Flight Test #1 Report

7/22/2019 Flight Test #1 Report

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AERSP 420Principles of Flight Test

Final Report - #1

Brian S. HarrellLinda John

October 23, 2013


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ABSTRACT

The Piper Arrow III-28R-201 belongs to a family of light aircraft design for flight

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

series of flight tests. Throughout the report, takeoff will be analyzed and compared to a

theoretical model. Furthermore, this report compares experimental data results to manufacturer

provided data in regards to pitot-static calibration and the power required to maintain level flight.

The takeoff roll test provided data to compare with the predicted values determined via

an algorithm and custom code implemented in MATLAB using characteristic quantities of the

Arrow III provided in the Pilots Operating Handbook. Upon inspection of this comparison, the

takeoff simulation was found to follow the same trend and be of the same numerical magnitudes

as the values found experimentally. Therefore, the simulation does accurately depict the Arrow's

behavior during the takeoff roll. Deviations from theoretical and experimental values could be

due to analytical error in area estimations, human error during the flight test, or the presence of

head or tail winds.

Similar to the takeoff roll data, the experimental values gathered during the pitot-static

calibration test were compiled and reduced in MATLAB in order to determine true airspeeds and

then converted into calibrated airspeed for comparison with the in flight indicated airspeed. It

was determined that the calibrated airspeed was in accordance with the indicated airspeed, falling

with 1.22% of each other. The aircraft airspeed indicator was thus correctly calibrated prior to

takeoff. Potential sources of error include not holding indicated airspeed completely constant as

well as deviations in static and pitot pressures due to variable pressure fields and angles of

attack. The level flight power required test yielded plausible values for equivalent power and

velocity required, but implausible values for coefficients A and B for the for the equation

Peq*Veq = A*(Peq^4)+B. The value of A and B turned out to be 10003 and 1.2378*(10^8)

respectively. This inaccuracy could be due to the inherent sensitivity of the equation's effect onthe values, specifically being multiplied and raised to the fourth power. Other potential errors

could arise from the utilization of charts to estimate power calculations, along with in-flight

errors such as not maintaining exactly constant altitudes or tail wind effects.


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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 predict the performance of a Piper Arrow III-28R-201 and compare it toexperimental data gathered in flight for takeoff

Collect and reduce flight test data for the Piper Arrow III-28R-201 for pitot-staticcalibration, and level flight power required and compare the experimental data results to

manufacturers documentation when appropriate

1.2 Description of Test AirplaneThe Arrow III 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, a 200 pound

luggage compartment, and a maximum takeoff weight of 2750 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 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 Arrow III incorporates a Lycoming 10-360-C 1C6 four-cylinder engine rated at 200

horsepower at 2700 rpm. The aircraft is equipped with McCauley 90DHA-16 propeller, which is

a constant speed, controllable pitch propeller with a maximum diameter of 74 inches. The

propeller control is located on the power quadrant between the throttle and mixture controls.

Engine controls consist of a throttle control, propeller control and a mixture control lever. The

throttle lever is used to adjust the manifold pressure. The propeller control lever is used to adjust

the propeller speed from high to low rpm. The mixture control lever is used to adjust the air to

fuel ratio. The horizontal stabilizer features a trim tab mounted on the trailing edge that providestrim control and pitch control forces. The rudder is of conventional design and includes a rudder

trim as well. Fuel is contained in two 38.5 U.S. Gallon tanks, one in each wing. Of the total 77

gallons, only 72 gallons are usable. The aircraft also has a system that supplies both pitot and

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

on the bottom of the left wing. The Arrow III uses a traditional flight control configuration.

A three-view drawing of the Arrow III is shown below in figure 1.


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Figure 1. Three-View drawing of the Piper Arrow III (test aircraft)


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1.3 Scope of TestThe flight test consists of three separate tests

Takeoff Roll Model (two sets of data taken) Pitot-Static Calibration Level Flight Power Required

An actual takeoff weight was determined to be 2514 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 20 gallons. All three tests had a combined duration of approximately one hour

and were filmed for later analysis. The level flight power required and pitot-static calibration

tests occurred at an altitude of about 3000 feet, both with gear up and flaps up. The takeoff roll

data was approximated based on the atmospheric conditions at the time of the experiment. All

tests were completed within the limitations of the Pilots Operating Handbook. Tables 1 and 2provide important atmospheric conditions and aircraft configurations during each specific flight

test.

Table 1. Atmospheric Conditions during Flight Tests

Abbreviation PA (feet) OAT (deg F) Density (slugs/ft^3)

Takeoff Test TO 1100 7072 0.002330.00244

Pitot-Static

Calibration

PS 28002900 70 0.00211

Level Flight

Power RequiredLFPR 27002900 6872 0.002100.002112

Table 2. Configurations during Flight Tests

Abbrev. Flaps Gear

TO Up Down

PS Up Up

LFPR Up Up


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Additional operating limitations and weights for the aircraft are shown in table 3 and

important physical parameters of the Arrow III are presented in table 4.

Table 3. Operating Limitations and Weights

Max Power

2700 RPM

29 in Manifold

Pressure

200 hp.

Max Takeoff Weight 2750 lbs.

Table 4. Important Physical Parameters of the Piper Arrow III

Name Abbreviation Value

Wing Planform Area S 170 ft^2

Surface Area SA 638.25 ft^2

Wing Span b 35.417 ft

Aspect Ratio AR 7.3786

Wing Span Efficiency Factor e 0.6


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1.4 Method of TestTakeoff

Following the performance of all pre-flight checks and procedures, team members

boarded the plane and taxied to the hold short line. At this point outside air temperature, pressure

altitude, and fuel level were recorded. Engine RPM should remain constant at 2700 for theduration of the takeoff test. The aircraft then pulled up to the first of several runway lights,

spaced 200 feet apart along the runway. The engine was run up to full power with the brake held.

A countdown of 3-2-1-Mark was called out by one of the team members and filming of the

dashboard began. On mark, the pilot released the brake and the aircraft began its roll down the

runway. At each runway light, one team member called out mark to indicate a data point, at

which airspeed and manifold pressure were recorded. The data recording continued until just

before the aircraft takes off, at which point the pilot aborted the first takeoff and repeated the

steps previously described for a second takeoff roll, which resulted in two sets of data. From the

data collected, plots of position versus time, velocity versus time, and velocity versus position

were generated and compared to calculated theoretical values. These theoretical plots were

derived from Newtons second law, which will be further explained in sections 2.1 and 2.2.

Pitot-Static Calibration

After the second set of takeoff data was gathered the pilot began takeoff and climbed to

an altitude of about 3000 feet. Once the aircraft was in steady flight, the pilot flew 4 consecutive

headings at a target air speed of 65 knots. Ideally these headings would be 240, 330, 060, and

150. After each heading was established, the following values were recorded for each heading

Indicated Air Speed GPS Track True Ground Speed Pressure Altitude Outside Air Temperature Manifold Pressure

From these values, true airspeed and wind speed can be determined using the methods described

in (Niewoehner, 2006).


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Level Speed Power Required

The aim of this portion of the flight test was to experimentally reduce data in order to

calculate flat plate area and span efficiency factor for the Arrow III. The raw data gathered

during the course of this flight test includes

Fuel Level Pressure Altitude Manifold Pressure RPM Outside Air Temperature

For this portion of the flight test, the pilot established a constant speed of about 65 kts. Once a

consistent heading and air speed had been established, a timer was started. At 0 seconds, 30

seconds, and 60 seconds mark was called out by the team member with the stopwatch and data

was recorded. At the 60 second mark, the deck angle was also 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 atwhich point the test was completed.

1.5 InstrumentationTable 5. List of Instruments used and the parameters that they were used to measure.

Parameter Instrument

Airspeed On-board ASI

Altitude On-board Altimeter

Manifold Pressure On-board gauge

Track On-board GPS

Ground-Speed On-board GPS

Time Hand-held Watch

Fuel Levels On-board fuel indicator

Deck Angle (iPhone App)

Outside Air Temperature On-board temperature gauge

Heading On-board heading indicator


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2.0 ANALYSISThe following describes the theory behind each of the three flight test experiments, as

well as the methods for reducing the pitot-static, and level flight power required data. The

following sections also describe the method used in writing code to analyze and simulate the

experiments done during the flight test. Several examples are given validating the analysis andthe code.

2.1 TheoryTakeoff Simulation

The primary theory behind the takeoff simulations is Newtons second law.

(1)

A quick free-body diagram analysis on the aircraft during ground roll and takeoff will show thatthe only two forces acting in the horizontal (x) direction are Thrust and Drag. With this in mind,

Eq. (1) becomes,

(2)

The thrust on the aircraft during takeoff can be determined based on the static thrust to

power loading, the power absorbed by the propeller and the thrust fraction. All of these

parameters were found in the Pilots Operating Handbook or in (McCormick, 2011). The actual

values used for calculating thrust will be further explained in section (2.2 Implementation).

The drag term in Eq. (2) must be calculated by evaluating Rolling Drag, Profile Drag, andInduced Drag separately and adding them together to get the total drag on the aircraft. The

Rolling Drag on the aircraft is

(3)

where W represents the gross weight of the aircraft and the coefficient of static friction, is

assumed to be 0.02. The Lift, referred to as L in Eq. (3) is

(4)

where is the density of the air at the time of the experiment, S is the wing planform area of the

aircraft, and the coefficient of lift for the aircraft is,


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The coefficient of lift was found by back calculating using Eq. (4) and assuming steady level

flight (L = W), using max takeoff weight, standard atmospheric properties and a cruise velocity

of 100 kts.

The Profile Drag on the aircraft is found using,

(5)

wheref, is the flat plate area of the aircraft. Flat plate area is found by multiplying the surface

area of the aircraft by the coefficient of skin friction.

Finally, the Induced Drag on the aircraft is

(6)

where

Summing the three components of drag found in Eq. (3), (5), and (6) results in an equation for

total drag as a function of velocity.

(7)


The purpose of the Pitot-Static experiment is to calculate a calibrated airspeed and

compare that with the indicated airspeed in the cockpit. This is done by flying a square flight

pattern at a specified, constant Indicated Airspeed, and collecting data during each leg of the

experiment. Representing each leg of the experiment as a vector with GPS ground speed as its

magnitude, and GPS track as the vector direction, the four legs of the experiment can be

combined to yield true airspeed and wind speed. The four data vectors are projected onto a

Cartesian plane with their roots at the origin. A circle can then be drawn through the tips of each


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data vector. The radius of this circle is representative of the true airspeed. Additionally, the

vector pointing from the origin of the Cartesian plane to the center of the circle is representative

of the wind speed and direction.

The primary reason for performing this calibration is error in the static pressure. This

error is the result of pressure fields surrounding the aircraft that interfere with static pressure

measured along the body of the aircraft

Once the true airspeed has been experimentally calculated, it can be converted to a

calibrated airspeed using,

(8)

where,

Ultimately, the calibrated airspeed should relate to the indicated airspeed in such a way that it

follows closely with the chart shown below in figure 2 (The New Piper Aircraft Inc., 2011).

Figure 2. Airspeed System Calibration chart for the Piper Arrow III. Note that it accounts for some

discrepancy between calibrated and indicated airspeed.


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Level Flight Power Required

The aim of the Level Flight Power Required (LFPR) portion of the flight test was to

reduce the experimental data in order to find the flat plate area and span efficiency factor of the

Arrow III. In the takeoff simulation, the values for flat plate area and span efficiency were

estimated. The experimental results from the LFPR portion of the flight test will be compared to

these estimates in order to ensure accuracy.

After power, pressure altitude and airspeed data have been gathered and reduced, a

relationship between equivalent power and equivalent velocity can be established according to,

(9)

where,

2.2 ImplementationTakeoff Simulation

Breaking the takeoff roll down into many small (0.01 second) time increments, the

horizontal acceleration of the aircraft can be calculated for each time step, where thrust and drag

are both functions of the horizontal velocity of the aircraft at time step k.

(10)

The thrust for each time step is calculated from the equation,

, (11)

where Static Thrust to Power Loading (McCormick, 2011) is

(12)

and Prop Power Absorbed (McCormick, 2011) is

(13)


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The thrust fraction is a function of velocity and is found by performing a linear curve fit on the

curve shown in figure 3 (McCormick, 2011).

Figure 3. Plot of Thrust Fraction versus Velocity (feet per second) for the Piper Arrow III

The resulting equation after performing the linear curve fit is

, (14)

where the velocity, V, is in units of feet per second.

Plugging Eq. (12)-(14) into Eq. (11), results in an equation for thrust as a function of

velocity. Equation (11) becomes

(15)

Additionally, by combining Eq. (3)-(6) into Eq. (7), the drag for each time step k, becomes


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(16)

Substituting Eq. (15)-(16) into Eq. (10), results in an equation for horizontal acceleration

at each time step that is dependent on the horizontal velocity at that time step. Now that an

expression for horizontal acceleration has been derived, it can be used to calculate velocity and

position at each future time step. The time step used in the theoretical takeoff model was

t = 0.01seconds.

(17)

(18)

(19)

Using Eq. (17)-(19), velocity, position and time can be calculated iteratively over a given time

interval to simulate the takeoff roll. The complete calculations can be seen in the Takeoff Code

in Appendix B.


Once the ground speed and GPS track have been found for each data point, they must be

converted to Cartesian coordinates using

(20)

(21)

After the data points have been converted to Cartesian coordinates, an initial guess vector was

created,

, (22)

where,


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Note: With the exception of extremely windy days, a good guess center point is the origin, (0,0).

This guess vector is then iterated using the equation below in order to zero-in on the

resulting vector containing actual airspeed (radius of the circle) and wind speed (from center of

circle).

, (23)

Note: \ represents a MATLAB operator finding thepseudo-inverse of J

where,

,(24)

, (25)

, (26)

, (27)

, (28)

where i represents each incremental data point (total of 4). Once Eq. (23)-(28) have been coded

into a program, one simply needs to iterate Eq. (23) in order to arrive at a final vector,


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(29)

where

Once a true airspeed had been calculated, the calibrated airspeed was hand calculated

using Eq. (8)


Once data had been gathered for the LFPR portion of the flight test, it was used to

calculate the equivalent velocity and equivalent power. These equivalent values represent the

theoretical velocity and power that the aircraft would have if it were flying at sea level at

standard atmosphere and standard weight. The equivalent velocity was calculated first using

, (30)

where,

Before calculating equivalent power, the power required during the flight test had to be estimated

using the IO-360 C1C6 Engine Chart, provided in class. Additionally, a change in power had tobe added or subtracted from the power required based on whether or not the aircraft changed

altitude during the course of the test. Total power required can be expressed as

Once had been determined for each of the data points, it could be plugged into


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(31)

in order to find equivalent power.

After this, and could be plotted against each other for each data pointgathered. A linear curve fit would then yield

, (32)

in which A and B are constant

coefficients

.

From there, flat plate area and span efficiency coefficient can be found based on the

coefficients, A and B, derived from Eq. (9).

(33)

, (34)

and

(35)

(36)

2.2.1 Verification ApproachTakeoff Simulation

After the takeoff code had been written, it was tested using realistic atmospheric

conditions in order to check that the simulation produced realistic values for velocity and

position over a short time period (approximately 30 seconds). The results from this test run

included position values of up to about 2000 feet, which is an accurate takeoff distance for the

Arrow III. Additionally, the test results show corresponding velocity values ranging up to about


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80 feet per second which is a realistic takeoff velocity for the Arrow III. The fact that test run

yielded real and reasonable results is verification that the code we developed is functional.


In order to verify the Pitot-Static Calibration code, we considered a best-fit circle based

on the following points: (70,0) (-10,80) (-90,0) (-10,-80), shown in figure 4.

Figure 4. A plot of the example used to validate the pitot-static code. The vectors extend from the center of

the circle to each of the four data points.

We know that the center point of this circle is located at, x=-10, y=0. We also know that the

radius must be 80 in order to satisfy the data points as closely as possible.

When the Pitot-Static Calibration code was run with those data points (as ground speeds

and GPS Track angles), we found a result that matched. Our results are shown below in figure 5.


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Figure 5. The resulting vector after the Pitot-Static Calibration code was run with the points,(-90,0) (-10,80)(70,0) (-10,-80). This result matches with what we already know to be the answer, validating and verifying

the code.


For the LFPR data reduction, our approach was verified simply based on the fact that our

results for flat plate area and for span efficiency factor were feasible values for a small propeller

aircraft like the Arrow III.

2.3 Example ResultsSeveral examples of our validation and verification results are shown below. Figures 6,

7, and 8 are sample results from our takeoff code. It is clear by examining these plots that the

results from the takeoff code are realistic for a small propeller aircraft like the Arrow III.

Additionally, figure 5 (above) shows our example result from the pitot-static calibration

code. The fact that figure 5 (above) returned an answer and furthermore returned the correct

answer, verifies and validates the code.

X_final =

80.0000

-10.0000

0

This Vector represents the radius of the circle (TAS (kts)):

r = 80 kts.

The Center of the Circle is located at, x = -10, y = 0


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Figure 6. Theoretical plot of position versus time. The slightly parabolic trend of the plot fits well with the

how the aircraft actually behaved during takeoff, verifying and validating the code.

Figure 7. Theoretical plot of velocity versus time. The shape of the curve, as well as the range of values

represented by the curve fit well with the how the aircraft actually behaved during takeoff, verifying and

validating the code.


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Figure 8. Theoretical plot of velocity versus position. The shape of the curve, as well as the range of values

represented by the curve fit well with the how the aircraft actually behaved during takeoff, verifying and

validating the code.


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3.0 RESULTS & DISCUSSIONTakeoff Simulation

Figures 9, 10, and 11 below show the theoretical takeoff simulations using the

atmospheric data at the time of the first takeoff roll. Experimental data from the first takeoff roll

is plotted on the same set of axes with the theoretical takeoff roll. Examining figure 9, one can

see that the experimental data follows a trend similar to the theoretical takeoff data. The

experimental position values tend to lie lower on the plot than the theoretical values. This is

likely the result of interference drag between the fuselage, landing gear and other instrumentation

mounted on the aircraft. Interference drag was not accounted for in the theoretical analysis.

Figure 10 shows a plot of velocity versus time for the first takeoff roll. Similarly to figure 9, the

experimental data lies slightly below the theoretical data. Again this is likely due to interference

drag on the aircraft that was not accounted for in the theoretical model of the takeoff roll.

Figure 9. A plot of position versus time for the 1stset of takeoff data. Note that the experimental data lies

slightly below the theoretical data.


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Figure 10. A plot of velocity versus time for the 1stset of takeoff data. Note that the experimental data lies


In figure 11 shown below, velocity is plotted against position for the first takeoff roll. Again, the

experimental data from the first takeoff roll is plotted on the same set of axes. The experimental

data follows a trend similar to that of the theoretical data, although the experimental data lies

below the theoretical takeoff roll, indicating that at each given position, the actual velocity of the

aircraft was slightly less than what was calculated in the theoretical model. Again this is likely

due to drag that was unaccounted for in the theoretical model.


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Figure 11. A plot of velocity versus position for the 1stset of takeoff data. Note that the experimental data

lies slightly below the theoretical data.

The same analysis was done using the atmospheric conditions at the time of the second takeoff

roll and the experimental data from the second takeoff roll. The results of this analysis are

shown below in figures 12, 13, and 14. The experimental data for the second takeoff roll tends

to be slightly less than the theoretical model, similarly to the first set of takeoff data. While both

the first and second sets of takeoff data follow similar trends, the second set of experimental data

lies closer to the theoretical model than the first set of data. This is due to the fact that the crew

had a better idea of how to properly execute the experiment during the second test.


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Figure 12. A plot of position versus time for the 2nd set of takeoff data. Note that the experimental data lies


Figure 13. A plot of velocity versus time for the 2nd set of takeoff data. Note that the experimental data lies



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Figure 14. A plot of velocity versus position for the 2nd set of takeoff data. Note that the experimental data

lies slightly below the theoretical data.


The pitot-static calibration data was reduced using the MATLAB code shown in

Appendix B. The test data (GPS Track, and Ground Speed) was plugged into the program with

an Indicated Air Speed of 65 knots and a tolerance of 0.5 knots; the results are shown in figure

15 below. An illustration of the best fit circle for our data points is also shown below in figure

16.

Figure 15. The resulting vector of the Pitot-Static Calibration data reduction.

X_final =

69.7342

6.7638

3.7529

This Vector represents the radius of the circle (TAS (kts)):

r = 69.73418 kts.

The Center of the Circle is located at,

x = 6.763753

y = 3.752868


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Figure 16. Best fit circle for the four experimental data points. The dotted vectors represent the

experimental data points while the solid vector represents the wind speed, and center of the circle

As shown above in figure 15, for an indicated airspeed of 65 knots, the true airspeed was 69.7

knots. Using Eq. (8), we found calibrated airspeed, shown below.

A comparison of the indicated, true and calibrated airspeeds are shown below in table 6. The

results of the pitot-static calibration show that the airspeed indicator inside of the cockpit is well

calibrated and accurate as it was within 1.22% of the calibrated airspeed we calculated. Whencompared to the plot shown in figure 2, one can see that the calibrated airspeed is expected to be

slightly higher than the indicated airspeed at a low velocity such as 65kts. This further confirms

the accuracy of our pitot-static calibration results.


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Table 6. Indicated, True and Calibrated airspeeds as well as percent error between the indicated and

calibrated airspeeds

Indicated Airspeed True Airspeed Calibrated Airspeed Error

65.0 kts 69.7 kts 65.8 kts 1.22%

Additionally, the center of the cirle, created by the four pitot-static data pointsis representative of

the wind speed during the experiment. Based on these coordinates, a wind speed and direction

were calculated. The resulting wind speed and direction are shown below,


After all of the experimental data had been converted to equivalent power and velocity

data using the equations given in the Implementation section (2.2), the data could be plotted and

analyzed. A plot of the and data points was then generated and a linear trend line

was fit to the data set using MATLAB. The resulting linear equation corresponds to Eq. (32).

The linear best fit equation as well as the plot of the data points are shown below in figure 17.

Figure 17. Plot of , with a linear trend line fitted to the data. Note

the equation for the best fit line in the upper left hand corner.


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Where,

Using Eq. (34) and (36), we calculated flat plate area and span efficiency coefficient based on the

coefficients A and B found above. The results of our calculations are shown below in table 7,

compared with the guesses used in the takeoff model.

Table 7. Estimated and calculated values for flat plate area and span efficiency factor. In both cases, therewere large amounts of error, largely due to poor experimental data.

Parameter Estimated Value LFPR Experimental Value Error

flat plate area, f 6.0634 0.081387 98.66%

span efficiency, e 0.6 -301.32 50120%


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4.0 CONCLUSIONSThroughout the entirety of this flight test, many things were learned, verified, and

accomplished. The aim of the takeoff test was to gather experimental data over the course of two

takeoff rolls, and compare that data to a theoretical takeoff model. The theoretical takeoff model

was computed via a custom code implemented in MATLAB and using equations and important

parameters from the POH for the Piper Arrow III. The results of the takeoff simulation seemed

to fit well with our experimental data. Based on the results from the takeoff test and simulation

we can conclude the following things:

The takeoff simulation produced using our code is in fact accurate and provides a realisticpicture of how the aircraft actually behaves during takeoff

There are other forces effecting the aircraft during takeoff that went unaccounted forincluding, increased drag forces and gravity forces due to the runway not being

completely level

While the takeoff test was successful in providing a realistic picture of takeoff for the Arrow III,there are some potential sources of error including:

Inaccuracies in the flat plate area estimation, leading to inaccuracies in the dragcalculations

Headwinds or Tailwinds exerting extra force Rounding and analytical error that could arise from using a non-infinitesimal time step Human error arising from the method of calling mark at each runway marker. Any swerving resulting in the aircraft not traveling in a straight line down the runway

Overall, the takeoff simulation and experiment was a success, although in the future, we would

suggest several changes. It would be beneficial and fairly simple to account for the wind at

takeoff in future iterations of this experiment. Additionally, GPS data could be used to measure

distance along the runway, making the timing of the data collection more accurate.

The goal of the pitot-static calibration portion of the flight test was to calibrate the

airspeed indicator, and in doing so, check that it had been calibrated correctly by the factory

before takeoff. After all necessary data had been gathered, a calibration code was written in

MATLAB to take the experimental ground speeds and tracks and convert them to a true airspeed.

The code was verified using a simple test case in which the answer (TAS output) was intuitive

and already known. Once the code was verified, it was run using the experimental data and a

true airspeed was found for the experiment. It was then converted to a calibrated airspeed andcompared with the indicated airspeed at which the pilot was flying. The results from this portion

of the test were accurate, yielding a calibrated airspeed within 1.22% of the indicated airspeed.

Some conclusions drawn from the pitot-static calibration are as follows:

The MATLAB code used to determine true air speed and wind speed is accurate The dashboard airspeed indicator had been correctly calibrated prior to takeoff


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Much of this difference is due to errors in the pitot-static system of the aircraftA few potential sources of error during the pitot-static calibration include:

Error resulting from the pilot not holding a constant IAS Errors in the data collection due to improper reading of the dashboard instrumentation

In future iterations of this experiment, it would be advisable to record angle of attack as well for

the data points gathered. It would also be advisable, if possible, to measure dynamic and static

pressure out in front of the aircraft using some kind of boom. This would eliminate any error

due to the pressure fields directly around the aircraft body.

The third and final portion of this flight test was the Level Flight Power Required test.

This test yielded reasonable values for equivalent power required and equivalent velocity

required, however, when the data was plotted, the resulting coefficients were very inaccurate.

We believe that the method of our test was correct, leading us to believe that the data gathered

was too inaccurate and discrete. Overall, after performing the LFPR test we can conclude that:

More data points at various speeds would improve our estimates for flat plate area andspan efficiency factor

The data gathered during the LFPR test is very sensitive due to the fact that during datareduction, it was multiplied and raised to the fourth power. This greatly expands any

small error in each data point

Some sources of possible error for the LFPR test include:

Inaccuracies in the power calculations due to utilizing a chart to estimate the power Inaccuracies in power due to the pilot not maintaining a constant altitude throughout the

test

In the future, this experiment could be improved fairly easily providing a more accurate method

for finding the power required by the engine during the flight test. Additionally, angle of attack

could have been better utilized by considering the way in which it affects the power data.

Finally, in future iterations of this test, the importance of maintaining a constant airspeed must be

stressed to the test pilot. Overall, many things were learned, and many conclusions were drawn

throughout the course of this test flight and the three experiments performed during flight.


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6.0 APPENDIXAppendix A: Raw Data Sheet


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Appendix B: Takeoff Code (MATLAB)% AERSP 420 -- Brian Harrell% Takeoff Model (Flight Test 1)

% Set constants for Piper Arrow III

S = 170;Surface_Area = 638.25;b = 35.417;AR = (b*b)/S;e = 0.6; %Estimate for low wing prop airplanemew = 0.02; %Assumed in class

% Set Precalculated ConstantsStatic_Thrust = 4.8;Prop_Power_Absorbed = 200*0.85;C_L = 0.477;

% Input Initial Atmospheric Conditions

Temp_F = input('Please enter the Outside Air Temperature at the time oftakeoff (degrees Fahrenheit) \n \n');Temp_R = Temp_F + 460;

Pressure_Alt = input('\n \nPlease input the Pressure Altitude in (feet) atthe time of takeoff \n \n');

Weight = input('\n \nPlease input the gross takeoff weight (lbs) for thetakeoff roll \n \n');

% Calculate air density% Gas constant for airR = 1716;

% Find air pressure in (in Hg)P_inHg = 29.92 - (Pressure_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);

% Coefficient CalculationsC_f = 0.0095; %GivenC_Di = (C_L*C_L)/(pi*AR*e);

% Calculate Flat Plate Areaf = C_f*Surface_Area;

% Set Initial Conditionstime = (0:0.01:30)';t_step = 0.01;

% Creates empty arrays for position, velocity, acceleration, Thrust and% all three DragsX = zeros(3001,1);V = zeros(3001,1);


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a = zeros(3001,1);Thrust = zeros(3001,1);D_r = zeros(3001,1);D_p = zeros(3001,1);D_i = zeros(3001,1);Drag = zeros(3001,1);

fori=1:3000

% Lift as a function of VelocityL = 0.5*Density*(V(i,1)*V(i,1))*S*C_L;

% Drag Calculations% Rolling DragD_r(i,1) = mew*(Weight - L);% Profile DragD_p(i,1) = (0.5*Density*(V(i,1)*V(i,1))) * f;% Induced DragD_i(i,1) = (0.5*Density*(V(i,1)*V(i,1))) * C_Di * S;% Total Drag

Drag(i,1) = D_r(i,1) + D_p(i,1) + D_i(i,1);

% Thrust Calculation based on the linear curve fit from Figure 6.21Thrust_Fraction = (-0.0039 * V(i,1)) + 1;Thrust(i,1) = Static_Thrust * Prop_Power_Absorbed * Thrust_Fraction;

% Acceleration Calculationa(i,1) = (Thrust(i,1)-Drag(i,1))/(Weight/32.2);

% Solves for the next step of position and velocityX(i+1,1) = (V(i,1)*t_step) + X(i,1);V(i+1,1) = (a(i,1)*t_step) + V(i,1);

end

% Experimental Data, Team #5%Takeoff #1Exp_Time_1 = [0, 7.09, 10.65, 13.51, 15.71, 17.56, 19.50, 21.42, 22.91,24.31];Exp_X_1 = [0, 200, 400, 600, 800, 1000, 1200, 1400, 1600, 1800];Exp_V_1_kts = [0, 20, 38, 46, 54, 58, 62, 64, 66, 70];%Takeoff #2Exp_Time_2 = [0, 7.52, 10.77, 13.21, 15.53, 17.50, 19.52, 21.34, 22.7, 23.8,24.88, 25.81];Exp_X_2 = [0, 200, 400, 600, 800, 1000, 1200, 1400, 1600, 1800, 2000, 2200];Exp_V_2_kts = [0, 20, 40, 47, 53, 57, 61, 64, 69, 70, 72, 74];

% Convert experimental Velocity from knots to feet per secondExp_V_1 = Exp_V_1_kts .* 1.6878;Exp_V_2 = Exp_V_2_kts .* 1.6878;

% Plotting the experimental Data versus the Theoretical Datafigure(1)plot(time, X, 'b', Exp_Time_1, Exp_X_1, '*-r')


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title('Position vs. Time')xlabel('Time (seconds)')ylabel('Position (feet)')legend('Theoretical Data (Run #1)', 'Experimental Set 1')

figure(2)

plot(time, V, 'b', Exp_Time_1, Exp_V_1, '*-r')title('Velocity vs. Time')xlabel('Time (seconds)')ylabel('Velocity (feet per second)')legend('Theoretical Data (Run #1)', 'Experimental Set 1')

figure(3)plot(X, V, 'b', Exp_X_1, Exp_V_1, '*-r')title('Velocity vs. Position')xlabel('Position (feet)')ylabel('Velocity (feet per second)')legend('Theoretical Data (Run #1)', 'Experimental Set 1')

**Note: When executing the code, you must adjust the arguments of the plot functions in order

to plot each experimental data set separately


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Appendix C: Pitot-Static Code (MATLAB)% AERSP 420 -- Brian Harrell% Find the center of a circle from (4) data points% Used to find True Airspeed and Winds

% Takes the GPS Track and IGS as inputsGPS_1 = input('\n\nPlease input the GPS Track of the first (1st) datapoint\n\n');IGS_1 = input('\n\nPlease input the Indicated Ground Speed of the first (1st)data point\n\n');GPS_2 = input('\n\nPlease input the GPS Track of the second (2nd) datapoint\n\n');IGS_2 = input('\n\nPlease input the Indicated Ground Speed of the second(2nd) data point\n\n');GPS_3 = input('\n\nPlease input the GPS Track of the third (3rd) datapoint\n\n');IGS_3 = input('\n\nPlease input the Indicated Ground Speed of the third (3rd)data point\n\n');

GPS_4 = input('\n\nPlease input the GPS Track of the fourth (4th) datapoint\n\n');IGS_4 = input('\n\nPlease input the Indicated Ground Speed of the fourth(4th) data point\n\n');

% Converts the IGS and Track to Cartesian pointsX_1 = IGS_1*sind(GPS_1);Y_1 = IGS_1*cosd(GPS_1);X_2 = IGS_2*sind(GPS_2);Y_2 = IGS_2*cosd(GPS_2);X_3 = IGS_3*sind(GPS_3);Y_3 = IGS_3*cosd(GPS_3);X_4 = IGS_4*sind(GPS_4);Y_4 = IGS_4*cosd(GPS_4);

% Takes the IAS for the experimentV_t = input('\n\nPlease enter the Indicated Airspeed that was held during theexperiment\n\n');

% Sets the fist "guess" x vectorx_w = 0;y_w = 0;X_guess = [V_t; x_w; y_w];

% Objective Function FF_1 = V_t - sqrt((X_1-x_w)*(X_1-x_w)+(Y_1-y_w)*(Y_1-y_w));F_2 = V_t - sqrt((X_2-x_w)*(X_2-x_w)+(Y_2-y_w)*(Y_2-y_w));F_3 = V_t - sqrt((X_3-x_w)*(X_3-x_w)+(Y_3-y_w)*(Y_3-y_w));F_4 = V_t - sqrt((X_4-x_w)*(X_4-x_w)+(Y_4-y_w)*(Y_4-y_w));

%Takes derivatives of F, to be used in the JacobiandF_V_t = 1;

dF_X_1 = (X_1-x_w)/sqrt((X_1-x_w)*(X_1-x_w)+(Y_1-y_w)*(Y_1-y_w));dF_X_2 = (X_2-x_w)/sqrt((X_2-x_w)*(X_2-x_w)+(Y_2-y_w)*(Y_2-y_w));


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X_final = X_plus_1;end

fprintf('\n\nThis Vector represents, The radius of the circle (True Airspeed,kts):\n\n r = %d kts.\n\nThe Center of the Circle is located at, x = %d, y =

%d', X_final(1), X_final(2), X_final(3));


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Appednix D: LFPR Code for curve fitting (MATLAB)% AERSP 420 -- Brian Harrell% Level Flight Power Required plotting and data reduction

% P equivalent and V equivalent data points for Team #5

P_ew = [121.39, 115.74, 120.30, 127.63, 125.52, 125.16];V_ew = [61.01, 70.54, 80.06, 89.54, 95.95, 108.14]; %in knots% Converts V_ew from knots to feet per secondV_ew_fps = V_ew.*1.6878;

P_ew_4 = P_ew .^ 4;P_ew_V_ew = [P_ew(1)*V_ew_fps(1), P_ew(2)*V_ew_fps(2), P_ew(3)*V_ew_fps(3),P_ew(4)*V_ew_fps(4), P_ew(5)*V_ew_fps(5), P_ew(6)*V_ew_fps(6)];

% Plots the arrays formed abovefigure(1)plot(P_ew_4, P_ew_V_ew, '*')title('P_ew*V_ew versus P_ew^4')

ylabel('P_ew*V_ew (hp*ft/second)')xlabel('P_ew^4 (hp^4)')legend('Experimental Data')

% Flat Plate Area and Span Efficiency Factor Calculation% Computing flat plate area and span efficiency factor based on the best% fit line

A = input('Please input the P_ew^4 term of the linear regression result\n');B = input('\nPlease input the constant term of the linear regression result(final term)\n');

% Input the span, and Ws value for the aircraft being analyzed

b = 35.417; %feetWs = 2500; %lbsrho_0 = 0.00237; %slugs/ft^3

% Calculates f and ef = (2*A)/rho_0;e = (2*(Ws/b)*(Ws/b))/(pi*rho_0*B);

sprintf('\nThe flat plate area of the aircraft is: %d feet^2\n\nThe spanefficiency factor for the aircraft is: %d \n', f, e)


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Appendix E: Flight Test Hazard Mitigation:

Flight Test #1 Report

Documents

Transcript of Flight Test #1 Report