Flight Test #2 Report

8/12/2019 Flight Test #2 Report

1/38

1

AERSP 420 Principles of Flight Test

Final Report - #2

Brian Harrell

Linda John

13 December 2013


2/38

2

ABSTRACT

The Piper Archer II-PA-28-181 belongs to a family of light aircraft design for flight

training, air taxi, and personal use. This report analyzes the performance of the Arrow II in a

series of flight tests. First, data on the performance of the aircraft during a stall simulation based

on atmospheric conditions will be analyses to determine the max lift coefficient and

consequential stall speed. Data from the climb rate test will be used to determine max climb

rates and climb rate speeds. Furthermore, this report compares experimental data results to

manufacturer provided data in the Pilot's Operating Manuel.

The experimental data is used in a stall simulation in MATLAB done using a code that is

attached at the end of this report. From this code, plots of lift coefficient versus angle of attack

are generated. The code also determines a stall angle of attack and a stall velocity for each of the

four stalls tests preformed. In comparison to the stall velocity given in the Pilots Operating

Handbook, the simulation results were within 3% of the provided values. The experimental data

for the climb test is used to determine a measured rate of climb for each test. This measured rate

of climb was then converted to an actual normalized rate of climb based on the air temperature at

altitude. MATLAB is once again used to plot these climb rates against velocity and compared

with the maximum climb rate and the maximum climb rate speed found in the Pilots Operating

Handbook. The results of the climb test experiment yielded a maximum climb rate of 749.3 feet

per minute compared to the given 700 feet per minute value, which is only 7% off. Finally, the

maximum climb rate speed provided is 76 knots. The experimental speed was found to be 75

knots, which is extremely close.

Potential sources of error in the experiment results could be due to inconsistencies in

maintaining constant speeds or altitudes, or human error in data collection. These errors could

be rectified by repeating the tests multiple times to reduce the severity of inconsistencies and by

running practice flight test prior to actual takeoff to ensure the team's preparedness.


3/38

3

1.0 INTRODUCTIONThe following describes the purpose of the flight test experiments, a breakdown of the

test aircraft, and the scope and methodology of the tests performed for analysis.

1.1 PurposeThe purpose of the combined analysis-flight test program is to:

Analytically determine the performance of a Piper Archer II-PA-28-181 and compare it toexperimental data gathered in flight for determining the maximum life coefficient and

resulting stall speed.

Collect and reduce flight test data for determining the maximum climb rate and maximumclimb rate speed for the Piper Archer II-PA-28-181 and compare the experimental data

results to values provided by the Pilot's Operating Handbook.

1.2 Description of Test AirplaneThe Archer II is a single engine, retractable landing gear, all metal airplane frequently

used for air taxi, flight training and personal use. It has seating for up to four people, 24 cubic

feet of baggage space, and a maximum takeoff weight of 2550 pounds. The aircraft is not

configured for stunt maneuvers since its structure is not designed for aerobatic loads. The

fuselage is a semi-monologue structure with a conventionally designed, semi-tapered wing,

which employs a NACA 652-415 laminar flow type airfoil section. The four-positioning wing

flaps are mechanically controlled by a handle located between the front seats. When fully

retracted, the right flap locks into place to provide a step for cabin entry. A vertical stabilizer,

all-movable horizontal stabilator and a rudder make up the empennage.

The Archer II incorporates a Lycoming O-360-A4A four-cylinder engine rated at 180

horsepower at 2700 rpm. The aircraft is equipped with a Sensenich 76EM8S5-0-60 propeller,

which is a fixed pitch propeller with a maximum diameter of 76 inches.. The horizontal

stabilizer features a trim tab mounted on the trailing edge that provides trim control and pitch

control forces. This tab is actuated by a control wheel on the floor between the front seats. The

rudder is of conventional design and includes a rudder trim as well. The flaps are manually

operated and spring-loaded to return to the up position.They have three extended positions, 10,

25, and 40 degrees. Fuel is contained in a single tank and of the total 50 gallon capacity, only 48


4/38

4

gallons are usable. The aircraft also has a calibrated system that supplies both pitot and static

pressure for the airspeed indicator and altimeter. Pitot static pressure is picked up by the probe

on the bottom of the left wing. The Archer II uses a traditional flight control configuration. A

three-view drawing of the Archer II is shown in figure 1.

Figure 1. Three view drawing of the Piper Archer II


5/38

5

1.3 Scope of TestThe flight test consists of two separate tests

Stall Test

Climb Rate Test

An actual takeoff weight was determined to be 2363 pounds and the altimeter was set at 29.92.

This weight includes the empty weight of the aircraft, the combined weight of the passengers and

pilot, and the weight of the fuel. At the time of takeoff the fuel level in the aircraft was at 25

gallons. Completing the two tests had a combined duration of approximately one hour and were

filmed for later analysis. The stall test occurred at altitude around 4300 feet. The climb test was

performed at altitude around 3800, 2400, and 4500 ft at the 0, 30 and 60 second time marks,

respectively. The outside air temperature during the time of the flight test was 20 degrees

Fahrenheit. All tests were completed with the both the gear down and flaps up and within the

limitations of the Pilots Operating Handbook. Tables 1 and 2 below list several important

parameters relating to the Piper Archer II.

Table 1. Operating Limitations and Weights for the Archer II

2700 RPMMax Power

180 hp.

Max Takeoff Weight 2550 lbs.

Table 2. Important Physical Parameters of the Piper Arrow II

Name Abbreviation Value

Wing Planform Area S 170 ft^2

Wing Span b 35 ft

Aspect Ratio A 7.2058

Oswalds Efficiency Factor e 0.6

NACA 652-415 Lift Curve Slope a 6.88 rad^-1


6/38

6

1.4 Method of TestStall Test

After the completion of the climb test, the team prepares for the start of the stall test. For

duration of this flight test, the indicated air speed should remain constant at around 65 knots andthe aircraft should be operating at full power. At this point, outside air temperature is recorded.

The pilot then maneuvers the aircraft to fly at a constant heading of 045. At this point the aircraft

is slowed down until stall is reached. At the moment of stall, the following values are recorded:

Pressure Altitude (feet) Indicated Airspeed (knots) Fuel Level (gallons) GPS Track Indicated Ground Speed (knots)

Once these values are recorded and stable flight is reached, the procedure is repeated for 3 other

headings: 135, 225, and 315. Following the collection of this data, the flight test is complete and

the aircraft is landed safely.

Climb Test

Following the completion of all necessary pre-flight checks and procedures, team

members board the aircraft and prepare for takeoff. At this point, outside air temperature and

initial fuel level are recorded. Once airborne, the aircraft is to climb to a stable cruise altitude

(around 4300 feet) in order to preform the climb test. The aircraft is flying at a constant speed of

65 knots with the gear down and the flaps up. Once in the correct configuration, the aircraft was

flown down to about 500 feet below the cruise altitude. Once this lower altitude is reached, video

taping of the flight test starts and the pilot begins a steady climb maneuver. At around 350 feet

below the cruise altitude the timer is started and the following data is recorded:

Pressure Altitude (feet) Outside Air Temperature (Fahrenheit) Indicated Ground Speed (knots) Fuel Level (gallons)


7/38

7

After 30 seconds of steady climb have passed on the timer, data for these parameters is taken

again, but this time RPM is also recorded. At 60 seconds, values for only pressure altitude and

outside air temperature are recorded. Once values were recorded for 0, 30, and 60 second marks,

the entire procedure was repeated at speeds increasing by 10 knot increments (75kts, 85kts,

95kts115kts) until wide open throttle was reached at which point the test was completed.

1.5 InstrumentationTable 3. Important Instruments and the parameters they were used to measure

Parameter Instrument

Airspeed On-board ASI

Altitude On-board Altimeter

RPM On-board gauge

Track On-board GPS

Ground-Speed On-board GPS

Time Stopwatch

Fuel Levels On-board fuel indicator

Outside Air Temperature On-board temperature gauge


8/38

8

2.0 ANALYSISThe following describes the theory behind the stall and climb tests as well as the data

reduction method used to analyze the climb test data. The following sections also describe the

code used to perform the stall simulation and how that relates to the stall experiment performedduring this flight test. Several figures and examples are given validating the code and overall

analysis method.

2.1 TheoryStall Test

The Primary theories behind the Stall Test and analysis are the Biot-Savart Law and the

Kutta Juokowski equation. To begin, the Biot-Savart Law describes the velocity of a fluid at any

radial point in a vortex. This is pertinent to predicting the stall of an aircraft because as the

aircraft moves through the air, the wing creates voticies originating from the wingtip, which

create downwash on the entire wing. This downwash is described by the Biot-Savart law using,

w ="

4#r, (1)

where !is the circulation of the vortex causing the downwash, and ris the radial disance from

the center of the vortex to the point being examined

Additionally, the Kutta Juokowski equation, given by,

L = "V#, (2)

describes the relationship between circulation, !,and lift,L. Based on Eq. (2) we can see that a

wing must create some circulation in order for it to produce lift. As the aircraft begins to stall

across the various sections of its wing, those sections will cease to produce circulation and

likewise, cease to produce lift.

Additionally, the lift on each wing segment of the aircraft can be expressed as,

L =1

2"V

2cC

l, (3)


9/38

9

where "is the air density at altitude, V is the velocity of the aircraft in feet per second, cis the

section chord length, and Clis the section lift coefficient.

By setting Eq. (2) and (3) equal to each other, an equation for circulation, !, can be

determined. Some simple algebra gives,

" =

1

2Vca

1+1

2ca(

1

"#y)

$

%

&&&&

'

(

))))

* (4)

where ais the lift-curve slope, #y, is the wing segment width and $is the angle of attack of the

wing segment. Equation (4) can be expressed in matrix form as,

!"= A

!"+

!X , (5)

Some simple matrix algebra yields,

!"= (I"A)

"1 !X , (6)

where

Anm=

1

2ac

nw

nm, (7)

and

!X

n=

1

2Va"c

n (8)

Additionally, in Eq. (6) the matrixIis an n-by-n identity matrix. In Eq. (8), $represents the

angle of attack of the wing section. In order to determine this angle of attack, one must consider

the effect of the flaps on the angle of attack of the wing.

For wing sections where the flaps affect the angle of attack, we must add an additional

factor, "finto the angle of attack when calculating the vector described in Eq. (8). The effect of

the flaps on the angle of attack is described by,

"f = "#$f (9)


10/38

10

Once we have determined the circulation matrix, !, we must next determine if any of the wing

segments have stalled, and ignore the lift contributions of each stalled segment. The segment lift

coefficient is determined for wing segment, iusing,

Cli= 2"i

Vci, (10)

and if (

Cl> 1.7) then we assume that the wing segment in question is stalled.

Additionally, we can calculate the lift on each wing segment using the equation,

Li= "V#

i, (11)

as well as the lift on the entire wing using the equation,

L = "V#ii=1

N

$ %y , (12)

where "i

is the circulation on wing segment i, andNis the number of segments that the wing has

been separated into.

After the lift on the wing has been determined, it can be used to find the lift coefficient,

CL

for the entire wing using the equation,

L =1

2"V

2SC

L, (13)

where S, is the planform area of the wing. This entire process can be repeated to generate a

relationship between CL

and $. From this relationship, CL max

can be determined and used to

calculate a theoretical VStall

which will be used to compare our experimental results to the Pilots

Operating Handbook.

Climb Test

The primary theory behind the climb test has to do with rate of climb derived from static

equilibrium equations. If in fact the forces on the aircraft are in equilibrium then we can assume,

T" D "W sin#= 0 (14)


11/38

11

where, T is thrust,Dis drag,Wis the weight of the aircraft and %is the angle of climb.

Additionally, if we are in equilibrium, then any forces normal to the direction of flight will

cancel out, leaving us with,

L = W cos" (15)

and because (R/C) = Vsin%, we know that,

R /C=T" D

WV (16)

Once we have determined the rate of climb, we must adjust it to account for the

atmospheric properties with which we are flying in. This conversion is done using,

R /C( )actual

= R /C( )measured

Tactual

Ts

(17)

where Ts=519degrees Rankine, which is the standard temperature of the atmosphere. Next we

must find the rate of increase of (R/C)with respect to gross weight given by,

"(R /C)

"W

#

$%&

'(W=actual

= "(R /C)

W"V

W

2CL

W#Ae (18)

whereA is the aspect ratio of the aircraft and eis Oswalds efficiency factor for the aircraft.Finally, we must use this rate to normalize the experimental climb rates for weight according to,

R /C[ ]Ws= (R /C)

actual+

"(R /C)

"W(W

actual#W

s) (19)


12/38

12

2.2 ImplementationStall Test

The stall test simulation was done using a custom code implemented in MATLAB. The

code took user input for several parameters including:

Pressure Altitude (feet) Outside Air Temperature (degrees Fahrenheit) Aircraft Weight (pounds) Indicated Airspeed at the time of stall (knots) Number of Wing Segments Flap Deflection (degrees)

The code takes the pressure altitude and temperature inputs and converts them to an air density to

be used throughout the simulation. Next, the indicated airspeed is converted from knots to feet

per second using,

Vfps = Vknots "1.6878, (20)

and wing segment width, #yis calculated by dividing the wingspan by the number of segments

used in the simulation. Next, an array is created containing the y-locations of the centers of each

wing segment along the wingspan. This is done using,

Yi= (i "1)#y +

#y

2, (21)

for wing segment i, across the entire wingspan.

Next, an array of chord lengths was created according to the geometry of the aircrafts

wing. This array was filled using a for loop and a series of nested if statements which can be

seen in further detail in the Stall Test Code in appendix B.After the chord length array had been completed, an angle of attack range was declared in

degrees,

" = [0 : 25] (degrees)


13/38

13

and converted from degrees to radians. The contribution of the flaps to the angle of attack was

also accounted for in this section of the code. First, the user was be prompted to enter the flap

deflection (

"f) in degrees. This flap deflection was then used to calculate the correction factor, &

based on the equation,

" = (4.8(10"6))(#f

3) " (0.00061)(#f

2)+ (0.014)(#f) +0.72 (22)

which was derived by digitizing the plot in (typeFlapAdjust.pdf) and performing a third degree

polynomial curve fit. The custom code used to derive this equation is shown in the Correction

Factor Calculation code in appendix C.

Next, the flap effectiveness factor, 'was determined for wing segment, i, using the

equation,

"i= 1"

#fi "sin(#fi )

$

%&'

()*, (23)

where,

"fi= cos"1

2c f

c i

#$%

&'("1

#$%

&'(, (24)

and the flap chord length, cf =0.9 feet. At this point, the effect of the tail on angle of attack can

be determined according to the equation,

"fi= " # $i # %f , (25)

and was then converted from degrees to radians for use in future calculations.

Next the custom code computed the downwash velocity contributions of each separate

wing segment on the other wing segments. This computation was done using two nested for

loops, which increment from 1 to N, and the equation,

w(i,j) = "1

4#

$

%&

'

()

1

(Yi" Yj +

*y

2)

" 1

(Yi"Yj"

*y

2)

$

%

&&&

'

(

)))

(26)


14/38

14

Another set of nested for loops was used to create theAmatrix described in Eq. (7). Both for

loops increment from 1 to N in order to create an N by N matrix.

In the next step of the simulation, a large for loop was used containing several other

important sub-algorithms, described in figure 2.

Figure 2. Describes the series of nested for loops used in the stall test code

After the loop described in figure (2) was completed, a plot of CL

versus $was generated

and analyzed to determine the maximum lift coefficient reached during the simulation. The

maximum lift coefficient was then used with the wing planform area, S, the air density, the

aircraft weight, W, and Eq. (13) to determine the theoretical stall velocity of the aircraft.

FOR loop, accounting for all angles of attack used in the simulationo FOR loop, accounting for all wing segments

! IF statement, used to determine the y-location along thewingspan

If we are examining the inner wing section, include thecontribution of the flaps in $

If we are examining the outer wing section, do notinclude the contribution of the flaps in $

! Calculate theX vector according to Eq. (8)o Calculate the circulation vector, !based on Eq. (6)o FOR loop, accounting for all wing segments

! Calculate the section lift coefficient, Claccording to Eq.(10)

! IF statement, used to determine if Clis above 1.7

If the above statement is true, set "i=0 for the wing

segment in question

o Calculate the lift on each wing segment using Eq. (11)o Calculate the total lift on the wing by summing the elements of the

segment lift vector created in the previous stepo Calculate C

Lfrom the total lift using Eq. (13)

END


15/38

15

Climb Test

The climb test was implemented using a custom code in MATLAB. Several important

physical parameters were hardcoded into the program including:

Wing Span (feet)

Planform Area (feet^2) Oswalds Efficiency Factor Aspect Ratio Standard Weight (lbs)

The experimental data for indicated airspeed, pressure altitude and weight were then hardcoded

into the program. The code then takes the atmospheric data and calculates the density of the air

for each of the climb tests. Next, a measured climb rate is determined by simply taking the

difference between the pressure altitude data points at 0 seconds and the pressure altitude data

points at 60 seconds.

Using the previously stated assumption that the forces during the climb are in

equilibrium, we can assume thatL = Wand that Eq. (13) holds true throughout this test. Eq. (13)

is then used to determine the lift coefficients for each of the climb tests.

At this point, Eq. (18) and (19) are used inside of for loops to determine the normalized

R/Cfor each climb test. The results were then plotted along with the raw experimental rate of

climb data and the rate of climb data from the Pilots Operating Handbook for the maximum

climb rate and maximum climb rate speed. The custom code used to process the data can be

seen in further detail in the Climb Test Code in appendix D.


16/38

16

2.2.1 Verification ApproachStall Test

The stall test simulation was verified via several plots used to check that the code was in

fact following its intended algorithm. In addition, a pause command was used in order to stepthrough the loops used in the code at the users convenience. The different plots used to verify

that the stall test simulation code worked properly are described in table 4.

Table 4. Shows the 5 figures produced during the stall test code and what those figures represent

Figure # Description of Plot

MATLAB Figure (1) Chord Length vs. Y-location

MATLAB Figure (2) Circulation, !vs. Y-location

MATLAB Figure (3) Section Lift Coefficient vs. Y-location

MATLAB Figure (4) Lift vs. Y-location (Lift Distribution)MATLAB Figure (5) Lift Coefficient, CL

vs. Angle of Attack, "

Climb Test

Looking at the climb rates determined from the code and comparing them to the

maximum climb rate found in the Pilots Operating Handbook, verified the climb test. All of our

experimental results were fairly close to this maximum climb rate except for our first data point,

which was the result of an error in data recording.

2.3 Example ResultsStall Test

For the stall test we expect to see a chord length plot that resembles the wing geometry of

the Piper Archer II. In addition, we expect to see plots of both circulation and lift across the

wing that have an elliptical shape at low angles of attack and begin to go to zero near the center

of the wing as the angle of attack is increased.

2.3.1 Verification ResultsThe stall test code was verified by generating several process plots and observing them as

the code worked through the angle of attack range. The process plots are shown at an angle of

attack of 0 and 18 degrees in figures 3 and 4. Note that in figure 3 you can see that the wing has


17/38

17

an elliptical lift distribution and in figure 4 the wing begins to lose lift in the center sections of

the wing due to an increased angle of attack.

Figure 3. Four process plots showing the chord length, circulation, section lift coefficient and lift distribution

across the wing. This process plot was taken at an angle of attack of 0 degrees. Note the elliptical shape of

the circulation and lift distribution plots.


18/38

18

Figure 4. Four process plots showing the chord length, circulation, section lift coefficient and lift distribution

across the wing. This process plot was taken at an angle of attack of 18 degrees. Note the gaps in the lift

distribution plot where the sig sections are stalled.


19/38

19

3.0 RESULTS & DISCUSSIONIn the following section, the results of our two flight test experiments, the stall test and

the climb test will be analyzed and discussed. Figures and tables of our experimental data will

be presented and discussed as well, along with comparisons between our experimental resultsand the theoretical results given by our stall test simulation and the Pilots Operating Handbook.

Stall Test

The stall test simulation was run four times using the atmospheric data from each of the

four stalls performed during the stall test experiment. A table of the experimental data for each

of the four stalls is shown in table 5.

Table 5. The pertinent experimental data for each of the four stalls.

Stall # PA (feet)OAT

(degrees F)Weight

(lbs)IAS(kts)

Number ofSegments

Flap Deflection,"f (degrees)

1 4380 20 2363 62 100 0

2 4340 20 2363 62 100 0

3 4280 20 2363 62 100 0

4 4300 20 2363 65 100 0

The resulting CL

vs. $plots generated by the stall test simulation are shown in figures 5,

6, 7 and 8. Each plot shows a linear relationship between CL

and $until the aircraft reaches its

maximum lift coefficient at which point, we see the plots drop off sharply. The maximum lift

coefficient values are illustrated on each of the plots using a pointer and a text box containing the

data for that specific data point.


20/38

20

Figure 5. Plot of Lift Coefficient vs Angle of Attack for the first set of stall data. Note the marker denoting a

maximum lift coefficient of 1. 551

Figure 6. Plot of Lift Coefficient vs Angle of Attack for the second set of stall data. Note the marker denoting

a maximum lift coefficient of 1. 551


21/38

21

Figure 7. Plot of Lift Coefficient vs Angle of Attack for the third set of stall data. Note the marker denoting a

maximum lift coefficient of 1. 551

Figure 8. Plot of Lift Coefficient vs Angle of Attack for the fourth set of stall data. Note the marker denoting

a maximum lift coefficient of 1. 551


22/38

22

Additionally, figures 9, 10, 11 and 12 show the results of each of the four stall test simulations.

We can see from these results that the aircraft reaches a maximum lift coefficient of

CLmax

=1.551

for each of the simulations. This result follows very closely with the data given in the Pilots

Operating Handbook.

Figure 9. MATLAB Command window for the first set of stall data, showing a max lift coefficient of 1.551

and a stall velocity of 53.558 knots

Figure 10. MATLAB Command window for the second set of stall data, showing a max lift coefficient of

1.551 and a stall velocity of 53.516 knots


23/38

23

Figure 11. MATLAB Command window for the second set of stall data, showing a max lift coefficient of


Figure 12. MATLAB Command window for the fourth set of stall data, showing a max lift coefficient of


Overall, we have a high confidence in the accuracy of our stall test simulation because our final

results follow closely with the data given in the Pilots Operating Handbook. Tables 6 and 7

show the final results of our stall test simulations as well as the actual values given in the Pilots

Operating Handbook. The lift coefficient values were derived using the parameters from our

flight tests, the stall velocity given in the Pilots Operating Handbook and Eq. (13).


24/38

24

Table 6. Experimental and Actual lift coefficients for stall in the Piper Archer II

Test # Experimental CL POH CL % Error

1 1.551 1.4688 5.60%

2 1.551 1.4688 5.60%

3 1.551 1.4688 5.60%

4 1.551 1.4688 5.60%

Table 7. Experimental and Actual stall velocities for the Piper Archer II

Test # Experimental VStall POH VStall % Error

1 53.558 55 2.62%

2 53.516 55 2.70%

3 53.454 55 2.81%

4 53.474 55 2.77%

Climb Test

After analyzing our climb test experimental data, we found that our results lined up well

with the parameters given in the Pilots Operating Handbook. Our raw experimental data, along

with our normalized results are plotted in figure 13. The maximum rate of climb is also plotted

at the maximum rate of climb speed per the Pilots Operating Handbook. While much of our

data lines up with what we expected based on the Pilots Operating Handbook, our first data

point is an outlier, leading us to believe that it is incorrect due to human error when recording the

data during the experiment.

Figure 13. Plot of (R/C)vs KIAS. Note the outlier at 65 knots and the POH value at 76 knots.


25/38

25

Additionally, we found that, disregarding our first data point, our maximum (R/C)

occurred at an indicated airspeed of 75 knots. This lines up with the Pilots Operating Handbook

considering that the given maximum rate of climb speed with flaps up is 76 knots. Table 8

shows the results of our rate of climb analysis, with a percent error calculated at 75 knots, where

we experienced our maximum rate of climb.

Table 8. Experimental and Actual maximum climb rates and maximum climb rate velocities for the Piper

Archer II

IAS (knots) (R /C)Ws (R/C) max (POH) % Error

65 1269.7 n/a

75 749.3 700 7.04%

85 565.8 n/a

95 723.7 n/a

105 469.5 n/a


26/38

26

4.0 CONCLUSIONSThroughout the course of this flight test, two experiments were performed. The first was

a stall test experiment in which the pilot flew four consecutive legs of a square flight pattern. On

each leg, the pilot attained steady, level flight and then slowed the aircraft down until it reachedstall. At the moment of stall, data was taken, including:

Indicated Airspeed (knots) Pressure Altitude (feet) Fuel Level (gallons) GPS Track Indicated Ground Speed (knots) Outside Air Temperature (degrees F)

This experimental data was then used in a stall simulation done using a custom code,

implemented in MATLAB. The results from this simulation included plots of lift coefficient

versus angle of attack, as well as a stall angle of attack, maximum lift coefficient and a stall

velocity computed for each of the four stalls. These results were then compared to the stall

velocity given in the Pilots Operating Handbook and were within 3% of the values stated by the

POH.

Some problems encountered during the stall test include:

Inconsistent pressure altitude due to pilot error Poor timing of the data gathering, resulting in data that does not represent the exact

moment of stall.

A slightly higher value of Lift because we did not account for the downward lift createdby the tail of the aircraft.

These problems could be eliminated by:

Running more tests in order to minimize error due to inconsistent pressure altitude Keeping coordinated video recordings of the airspeed indicator as well as the altimeter.

This would counteract some of the human error involved in calling out and recording the

data during the flight test

Using more in depth analysis to account for the downward lift caused by the tail


27/38

27

The second of the two flight tests was a climb test. The climb test was performed at 10

knot increments from 65 knots up to wide open throttle. To execute the climb test, the pilot

would achieve steady level flight approximately 300 feet below the target altitude. The pilot

would then allow the aircraft to climb for one minute. At the 0 second, 30 second, and 60 second

marks, data was taken including:

Indicated Airspeed (knots) Pressure Altitude (feet) Fuel Level (gallons) Outside Air Temperature (degrees F)

This experimental data was then used to determine a measured rate of climb for each test. This

measured rate of climb was then converted to an actual rate of climb based on the air temperature

at altitude. Next, several aircraft parameters and the actual climb rate were used to determine the

rate of change of the climb rate with respect to the aircraft gross weight. This rate of change was

in turn used to normalize the actual climb rates for weight. Finally, these normalized climb rates

were plotted against velocity and compared with the maximum climb rate and the maximum

climb rate speed found in the Pilots Operating Handbook. The results of the climb test

experiment yielded a maximum climb rate of 749.3 feet per minute, which was only 7.04% off of

the given value of 700 feet per minute. Additionally, the maximum climb rate speed found in the

climb test experiment was approximately 75 knots as compared to the POH value of 76 knots

with flaps up.

Some problems encountered in the climb test experiment included:

An inconsistent indicated airspeed due to pilot error Poor data gathering methods which resulted in a severe outlier in our data An inconsistent starting point (PA) for each of the climb tests

These problems could be eliminated by:

Performing more climb tests to reduce error due to inconsistent indicated airspeed Video recordings of the airspeed indicator as well as the altimeter to ensure that recording

errors due not diminish the integrity of the experiment

A greater attention to detail on the part of both the pilot and crew to ensure that each testbegins at the same pressure altitude as the one before it


28/38

28

5.0 REFERENCESArcher PA-28-181 Pilot's Operating Handbook. The New Piper Aircraft Inc., Publications

Department. Rev 24, Oct. 24, 2011.

McCormick, Barnes W. AIAA (2011), Introduction to Aeronautics and Flight Testing. 51-55.


29/38

29

6.0 APPENDIXAppendix A: Raw data sheet


30/38

30

Appendix B: Stall Test Code% AERSP 420 -- Brian Harrell% Stall Test Code% The stall test was performed in a Piper Archer II. Some important% parameters for the Archer II are hard-coded into the program below.b = 35; % Wing Span (in feet)

S = 170; % Wing Area (feet^2)%%%%%% LIFT CURVE SLOPE (a) %%%%%%% For the NACA 652-415 airfoila = 6.88; % C_L per radian (derived in class)

% USER INPUT% Calculates density using the Density_Calculator.m code that I wrote% for previous flight tests%%% AERSP 420 -- Brian Harrell %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Density Calculator%input('Please input the pressure altitude in (feet)\n');Press_alt = 4300;%input("Please input the outside air temperature in (degrees Fahrenheit)\n");Temp_F = 20;

%%% Convert to degrees RankineTemp_R = Temp_F + 460;

R = 1716; %Gas constant for air%%% Find air pressure in (in Hg)P_inHg = 29.92 - (Press_alt/1000);%%% Convert from (in Hg) to (psf)P_psf = P_inHg * 70.7261979206;

%%% Use ideal gas law to determine density at altitudedensity = P_psf / (R*Temp_R);%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Takes user input for the Weight of the aircraft at the time of stall%input("Please input the Weight (in lbs) at the time of stall\n")W = 2363; %pounds

% Takes user input for the Indicated Airspeed at the time of stall%input("Please input the Indicated Airspeed (in knots) at the time ofstall\n")V_kt = 65;V_fps = V_kt*1.6878; % feet per second

% Takes user input for the number of wing segments you wish to use, delta_y% represents the width of each wing segment%input('Please input the number of segments (N) you would like to use\n');N = 100;delta_y = b/N;

%%%%%% Y ARRAY %%%%%%% Creates an empty array for the y-values of each segment. To be filled in% the for loop belowY = zeros(N,1);

% For loop filling the y-array. The filled y-array will have the


31/38

31

% y-coordinate of THE CENTER of each segment across the wingfori=1:N

Y(i,1) = ((i-1)*delta_y) + (delta_y/2);

end

%%%%%% CHORD LENGTH ARRAY %%%%%%% Creates an empty array for the chord length values. To be filled in the% for and if loops belowc = zeros(N,1);

% The for loop below will increment from 1 to the number of wing segments% and the nested if loops will determine the correct chord length depending% on the horizontal (y-location) of the segment across the wingforj=1:N

%Left wingtip to end of taper on left wingifY(j,1)


32/38

32

% under the curve is flled in to represent the solid wing.figure(1)area(Y, c)title('Chord Length vs Y-Location (along the wingspan)')ylabel('Chord Length (feet)')xlabel('Y-Distance (along the wingspan, in feet)')

%%%%%% ANGLE OF ATTACK %%%%%%% Start by choosing a range of angles of attack to analyzealpha_d = 0:25; %degreesalpha_r = (pi/180).*alpha_d; % in radians

% Must next calculate the change in angle of attack along the wing for eachwing% section due to the flap deflection.% Using the equation alpha_f = nu*tau*theta_flaps%input('Please input the flap deflection in degrees\n');d_f = 0;% Calculate the correction factor (nu) from the typeFlapAdjust.pdf file% see typeFlapAdjust.m for details on how the equation below was foundnu = ((4.8*10^-6)*(d_f*d_f*d_f)) - (0.00061*d_f*d_f) + (0.014*d_f) + 0.72;

% the flap chord length was found to be 0.9 feet based on the three view% drawing of the test airplanec_f = 0.9;% calculate flap effectiveness factor (tau) as a function of the flap to% wing chord ration (c_f/c). Data and equations based on TauCalc.pdf,% found on the Angel sitetheta_f = acos(((2*c_f)./c) - 1);tau = 1 - ((theta_f - sin(theta_f))/pi);fori=1:N

alpha_fd(i) = nu*tau(i)*d_f; %degreesend

alpha_fr = alpha_fd.*(pi/180); %radians% The flaps will take effect below when determining the X matrix

%%%%%% DOWNWASH VELOCITY (w) %%%%%%% Computes the downwash velocity to be used in each element of the (A)% matrix. According to the equations derived in class.% First we will create an array of zeros to hold the (w) valuesw = zeros(N,N);% Calculates downwash velocity for each location span wise across the wingfori=1:N

forj=1:Nw(i,j) = -(1/(4*pi))*((1/(Y(i)-Y(j)+(0.5*delta_y))) - (1/(Y(i)-Y(j)-

(0.5*delta_y))));

endend

% Next we want to calculate all of the circulation values (expressed as J)% across the wing. This will be done using the equation% J = (I-A)^(-1) * (X), where J, A and X are vectors and I is an identity% matrix. The Matrixes are calculated separately in the steps below.

%%%%%% MATRIX A %%%%%%% First we will create a matrix of zeros to hold the (A) values


33/38

33

A = zeros(N,N);% fills the matrix Afork=1:N

forl=1:NA(k,l) = 0.5*a*c(k)*w(k,l);

endend

%%%%%% IDENTITY MATRIX (N by N size) %%%%%%I = eye(N);% The loop below will determine, the X matrix, the circulation matrix, the% section and wing lift coefficients, and the section and wing lift for% each angle of attack and wing sectionX = zeros(N,1);J = zeros(N,1);L = zeros(length(alpha_r),1);

form=1:length(alpha_r)

%%%%%% VECTOR X %%%%%%form_1=1:N

if(Y(m_1,1)>=8.92) && (Y(m_1,1) 1.7)J(m_2)=0;

endendfigure(3)plot(Y, C_l)title('Section Lift Coefficient vs. Y-Location (along the wingspan)')ylabel('Section Lift Coefficient C_l')xlabel('Y-Distance (along the wingspan, in feet)')

% Next I will create a vector of lift values for each segment based onthe


34/38

34

% circulation values. This will be used to plot a lift distributionacross

% the span of the aircraft%%%%%% WING SEGMENT LIFT %%%%%%L_s = (density*V_fps*delta_y).*J;

% WATCH THIS PLOT AND YOU WILL SEE THE WING SECTIONS STALLING%%%%%% LIFT DISTRIBUTION PLOT %%%%%%figure(4)plot(Y, L_s)title('Lift Distribution Plot (along the wingspan)')ylabel('Cross-Section Lift (lbs/ft')xlabel('Y-Distance (along the wingspan, in feet)')% THROW IN A PAUSE SO YOU CAN SEE PROGRESSION OF STALL IN PLOTSpause()

%%%%%%% TOTAL LIFT %%%%%%L(m,1) = sum(L_s);

%%%%%% WING LIFT COEFFICIENT %%%%%%% Calculates the C_L for the entire wing for each angle of attack

iteration% Must first create an empty array for the C_L valuesC_L(m,1) = (2*L(m,1))/(density*V_fps*V_fps*S);

end

%%%%%% LIFT COEFFICIENT versus ALPHA (entire wing) %%%%%%figure(5)plot(alpha_d,C_L)title('C_L versus AoA for the Piper Archer II')legend('Theoretical Model')xlabel('Angle of Attack (degrees)')ylabel('Lift Coefficient (C_L)')

%%%%%% EXPERIMENTAL DATA COMPARISON %%%%%%% Assuming steady level flight, we can assume that% L = W = 0.5*density*V^2*S*C_L% Based on this equation, we can determine the aircrafts stall Velocity% based on its physical properties and the C_Lmax determined from the plot% above.C_Lmax = max(C_L);sprintf('\nThe max Lift Coefficient for the wing is, %d \n', C_Lmax)V_stall = sqrt(W/(0.5*density*S*C_Lmax)); %feet per secondV_stall_kts = V_stall/1.6878; %knotssprintf('\nThe stall Velocity of the aircraft based on the C_L vs alpha plot

is, %d knots\n', V_stall_kts)


35/38

35

Appendix C: Correction Factor Code

% AERSP 420 -- Brian Harrell% Find correction factor (nu) as a function of flap deflection. Data points% gathered from the plot of nu versus flap deflection found on% typeFlapAdjust.pdf on the Angel site

% Data points gathered from the plot (done by hand)nu = (10:2:70);d_f = [.82, .81, .80, .79, .78, .77, .76, .75, .74, .72, .70, .69, .67, .65,.64, .62, .59, .56, .53, .50, .47, .44, .41, .39, .38, .37, .36, .35, .35,.34, .34];

plot(nu, d_f, '*')ylabel('Correction Factor (nu) (dimensionless)')xlabel('Flad Deflection (d_f) (degrees)')legend('Visual Data Points')


36/38

36

APPENDIX D: Climb Test Code% AERSP 420 -- Brian Harrell% Climb Test Code% The climb test was performed in a Piper Archer II. Some important% parameters for the Archer II are hard-coded into the program below.b = 35; % Wing Span (in feet)

S = 170; % Wing Area (feet^2)e = 0.6; %Oswald's Efficiency Factor (estimated)AR = 7.3786; %Aspect Ratio

% Some standard atmospheric properties that will be needed in the analysis% belowT_s = 519; %degrees RR = 1716; %Gas constant for airW_s = 2500; %standard weight, lbs

% USER INPUT% Calculates density using the Density_Calculator.m code that I wrote% for previous flight tests%%% AERSP 420 -- Brian Harrell %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%% Density Calculator%input('Please input the pressure altitude in (feet)\n');PA_0s = [3240, 3840, 3840, 3860, 3820]; %Initial PA (feet)%input("Please input the outside air temperature in (degrees Fahrenheit)\n");Temp_F = [24, 21, 21, 21, 21];%%% Convert to degrees RankineTemp_R = Temp_F + 460;%%% Find air pressure in (in Hg)fori=1:5

P_inHg(i) = 29.92 - (PA_0s(i)/1000);end%%% Convert from (in Hg) to (psf)P_psf = P_inHg .* 70.7261979206;

%%% Use ideal gas law to determine density at altitudefori=1:5

density(i) = P_psf(i) / (R*Temp_R(i));end%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

IAS = [65, 75, 85, 95, 105]; %Experimental Airspeed (knots)IAS_fps = IAS.*1.6878;PA_60s = [4540, 4610, 4420, 4600, 4300]; %Final PA (feet)W = [2387, 2381, 2375, 2369, 2369]; %lbs

% Find the measured Rate of ClimbRC_meas = PA_60s - PA_0s; %feet per minute

% Find the actual Rate of Climbfori=1:5

RC_actual(i) = RC_meas(i)*(Temp_R(i)/T_s);end% Calculate Lift coefficient for each climb test, using L=W (not sure if% this si the correct way to determine lift coefficient.fori=1:5

CL(i)= (2*W(i))/(density(i)*IAS_fps(i)*IAS_fps(i)*S);end% Calculate the rate of increase of rate of climb with respect to gross


37/38

37

% weightfori=1:5

dRC_dW(i) = (-RC_actual(i)/W(i))-((IAS_fps(i)*2*CL(i))/(W(i)*W(i)*pi*AR*e));end% Next we must use this rate of change to normalize the climb rate for% weightfori=1:5

RC_Ws(i) = RC_actual(i) + (dRC_dW(i)*(W(i)-W_s));end% Data from the pilot's operating handbook regarding the best rate of climb% and the best rate of climb speedRC_max = 700; % feet per minuteRC_max_V = 76; %knots

figure(1)plot(IAS, RC_Ws, '-*', RC_max_V, RC_max, 'square')title('Rate of Climb vs. Indicated Airspeed')xlabel('Indicated Airspeed (kts)')ylabel('Rate of Climb (feet per minute)')

legend('Experimental Results', 'POH Data')


38/38

APPENDIX E: Hazard Mitigation

Hazard Mitigation Team 5

1. Risk: Phone camera battery dies/ doesn't workProbability Rank: 1Severity Rank: 3

Mitigation: Bring a spare phone or an actual digital camera

2. Risk: Stall Test Video recorder does not capture all of the necessary instrumentsProbability Rank: 4

Severity Rank: 2Mitigation: Record Right and Left side of the dashboard with two separate cameras

3. Risk: Stall Test Airplane does not remain in 1 g flight throughout the maneuver, causingstall at a lower or higher speed than in steady, level flight

Probability Rank: 2

Severity Rank: 4Mitigation: Check that the climb rate remains constant and repeat data points if necessary

4. Risk: Climb Test Not hitting target altitude at the 30 second mark because the airplane isnot climbing at the prescribed 700ft per minute

Probability Rank: 3

Severity Rank: 3Mitigation: Talk to the pilot about consistency with respect to the climb rate and repeat

the step if necessary

Flight Test #2 Report

Documents

Transcript of Flight Test #2 Report