flight test report

7/28/2019 Flight Test Report

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AERSP 420Principles of Flight Test

Final Report

Matthew Drury

12/20/12


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ABSTRACT

The Cessna 172R is a very popular aircraft for both training and personal use. For this

reason, the C172R was the aircraft chosen by the Pennsylvania State Universitys

Fundamentals of Flight Testing course to use as a test platform. Tests conducted

examined dynamic and static stability, takeoff, rate of climb, cruise power required, pitot

static calibration and stall characteristics of the C172R. The experimental data gathered

was compared to analytical computer models produced by the students in the course.

These results were also compared to published results from prior years.

1.0 INTRODUCTIONThis section describes the purpose of the flight tests conducted, a description of the test

airplane and description of all tests conducted.

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

Analytically predict the performance of a C172R and compare it to experimentaldata gathered in flight for takeoff, stall series, and static and dynamic stability

Collect and reduce flight test data for the C172R for pitot-static calibration, cruisepower, and climb performance, and compare to manufacturers documentation

1.2 Description of Test AirplaneThe Cessna C172R is an all metal, semimonocouque, high wing single engine airplanedesigned for utility and training purposes. The test airplane, tail number N2254U, was

manufactured in 1996. It is powered by a Lycoming IO-360-L2A engine rated at 160BHP with a two blade fixed pitch-propeller. Maximum takeoff weight for the C172R is

2450 lbs with a useful load of 818 lbs. The cockpit seats a maximum of four and provides

dual controls in the front seats. Flight controls include conventional ailerons, rudder and

elevator, all operated through cables and mechanical linkages. The ailerons and elevatorare controlled by a yoke and the rudder by rudder pedals. Also included in the flight

control system is an electrically controlled flap system and mechanical elevator trim The

flaps maybe selected in increments up to Taxiing is accomplished using a

combination of rudder inputs and differential braking to maneuver the steerable nose

wheel.


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Figure 1: Three view of C172R.


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1.3 Scope of TestThree flights were conducted, each approximately 1 hour in duration. The first flightmeasured takeoff distance, pitot static calibration and cruise power required. The second

measured stall and climb profile, while the final flight investigated the static and dynamic

stability of the aircraft. Table 1 summarizes airplane configurations and altitudes for allconducted tests. Table 2 shows relevant limitations that were considered for all flights.

Table 1: Relevant configurations and altitudes for conducted tests

Test Description Flaps Pressure Altitude

Takeoff Roll 10 1040

Pitot Calibration 0 4000Cruise Power Required 0 4000

Stall 0 5000Climb 0 5000Stick Position 0 4000

Phugoid 0 4000

Table 2: Relevant Limitations

Forward CG Limit 40 inches aft of datum

Aft CG Limit 47. 3 inches aft of datum

Load Factor +3.8, -1.52

Stall Speed in Cruise (VS1) 44 knotsMax Weight 2450 lbs


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1.4 Method of TestTakeoff Roll:

Take off was started with brakes held while power was increased to wide open throttle

(WOT) at which time brakes were released. A stopwatch with equipped with a lapfunction was used to track the time between each runway light (200 ft). Once 60 knots

was reached, the takeoff was aborted. Also, GPS Essentials, an Android based

application, was used to collect position and velocity. It was later discover that there wasan error in data recording, therefore no GPS takeoff data was obtained. This samemethod was conducted a second time but with the exception of the aborted takeoff.

Pitot Static Calibration:

Calibration of the C72Rs pitot system was tested by flying the cardinal headings at an

indicated airspeed (IAS) of 50 knots. Heading and IAS were recorded on each leg along

with GPS acquired true airspeeds (GS) and bearing. The GPS ground speeds recordedwere reduced using a least squares method to determine TAS, CAS and a calibration

factor.

Cruise Power Required:

Cruise power required for straight and level flight was calculated starting at 50 KIAS

increasing by 10 knots up to 110 KIAS. Pressure altitude, outside air temperature, RPM,IAS and angle of attack were recorded at 0, 30 and 60 seconds. These values were used

along with properties of the C172R to develop a power required curve and determine

equivalent flat plate area and Oswalds efficiency factor

Stall:

Stall performance of the C172R was studied at a pressure altitude of 5000 ft. Power-offstalls were performed on three different legs, each 45 apart. IAS, pressure altitude,

heading, and GPS acquired heading and speed were recorded on each leg.

Rate of Climb:

The climb performance of the C172R was tested using the saw tooth climb method

outlined inIntroduction to Flight Testing and Applied Aerodynamics. The target pressurealtitude that data would be recorded at was 5000 ft and the altitude below the target

altitude was calculated using theoretical rate of climb data. Once the starting altitude was

established, pressure altitude, IAS, RPM, heading, vertical speed indicator readings(VSI), and GPS TAS were recorded at the 0, 30 and 60 second marks. This was done

starting at 60 KIAS up to 100 KIAS increasing by 10 knot increments.


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Phugoid:

To determine the dynamic stability characteristics of the C172R two variations of acontrol fixed phugoid were performed. The airplane was trimmed at 80 KIAS and the

position of the yoke column at the dash was noted. Once trimmed at 80 KIAS, the yoke

was pulled back until 60 KIAS was reached, at which time the yoke was pushed forwardto the position noted earlier and held there until oscillations damped out. Accelerometerdata was recorded along with a video recording of the airplanes ASI and altimeter This

process was repeated for a trim speed of 100 KIAS and a aft yoke speed of 80 KIAS.

Stick Position:

To determine the static stability of the C172R the airplane was slowed to 60 KIAS and

yoke position from the dash was measured. Airspeed was increased by 10 knotincrements and the process was repeated up to 110 KIAS.


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1.5 InstrumentationData was gathered using the instruments listed below in Table 3 and recorded on datasheets during the test flight and processed later using student developed computer

programs.

Table 3: Instrumentation List

Parameter SourceAirspeed Production airspeed indicatorAltitude Production altimeterRate of Climb Production VSIRPM Production tachometerFuel Quantity Production fuel gageFlap Position Production indicatorsTime Wrist watchGround Speed/ Latitude/

LongitudeAndroid powered cell phone

Acceleration Android powered cell phoneYoke Position RulerDeck AngleHeading

Android powered cell phoneProduction directional gyro


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2.0 ANALYSISThis section describes the theory used to predict test results. All predicted resultsare compared to actual data and presented in Results and Discussion.

2.1

Theory


To calibrate the C72Rs pitot static system, the cardinal headings were flown at aconstant IAS and pressure altitude while GPS derived bearing and ground speeds

were recorded for each leg. This data was used along with a least squares fitting

method to determine TAS. A custom MATLAB code was written using the method

described in this section to calculate the pitot static calibration factor.

The north-south and east-west components of the

th

i ground speed vector are denotediy and ix respectively in

22 )()( byaxL iii

while a and b are the east-west and north-south coordinates of the circle formed by

the ground speed vectors.

An arbitrary value of a and b were chosen initially, and fixed point iteration was used

to calculate the actual values. The number of headings flown is denoted by m, thisnumber was 4 for the tests flown in this report. Once the correct center of the circle

was found usingaLLxa

bLLyb

the vector from the center of the circle to the point where the ground speed vectorsjoin is the wind vector.

The radius of the circle is TAS. CAS was then found using

TASCAS

where is the ratio of density at sea level on a standard day to measured density.

Intermediate calculations used are shown below as Equations (5)-(9).

m

i

ixm

x1

1


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m

mi

iym

y1

m

i

iLm

L1

1

m

i i

iaL

xa

mL

1

1

m

i i

ib

L

yb

mL

1

1


Cruise power required for the C172R was used to determine equivalent flat plate areaand Oswalds efficiency factor This was done by reducing the data gathered during

testing to a standard velocity ( ), weight, and power ( ). Equivalent airspeedwas found using

W

Wvv sew

where sW is the standard weight of the 172R which is 2450 lbs. The equivalent power

required at sea level was found using

2

3

W

WPP sew

where P is the actual power produced during the test flight and v is IAS. The actual

power produced was calculated using

nD

vJ

1305.01459.03167.04399.01639.0234

JJJJCT

TCDpropnT42

Wt

hTvPrequired

where J is the advance ratio of the propeller, n is the RPM converted to revolutions

per second, Dprop is the diameter of the propeller (6.25 ft), and TC is the thrust

coefficient. In Equation (15), the second term is the correction for any altitude gained

during the flight. The TC Equation was measured by B.W. McCormick and given in

[3].


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Rate of Climb:

Predicted values for rate of climb were found starting with

for the C172R was calculated using Figure 2 shown below. This curve wasgiven in [3]. To generate this curve one must iterate over RPM to find the point where

the SHP and BHP curves intersect as seen in Figure 3. CP is then calculated using

0792.00119.01 JCP

0907826.00464073.0100686.02

2 JJCP

Advance ratio and thrust are then calculated for each velocity using Equations (12)-(14). For this test the airplane would be trimmed for various speeds and rate of climb

would be recorded for each. Therefore, was calculated by multiplying total drag

by a wide range of speeds. The predicted rate of climb values were then used to

determine the altitude the saw-tooth climb would be started at for each configuration.All values of rate of climb and speed were reduced to standard values using Equations

(10) and (11).

0 20 40 60 80 100 120 1400

20

40

60

80

100

120

140

Velocity (knots)

HP

Figure 2: Power available for C172R, used to predict rate of climb.


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Static Stability (Stick Position):

To determine the neutral point of the test aircraft, a range of airspeeds are flown while

holding altitude constant and measuring the distance from the dash to yoke for each

speed. These distances are then plotted against plotted against CL. This shows how CMvaries with CL for this particular CG location. Because the pitching moment does notchange when the CG is located at the neutral point of the aircraft, CL will not vary with

stick position at this point. By moving the CG fore and aft and plotting the various cases,

the CG location that gives 0LdC

dsis the neutral point. The neutral point of the C172R

was calculated in [3] to be 1.98 feet aft of the leading edge of the mean aerodynamic

chord of the wing.

Dynamic Stability (Phugoid):

To predict the phugoid mode of the C172R longitudinal equations of motion were used to

model the accelerations of the aircraft. Acceleration in the longitudinal direction is given

by

ou gXuXu cos

and the acceleration of the pitch attitude is given by

MMMM q

The previous two equation are linked by the time rate of change of angle of attack which

can be found using

ZgZZZuZu

oqu

o

sin1

For the flight test that would be flown, it would be assumed that the phugoid was control

fixed therefore, all terms with will drop out.

In addition to this model, a simple undamped model was constructed using the Lorentz

Approximation for a phugoid which is given by

2

2

g

uT o


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where uois the trimmed velocity This was used to determine the frequency, , and inturn plot the acceleration using

)cos( tAx

Note: A working analytical phugoid model described above was not obtained by the time

this report was written.


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2.2 ImplementationTake Off:

Takeoff was modeled using a custom MATLAB code that took in pressure altitude and

outside air temperature and calculated drag, thrust, RPM, shaft horsepower (SHP), andposition during the takeoff roll. This was done using the fact that the total forces acting

on the aircraft vary with lift as

)( LWF

Starting from rest, RPM was calculated by iterating brake horsepower (BHP) and SHP

until the two values were equal, using

26922

637511793750

28335002050306102 ne.nPAe.n.PAe.PA..BHP

pCDnSHP

53

The variations of BHP and SHP with RPM are shown in Figure 3 below.

400 600 800 1000 1200 1400 1600 1800 2000 2200 24000

20

40

60

80

100

120

140

160

RPM

HP

SHP

BHP

Figure 3: Variation of SHP and BHP with RPM.


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Equation (25) was found by applying a curve fit to the performance chart for the

Lycoming IO-360 engine. This chart can be found in figure A1 of the Appendix. The

power coefficient (Cp) is a piecewise function, shown in Figure 4 below. This graph wasgiven in [3].

0 0.2 0.4 0.6 0.8 1 1.20

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

J

Cp

Figure 4: Power coefficient for C172R propeller.

This RPM value was then used to calculate advance ratio, thrust, and drag for each

velocity using Equations (12), (14), and

)( DiSCfqD

Note that the CL used was calculated for 80% power at a pressure altitude of 8000 feet,

this selection was taken from the C172R POH. Figure 5 illustrates this process. Relevant

airplane parameters used can be found in table A1.


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Iterate to find RPM

Coefficients of

Thrust and Power

Thrust, HP

Forces, acceleration,

distance

Loop over

velocity

Output

Input:

OAT, PA, W

Figure 5: Takeoff simulation flow chart.

Stall:

To predict stall characteristics of the C172R a custom MATLAB code was written. The

purpose of this code was to calculate the Cl distribution across the wing and check if thisCl was greater than Cl,max for the NACA 2412airfoil that is used on the C172R. In orderto calculate the section lift coefficient along the span, the circulation was calculated at a

finite number of points along the span. The circulation at point is given by

vCc lii2

1


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where ci is the chord of the section, and C l is the section lift coefficient. Cl can also be

denoted as

aCl

Where a is the lift curve slope of the NACA 2412, the airfoil used on the C172R. Thevariation of chord and twist along the span of the C72R was found using figures in

and assuming a linear progression from a washout of- at the wingtips to at the root

These can be seen below in Figures 6 and 7.

0 5 10 15 20 25 30 35 403.6

3.8

4

4.2

4.4

4.6

4.8

5

5.2

5.4

5.6

Span (ft)

Chord(ft)


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0 5 10 15 20 25 30 35 40-3

-2.5

-2

-1.5

-1

-0.5

0

Span (ft)

Twist(degrees)

Figure 7: Twist variation along span

Because stall of the entire wing, not a two dimensional airfoil, is being predicted the

influence of vortices across the wing must be accounted for. This effect is known as

downwash and is denoted by W. This can be accomplished by modifying Equation (30)to

where is the angle of attack of plus the twist of the wing at i. W(i,j) is the velocityinduced at a point i by a vortex (j) at point j and is given by

where y(i) is the span wise location being effected by the vortex (j) at the location y(j)

and is the width of the vortex. This can be written as a system of linear algebraicequations,

where


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for ij

for i=j

The lift coefficient can then be calculated along the span by rearranging Equation #. If the

local Cl was found to be greater than Cl,max of the airfoil, the local Cl is set equal to Cl,max.The result of the custom MATLAB code created to perform the process just described is

shown below in Figures 8 and 9.

0 5 10 15 20 25 30 351

1.1

1.2

1.3

1.4

1.5

1.6

Span (ft)

Cl

8 S =5 z .

igure shows the lift coefficient across the span at an angle of attack of This value

was chosen using the lift curve slope of the NACA 2412 as the angle of attack at which

the airfoil would stall. As can be seen, the lift increases toward the root due to the

decreasing twist of the wing.


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0 2 4 6 8 10 12 14 16 18 20-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

Angle of Attack (deg)

CL

Figure 9: Predicted CL at zero degrees of flaps.


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2.2.1 Verification ResultsPitot Static Calibration:

To verify that the custom MATLAB code used to determine pitot static calibration factor

was accurate, velocity magnitudes of 80 knots and 50 knots were chosen for headings of

North/South and East/West respectively. The radius of the circle fit to these data pointsby the least squares method was calculated to be 65 knots, which is the average of the

four airspeeds. This can be seen below in Figure 10.

-80 -60 -40 -20 0 20 40 60 80-100

-80

-60

-40

-20

0

20

40

60

80

100

Velocity (knots)

Velocity

(knots)

Figure 10: Verification of least squares calculation in pitot static calibration MATLAB code.

Wind speeds are found by calculating the distance from the center of the least squares

circle to the center of the circle centered at the origin. Figure 10 gives a wind speed of

zero, which seems to be correct as the above situation would require wind to come fromboth the East and West at the same speed. This scenario is very unlikely in nature and the

calculations in the MATLAB code would cancel the two wind speeds. Therefore a second

verification was conducted using wind velocities to verify the shifting of the least squarescircle. Parameters were selected such that a North shift on the least squares circle wouldoccur, i.e. winds from the South. The result of this test is shown below in Figure 11 and

Table 4.


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-100 -80 -60 -40 -20 0 20 40 60 80 100

-100

-50

0

50

100

Velocity (knots)

Velocity

(knots)

Headings

Non-Corrected

Least Squares

Figure 11: Verification of least squares circle shift using wind speed and direction.

Table 4: Inputs and results of least squares circle shifting verification.

Parameter Input Results

North Airspeed 100 knots --

South Airspeed 85 knots --West Airspeed 90 knots --

East Airspeed 90 knots --

Wind Direction --

Wind Speed -- 3.8 knots

True Airspeed -- 91 knots


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3.0 RESULTS & DISCUSSION

Take Off:

Take off data was to originally be taken via GPS Essentials, however, difficulties wereencountered during testing and no GPS data was gathered. The data shown below was

taken by hand by reading the instruments and using a stopwatch. It is presented along

with the predicted curves in Figures 12-14. The measured data does indeed line up withthe predicted values; however the GPS data would most likely have been much closer.

0 200 400 600 800 1000 1200 14000

10

20

30

40

50

60

70

Distance (ft)

Velocity

(kts)

Predicted

Aborted T/O

T/O

Figure 12: Variation of IAS with distance during takeoff roll.


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0 5 10 15 20 250

200

400

600

800

1000

1200

1400

Distance(ft)

Time (sec)

Predicted

Aborted T/O

T/O

Figure 13: Take off distance vs time.

0 5 10 15 20 250

10

20

30

40

50

60

70

Velocity

(kts)

Time (sec)

Predicted

Aborted T/O

T/O

Figure 14: IAS variation with time during takeoff roll.


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The ground speeds recorded during the pitot static calibration test flight are show below

in Table 5. The goal of this test was to calculate a calibration factor for this flight

condition. The results of entering the values shown in Table 5 into the custom leastsquares MATLAB code are summarized below in Table 6. This test was conducted at apressure altitude of 4000 feet; winds at altitude were calculated to be 287 at 18.5 knots by

the custom MATLAB code. The substantial tail wind encountered while flying East is

easily seen in Figure 15 below via the shift of the least squares circle to the East.

Table 5: Values of ground speeds and corresponding headings from test flight

Direction Ground SpeedNorth 23.2 ktsEast 69.8 ktsWest 37.6 ktsSouth 46.1 kts

Table 6: Results of pitot static calibration test flight

Parameter

OAT IAS 50 ktsTAS 47 ktsCAS 45 ktsCorrection Factor 0.89

A constant IAS of 50 knots was held as the cardinal headings were flown for 30 seconds

during this test. Note that the correction factor calculated only holds for these flying

conditions, i.e. zero flaps and 50 KIAS. In order to produce a calibration curve across theentire operating range of this aircraft, data would need to be taken at airspeeds spanning

this range.


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-60 -40 -20 0 20 40 60 80-60

-40

-20

0

20

40

60

Velocity (knots)

Velocity(knots)

Headings

Non-Corrected

Least Squares

Figure 15: Least squares circle for pitot static system calibration test flight.


The main objective of the cruise power required test was to experimentally determineOswalds efficiency factor and equivalent flat plate area of the C72R Power required

was found using Equations (12)-(15) for each velocity flown. These values were then

reduced to standard values using Equations (10) and (11). When is plotted against

, a linear curve is obtained and given by

Taking points from the experimental data shown in Figure 16 and using Equation (34), a

value of 0.56 was found forOswalds efficiency factor along with an equivalent flat plate

area of 4.52 .


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0 1 2 3 4 5 6 7 8 9 10

x 108

1

2

3

4

5

6

7

8

9x 10

6

Vew

4

Pew

Vew

Measured Data

Measured Trend

Published Data

P q O y

Rate of Climb:

The rate of climb test conducted was a saw tooth climb with important parameters

recorded at the 0, 30 and 60 second marks. The actual rate of climb was found by

measuring the time it took to climb from the starting PA to the PA at the 30 second mark.This process was repeated from the 30 second mark to the 60 second mark and then

averaged with the first value to give rate of climb for that velocity. These values were

then reduced and plotted along with predicted values and VSI readings in Figure 17. Asyou can see there is a large drop in rate of climb at 60 knots, this is most likely do to wind

gusts at the instant of data recording. In a real flight testing program this test would be

repeated to obtain more consistent data.


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40 50 60 70 80 90 1000

100

200

300

400

500

600

700

Velocity (knots)

R/C

(fpm)

Predicted

Measured

VSI

Figure 17: Comparison of measured to predicted values of rate of climb reduced to standard values.

Stall:

To measure stall of the C172R, three headings 45 apart were flown while a power-off

stall was executed on each heading. At stall break IAS, ground speed and pressurealtitude were recorded. These parameters were used as inputs for the custom MATLAB

code developed for pitot static calibration. The results are categorized in Table 7 below.

Table 7: Data produced by pitot static calibration MATLAB code for stall tests

Parameter

OAT PA 5000 ftIAS 55 kts

TAS 62 ktsCAS 57 kts


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-80 -60 -40 -20 0 20 40 60 80 100-80

-60

-40

-20

0

20

40

60

80

Velocity (knots)

Velocity(knots)

Headings

Non-Corrected

Least Squares

Figure 18: Airspeed calibration circles produced during stall tests

On each leg of the test, stall break was recorded from the ASI to be 55 KIAS. Using

Figure 9, a weight of 2601 lbs, and choosing 1.6 as the CL for stall, the predicted stall

speed was calculated to be 57 KTAS. This prediction is reasonable when taking into

account all sources of possible error in the two custom MATLAB codes that weredeveloped to predict this value along with human error when recording in flight data.

Static Stability (Stick Position):

To calculate neutral point of the C172R, the test performed would have been required to

be repeated multiple times with various CG locations. However, only one test wasperformed to serve as a learning experience.

Before takeoff, the distance from the dash to the yoke was measured with a ruler forvarious elevator deflections. These values were used to generate Figure 19, where the

convention for negative deflection is trailing edge down. Figure 20 shows the elevator

deflection variation with CL.


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3 4 5 6 7 8 9 10-30

-20

-10

0

10

20

30

40

50

ElevatorDeflection(degrees

)

Yoke Position (in)

Figure 19: Elevator deflection as a function of yoke position measured from dash.

0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.34.6

4.8

5

5.2

5.4

5.6

5.8

6

6.2

6.4

6.6

CL

YokePosition(inche

s)

Experimental

Linear Fit

Figure 20: Yoke position variation with CL

The data shows a linear trend with the exception of one outlying data point at CL=0.95.

This is most likely due to an unintentional perturbation from the selected cruise altitude.

As stated earlier, in order to experimentally determine the location of the neutral point


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this test would need to be repeated again for different CG locations until a curve of

0LdC

dswas obtained.

Dynamic Stability (Phugoid):

The phugoid mode of the C172R was tested at trim velocities of both 80 knots and 100

knots. Accelerometer malfunctions were encountered during the test flight; therefore no

accelerometer data was gathered. The data presented below was borrowed from anotherflight test group that flew the same day. This data was reduced and compared to results

for both a simple undamped model and results from [3] for a similar test. The results are

shown below in Table 8 and Figures 21-23.

Table 8: Comparison of relevant data for 80 knot phugoid

Variation Period (seconds) thalf

Experimental 22.5 28Published [3] 32 58Undamped 18.65 --

10 20 30 40 50 60 70 80 90 100 1100.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

Time (seconds)

Acceleration(ft/s

2)

Experimental

Undamped Simple

Figure 21: Experimental phugoid data compared to the undamped simple model for a trim speed of

80 knots


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In Figure 21 the experimental results are compared to the undamped simple model. The

periods of these two curves match most closely out of the three compared methods.

10 20 30 40 50 60 70 80 90 100 110

0.7

0.8

0.9

1

1.1

1.2

1.3

Time (seconds)

Acceleration(ft/s

2)

Experimental

Published

Figure 22: Experimental phugoid data compared to a similar test presented in [3] for a trim speed of

80 knots.

In Figure 22, the experimental data is compared to the data published in [3]. Theamplitudes match fairly well, but the period of the experimental data is much smallerthan the published data, therefore the time to half is much shorter.


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10 20 30 40 50 60 70 80 90 100 1100.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

Time (seconds)

Acceleration(ft/s

2)

Undamped

Published

Figure 23: Published data from [3] for a phugoid with a trim speed of 80 knots compared to an

undamped simple model.

As seen, there is a large error between the time to half from [3] and the experimental timeto half. There are many possible sources of error, but after discussing the results with the

group that gathered the data, it was decided that the most likely cause of the large

discrepancy in data is the placement of the accelerometer. The accelerometer was placedon the seat of the cockpit; therefore the cushion would have acted as a damper and

absorbed most of the acceleration. For more accurate results the accelerometer should

have been placed on a more rigid surface, such as the floor. It would also be desirable tohave multiple accelerometers for redundancy purposes. This would also help to find the

best location to place an accelerometer for future tests of this nature.


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4.0 CONCLUSIONSThe performance characteristics of the Cessna C172R investigated in this course included

takeoff, rate of climb, cruise power required, stall, pitot static calibration and both staticand dynamic stability. Computer generated models for takeoff, and stall were compared

to measured in flight data. These models were found to be accurate representations of the

experimental data. A calibration factor for the pitot static system was found using acustom MATLAB code and GPS derived ground speeds and headings. Determining

equivalent flat plate area and Oswalds efficiency factor was the goal of the cruise power

required test. The experimental results were found to be close to published data for the

C172R, but some error was present. A stick position test was used to measure the staticstability of the aircraft. This test was meant to find the location of the neutral point;

however this test would need to be repeated multiple times for different CG locations to

do this. Because this would require a considerable amount of time and money, this test

was only conducted once as a learning experience. The dynamic stability of the C172Rwas measured via the phugoid mode. Control fixed phugoids with trim speeds of both 80

and 100 knots were performed but only data from the 80 knot variation was gathered.

From this period and time to half were found and compared to published data.

In each test flight conducted, problems were encountered. The most prominent error was

the malfunctions in data gathering in flight. This could have been avoided or mitigated agreat deal by ensuring all members of the group knew exactly how to work all data

gathering devices. A simple way to verify that these devices are gathering data also

would have been valuable. The groups understanding of the methods of each test was

also found to be very important, and the ability of the group to be able to convey theseprocedures to the pilot even more so. If the procedure was not fully understood by the

group, the data suffered.

During the three test flights, only a few large errors in data were present and not

discovered until the flight had ended. In a traditional flight test program these tests would

be conducted again to obtain better data, but this was not possible in this course. Some of

these errors were due to the lack of understanding of the group and therefore the pilot ofthe procedures of the test. Others, such as wind gusts, were uncontrollable events that

would simply require a re-test.


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5.0 REFERENCESNiewoehner, Robert. (2006). "Refining Satellite Methods for Pitot-Static

Calibreation."Journal of Aircraft, Engineering Notes.Lewis, Gregory. (2003). "Using GPS to Determine Pitot-Static Errors." National Test

Pilot School: http://www.ntps.edu/information/downloads.

McCormick, B.W.(2011)."Introduction to Flight Testing and Applied Aerodynamics."AIAA Educational Series.


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6.0 APPENDIXRaw data sheets (shared by team)

Hand-cranked dataRisk analysis (shared by team)

Table A1: Properties of C172R

Parameter Symbol Value UnitsStandard WeightWing Area

Wing Span

Oswalds Efficency actor

Aspect Ratio

Propeller Diameter

Equivalent Flat Plate Area

Sb

eAR

Dpropf

2450174

36.08

7.486.256.25

6

lbs

ft

N/AN/A

ft

Figure A1: Lycoming IO-360 power curve, used to find BHP for C172R.


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Custom MATLAB Codes


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Pitot Static Calibration

% Matt Drury% AERSP 420% 12/14/12%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

clc;clear;close all

OAT=33; % outside air temperature [F]PA=4000; % pressure altitude [ft]KIAS=50; % indicated airspeed [knots]n=4; % number of headings flownR=1716; % gas constant

pratio=((4e-10*PA^2)-(4e-5*PA)+1.0134);tR=OAT+460; % temperature [R]P=pratio*2116; % pressure [psf]dens=P/(R*tR); % density [slug/ft3]rho_s=0.00237; % sea level density [slug/ft3]sigma=dens/rho_s; % density ratio

% Headings and correspoding ground speeds% Input manuallyH=[0;90;180;270];

GS=[23.3;69.8;37.6;46.1];

% Converts from compass heading to traditional coordinatesfor i=1:n

if H(i) =0theta1(i)=90-H(i);

elseif H(i) >90 && H(i)


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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Least Squares Circle calculations%

tol=1e-6; % tolerance used for iterationa=0;b=0;for i=1:500

for k=1:nL(k)=sqrt((x(k)-a).^2+(y(k)-b).^2);

endLsum=0;xsum=0;ysum=0;xa=0;yb=0;

for k=1:nLsum=Lsum+L(k);xsum=xsum+x(k);ysum=ysum+y(k);xa=xa+((a-x(k))/(L(k)));yb=yb+((b-y(k))/(L(k)));

end

xbar=(1/n)*xsum;ybar=(1/n)*ysum;Lbar=(1/n)*Lsum;La=(1/n)*xa;Lb=(1/n)*yb;a1=xbar+(Lbar*La);b1=ybar+(Lbar*Lb);

if abs(a-a1)>tol && abs(b-b1)>tola=a1;b=b1;

elsebreakend

end

% Plot circlestheta=linspace(0,2*pi,100);x1=Lbar*cos(theta);x2=Lbar*cos(theta)+a1;y1=Lbar*sin(theta);y2=Lbar*sin(theta)+b1;plot(x,y,'*',x1,y1,'-',x2,y2,'--')xlabel('Velocity (knots)');ylabel('Velocity (knots)');legend('Headings','Non-Corrected','Least Squares')


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% Output% Units are in knots and degrees, wind direction is direction% wind is blowing from.TAS=Lbarwind_speed=sqrt((a1^2)+(b1^2))

wind_direction=atand(a1/b1)+360CAS=TAS*sqrt(sigma)correction_factor=CAS/KIAS


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Takeoff:

% Takeoff Model% Matt Drury% AERSP 420% 12/20/12

clc;clear;close all%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%Constants for C172R

W=2450; % Weight [lbs]S=174; % Wing area [sqft]AR=7.48; % Aspect Ratiof=6.25; %flat plate area [sqft]Dprop=6.25; % prop diameter [ft]u=0.02; % friction coefficient

e=0.8; % Oswalds efficiency factorCL=0.359; % crusie(const. during takeoff)g=32.2;R=1718; % Gas constant%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%k=100;PA=5000; % Pressure altitude [feet]OAT=45; % Outside air temperature [F]tol=0.1; %tolerance for itterationPo=2116; % Standard atmospheric pressure [psf]templaps=(460+59)-(3.57/1000)*PA; % Lapse rate temperature [R]theta=templaps/(460+59);P=Po*(theta^5.256); % Actual temperature [R]rho=P/(R*(OAT+460)); % density [slug/ft3]n=linspace(0,2400,k);n1=zeros(size(n));v=linspace(0,100,k); % Velocity [fps]v_kts=v/1.69; % Velocity [kts]

% Itterate over velocityfor j=1:k

q(j)=0.5*rho*(v(j)^2); % dynamic prssureL(j)=q(j)*S*CL; % liftCdi=0.5*((CL^2)/(pi*AR*e)); % induced drag, multiplied by 0.5

because of ground effectD(j)=q(j)*(f+(S*Cdi))+(u*(W-L(j))); % total drag

for i=1:k

J(i)=v(j)/((n(i)/60)*Dprop);

if J(i)


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CP(i)=(-0.100686*J(i)^2)+(0.0464073*J(i))+0.0907826;%... quadratic portion of Fig 3.13, power coefficient

end

SHP(i)=(1/550)*rho*((n(i)/60)^3)*(Dprop^5)*CP(i); % shafthorsepower

BHP(i)=(-102.306)-(0.00205*PA)+((5.33e-8)*(PA^2))+(0.179375*n(i))-((1.375e-6)*(n(i)*PA))-(0.0000291667*(n(i)^2)); %brake hp

end

% Function that calculates intersection of two curves,finds

% actual RPM[xout,yout]=intersections(n,SHP,n,BHP,1);n1(j)=xout(end);J(j)=v(j)/((n1(j)/60)*Dprop);

% Creates peacewise CP curve for actual RPMif J(j)


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figureplot(t,distance,'-',t2,D2,'*--',t3,D3,'o:')ylabel('Distance (ft)')xlabel('Time (sec)')legend('Predicted','Aborted T/O','T/O')

figureplot(t,v_kts,'-',t2,IAS2,'*--',t3,IAS3,'o:')ylabel('Velocity (kts)')xlabel('Time (sec)')legend('Predicted','Aborted T/O','T/O')


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Stall Prediction:

% Stall Prediction% Matt Drury% AERSP 420% 12/20/12

clc;clear allclose alldf=0; % Flap deflection [deg]n=100;AOA=linspace(0,20,n); % Angle of attack [deg]b=37.42; % Wingspan [feet]b_seg=b/n; % Width of segment [feet]temp_b=0; % PlaceholderS=174; % Wing Area [ft2]

% Loops over angle of attackfor jj=1:n

% Creates wingfor i=1:n

x_mid(i)=(b_seg/2)+temp_b;temp_b=temp_b+b_seg;

if (x_mid(i)>=0) && (x_mid(i)10.25) && (x_mid(i)=30twist(i)=(0.1773*x_mid(i)-3)+((1.583/5.77)*df);

elsetwist(i)=(0.1773*x_mid(i)-3)+((1.1/5.29)*df);

endelseif (x_mid(i)>16.92) && (x_mid(i)20.5) && (x_mid(i)=30

twist(i)=(-0.1773*x_mid(i)+3.635)+((1.583/5.77)*df);else

twist(i)=(-0.1773*x_mid(i)+3.635)+((1.1/5.29)*df);end

elseif (x_mid(i)>27.17) && (x_mid(i)


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twist(i)=(-0.1773*x_mid(i)+3.635);endC(i)=2/(c(i)*0.103);

end

for i=1:nfor j=1:n

W(i,j)=(1/(4*pi))*((1/(x_mid(j)-x_mid(i)+(b_seg/2)))-(1/(x_mid(j)-x_mid(i)-(b_seg/2))));

endend

Z=diag(C);A=(W+Z);alpha=twist+AOA(jj);gamma=inv(A)*alpha';

clmax=1.6;CLW=0;

% Calculate Cl across wingfor i=1:n

cl(i)=2*gamma(i)/c(i);

if cl(i)>clmaxcl(i)=clmax;

elsecl(i)=cl(i);

end

CLW(i)=c(i)*cl(i);

end

CLW2(jj)=sum(CLW)*b_seg/S; % total lift coefficeint of wing

end

plot(x_mid,c)xlabel('Span (ft)');

ylabel('Chord (ft)');

figure;plot(x_mid,twist)xlabel('Span (ft)');ylabel('Twist (degrees)');


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figure;plot(x_mid,cl)xlabel('Span (ft)');ylabel('C_{l}');

figure;plot(AOA,CLW2)xlabel('Angle of Attack (deg)');ylabel('C_{L}');


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Data Sheets:


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