Airspeed (mph)

Heading (deg)

OAT (°C)

RPM

1 0 1000 60 200 14.0 2200

2 30 1200 60 200 13.6 2200

3 60 1330 60 200 13.3 2150

4 90 1460 60 200 13.1 2150

5 120 1580 60 200 12.8 2150

6 150 1720 60 200 12.6 2150

7 180 1860 60 200 12.3 2150

Table 16: Collected Data – Flight Test 4 – Lower Altitude Heading 20

Test Pt Time (sec)

Altitude (ft)

Airspeed (mph)

Heading (deg)

OAT (°C)

RPM

1 0 1000 60 20 14.0 2100

2 30 1160 60 20 13.7 2100

3 60 1300 60 20 13.4 2100

4 90 1480 60 20 13.0 2100

5 120 1610 60 20 12.8 2100

6 150 1760 60 20 12.5 2100

7 180 1900 60 20 12.2 2100

65


Table 17: Collected Data – Flight Test 5 – Higher Altitude

Test Pt Time (sec)

Airspeed (mph)

Altitude (ft)

Heading (deg)

RPM

1 0 40 3500 210 2000

2 5 41 3500 210 2000

3 10 48 3500 210 2000

4 15 53 3500 210 2000

5 20 55 3500 210 2000

6 25 61 3500 210 2000

7 30 70 3500 210 2000

8 35 75 3500 210 2000

9 40 80 3500 210 2000

10 45 82 3500 210 2000

11 50 86 3500 210 2000

12 55 88 3500 210 2000

Table 18: Collected Data – Flight Test 5 – Lower Altitude

Test Pt Time (sec)

Airspeed (mph)

Altitude (ft)

Heading (deg)

RPM

1 0 40 500 200 2100

2 5 50 500 200 2100

3 10 60 500 200 2100

4 15 65 500 200 2100

5 20 72 500 200 2100

6 25 77 500 200 2100

7 30 80 500 200 2100

8 35 84 500 200 2100

9 40 86 500 200 2100

10 45 88 500 200 2100

66


Table 19: Collected Data – Flight Test 6 – Climb - Forward C.G.

Test Pt Condition Altitude (ft)

Airspeed (mph)

Stick Force (lbs)

Stick Displacement

(in)

1 Trim 2000 70 0 6.75

2 Above Trim (10) 2060 80 2.3 6.5

3 Below Trim (10) 2260 60 -3.5 7.25

4 Above Trim (20) 2280 90 5.0 6.1875

5 Below Trim (20) 2500 50 -6.5 7.75

6 Free Return Above

2760 74 0 6.5

7 Free Return Below

2740 68 0 6.75

Table 20: Collected Data – Flight Test 6 – Climb - Aft C.G.


Airspeed (mph)

Stick Force (lbs)

Stick Displacement

(in)

1 Trim 1540 70 0 6.5

2 Above Trim (10) 1640 80 2.5 6.5

3 Below Trim (10) 1780 60 -4.0 7.0

4 Above Trim (20) 1800 90 5.6 6.0

5 Below Trim (20) 2010 50 -7.7 7.375

6 Free Return Above

1800 73 0 6.5

7 Free Return Below

2100 67 0 6.75

67

Table 21: Collected Data – Flight Test 6 – Power Approach - Forward C.G.


Airspeed (mph)

Stick Force (lbs)

Stick Displacement

(in)

1 Trim 2600 70 0 7.0

2 Above Trim (10) 2400 60 -4.5 7.5

3 Below Trim (10) 1900 80 1.5 6.5

4 Above Trim (20) 1700 50 -7.0 8.25

5 Below Trim (20) 1040 90 4.6 6.25

6 Free Return Above

1500 73 0 6.75

7 Free Return Below

700 78 0 6.75

Table 22: Collected Data – Flight Test 6 – Power Approach - Aft C.G.


Airspeed (mph)

Stick Force (lbs)

Stick Displacement

(in)

1 Trim 2300 70 0 6.625

2 Above Trim (10) 2100 60 -4.5 7.125

3 Below Trim (10) 1800 80 2.2 6.375

4 Above Trim (20) 1640 50 -7.8 7.875

5 Below Trim (20) 1120 90 4.1 6.125

6 Free Return Above

1500 68 0 6.750

7 Free Return Below

86070 76 0 6.500

68


Table 23: Collected Data – Flight Test 7 – Forward C.G.

Test Pt Time (sec)

Airspeed (mph)

Altitude (ft)

1 0 74 1600

2 5 67 1600

3 10 76 1600

4 15 73 1600

5 20 67 1610

6 25 70 1620

7 30 75 1610

8 35 74 1610

9 40 72 1620

10 45 70 1620

11 50 72 1620

12 55 73 1620

13 60 73 1620

69

Table 24: Collected Data – Flight Test 7 – Aft C.G.

Test Pt Time (sec)

Airspeed (mph)

Altitude (ft)

1 0 74 1080

2 5 66 1160

3 10 79 1120

4 15 74 1140

5 20 68 1180

6 25 70 1180

7 30 74 1160

8 35 74 1160

9 40 72 1180

10 45 70 1190

11 50 72 1200

12 55 73 1200

13 60 73 1200

70


Table 25: Collected Data – Flight Test 8 – Forward C.G

Test Pt Time of Day Stick Force (lbs)

Yoke Position (in)

Elevator Position

(deg)

Nz (g)

Trim 7:24:45 0 6.3125 0 1.00

Windup Turn Left 30°

7:25:10 10.0 8.000 8.29 1.18


7:25:55 13.5 8.500 10.79 1.33


7:26:15 20.0

9.000 13.29 1.63

Table 26: Collected Data – Flight Test 8 – Aft C.G

Test Pt Time of Day Stick Force (lbs)

Yoke Position (in)

Elevator Position

(deg)

Nz (g)

Trim 8:48:00 0 6.3125 0 1.00

Windup Turn Right 30°

8:48:16 10.5 7.500 5.78 1.21


8:48:25 18.0 8.000 8.29 1.42


8:48:42 21 8.500

10.79 1.67

71


Table 27: Collected Data – Flight Test 9 – Forward C.G

Table 28: Collected Data – Flight Test 9 – Aft C.G

Time to damp Dutch Roll oscillation

15 sec

Time to damp Dutch Roll oscillation

15 sec

72

Appendix D

Data Reduction Techniques


a. DETERMINE ANGULAR DIFFERENCE BETWEEN AIRPLANE

MAGNETIC HEADING AND GPS MAGNETIC TRACK

Obtain the angular difference between the collected GPS track and

magnetic heading by using the following formula:

𝐴𝐷 = 𝐺𝑃𝑆 𝑇𝑟𝑎𝑐𝑘 − 𝐻𝑒𝑎𝑑𝑖𝑛𝑔

b. CALCULATE CORRECTED GROUND SPEED

Calculate corrected ground speed by using the following formula on the

previously determined angular difference (AD):

𝐺𝑆𝐶 = 𝐺𝑆𝐺𝑃𝑆 cos(𝐴𝐷)

c. CALCULATE ATMOSPHERIC PRESSURE RATIO

Calculate the atmospheric pressure ratio using the following formula with

the previously determined instrument corrected altitude:

𝛿 = [1.0 − (6.87535 𝑥 10−6 )𝐻𝐼𝐶]5.2561

d. CALCULATE THE ATMOSPHERIC TEMPERATURE RATIO

73

Calculate the atmospheric temperature ratio using the collected outside air

temperature with following formula:

𝜃 = (273.15 + 𝑂𝐴𝑇)

288.15

e. CALCULATE THE SQUARE OF THE ATMOSPHERIC DENSITY RATIO

Calculate the square of the atmospheric density ratio using the atmospheric

pressure ration and the atmospheric temperature ratio calculated above and

the following formula:

√𝜎 = √𝛿

𝜃

f. CALCULATE CALIBRATED AIRSPEED

Calculate the calibrated airspeed VC using corrected ground speed and theta

with the following formula (note that VC is in knots):

𝑉𝐶 = 𝐺𝑆𝐶(√𝜎)

g. CALCULATE AVERAGE CALIBRATED AND INSTRUMENT

CORRECTED AIRSPEEDS

Calculate average calibrated airspeed (VC) and average instrument

corrected airspeed (VIC) using the following formulas (note that VC and VIC

are in knots):

𝑉𝐶 = 𝑉𝐶ℎ𝑒𝑎𝑑𝑖𝑛𝑔

+ 𝑉𝐶𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 ℎ𝑒𝑎𝑑𝑖𝑛𝑔

2

74

𝑉𝐼𝐶 = 𝑉𝐼𝐶ℎ𝑒𝑎𝑑𝑖𝑛𝑔

+ 𝑉𝐼𝐶𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 ℎ𝑒𝑎𝑑𝑖𝑛𝑔

2

Convert 𝑉𝐶 and 𝑉𝐼𝐶 from knots to MPH by multiplying by 1.15. These

values will be used in the next step.

h. CALCULATE POSITION CORRECTION

Calculate the position correction (∆VPC) using the following formula using:

∆𝑉𝑃𝐶 = 𝑉𝐶 − 𝑉𝐼𝐶

i. GENERATE A PLOT OF AVERAGE INDICATED AIRSPEED (Vi) vs

POSITION CORRECTION (∆VPC) FOR FLAPS UP AND FLAPS DOWN

Plotting the previously collected data to produce a graph of indicated

airspeed vs. position correction.

75


a. CALCULATE THE WEIGHT CORRECTED STALL SPEEDS

The weight corrected stall speeds are calculated from the following

formula:

𝑉𝑆 = 𝑉𝐶 √𝑊𝑆

𝑊𝑇

where:

VS = Weight corrected stall speed

VC = Calibrated stall speed

Ws = Standard gross weight

WT = Weight of aircraft at moment speed was recorded.

The value of WS used was 1300 lbs. To calculate WT, the weight of fuel

burnt at a test point was subtracted from the takeoff weight.

b. CALCULATE MAX COEFFICIENT OF LIFT

The max coefficient of lift is calculated from the following formula:

𝐶𝐿,𝑚𝑎𝑥 =2𝑊𝑇

𝑆𝜌𝑆𝐿𝑉𝐶2

where:


S = Total surface area of the wings.

𝜌𝑆𝐿= Air density at sea level.

VC = Calibrated airspeed in ft/sec.

76


a. BREAK HORSE POWER CALCULATION

An engine power chart was unavailable to use in the determination of brake

horsepower, as is normally done for this flight test. After discussions with

Dr. Ralph Kimberlin, Professor, Aerospace Engineering at Florida Institute

of Technology, it was decided to use a brake horse power of 65 at max

RPM in the calculations, and interpolate the horse power for other RPMs

from this max value. In the case of this flight test, max RPM was 2270.

b. CALCULATE DENSITY RATIO

The Density Ratio was calculated from the following formula:

𝜎 =𝛿

𝛩

𝛿 = [1.0 − (6.87535𝑥10−6) ∗ Hpi]5.2561

(Hpi is pressure altitude)

𝜃 =273.15+𝑇𝑎𝑖

288.15, (TAI is temperature at altitude)

c. CALCULATE WEIGHT RATIO

The weight ratio was calculated from the following formula:

𝑊𝑒𝑖𝑔ℎ𝑡 𝑅𝑎𝑡𝑖𝑜 = 𝑊𝑇

𝑊𝑆

WT is weight of the aircraft at the data point, WS is the max gross

weight of the aircraft at takeoff.

77

d. CALCULATE PIW, VIW, and NIW

Weight corrected power (PIW) was calculated from the following formula:

𝑃𝐼𝑊 = 𝐵𝐻𝑃𝑇∗ √𝜎𝑇

(𝑊𝑇𝑊𝑆

)1.5

Weight correct airspeed (VIW) was calculated from the following formula:

VIW = VC

√WTWS

Weight correct airspeed (NIW) was calculated from the following formula:

NIW = RPM √𝜎

√WTWS

e. Generate plots for PIW vs VIW, PIW vs NIW, and NIW vs VIW.

f. Generate plot of density altitude vs true airspeed.

78


a. PLOT TIME vs ALTITUDE

Plot the time vs. instrument collected altitude. The two sets of higher altitude

data points were plotted on the same graph, using a second order polynomial

trend line, and the equation of the line was displayed. The same procedure was

repeated for the lower altitude data points

b. DERIVATIVES OF CURVE FIT EQUATIONS

Take the derivative of each of the curve fit equations from the equations

generated in step (a).

c. DETERMINE RATE OF CLIMB FOR EACH DATA SET

Take an intermediate altitude between the start of the climb and the end of the

climb for each of the data sets (higher altitudes and lower altitudes), and solve

the curve fit equations from step (b) for time.

Plug in the times from above into the rate of time equations from step (a) to

determine rate of climb (ROC).

d. DETERMINE AVERAGE RATE OF CLIMB

Determine the average rate of climb by using the calculated rate of climb for both

the lower and higher altitude.

79

e. DETERMINE AMBIENT TEMPERATURE AT SELECTED ALTITUDES

From the collected data, interpolate the average ambient temperature at the

lower and higher altitudes respectively.

f. DETERMINE TEMPERATURE CORRECTED RATE OF CLIMB

Determine the temperature at altitude on a standard day using the following

equation:

Ts (°C) = −2 ∗ 𝐻𝑝

1000+ 15

g. CALCULATE DENSITY RATIO

Calculate the density ratio from the following formula:

𝜎 =𝛿

𝛩

where, 𝛿 = [1.0 − (6.87535𝑥10−6) ∗ Hpi]5.2561

(Hpi is pressure altitude)

and, 𝜃 =273.15 + 𝑇𝑎𝑖


80

h. CALCULATE AIRCRAFT WEIGHT AT SELECTED ALTITUDE - WT

Determine the instantaneous weight of the aircraft at the selected altitude

through interpolation by using the starting weight of the airplane, the fuel spent

during the flight, and the time of day that a reading was taken.

i. DETERMINE WEIGHT CORRECTED RATE OF CLIMB - CIW

The instrument corrected rate of climb is calculated from the following

formula:

CIW = 𝑅𝑂𝐶𝑇𝐶∗ √𝜎

√𝑊𝑇𝑊𝑆

where:

ROCTC = Temperature corrected rate of climb

= Density ratio

Ws = Standard gross weight


j. DETERMINE WEIGHT CORRECTED POWER - PIW

Instrument and weight corrected power is calculated from the following

equation:

PIW = 𝐵𝐻𝑃𝑡∗ √𝜎

(𝑊𝑇𝑊𝑆

)1.5

BHP was determined to be 65 the max rpm of 2270 from the level flight

performance flight test,

k. PLOT CIW vs PIW

81


a. PLOT CALIBRATED AIRSPEED IN FT/SEC VS TIME

b. TAKE DERIVATIVES OF CURVES TO DERIVE ACCELERATION

Take the derivative of the trend line equations from step (a) to derive the

acceleration equations. The y term in the equation can be converted to v for

velocity and the x term can be converted to t for time before taking the

derivative.

c. USE ACCELERATION EQUATIONS TO DERIVE VELOCITY AT EACH

TIME

Use the acceleration equations derived in step (b) to get the acceleration for

each time the velocity was recorded in the flight data, by substituting in the

time.

d. CALCULATE DENSITY RATIO

Calculate the Density Ratio was calculated from the following formula:

𝜎 =𝛿

𝛩

where, 𝛿 = [1.0 − (6.87535𝑥10−6) ∗ Hpi]5.2561, (Hpi is pressure altitude)

and, 𝜃 =273.15+𝑇𝑎𝑖


82

e. CALCULATE TRUE AIRSPEED VT IN FT/SEC

Calculate the true airspeed using the following formula:

𝑉𝑡 = 𝑉𝑐

√𝜎

f. CALCULATE TEST WEIGHT WT AT MIDPOINT OF LEVEL

ACCELERATION

Calculate the test weight by subtracting the weight of fuel spent at the time of

the data collection.

g. CALCULATE THRUST HP IN EXCESS

Calculate thrust HP in excess by the following formula:

𝐹𝐻𝑃𝑒𝑥𝑐𝑒𝑠𝑠 = (𝑊𝑇

𝑔) (

𝑑𝑣

𝑑𝑡) 𝑉𝑇 ∗

1 𝐻𝑃

550 𝑓𝑡∗𝑙𝑏𝑠/𝑠𝑒𝑐 , where g = 32.2 ft/s2

h. CALCULATE THRUST HP IN EXCESS FOR NON-STANDARD WEIGHT

The correction for Thrust HP corrected for non-standard weight is:

(𝐹𝐻𝑃𝑒𝑥𝑐𝑒𝑠𝑠)𝑤𝑐 0 = 𝐹𝐻𝑃𝑒𝑥𝑐𝑒𝑠𝑠

(𝑊𝑇𝑊𝑆

)

32

83

i. CALCULATE RATE OF CLIMB

The rate of climb is given by the following equation:

𝑅𝑂𝐶 = (𝐹𝐻𝑃𝑖𝑛𝑒𝑥𝑐𝑒𝑠𝑠)𝑤𝑐

𝑊𝑠∗

550 𝑓𝑡∗𝑙𝑏𝑠/𝑠

1 𝐻𝑃∗

60𝑠

1 𝑚𝑖𝑛

j. PLOT RATE OF CLIMB VS CALIBRATED AIRSPEED

1. Plot ROC vs. calibrated airspeed by graphing the previous data using a

polynomial of order 2.

2. Plot the max points on each curve.

A line drawn through these points will show the best rate of climb (Vy).

The coordinates of the max point can be calculated as follows:

x value

Use the a and b quadratic values from the equation of the curves, and plug

into the following formula:

𝑥 = − 𝑏

2𝑎

y value

Plug x into the equation of the curve.

Plot these two points on the graph and draw a trendline between them. The

point that the line crosses the x-axis is the best rate of climb speed.

84

3. Plot the tangent points on each curve for a line drawn from the origin.

A line drawn through these points will show the best angle of climb (Vx).

To calculate the tangent points, use the following formula:

𝑦′ = 𝑦2−𝑦1

𝑥2−𝑥1

(derivative of equation = slope of line from origin)

Example:

Derivative of equation

y = -0.4594x2 + 55.281x – 1358.4

y’ = -0.9188x + 55.281

Slope of tangent line

The two points of the line are: (0,0) and (x, -0.4594x2 + 55.281x

– 1358.4)

Plugging into the slope formula, and doing the algebra yields a

slope of:

−0.4594x2 + 55.281x – 1358.4

𝑥

85

Equating the two results in a and b above, and doing the algebra

yields:

x = 54.4

Plugging x into the original curve equation yields:

y = 309

The tangent point for a line drawn from (0, 0) is (54.4, 309) for the

3500 ft curve.

k. PLOT PRESSURE ALTITUDE VS VX AND VY

Plot best rate of climb (Vy) and best angle of climb (Vx) using the max points

and tangent points x-values and the pressure altitudes for the y values.

The point where Vx and Vy meet is the theoretical maximum altitude.

The Vy line indicates the Best rate of climb airspeed.

l. PLOT WEIGHT CORRECTED THRUST HP VS CALIBRATED AIRSPEED

Plot weight corrected thrust HP vs calibrated airspeed using the previously

reduced data.

86


STICK-FIXED DATA - CLIMB

a. CALCULATE CALIBRATED AIRSPEEDFOR EACH DATA POINT

Determine the calibrated airspeed for each collected airspeed using the position

correction charts shown earlier. The formula for this calculation is:

b. CALCULATE TEST WEIGHT AT EACH POINT

The test weight at each point can be determined for each point by the following

formula:

𝑊𝑇 = 𝑊𝑠𝑡𝑎𝑟𝑡 − 𝑊𝑓𝑢𝑒𝑙 𝑏𝑢𝑟𝑛𝑒𝑑

c. CALCULATED LIFT COEFFICIENT AT EACH POINT

Using the calibrated airspeed and test weight calculated above, determine the lift

coefficient at each point using the following formula:

𝐶𝐿 = 2∗ 𝑊𝑇

𝜌𝑆𝐿 ∗ 𝑉𝐶2 ∗ 𝑆

ρSL = 0.0023769 𝑙𝑏 ∗ 𝑠𝑒𝑐2

𝑓𝑡4 (sea level density)

S = 174.5 𝑓𝑡2 (wing area)

87

d. PLOT CALIBRATED AIRSPEED VS ELEVATOR POSITION FOR EACH

C.G. IN CLIMB CONFIGURATION

Generate a plot of calibrated airspeed (Vc), vs. elevator position for each C.G.

using the calculated calibrated airspeed and collected elevator position. Fit a

smooth curve through the data, and include the equations of the generated

lines.

e. PLOT COEFFICIENT OF LIFT VS ELEVATOR POSITION

Plot elevator position δe, vs. calculated CL for each C.G. and fit a smooth curve

through the data. Include the equations of the generated lines. Note that the

curves should come to a point where CL is 0.

f. DETERMINE THE SLOPES AT EVEN INCREMENTS OF COEFFICIENT

OF LIFT

Determine the slope, 𝑑 𝛿𝑒

𝑑𝐶𝑙, at even increments of CL. Take the derivative of

the line equations in step V above, then plug in even increments of CL to

calculate the slope at that point. In this case, a CL of 0.2, 0.4, 0.6, and 0.8 were

used.

g. PLOT SLOPE VS C.G. POSITION

Plot slope vs. C.G. position from the data calculated in step VI above and

connect lines of constant CL. The point where the lines have a slope of zero

are the stick-fixed neutral points.

88

Add a second x-axis, C.G. in %MAC. C.G. in inches is related to C.G.

%MAC using the following equation:

𝐶. 𝐺. (%𝑀𝐴𝐶) = 𝐶.𝐺.(𝑖𝑛)−𝑙𝑒𝑎𝑑𝑖𝑛𝑔 𝑒𝑑𝑔𝑒 𝑜𝑓 𝑀𝐴𝐶

𝑀𝐴𝐶∗ 100

MAC = 63.84 in, leading edge of MAC = 77.6 in aft

h. PLOT NEUTRAL POINTS

Plot the neutral points obtained from the previous graph in %MAC vs. CL and

smooth a curve through the data. Include an indication of the aft C.G. limit

and the trim value of CL.

i. REPEAT THE ABOVE STEPS FOR THE POWER APPROACH DATA

Repeat all of the above steps using the power approach data, and determine the

neutral points.

89

STICK-FREE DATA - CLIMB

a. PLOT STICK FORCE VS CALIBRATED AIRSPEED

Plot stick force (FS) vs. calibrated airspeed (VC) for each C.G. in the climb

configuration, and smooth a curve through the data. Include the equation of

the lines in the plot.

b. PLOT FS/q FROM CURVE FITS VS CALCULATED CL FOR EACH C.G.

Using the curve equations in step IX, recalculate FS for each VC , then calculate

FS/q.

𝑞 = 1

2 𝜌𝑆𝐿 𝑉𝐶

2

Plot CL vs FS/q for each C.G. Fit a smooth curve through the data, and show

the equations of the curves on the plot.

c. DETERMINE THE SLOPES AT EVEN INCREMENTS OF COEFFICIENT

OF LIFT

Determine the slope, 𝑑 𝐹𝑠

𝑑𝐶𝑙, at even increments of CL. Take the derivative of

the line equations in step X above, then plug in even increments of CL to

calculate the slope at that point. In this case, a CL of 0.2, 0.4, 0.6, and 0.8 were

used.

90

d. PLOT SLOPES VS C.G. POSITION

Plot slope vs. C.G. position from the data calculated in step XI and connect

lines of constant CL. The point where the lines have a slope of zero are the

stick-free neutral points.

Add a second x-axis, C.G. in %MAC. C.G. in inches is related to C.G.

%MAC using the following equation:

𝐶. 𝐺. (%𝑀𝐴𝐶) = 𝐶. 𝐺. (𝑖𝑛) − 𝑙𝑒𝑎𝑑𝑖𝑛𝑔 𝑒𝑑𝑔𝑒 𝑜𝑓 𝑀𝐴𝐶

𝑀𝐴𝐶∗ 100

MAC = 63.84 in, leading edge of MAC = 77.6 in aft

e. PLOT NEUTRAL POINTS

Plot the neutral points obtained from the previous graph in %MAC vs. CL and

smooth a curve through the data. Include an indication of the aft C.G. limit

and the trim value of CL.

f. REPEAT THE ABOVE STEPS FOR THE POWER APPROACH DATA

Repeat all of the above steps using the power approach data, and determine the

neutral points.

91


a. PLOT TIME VS. COLLECTED AIRSPEED

Plot time vs. airspeed, using the collected data. Also determine the period and

half-cycle amplitudes of the wave from the plot.

b. DETERMINE THE DAMPING FACTOR

Calculate the half-cycle amplitude ratio between successive half-cycle

amplitudes using the graph generated in step (a) above:

𝐴𝑣𝑒𝑟𝑎𝑔𝑒 = (𝑋1

𝑋2,

𝑋2

𝑋3,

𝑋3

𝑋4) / 3

Look up the averaged half-cycle amplitude ratio value in the chart below to

determine the damping factor:

Figure 33: Half Cycle Amplitude vs Damping Factor

92

c. DETERMINE THE DAMP FREQUENCY (ωd) AND NATURAL

FREQUENCY (ωn)

Damp Frequency

𝑤𝑑 = 2𝜋

𝑇, where T = peak to peak period

Natural Frequency

𝑤𝑛 = 𝑤𝑑

√1− 𝜁2 , where 𝜁 is the damping factor calculated from Figure 5.


STICK-FIXED DATA

a. PLOT ELEVATOR POSITION VS ACCELERATION

Plot elevator position vs NZ for both the pull-up and push-over data for each

C.G. Fit a smooth curve through the data for NZ values greater than 1 for each

C.G., and include the equation of the curves on the plot.

b. TAKE THE SLOPE OF EACH EQUATION AT EVEN INCREMENTS OF

ACCELERATION

Take the or derivative of each equation above, and calculate the slope at even

increments of NZ.

93

For example:

Line equation: y = -0.3571x2 + 2.5074x + 10.276

Derivative: y’ = -0.7142x + 2.5074

c. PLOT SLOPE FOR EACH ACCELERATION VS C.G.

Plot the slope for each NZ vs. C.G., and extend these lines to the x-axis to

determine the maneuvering points.

d. PLOT MANEUVER POINTS VS ACCELERATION

Using the maneuver points obtained above, plot NZ vs. maneuver points.

STICK-FREE DATA

e. PLOT STICK FORCE VS ACCELERATION

Plot FS vs NZ for both the pull-up and push-over data for each C.G. Fit a smooth

curve through the data for NZ values greater than 1 for each C.G., and include the

equation of the curves on the plot.

94

f. TAKE THE SLOPE OF EACH EQUATION AT EVEN INCREMENTS OF

ACCELERATION

Take the or derivative of each equation above, and calculate the slope at even

increments of NZ.

For example:

Line equation: y = -0.3571x2 + 2.5074x + 10.276

Derivative: y’ = -0.7142x + 2.5074

g. PLOT SLOPE FOR EACH ACCELERATION VS C.G.

Plot the slope for each NZ vs. C.G., and extend these lines to the x-axis to

determine the maneuvering points.

h. PLOT MANEUVER POINTS VS ACCELERATION

Using the maneuver points obtained above, plot NZ vs. maneuver points.

95


There is no data reduction required for this test flight due to the lack of an

automatic data recording device.

96

Appendix E

Reduced Data


Table 29: Reduced Data - Position Correction Using GPS Method

AD

(angular difference)

15 24 19 25 17 28 26 25 21 35

GSc (groundspeed

corrected) 71.5 65.8 68.1 60.7 65.0 54.7 52.1 56.2 53.2 41.8

δ (atmospheric

pressure ratio)

0.9455 0.9487 0.9462 0.9449 0.9449 0.9449 0.9452 0.9452 0.9452 0.9459

Θ (atmospheric

temp ratio)

0.9843 0.9843 0.9843 0.9843 0.9843 0.9843 0.9843 0.9843 0.9843 0.8438

√σ (sqrt sigma)

0.9801 0.9817 0.9804 0.97974 0.97974 0.97974 0.97992 0.97992 0.97992 0.98028

Vc (calibrated

airspeed in knots)

70.06 64.57 66.75 59.49 63.71 53.63 51.08 55.06 52.15 40.95

Vc avg (average

calibrated airspeed in

knots)

67.31 63.12 58.67 53.07 46.55

Vc avg (average

calibrated airspeed in

mph)

77.41 72.59 67.47 61.03 53.53

Vic avg (average

instrument corrected airspeed in mph)

82 76 70 63 55

Vi avg (mph)

82 76 70 63 55

∆Vpc -4.59 -3.41 -2.53 -1.97 -1.47

97


Table 30: Reduced Data – Determination of Stall Speeds

Wto

Takeoff Weight

(lbs) 1231 1231 1231 1231 1231 1231 Wt

Weight at stall (lbs) 1209.6 1207.5 1205.4 1203.3. 1201.3 1199.2 ∆Vpc

Stall Airspeed (interpolated) -2.5 -2.5 -2.7 -2.2 -2.2 -2.1

Vst stall calibrated

stall airspeed (calculated) 32.5 32.5 31.3 35.8 35.8 36.9

Vs weight

corrected stall airspeed

(mph) 33.7 33.7 32.6 37.2 37.2 38.4 Vs

wgt corrected stall speed

(ft/sec) 49.4 49.4 47.7 54.5 54.6 56.3 Wing Area (sq. feet) 183.0 183.0 183.0 183.0 183.0 183.0

density at sea level 0.0023769 0.0023769 0.0023769 0.0023769 0.0023769 0.0023769 CL, MAX 2.282 2.275 2.432 1.860 1.853 1.739

98


Figure 34: Brake HP vs Propeller Load

0

10

20

30

40

50

60

70

80

90

1500 1700 1900 2100 2300 2500

Bra

ke H

ors

ep

ow

er

Propeller Load

Brake HP vs Propeller Load

99

Table 31: Reduced Data – Determination of Level Flight Performance

∆Vpc for A/S -5.0 -3.5 -2.9 -2.4 -1.7 -1.8 Calibrated A/S

(mph) 78.0 71.5 68.1 64.6 56.3 41.2 Inst. Correction for

Altitude 0.0 0.0 0.0 0.0 0.0 0.0

Corrected Altitude 3500 3500 3500 3500 3500 3500 Break H.P.

(interpolated fr) 65 63 60 57 54 52 Ts

(°C) 8.0 8.0 8.0 8.0 8.0 8.0 Adjusted Brake H.P

per temp 64.2 62.2 59.3 56.3 53.3 51.4 δ

(atmospheric pressure ratio) 0.8798 0.8798 0.8798 0.8798 0.8798 0.8798 Θ

(atmospheric temp ratio) 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 σ

(density ratio) 0.8798 0.8798 0.8798 0.8798 0.8798 0.8798

time of day 8:20:00am 8:20:30am 8:21:00am 8:21:30am 8:22:00am 8:22:30am

Mins after engine start 71.0 71.5 72.0 72.5 73.0 73.5 Wto

Takeoff Weight (lbs) 1231 1231 1231 1231 1231 1231 Wt

aircraft weight at data point (lbs) 1194.0 1193.7 1193.4 1193.2 1192.9 1192.7

Wt/Ws weight ratio 0.9177 0.9175 0.9173 0.9171 0.9169 0.9167

Piw instrument and

weight corrected HP 68.5 66.4 63.3 60.1 57.0 54.9 Viw

instrument and weight corrected airspeed

(mph) 81.4 74.7 71.1 67.5 58.8 43.0 Niw

instrument and weight corrected RPM 2222.6 2154.3 2056.6 1958.9 1861.2 1763.4

100

Table 32: Density Altitude vs True Airspeed

Standard Altitude

(ft)

BHPs from chart

SQRT of Density

Ratio Piw

Niw from graph

Viw from graph

True Airspeed

(mph)

75% Power

0 48.8 1.0000 48.8 1994.16 67.6 67.6

2000 48.8 0.9643 47.0 1970.13 65.8 68.2

4000 48.8 0.9293 45.3 1946.65 63.9 68.7

6000 48.8 0.8952 43.6 1923.69 61.8 69.0

8000 48.8 0.8618 42.0 1901.27 59.7 69.3

10000 48.8 0.8293 40.4 1879.37 57.5 69.3

65% Power

0 42.3 1.0000 42.3 1904.51 60.0 60.0

2000 42.3 0.9643 40.7 1883.69 57.9 60.1

4000 42.3 0.9293 39.3 1863.33 55.8 60.0

6000 42.3 0.8952 37.8 1843.44 53.6 59.9

8000 42.3 0.8618 36.4 1824.01 51.4 59.6

10000 42.3 0.8293 35.0 1805.03 49.1 59.2

55% Power

0 35.8 1.0000 35.8 1814.86 50.3 50.3

2000 35.8 0.9643 34.5 1797.24 48.1 49.9

4000 35.8 0.9293 33.2 1780.02 46.0 49.4

6000 35.8 0.8952 32.0 1763.19 43.7 48.9

8000 35.8 0.8618 30.8 1746.75 41.5 48.2

10000 35.8 0.8293 29.6 1730.69 39.3 47.4

101


Table 33: Reduced Data - Climb Performance

Higher Altitude 200 Degree Heading

Time 0 30 60 90 120 150 180

Altitude 3500 3660 3800 3900 4010 4130 4240

Heading 200 200 200 200 200 200 200 Selected Altitude

(ft) 3830 Rate of Climb

(ft/min) 250.0

Avg Rate of Climb (ft/min) 221.0 Ta

Ambient Temp at selected Altitude (°C) 7.3

Average Ambient Temp at Selected Altitude

(°C) 7.6 Ts

Std. Temp at Selected Altitude (°C) 7.3

ROCTC Temp Corrected Rate of Climb

(ft/min) 221 δ

(atmospheric pressure ratio) 0.8691 Θ

(atmospheric temp ratio) 0.9743 σ

(density ratio) 0.8920

Mins after engine start 36 Wt

aircraft weight at data point (lbs) 1212

Wt avg (lbs) 1210

Wt/Ws - Weight Ratio 0.9303 Ciw - Weight Corrected ROC

(ft/min) 216 BHPt

(Interpolated from max of 65) 60.1 Piw

instrument and weight corrected HP 63.3

102


Higher Altitude – 20 Degree Heading

Time 0 30 60 90 120 150 180

Altitude 3500 3640 3710 3820 3900 4000 4100



(ft/min) 192

Avg Rate of Climb (ft/min) 221 Ta



(°C) 7.9 Ts



(ft/min) 221 δ




Mins after engine start 42 Wt


WT avg (lbs) 1210


(ft/min) 216 BHPt


(instrument and weight corrected HP 63.3

103


Lower Altitude – 200 Degree Heading

Time 0 30 60 90 120 150 180

Altitude 1000 1200 1330 1460 1580 1720 1860



(ft/min) 279.0




(°C) 13.3 Ts



(ft/min) 291 δ




Mins after engine start 52.5 Wt


WT avg (lbs) 1202


(ft/min) 295 BHPt



104


Lower Altitude – 20 Degree Heading

Time 0 30 60 90 120 150 180

Altitude 1000 1160 1300 1480 1610 1760 1900



(ft/min) 301.0




(°C) 13.3 Ts



(ft/min) 291.2 δ




Mins after engine start 56.5 Wt


WT avg (lbs) 1202


(ft/min) 295 BHPt



105


Table 37: Reduced Data – Level Acceleration Higher Altitude

position correction for airspeed -2.04 -1.96 -1.61 -1.57 -1.61 -1.88

Calibrated Airspeed (mph) 38.0 39.0 46.4 51.4 53.4 59.1

Calibrated Airspeed (ft/sec) 55.7 57.3 68.0 75.4 78.3 86.7

dv/dt (ft/sec2) 0.825 1.127 1.353 1.505 1.581 1.583 δ

atmospheric pressure

ratio 0.8798 0.8798 0.8798 0.8798 0.8798 0.8798 Θ

atmospheric temp ratio 0.9826 0.9826 0.9826 0.9826 0.9826 0.9826 σ

(density ratio) 0.8954 0.8954 0.8954 0.8954 0.8954 0.8954 True Airspeed

(ft/sec) 58.8 60.5 71.9 79.7 82.8 91.6 Weight at midpoint of level acceleration

(lbs) 1195.0 1195.0 1195.0 1195.0 1195.0 1195.0

Thrust HP in excess 3.28 4.60 6.57 8.09 8.83 9.79 Weight corrected

Thrust HP in excess 3.7 5.2 7.5 9.2 10.0 11.1

ROC (ft/min) 94.4 132.5 189.1 233.1 254.4 281.9 position correction

for airspeed -2.04 -1.96 -1.61 -1.57 -1.61 -1.88

106

Table 38: Reduced Data – Level Acceleration Higher Altitude (Continued)



Calibrated Airspeed (ft/sec) 98.6 104.9 110.9 113.2 117.8 120.0

dv/dt (ft/sec2) 1.509 1.361 1.137 0.839 0.465 0.017 δ


ratio 0.8798 0.8798 0.8798 0.8798 0.8798 0.8798 Θ


(density ratio) 0.8954 0.8954 0.8954 0.8954 0.8954 0.8954 True Airspeed


(lbs) 1195.0 1195.0 1195.0 1195.0 1195.0 1195.0



ROC (ft/min) 305.8 293.2 259.1 195.1 112.6 4.2

107

Table 39: Reduced Data – Level Acceleration Lower Altitude



Calibrated Airspeed (ft/sec) 55.7 71.0 85.3 92.1 101.2 107.3 dv/dt

(ft/sec2) 3.403 2.768 2.209 1.724 1.315 0.980 δ


ratio 0.9821 0.9821 0.9821 0.9821 0.9821 0.9821 Θ


density ratio 0.9787 0.9787 0.9787 0.9787 0.9787 0.9787 True Airspeed


(lbs) 1191.9 1191.9 1191.9 1191.9 1191.9 1191.9



ROC (ft/min) 372.7 386.7 370.8 312.4 261.6 206.9

108

Table 40: Reduced Data – Level Acceleration Lower Altitude (Continued)

position correction for airspeed -4.39 -5.24 -5.71 -6.20

Calibrated Airspeed (mph) 75.6 78.8 80.3 81.8

Calibrated Airspeed (ft/sec) 110.9 115.5 117.8 120.0 dv/dt

(ft/sec2) 0.721 0.536 0.427 0.392 δ

(atmospheric pressure

ratio) 0.9821 0.9821 0.9821 0.9821 Θ

(atmospheric temp ratio) 1.0035 1.0035 1.0035 1.0035 σ

(density ratio) 0.9787 0.9787 0.9787 0.9787 True Airspeed

(ft/sec) 112.1 116.8 119.0 121.3 Weight at midpoint of level acceleration

(lbs) 1191.9 1191.9 1191.9 1191.9

Thrust HP in excess 5.44 4.21 3.42 3.20 Weight corrected

Thrust HP in excess 6.2 4.8 3.9 3.6

ROC (ft/min) 157.2 121.8 98.8 92.5

109


Table 41: Reduced Data - Stick Fixed Longitudinal Static Stability – C.G. 16.06

VC

(Calib. AS) 67.3 75.6 58.2 83.3 48.4 70.7 65.5

WT (Test Weight)

1223.4 1223.0 1222.7 1222.3 1222.0 1221.3 1220.6

CL (Coefficient

of Lift) 0.6064 0.4795 0.8095 0.3951 1.1682 0.5480 0.6379

Table 42: Reduced Data – Stick Fixed Longitudinal Static Stability – C.G. 16.70

VC

(Calib. AS) 67.3 75.6 58.2 83.3 48.4 69.8 64.6

WT (Test Weight)

1205.7 1205.6 1205.4 1205.2 1205.0 1204.7 1204.3

CL (Coefficient

of Lift) 0.5976 0.4727 0.7981 0.3896 1.1520 0.5538 0.6468

110


Table 43: Reduced Data – Longitudinal Dynamic Stability

Damping Factor ωd ωn

Climb 0.125 0.2618 0.2618

Power Approach 0.150 0.2639 0.2648


Table 44: Derivatives of Equations – Stick Fixed

Forward C.G. (16.06 in) y’ = -88.574x + 137.01

Aft C.G. (17.26 in) y’ = -37.972 x + 66.347

Table 45: Derivatives of Equations – Stick Free

Forward C.G. (16.06 in) y’ = -76.14x + 131.12

Aft C.G. (17.26 in) y’ = -102.04 x + 148.47

111


There is no reduced data for this flight test.

flight testing of the piper j4a cub coupe

Documents