advanced aerodynamics lab report

RMIT University School of Aerospace, Mechanical and Manufacturing Engineering

Advanced Aerodynamics Lab ReportAERO2358Dr. John Watmuff

Andrew Pandelis 3378766Angus Muffatti 3330774Daniel Chadwick 3332866Isaiah Marquez 3378780Daniel D'Cruz 3298430

April 28 2014

1


Table of ContentsIntroduction...........................................................................................................................................3

Background Information........................................................................................................................4

Theoretical Estimates Calculations........................................................................................................8

Description of Apparatus.....................................................................................................................14

Experimental Procedures....................................................................................................................18

Experimental forces and moments......................................................................................................23

Cm vs Alpha.........................................................................................................................................35

Cm vs Del E..........................................................................................................................................42

Experimental Vs Theoretical................................................................................................................50

Discussion............................................................................................................................................51

Conclusion...........................................................................................................................................52

References...........................................................................................................................................53

2


INTRODUCTION

A model of the P-51D aircraft was tested in the RMIT wind tunnels, using the

experimental values obtained, this report will detail the configurations of the model aircraft

and quantify the experimental values of certain longitudinal stability derivatives.

The main objective of this laboratory demonstration is to compare the theoretical and

experimental estimates of certain longitudinal stability derivatives with an aim to predict the

motion history of the pitch-constrained scale wind-tunnel model of the P-51D

An aircraft's stability is expressed in relation to each axis: lateral stability - stability in roll,

directional stability - stability in yaw and directional stability - stability in pitch. Lateral and

directional stability are interdependent and thus the most important is the longitudinal

stability.

The longitudinal stability of an aircraft refers to the pitching plane's stability; this

plane describes the position of the aircraft's nose in relation to its tail in the horizon. If an

aircraft is longitudinally stable, a small increase in the angle of attack will cause the pitching

moment on the aircraft to change so that the angle of attack decreases. Similarly, this also

works backwards where if the angle of attack decreases even slightly, this will cause the

pitching moment to change so that the angle of attack increases.

The pitch moment works in conjunction with the elevator, angle of attack and the rate of

pitch. This simply means that stability will be affected from any variations of those

components.

A slight change in certain factors such as airspeed (u0), pressure (Q), wing's surface area (S),

mean aerodynamic chord (c ¿ can all affect the pitch moment and therefore alter an aircraft's

longitudinal stability.

3


BACKGROUND INFORMATION

P-51D

The P-51 Mustang was American long-range fighter jet. It was designed and created

by North American Aviation by the request of the British Purchasing Commission. This

fighter-bomber took its first flight on the 26th October 1940. The P-51 was originally

designed to have an AllisonV-1710 engine; however, with this engine limiting the aircrafts

high altitude performance the Rolls Royce Merlin was fitted for both the P-51B and the P-

51C models, which drastically improved the high altitude performance. The iconic P-51D

utilized the Packard V-1650-7 engine, which was merely a license-built version if the Rolls

Royce Merlin. The P-51D was armed with six .50 calibre M2 Browning machine guns which

is a weapon still used on today’s fighter jets.

P-51D Specifications

First Flight May 20, 1941

Wingspan 37 feet

Wing area 233 square feet

Length 32 feet

Horizontal Stabilizer Span 13 feet

Height 8 feet and 8 inches

Power Plant Packard V-1650 "Merlin" with 1,695-hp V-12

Speed 437 mph

Landing Gear Hydraulically operated

Propeller Hamilton Stanford, four blade. 11 feet and 2 inches

Maximum Take-off Mass 12, 100 lbs

Cruise Speed 275 mph

Stall Airspeed (flaps up, down) 95 mph, 102 mph

Range 1650 miles

Maximum Altitude (Ceiling) 41, 900 feet

Table 1: P-51D Specifications

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The P-51 mustang is the answer to the allies’ need of an effective bomber escort, with

the assistance of external fuel tanks, its impressive ability for reasonably long range flight

could accompany bombers all the way to Germany and back. It wasn’t long before it was

evident that the P-51 was far superior to the older P-47 and by the end of 1944, the mustang

was utilized by 14 out of the 15 thunderbolt and lightning groups. From a more technical

perspective, the U.S air force flight test engineers concluded that "The rate of climb is good

and the high speed in level flight is exceptionally good at all altitudes, from sea level to

40,000 feet. The airplane is very manoeuvrable with good controllability at indicated speeds

to 400 MPH. The stability about all axes is good and the rate of roll is excellent, however, the

radius of turn is fairly large for a fighter. The cockpit layout is excellent, but visibility is poor

on the ground and only fair in level flight." This plane dominates at a deadly pace and an

unparalleled manoeuvrability that made it a crucial asset not only to the United States, but

also to many allied forces.

Figure 1: North-American P-51 Mustang

The United Kingdom where the first to operate this historical aircraft with the

Mustang Mk I entering service in 1941, however, having the altitude issues at this time the

aircrafts where only operated by Army Co-operation command and where not used by

Fighter command until 1942 where they undertook their first reconnaissance mission over

Germany. It wasn’t until late 1943 when the English started using their vast amount of P-

51Bs and P-51Cs, which were known to the Royal Air Force (RAF) as Mustang Mark IIIs.

5


France first started incorporating the P-51 mustangs in their Tactical Reconnaissance

Squadron for various photograph-mapping missions over Germany. These planes stayed in

service until the early 1950s.

Figure 2: P-51D Side View

The Chinese nationalist air force used the P-51 during the war against Japan in the

later part of the Sino-Japanese war. They continued to use them against communist rebels,

however where overpowered and where required to retreat to Taiwan in 1949. Pilots that

where still loyal to the nationalist forces transported most of the mustangs to Taiwan where

they were used primarily for defence.

This ionic plane was revolutionary to say the least having moulded history with its incredible

abilities. The P-51 Mustang was not only one of the greatest aviation and engineering

achievements in history, but it also set the bar for future generations of fighter jets.

6


TABLE OF ACRONYMS

AR Aspect Ratio

CoM Centre of Mass

EoM Equations of Motion

PID Proportional-Integral-Differential (Pitch Controller)

USAAF United States of America Air Force (WWII Acronym)

USB Universal Serial Bus

PWM Pulse Width Modulation

TABLE OF NOMENCLATURE

α Angle of attack

δ Angular displacement of control surface

θ, ϑ Pitching angle

∆θ& Rate of change of pitch angle

∆q& Rate of change of pitch

E Elevator component ( δ E represents elevator deflection)

b Wingspan

c Mean aerodynamic chord

CLWB Wing Body lift coefficient

CLT Tail lift coefficient

CM Pitching moment coefficient

CMα Coefficient of pitching moment due to angle of attack

CM q Coefficient of pitching moment due to pitch rate

CM δ E Coefficient of pitching moment due to elevator deflection

M α Pitching moment due to angle of attack

M q Pitching moment due to pitch rate

Mδ E Pitching moment due to elevator deflection

q Dynamic Pressure

S Surface Area of main wing

u0 Incident airspeed generated by wind tunnel

VH Vertical tail volume coefficient

Iyy Second inertial moment of area

7


THEORETICAL ESTIMATES CALCULATIONS

The longitudinal derivatives theoretically are a major necessity for comparison and testing the

accuracy of the practical experiment and overall determination of the aircrafts longitudinal

aerodynamic features. In order to achieve this we calculated the various Moments using data

from the CAD model as well as theoretically estimated some of the other features. Our

primary aim was to calculate the Mα, Mq & MδE.

Figure 3: P-51D CAD model

The data from the CAD model were measured for various magnitudes and tabulated along

with its Inertia Along the 3 axes. This made our calculations easier as getting our primary

data was not a problem. And working backwards from our final derivate formulas, we were

able to establish the various longitudinal stability derivatives.

Recorded Data

8


Quantity Value Units

Mean aerodynamic chord, c 0.0704715 m

Distance from CG to AC of tail, lt 0.1423064 m

XAC0.0176179 m

XCoM0.0232556 m

Wing area, S 0.02828 m2

Tail area, St 0.005478 m2

Horizontal tail volume coefficient, VH 0.3911593

Elevator area 0.002619 m2

Area fixed horizontal stab 0.002859 m2

Aspect ratio AR 5.6944584

Moment of inertia about y axis Iyy0.0015233

Change in downwash to AoA d3/da 0.4079202

Air density rho 1.225 Kg/m3

dCLt/dδE2.8207997

Flap effectiveness parameter, τ 0.65

Elevator (control surface area / lifting surface area) 0.4780942

Root chord 0.099745 m

Tip chord 0.045376 m

Taper ratio 0.45492005

Tail span 0.13548 m

Span b 0.401297 m

Chord tail 0.04043401 m

Flight speed, u035 m/s

Cl α wing4.58 /rad

Clα tail5.73 /rad

CmδE-0.99304377

Efficiency factor of tail η 0.9

Cmq -6.17015456

CL α wing 3.64877822/rad

CLα tail 4.3396918/rad

Cmα-0.61265343

Mw -17.1830211 m/s

9


Dynamic pressure Q 750.3125 Pa

Mα -601.405739 s2

Mq -6.09767391 s

MδE -974.812502 s2

Table 2: Quantity Values

Recorded Data 2

Location with respect to the CoM (m)

Mass Element Mass (kg) X Y Z Component of inertia

Servo 0.008 -0.025 0 0.027 1.08E-05

Ballast 0.048 0.055 0 0 0.00015

Spinner 0.05 0.115 0 0 0.00066

Top Half 0.17293 -0.0038 0 0.00232 3.37E-06

Bottom Half 0.08223 0.01829 0 0.01039 3.64E-05

Top fuselage 0.04918 0.03128 0 -0.0177 6.36E-05

Horizontal

Stabilizer

0.01174 -0.1493 0 -0.0248 0.000269

Elevator 0.00379 -0.1731 0 -0.2414 0.000334

Total Mass 0.42586 Value used in calculation Iyy = 0.00152

Center of Rotation (CoR) 0.02432 0 -0.0054 IyyCoR = 0.00179

Table 3: Mass Element table

Calculations

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1) Pitching Moment due to change in ‘α’ (M α).

M α=u0 M w

Where,

U0 = Flow Velocity

Mw= Downward velocity Pitching Moment

M w=CM α

Q∗S∗cu0∗I yy

CM α=Pitching Moment Coefficient due ¿change∈ Angle of Attack (α )

c=Mean Aerodynamic Chord

S = Area of Wing Body

Iyy= Moment of Inertia about the Y axis

Q = Dynamic Pressure

CM α=CLαwing( XCoM

c−

X Ac

c )+Cmαfus−η V H CLαTail(1− dε

dα )

CLαwing=Coefficient of Lift of the wing (3 D )

CLαTail=Coefficient of Lift of the tail(3 D)

η = Tail Efficiency

V H=TailVolume Ratio=ltail S tail

Swingc

11


Stail = Tail Area

ltail = the distance from the Pivot point to the aerodynamic centre of the tail

For the 3D coefficient of lift for the wing and tail the formula is similar,

CLαwing=

C lαwing

1+C lαwing

πAR

From utilizing the above formulae and data from the table we were able to calculate the

pitching moment due to change in Angle of Attack (α).

2) Pitching Moment Due to Pitch Rate (Mq)

M q=Cmq

c2u0

(QS c )/I yy(s−1)

Cmq=−2η CLαTail

V H

lTail

c

3) Pitching Moment Due to Elevator Deflection

12


M δE=Cmδ

E

QS cI yy

(s−2 ¿

CmδE

=−η V H

dCLTail

d δE

d C LTail

d δE

=τ CLαTail

Where, τ , is the flap effectiveness parameter

Calculated Pitch Moments

Flow Velocity 15 m/s

M α -110.462279 /s2

M q -2.61328882 /s

M δE-179.047194 /s2

Flow Velocity 25 m/s

M α -306.839663 /s2

M q -4.35548136 /s

M δE-497.353318 /s2

Flow Velocity 35 m/2

M α -601.405739 /s2

M q -6.09767391 /s

M δE-974.812502 /s2

Table 4: Pitch Moment Answers

DESCRIPTION OF APPARATUS

13


Wind Tunnel

The wind tunnel provided by RMIT that was used in the lab test had a test section of 2m wide

x 1.6m long. This wind tunnel is capable of producing wind speeds of up to 150 km/hr.

Figure 3: Wind Tunnel Test Section

The wind tunnel used in RMIT is a closed loop wind tunnel; in a closed-loop wind tunnel,

the moving air is brought back to the fan and is continuously re-circulated through the tunnel.

A close-looped tunnel efficiently produces long test times.

Figure 4: Closed Loop Wind Tunnel

Force Balance

14


The Force/Torque: Nano17 titanium sensor is a 6-axis sensor that is capable of measuring the

forces and moments with 6 degrees of freedom. In our case the force balance will be

measuring the forces in the X, Y, Z directions and also the moments, which will produce the

data as a time series to a connected computer.

Figure 5:Force balance on test model Figure 6: Force Balance

Wing-tip Potentiometer

The potentiometer is connected to the pivot shafts that are connected to the wing tips; these

constrain the model to rotate about the y-axis/pitch axis. The potentiometer, which is a

rotational variable resistor, is being used to determine the pitch angle in response to elevator

deflection. The output voltage from this device is converted to pitch angle using a simple

voltage divider rule.

Figure 7:Potentiometer coupled to the wing tip

Microcontroller

15


The Arduino microcontroller takes an input signal from the user, which in this case, is the

desired pitch angle via a control. This is then converted to a signal with a proportion to the

difference between the current pitch angle and the desired pitch angle. The microcontroller

has a proportional-integral-derivative (PID) controller implemented in the on-board software;

the output signal of this controller is the required servo angle, θservo, in degrees. A second

software function converts this into a pulse width modulation (pwm) signal required for the

servo input.

Figure 8: Arduino Microcontroller

Servo and Control Rod

The servo is responsible for deflecting the elevator using the control rod; the amount of

deflection required is determined by the pulse width modulation signal, which is received

from the microcontroller.

Figure 9:Control connection to elevator Figure 10: Location of servo

16


Model Pitch Constraining Rig

The constraining rig is a vital part of this experiment as it ensures that there is a stable base in

order to yield better accuracy of the results. The potentiometer and wingtips are connected to

the structure as seen in figure 11 below.

Figure 11: Pitch constraining rig

Rod Support

The rod support ensures the model has a stable base and is fixed in the rig to eliminate any

discrepancies in the data that will be generated. The rod support has a pivot point so that the

angle of attack can be altered in order to obtain the forces acting on the aircraft at multiples

angles of attack.

Figure 12: Support rod Pivot Point

17


EXPERIMENTAL PROCEDURES

1. Ensure the model, P-51, is mounted to the force balance using a short rod. This device

allows for the measurement of both forces and moments, three of these being components of

forces applied to the plane and the other three being components of moment applied. Mount

the complete assembly on an adjustable sting, which will allow for a variation in the angle of

attack.

2. The rods that are connected to each of the ends of the wings allow the model plane to

rotate about the y-axis. A rotational variable resistor known as a potentiometer that is

connected to either one of the rods, which is also connected to the wings, measures this

rotation. By using the voltage divider rule the pitching angle can be derived by using the

voltage output of the potentiometer. With the potentiometer determining the current pitching

angle of the P-51, the microcontroller will determine the error signal between the desired

pitch angle and the actual pitch angle, this in turn will be sent to the PID controller. The

readings calculated by the PID controller are directly proportional to the commanded servo

angle θservo (degrees). Other software, which is also on-board the microcontroller allows the

servo angle to be converted to what is known as servo pulse width modulation signal. This is

the procedure required for operating the servo.

3. After ensuring that all the electronics are working correctly, a serial interface program will

be used connected to the assembly. Enter the desired pitch angle and the computer will send

this command through the microcontroller via USB.

4. All six components (forces and moments) are logged in a time series. Having many values

for all six components allows for the calculation of an average magnitude for the six forces

and moments acting on the plane.

5. Transducers are susceptible to high frequency electronic noise and drift. Both these

phenomena can interfere with result so precautions must be taken. To guarantee that these

two things do not hinder our results, samples of the force balance readings must be taken

without any wind and without any load being applied to the model. (The procedure to solve

the problems with wind can be seen in the workings below) Subtracting these wind-off forces

will account for the effects of drift.

18


Factors Affecting Quality

Flow quality

Over the course of this testing there are some factors that may affect the accuracy and

precision of our results. One of the hardest to sources of error to measure is the quality of the

laminar flow in the test section. Closed-loop wind tunnels are capable of producing flow with

turbulent flow percentage between 0.5-2% (Advanced thermal solutions, 2012) which is

relatively low in low speed wind tunnels. This turbulent flow would affect the test results

marginally, but not to a degree that would significantly alter the measurements.

Figure 13: Schematics of wind tunnel with turbulence reducing design

(advanced thermal solutions, 2012)

19


Equipment calibration

The measuring equipment may be a source of error if the devices are poorly calibrated or

have a manufactured systematic error. The F/T: Nano17 Titanium sensor has the ability to

resolve down to a 0.149 gram-force and near-zero noise distortion (ATI Industrial

Automation, 2014), which will give a reasonably accurate result given that it is in perfect

working order.

Linkage

A major part of the results is based on the elevator deflection, which is controlled by a very

simple mechanical link. Ensuring this link produces input angle before the test will eliminate

this as a potential source of error.

Low Reynolds Number – Trip wire

Due to the low speed of the wind tunnel and the small scale of our model it is very difficult to

replicate the Reynolds number of the full size aircraft. Different methods have been used to

try replicating the flow separation in small-scale tests by attaching a boundary layer leading-

edge trip to increase the boundary layer thickness. This trip will allow a boundary layer

transition to turbulent flow at relatively low speeds (Rona & Soueid, 2010). Common trips

that have been tested are sandpaper, silicon granules and a trip wire. In this test a trip-wire

has been used which will increase Reynolds number, which will result in a closer replication

of the flow over a full-scale aircraft at high speeds. If the trip wire is not set up correctly and

too much turbulent flow is produced, this may affect the measurements due to the turbulent

flow altering the forces acting on the wing altering the actual aerodynamic forces of the

aircraft.

20


Drift

The force balance also suffers from a problem known as drift, this occurrence is discussed

further when the mean and RMS values are calculated and how to eliminate drift as a source

of error. Table 2 shows the average values for the measurements with the wind off, in theory

these values should remain constant if the conditions are unchanged. As shown in Table 2 the

values vary which suggests that the position or orientation of the model may have been

slightly altered, to take this into account as a possible source of error in the measured

calculations a 95% confidence interval has been calculated. Therefore when the drift is being

eliminated, to obtain maximum accuracy this confidence interval should be noted. In this case

we are only focussing on the moment about the Y-axis (pitching moment) which has a

relatively low confidence interval that would not cause significant error in our measurements

therefore it can be ignored.

Wind Off

Force X

direction

Force Y

direction

Force Z

direction

Moment about

the X-axis

Moment about

the Y-axis

Moment about

the Z-axis

Test 1 0.028310041 0.01811601 0.089125675 -0.000552377 -5.48427E-05 0.000235214

Test 2 0.011644781 -0.004370597 0.13265941 0.000102094 0.000588598 0.000752102

Test 3 0.028310041 0.01811601 0.089125675 -0.000552377 -5.48427E-05 0.000235214

Test 4 0.011644781 -0.004370597 0.13265941 0.000102094 0.000588598 0.000752102

Average 0.019977411 0.006872707 0.110892543 -0.000225141 0.000266878 0.000493658

Stdev 0.009621692 0.012982649 0.025134214 0.000377859 0.000371491 0.000298425

Confidence

Interval ± 0.02886508 ± 0 .038947946 ± 0.075402641 ± 0.00113358 ± 0.001114472 ± 0.00089528

Table 5: Repeat test data for wind off condition

21


Repeatability

Repeatability is the ability to repeat the same measurements under certain conditions. These

repeatability conditions state that the same operator must take the measurements in the same

lab, same equipment and procedure (Pandiripalli, 2010). The overall repeatability of the test

cannot be calculated due to their being two different conditions, wind on and wind off. The

repeatability of these two conditions is directly related to the standard deviation between the

repeat tests, the confidence interval calculated for each independent force using a significance

level of 0.95 meaning 95% of the data will lie between these intervals. Table 1 shows the

average force plus or minus the confidence interval for the four repeat tests, the measurement

that is the main focus of this test is the moment about the Y-axis which has a relatively large

confidence interval. Due to the small scale of this test this interval should be taken into

account. The 95% interval is represented graphically in Figure 2 as a normal distribution

curve, with the values at each standard deviation presented in Table 3.

Wind On

Force X

direction

Force Y

direction

Force Z

direction

Moment about

the X-axis

Moment about

the Y-axis

Moment about

the Z-axis

Test 1 -0.330904586 0.043191308 6.051690684 0.012199536 -0.038229987 -0.001598755

Test 2 -0.32691614 0.043309695 6.007004294 0.012077555 -0.042624876 -0.001773912

Test 3 -0.352473091 0.016492863 6.080261077 0.013739574 -0.041933998 -0.001276483

Test 4 -0.329133144 0.03064805 6.146087448 0.014662234 -0.026099067 -0.00142624

Average -0.33485674 0.033410479 6.071260876 0.013169725 -0.037221982 -0.001518848

Stdev 0.011857038 0.012747494 0.05828642 0.001249855 0.007662238 0.000215066

Confidence

Interval ± 0.035571113 ± 0.038242483 ± 0.17485926 ± 0.003749565 ± 0.022986714 ± 0.000645197

Table 6: Repeat Data for Wind On Condition

22


Standard Deviation Score Normal Distribution

-4 -0.067870934 0.017466206

-3.5 -0.064039815 0.11389397

-3 -0.060208696 0.578401304

-2.5 -0.056377577 2.287621533

-2 -0.052546458 7.046370391

-1.5 -0.048715339 16.90336384

-1 -0.04488422 31.57964116

-0.5 -0.041053101 45.94810677

0 -0.037221982 52.06602611

0.5 -0.033390863 45.94810677

1 -0.029559744 31.57964116

1.5 -0.025728625 16.90336384

2 -0.021897506 7.046370391

2.5 -0.018066387 2.287621533

3 -0.014235268 0.578401304

3.5 -0.010404149 0.11389397

4 -0.00657303 0.017466206

Table 7:Normal Distribution of Wind on Repeat Data for the Moment about the Y-axis

-0.08 -0.07 -0.06 -0.05 -0.04 -0.03 -0.02 -0.01 0

Figure 14: 95% confidence interval for moment about the Y-axis

23


EXPERIMENTAL FORCES AND MOMENTS

Mean

In order to simplify data and make it more user friendly, we firstly have to find the mean

(average) of the data. The force balance used for the experiment measures the data repeatedly

and shows all of the fluctuations that occur during that time. Hence, taking the mean should

provide an estimate as to what the average forces are, during that time interval for the set

angle of attack or elevator angle. In order to do this we went about calculating the area using

the trapezoidal rule and dividing it into 473 equal parts. This was then compared to the mean

using the standard method and further checked for accuracy.

To calculate the trapezoidal area we first need to get our step size, this is done using the

formula:

∆ x=b−an

Where, b = last recorded data point

a= initial recorded data point

n=number of strips

After getting our step size we then using the trapezoidal rule formula and calculate the area

under our data curve.

∆ x2

¿

24


Once the area is calculated we can derive our mean by simply dividing the area and by taking

away one from the number of recorded data.

Mean= AreaN−1

RMS

The Root Mean Square (RMS), also known as the quadratic mean, is the average calculated

when the data set has a lot of fluctuations. Especially when the data moves between the

positive and negative during measurement, like a sinusoidal wave. In order to calculate the

RMS of our data we used a simple and effective RMS formula:

RMS=√ f x02+f x1

2+ f x22+…+ f xn

2

Number of Data Recorded

Drift and Noise

The calculations need to be altered with respect to drift as there could be existing drift or

noise within the wind tunnel prior to the commencement of the experiment.

These factors always interfere with the integrity of the data tabulated at the end of the

experiment. To get rid of drift and noise effects the force balance measurements were

recorded before and after the experiment, i.e.,

Factual=FWind on−FWind off

The same method was carried out to calculate the actual moments as well

M actual=M Wind on−M Wind off

25


Data Quality

Data quality measurements were done in order to check how far our actual values are from an

acceptable range. Dividing the RMS over the Mean enabled us to acquire a more accurate

data quality. The data that equates closer to 1 are presumed to be relatively good and

acceptable for the experiment.

Data Quality= RMSMean

Angle of

Attack

Data Mean

(off)

RMS

(off)

Mean

(on)

RMS

(on)

Quality

(off)

Quality

(on)

0.3

Fx-0.04698568 0.056586246 -0.86364647 0.86641658 -1.20432956 -1.00320745

Fy -0.0377554 0.04402959 -0.06033362 0.144103345 -1.16617993 -2.38844152

Fz -0.0712203 0.104596631.99054702

51.992968121

-1.46863506 1.001216297

Tx 0.000333473 0.0010584630.01267159

90.018842226

3.174059069 1.486965141

Ty 0.000420925 0.000788686 -0.12032226 0.120494425 1.873697214 -1.00143081

Tz -0.00038261 0.000520769 -4.59E-07 0.007736779 -1.36108904 -16853.2308

Table 8: Data Quality Example

The discrepancies in the data quality at certain spots are due to fluctuations within the wind

tunnel and at some spots, this obviously have affected the quality of the data significantly.

26


Calculated Data

1. Varying Angle of Attack

Angle of Attack

Data Mean (off) RMS (off) Mean (on) RMS (on)

0.3

Fx -0.046985682 0.056586246 -0.863646472 0.86641658

Fy -0.0377554 0.04402959 -0.060333629 0.144103345

Fz -0.0712203 0.10459663 1.990547025 1.992968121

Tx 0.000333473 0.001058463 0.012671599 0.018842226

Ty 0.000420925 0.000788686 -0.120322266 0.120494425

Tz -0.000382612 0.000520769 -4.59E-07 0.007736779

2

Fx -0.039902846 0.051963012 -0.7455381 0.75232132

Fy -0.00127395 0.023820056 0.00380132 0.1324861

Fz -0.134750391 0.151481552 3.29663982 3.29820294

Tx 0.000772268 0.001116131 0.01217275 0.01813789

Ty 0.000712018 0.000876288 -0.097375 0.09790305

Tz -0.000395264 0.000497702 -0.0005264 0.01098305

4

Fx 0.00970643 0.03441805 -0.4959374 0.50457367

Fy -0.0384456 0.04685305 -0.0250547 0.15027446

Fz -0.0496022 0.0936422 5.03348321 5.0344938

Tx 0.00503905 0.00531427 0.01775956 0.02372547

Ty 0.00139994 0.00176525 -0.0611797 0.06181862

Tz 0.00075454 0.00087879 -0.0006363 0.00992038

27


6.1

Fx 0.06930005 0.07731067 -0.1737987 0.19097755

Fy 0.03786172 0.04592361 0.05395597 0.12826804

Fz 0.07080594 0.10820409 6.75249412 6.76744398

Tx 0.00171086 0.00190003 0.01463158 0.0190158

Ty 0.00158878 0.0016895 -0.0227462 0.02396071

Tz 0.00054562 0.00065273 -0.0016704 0.01158755

8

Fx -0.0577762 0.06579474 -0.0111083 0.08074491

Fy -0.0314337 0.03867139 -0.017648 0.1708552

Fz 0.07712771 0.10820007 8.08488351 8.08555758

Tx 1.01E-05 0.00081256 0.01193277 0.02117678

Ty 8.43E-05 0.00047487 0.01401353 0.01588458

Tz 0.00028783 0.00043184 -0.0020258 0.01497464

10

Fx -0.0191087 0.04283723 0.35537997 0.36145426

Fy 0.0780545 0.0816325 0.08356053 0.15032691

Fz 0.13735282 0.15809701 9.3439296 9.34433181

Tx -0.0042268 0.00437825 0.00484711 0.0134266

Ty -0.0069322 0.00727058 0.05318312 0.05357541

Tz -0.000387 0.00053974 -0.0017549 0.01319431

Table 9: Calculated Data for Varying AoA

2) Elevator angle changing with Angle of attack at 0.3 degrees

28


Elevator Data Mean (off) RMS (off) Mean (on) RMS (on)

0

Fx 0.03512613 0.04576137 -0.7829603 0.78630889

Fy 0.04554277 0.05102774 0.0428672 0.13508016

Fz 0.11338087 0.14356424 2.21199777 2.21425332

Tx 0.00112758 0.00150574 0.01229549 0.01844999

Ty -0.00035 0.00079623 -0.0995397 0.09976264

Tz 0.00050895 0.00064533 0.00114523 0.00840498

4.1

Fx -0.0493484 0.06020544 -0.8453816 0.84890488

Fy -0.0340282 0.0424589 -0.0060608 0.1179919

Fz 0.13315176 0.15636052 2.08005206 2.08257864

Tx 0.00087366 0.00113107 0.010301 0.01634015

Ty 0.00011817 0.00061978 -0.1456107 0.14576766

Tz 0.00062057 0.000716978 0.00204854 0.0073027

4.3

Fx -0.0407299 0.05169733 -0.7910104 0.79470157

Fy -0.0125647 0.02512264 0.03036458 0.13653872

Fz 0.14901834 0.17167739 2.46986723 2.47201407

Tx -0.0003523 0.00104628 0.01321421 0.01935803

Ty 0.00033702 0.00064467 -0.0568792 0.05728723

Tz 0.00039439 0.00055521 7.34E-05 0.00905867

7.9 Fx -0.0493484 0.06020544 -0.9281221 0.93231398

29


Fy -0.0340282 0.0424589 -0.0225814 0.11586053

Fz 0.13315176 0.15636052 1.81967054 1.82238895

Tx 0.00087366 0.00113107 0.00780928 0.01431143

Ty 0.00011817 0.00061978 -0.2060659 0.20620386

Tz 0.00062057 0.00071697 0.004438 0.0077539

8.9

Fx -0.0408584 0.05169733 -0.8159015 0.82003421

Fy -0.0126044 0.02512264 0.04015511 0.12905737

Fz 0.14948843 0.17167739 2.69483299 2.69665155

Tx -0.0003534 0.00104628 0.01500936 0.01990107

Ty 0.00033808 0.00064467 -0.0010192 0.0076689

Tz 0.00039563 0.00055521 -0.0004393 0.01048086

11.5

Fx -0.0493484 0.06020544 -0.9580186 0.96148289

Fy -0.0340282 0.0424589 -0.0310396 0.11829027

Fz 0.13316176 0.15636052 1.73085563 1.73354375

Tx 0.00087366 0.00113107 0.00746893 0.01447754

Ty 0.00011817 0.00061978 -0.2228302 0.2229376

Tz 0.00062057 0.00071697 0.00564332 0.01110972

13.6

Fx -0.0407299 0.05169733 -0.8641081 0.86772956

Fy -0.0125647 0.02512264 0.05001416 0.11093155

Fz 0.14901834 0.17167739 2.90774062 2.90915024

Tx -0.0003523 0.00104628 0.01729261 0.02029803

Ty 0.00033702 0.00064467 0.04651304 0.04698827

Tz 0.00039439 0.00055521 -0.0013357 0.00708795

14.8Fx -0.0493484 0.06020544 -0.996548 1.00106449

Fy -0.0340282 0.0424589 -0.0315008 0.11737656

30


Fz 0.13315176 0.15636052 1.63913017 1.64241703

Tx 0.00087366 0.00113107 0.00630117 0.01339783

Ty 0.00011817 0.00061978 -0.2447933 0.24493561

Tz 0.00062057 0.00071697 0.00618468 0.01007277

18.7

Fx -0.0408584 0.05169733 -0.9184086 0.92117253

Fy -0.0126044 0.02512264 0.06040042 0.13962282

Fz 0.14948843 0.17167739 3.03044543 3.03191905

Tx -0.0003534 0.00104628 0.01918841 0.02359609

Ty 0.00033808 0.00064467 0.07384452 0.07410657

Tz 0.00039563 0.00055521 -0.0023338 0.00787925

Table 10: Calculated Data for Varying Elevator Angle

3) Changing Elevator angle with Angle of attack at 5 degrees

31


Elevator Data Mean(off) RMS(off) Mean(on) RMS(on)

0

Fx 0.028310588 0.041705156 -0.330539026 0.339681554

Fy 0.018105813 0.028856354 0.04290192 0.13959575

Fz 0.088949966 0.120748577 6.04528698 6.04607779

Tx -0.00055348 0.000920942 0.012207862 0.01876994

Ty -0.000055608 0.000530156 -0.03819059 0.0388994

Tz 0.00023442 0.00041986 -0.0016076 0.00945575

4.1

Fx 0.028311 0.041705156 -0.356914008 0.365699436

Fy 0.18105813 0.028856354 0.03808199 0.123876106

Fz 0.088949966 0.120748577 5.872540547 5.873376289

Tx -0.00055348 0.000920943 0.010761499 0.016568039

Ty -5.56078E-05 0.000530156 -0.079841238 0.080209588

Tz 0.000234422 0.000419863 -0.000746881 0.010392749

4.3

Fx 0.1169757 0.036205282 -0.332185476 0.344261675

Fy -0.004327195 0.02622378 0.027164674 0.138342589

Fz 0.132410516 0.154919326 6.315984361 60316953397

Tx 0.001019954 0.001303715 0.015737618 0.021293423

Ty 0.000586904 0.00078367 0.01975302 0.021737681

Tz 0.000750898 0.000820002 -1.87E-03 0.012759533

7.9 Fx 0.028310588 0.041705156 -0.428069526 0.43647113

32


Fy 0.018105813 0.028856354 0.029704462 0.171277906

Fz 0.088949966 0.120748577 5.695981966 5.6965422

Tx -0.00055348 0.000920942 0.008059964 0.019769977

Ty -0.000055608 0.000530156 -0.126621632 0.126914942

Tz 0.000234422 0.000419863 0.000711753 0.011646944

8.9

Fx 0.01169757 0.036205282 -0.359832764 0.365097271

Fy -0.004327195 0.02622378 0.035400788 0.126062263

Fz 0.132410516 0.154919326 6.540855106 6.541695393

Tx 0.001019954 0.001303715 0.018718713 0.022557673

Ty 0.000586904 0.00078367 0.073840275 0.074088236

Tz 0.000750898 0.000820002 -0.002806726 0.012932775

11.5

Fx 0.028310588 0.041705156 -0.48315371 0.492293637

Fy 0.018105813 0.028856354 0.018549877 0.158813282

Fz 0.088949966 0.120748577 5.554766432 5.555515627

Tx -0.00055348 0.000920942 0.007614651 0.018069708

Ty -5.5608E-05 0.000530156 -0.154686987 0.15497725

Tz 0.000234422 0.000419863 0.002747951 0.008702491

13.6 Fx 0.01169757 0.036205282 -0.408581615 0.414571547

33


Fy -0.004327195 0.02622378 0.042747953 0.137872495

Fz 0.132410516 0.154919326 6.726861823 6.727623793

Tx 0.001019954 0.001303715 0.020473033 0.024509457

Ty 0.000586904 0.00078367 0.120401259 0.120562529

Tz 0.000750898 0.000820002 -0.003760003 0.010750215

14.8

Fx 0.028310588 0.041705156 -0.503556902 0.513762972

Fy 0.018105813 0.028856354 0.013882405 0.141440815

Fz 0.088949966 0.120748577 5.498618464 5.499584926

Tx -0.00055348 0.000920942 0.007476593 0.016358228

Ty -5.5608E-05 0.000530156 -0.166280013 0.166599125

Tz 0.000234422 0.000419863 0.003090666 0.011894883

18.7

Fx 0.01169757 0.036205282 -0.46725399 0.473279577

Fy -0.004327195 0.02622378 0.049947956 0.1455884

Fz 0.132410516 0.154919326 6.886474671 6.887204829

Tx 0.001019954 0.001303715 0.022410034 0.026554173

Ty 0.000586904 0.00078367 0.147625607 0.14777559

Tz 0.000750898 0.000820002 -0.004694543 0.012022215

Table 11: Calculated Data for Changing Elevator Angle

CM VS ALPHA

34


Resolving and rotating data

The location of the force balance must be taken into account when analysing the data to

ensure the pitching moment used in the calculations is about the CG. Resolving the forces

and moments back to the CG involves a simple translational matrix.

Figure 15:Force balance with respect to CG

Using the measurements in the above diagram the general transformation matrix can be

formed and be applied to the data.

35


[M x

M y

M z]

cg

=[M x

M y

M z]fb

−[−0.00550

0.095 ]×[Fx

F y

F z]

The force balance has been setup in such a way that it rotates with the rod when the angle of

attack is altered. To account for this we have to rotate the axis to align it with the wind

direction with a rotational matrix.

Where α is the angle of attack

The calculations below for angle of attack 2 degrees, demonstrating the process used to

resolve and rotate all sets of data.

36


Resolving to CG using transformation matrix

[M x

M y

M z]

cg

=[ 0.01116791−0.09918970.00063628 ]

fb

−[−0.00550

0.095 ]×[−0.81808643−0.00267557

2.0986169 ]

Rotating to align with direction of the wind

[Fx

F y

F z]Wind

=[cos(2) 0 −sin(2)0 1 0

sin(2) 0 cos (2) ]×[−0.81808643−0.00267557

2.0986169 ]fb

Angle of Attack Force/Moment Raw Mean Force/Moment Rotated and

Resolved Mean

2

Fx -.81666079 Fx -1.389479758

Fy -.022578229 Fy -.022578229

Fz 2.061767325 Fz 1.728341792

Mx 0.012338126 Mx -.188021404

My -.120743191 My -.321102721

Mz 0.000382153 Mz -.199977377

Table 12: Rotated and Resolved Data for AoA 2 degrees

AoA(Deg

)Data Mean(off) RMS(off) Mean(on) RMS(on) Mean On - Off

37


0.3

Fx -0.0469857 0.05658625 -0.8636465 0.86641658 -0.81666079Fy -0.0377554 0.04402959 -0.0603336 0.14410335 -0.022578229Fz -0.0712203 0.10459663 1.99054703 1.99296812 2.061767325Tx 0.00033347 0.00105846 0.0126716 0.01884223 0.012338126Ty 0.00042093 0.00078869 -0.1203223 0.12049443 -0.120743191Tz -0.0003826 0.00052077 -4.59E-07 0.00773678 0.000382153

2

Fx -0.0399028 0.05196301 -0.7455381 0.75232132 -0.705635254Fy -0.001274 0.02382006 0.00380132 0.1324861 0.00507527Fz -0.1347504 0.15148155 3.29663982 3.29820294 3.431390211Tx 0.00077227 0.00111613 0.01217275 0.01813789 0.011400482Ty 0.00071202 0.00087629 -0.097375 0.09790305 -0.098087018Tz -0.0003953 0.0004977 -0.0005264 0.01098305 -0.000131136

4

Fx 0.00970643 0.03441805 -0.4959374 0.50457367 -0.50564383Fy -0.0384456 0.04685305 -0.0250547 0.15027446 0.0133909Fz -0.0496022 0.0936422 5.03348321 5.0344938 5.08308541Tx 0.00503905 0.00531427 0.01775956 0.02372547 0.01272051Ty 0.00139994 0.00176525 -0.0611797 0.06181862 -0.06257964Tz 0.00075454 0.00087879 -0.0006363 0.00992038 -0.00139084

6.1

Fx 0.06930005 0.07731067 -0.1737987 0.19097755 -0.24309875Fy 0.03786172 0.04592361 0.05395597 0.12826804 0.01609425Fz 0.07080594 0.10820409 6.75249412 6.76744398 6.68168818Tx 0.00171086 0.00190003 0.01463158 0.0190158 0.01292072Ty 0.00158878 0.0016895 -0.0227462 0.02396071 -0.02433498Tz 0.00054562 0.00065273 -0.0016704 0.01158755 -0.00221602

8

Fx -0.0577762 0.06579474 -0.0111083 0.08074491 0.0466679Fy -0.0314337 0.03867139 -0.017648 0.1708552 0.0137857Fz 0.07712771 0.10820007 8.08488351 8.08555758 8.0077558Tx 1.01E-05 0.00081256 0.01193277 0.02117678 0.011922685Ty 8.43E-05 0.00047487 0.01401353 0.01588458 0.013929261Tz 0.00028783 0.00043184 -0.0020258 0.01497464 -0.00231363

10

Fx -0.0191087 0.04283723 0.35537997 0.36145426 0.37448867Fy 0.0780545 0.0816325 0.08356053 0.15032691 0.00550603Fz 0.13735282 0.15809701 9.3439296 9.34433181 9.20657678Tx -0.0042268 0.00437825 0.00484711 0.0134266 0.00907391Ty -0.0069322 0.00727058 0.05318312 0.05357541 0.06011532Tz -0.000387 0.00053974 -0.0017549 0.01319431 -0.0013679

Table 13: Experimental Values for Cm vs Alpha

Moment Resolving Matrix

-0.0055 0 0.095

38


Angle (deg) Axis Rotation Matrix

0.3

0.95533649 0 -0.2955202

0 1 0

0.29552021 0 0.95533649

2

-0.4161468 0 -0.9092974

0 1 0

0.90929743 0 -0.4161468

4

-0.6536436 0 0.7568025

0 1 0

-0.7568025 0 -0.6536436

6.1

0.98326844 0 0.1821625

0 1 0

-0.1821625 0 0.98326844

8

-0.1455 0 -0.9893582

0 1 0

0.98935825 0 -0.1455

10

-0.8390715 0 0.54402111

0 1 0

-0.5440211 0 -0.8390715

Real Force Values

AoA (Deg) Data Real Force (N) unit coefficients value

39


0.3

Drag -1.389479758 N cd -0.1327918Fy -0.022578229 N

Lift 1.728341792 N cl 0.16517659L (moment) -0.188021404 Nm

M (moment) -0.321102721 Nm Cm -0.4354611N (moment) -0.199977377 Nm

2

Drag -2.826506411 N cd -0.2701275Fy 0.00507527 N

Lift -2.069594502 N cl -0.1977899L (moment) -0.318462582 Nm


4

Drag 4.177402586 N cd 0.39923187Fy 0.0133909 N



6.1

Drag 0.978121723 N cd 0.09347851Fy 0.01609425 N



8

Drag -7.929329419 N cd -0.7578013Fy 0.0137857 N



10 Drag 4.694349346 N cd 0.44863616Fy 0.00550603 N



Plot of Cm vs Alpha

40


0 2 4 6 8 10 12

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

f(x) = − 0.0696007404818489 x − 0.442223029527592

Series2Linear (Series2)

From the graph above Cm_alpha = - .0696

CM VS DEL E

41


Elevator Data Mean(off) RMS(off) Mean(on) RMS(on) Mean(on-off)

0

Fx 0.03512613 0.04576137 -0.7829603 0.78630889 -0.81808643Fy 0.04554277 0.05102774 0.0428672 0.13508016 -0.00267557Fz 0.11338087 0.14356424 2.21199777 2.21425332 2.0986169Tx 0.00112758 0.00150574 0.01229549 0.01844999 0.01116791Ty -0.00035 0.00079623 -0.0995397 0.09976264 -0.0991897Tz 0.00050895 0.00064533 0.00114523 0.00840498 0.00063628

4.1

Fx -0.0493484 0.06020544 -0.8453816 0.84890488 -0.7960332Fy -0.0340282 0.0424589 -0.0060608 0.1179919 0.0279674Fz 0.13315176 0.15636052 2.08005206 2.08257864 1.9469003Tx 0.00087366 0.00113107 0.010301 0.01634015 0.00942734Ty 0.00011817 0.00061978 -0.1456107 0.14576766 -0.14572887Tz 0.00062057 0.00071698 0.00204854 0.0073027 0.00142797

4.3

Fx -0.0407299 0.05169733 -0.7910104 0.79470157 -0.7502805Fy -0.0125647 0.02512264 0.03036458 0.13653872 0.04292928Fz 0.14901834 0.17167739 2.46986723 2.47201407 2.32084889Tx -0.0003523 0.00104628 0.01321421 0.01935803 0.01356651Ty 0.00033702 0.00064467 -0.0568792 0.05728723 -0.05721622

Tz0.00039439

0.000555217.34E-05 0.00905867

-0.000321007

7.9

Fx -0.0493484 0.06020544 -0.9281221 0.93231398 -0.8787737Fy -0.0340282 0.0424589 -0.0225814 0.11586053 0.0114468Fz 0.13315176 0.15636052 1.81967054 1.82238895 1.68651878Tx 0.00087366 0.00113107 0.00780928 0.01431143 0.00693562Ty 0.00011817 0.00061978 -0.2060659 0.20620386 -0.20618407Tz 0.00062057 0.00071697 0.004438 0.0077539 0.00381743

8.9

Fx -0.0408584 0.05169733 -0.8159015 0.82003421 -0.7750431Fy -0.0126044 0.02512264 0.04015511 0.12905737 0.05275951Fz 0.14948843 0.17167739 2.69483299 2.69665155 2.54534456Tx -0.0003534 0.00104628 0.01500936 0.01990107 0.01536276Ty 0.00033808 0.00064467 -0.0010192 0.0076689 -0.00135728Tz 0.00039563 0.00055521 -0.0004393 0.01048086 -0.00083493

11.5 Fx -0.0493484 0.06020544 -0.9580186 0.96148289 -0.9086702Fy -0.0340282 0.0424589 -0.0310396 0.11829027 0.0029886

42


Fz 0.13316176 0.15636052 1.73085563 1.73354375 1.59769387Tx 0.00087366 0.00113107 0.00746893 0.01447754 0.00659527Ty 0.00011817 0.00061978 -0.2228302 0.2229376 -0.22294837Tz 0.00062057 0.00071697 0.00564332 0.01110972 0.00502275

13.6

Fx -0.0407299 0.05169733 -0.8641081 0.86772956 -0.8233782Fy -0.0125647 0.02512264 0.05001416 0.11093155 0.06257886Fz 0.14901834 0.17167739 2.90774062 2.90915024 2.75872228Tx -0.0003523 0.00104628 0.01729261 0.02029803 0.01764491Ty 0.00033702 0.00064467 0.04651304 0.04698827 0.04617602Tz 0.00039439 0.00055521 -0.0013357 0.00708795 -0.00173009

14.8

Fx -0.0493484 0.06020544 -0.996548 1.00106449 -0.9471996Fy -0.0340282 0.0424589 -0.0315008 0.11737656 0.0025274Fz 0.13315176 0.15636052 1.63913017 1.64241703 1.50597841Tx 0.00087366 0.00113107 0.00630117 0.01339783 0.00542751Ty 0.00011817 0.00061978 -0.2447933 0.24493561 -0.24491147Tz 0.00062057 0.00071697 0.00618468 0.01007277 0.00556411

18.7

Fx -0.0408584 0.05169733 -0.9184086 0.92117253 -0.8775502Fy -0.0126044 0.02512264 0.06040042 0.13962282 0.07300482Fz 0.14948843 0.17167739 3.03044543 3.03191905 2.880957Tx -0.0003534 0.00104628 0.01918841 0.02359609 0.01954181Ty 0.00033808 0.00064467 0.07384452 0.07410657 0.07350644Tz 0.00039563 0.00055521 -0.0023338 0.00787925 -0.00272943

Moment Resolving Matrix

Moment Resolving Matrix-0.0055 0 0.095

Angle (degrees) Axis Rotation Matrix

0.3

0.95533649 0 -0.2955202

0 1 0

0.29552021 0 0.95533649

0.3 Degrees Angle of Attack

angle of attack = 0.3 deg

43


Elevator Data Real Forces (N) Unit

Coefficients ValueCm due to AoA

Cm due to elevator delection

0

Drag -1.401731518 N cd -0.1339626Fy -0.00267557 N


M (moment) -0.303057781 Nm Cm -0.4109896 -0.43546110.024471513

N (moment) -0.203231801 Nm

4.1

Drag -1.335827942 N cd -0.1276643Fy 0.0279674 N


M (moment)-0.335062581

NmCm -0.4543927 -0.4354611

-0.018931562

N (moment) -0.187905741 Nm

4.3

Drag -1.402628082 N cd -0.1340483Fy 0.04292928 N


M (moment) -0.281823407 Nm Cm -0.3821927 -0.43546110.053268353

N (moment) -0.224928194 Nm

7.9

Drag -1.33792496 N cd -0.1278647Fy 0.0114468 N


M (moment)-0.371236609

NmCm -0.5034498 -0.4354611

-0.067988705

N (moment) -0.161235109 Nm

8.9

Drag -1.492627704 N cd -0.1426495Fy 0.05275951 N

Lift 2.202619638 N cl 0.21050304

44


L (moment) -0.23070771 Nm

M (moment) -0.24742775 Nm Cm -0.3355473 -0.43546110.099913771

N (moment) -0.2469054 Nm

11.5

Drag -1.340236621 N cd -0.1280856Fy 0.0029886 N


M (moment)-0.379726974

NmCm -0.514964 -0.4354611

-0.0795

0285N (moment) -0.151755854 Nm

13.6

Drag -1.601861417 N cd -0.1530889

Fy 0.06257886 N


M (moment) -0.220431177 Nm Cm -0.2989361 -0.43546110.136524977

N (moment) -0.268337287 Nm

14.8

Drag -1.349941391 N cd -0.1290131Fy 0.0025274 N


M (moment)-0.393189017

NmCm -0.5332204 -0.4354611

-0.097759301

N (moment) -0.142713437 Nm

18.7

Drag -1.689736735 N cd -0.1614871Fy 0.07300482 N


M (moment)-0.205011001

NmCm -0.2780242 -0.4354611

0.157436935

N (moment) -0.281246871 Nm

Plot of Cm vs Del E (0.3 degrees)

45


0 2 4 6 8 10 12 14 16 18 20

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

f(x) = 0.00358051340489022 x − 0.0102904325913384Series2Linear (Series2)

From the graph above, Cm_del.E = .0036

5 Degrees Angle of Attack

46


Elevator Data Real Force (N) Unit

Coefficients ValueCm due to AoA

Cm due to elevator delection

0

Drag 5.609884085 N cd 0.53613327Fy 0.024796107 N

Lift 2.033697181 N cl 0.19435922L (moment) 0.010787669 Nm

M (moment)-0.037998603

NmCm -0.0515315 -0.7902

0.738668473

N (moment) 0.030917834 Nm

4.1

Drag 5.436751635 N cd 0.51958711Fy -0.14297614 N


M (moment) -0.080571999 Nm Cm -0.1092671 -0.79020.680932

874N (moment) 0.030828445 Nm

4.3

Drag 5.802169023 N cd 0.55450983Fy 0.031491869 N


M (moment) 0.019339321 Nm Cm 0.02622688 -0.79020.816426

879N (moment) 0.031386482 Nm

7.9

Drag 5.247261313 N cd 0.50147763Fy 0.011598649 N


M (moment)-0.126502231

NmCm -0.1715551 -0.7902

0.618644927

N (moment) 0.031316007 Nm

8.9

Drag 6.039823973 N cd 0.57722237Fy 0.039727983 N


M (moment)0.073471876

NmCm 0.09963835 -0.7902

0.889838345

N (moment) 0.031688821 Nm

47


11.5

Drag 5.096221009 N cd 0.4870428Fy 0.000444064 N


M (moment) -0.154628937 Nm Cm -0.2096989 -0.79020.580501

101N (moment) 0.03257552 Nm

13.6

Drag 6.204362124 N cd 0.59294718Fy 0.047075149 N


M (moment) 0.120073269 Nm Cm 0.16283648 -0.79020.953036

483N (moment) 0.031758581 Nm

14.8

Drag 5.036591745 N cd 0.48134406Fy -0.004223408 N


M (moment) -0.166247634 Nm Cm -0.2254555 -0.79020.564744

49N (moment) 0.032609421 Nm

18.7

Drag 6.340775625 N cd 0.60598414Fy 0.054275151 N


M (moment) 0.147337217 Nm Cm 0.19981029 -0.79020.990010

286N (moment) 0.031701912 Nm

Plot of Cm vs Del E (5 degrees)

48


0 2 4 6 8 10 12 14 16 18 200

0.2

0.4

0.6

0.8

1

1.2

f(x) = 0.00706606079340735 x + 0.693407551478105

Series2Linear (Series2)

From the above graph, Cm_del.E = 0.0071

Similarities or Differences

Based on the two graphs, the different angle of attacks still showed a very similar pattern and

trend. Not only are the values of the coefficient of pitching moment due to the elevator's

deflection are both very homogenous, it also fluctuates at the same point when the elevators

are on the same angle.

EXPERIMENTAL VS THEORETICAL

49


Firstly, the pitch moment coefficient due to the angle of attack, Cmα, displays a negative

linear trend with a value of -.0696; this negative slope for a positive value of alpha indicates

that there is stability in pitching. Compared to the experimental values, our derived

theoretical value was out by a factor of 10, where the experimental values are -.61. By

calculating the percentage error (calculated percentage error = (|theoretical-experimental|)/(|

theoretical|), it gives an error of 88.6395% which is a huge difference.

As for the coefficient of pitching moment due to the elevator's deflection, CmδE

, the

experimental values and theoretical values are completely different. The theoretical value of

CmδE

was 0.0071 while the experimental value was -0.993, obviously one of these two values

are wrong. The graph shows an escalating and declining pattern, which means the pitch of the

test model is completely unstable. Some assumptions could be the external factors in the

experiment that produced the experimental values to be different such that there were no

proper controls implemented to reduce the effect of drift in the model plane; another could

have been the placement of the force balance under the aircraft was not a very ideal position

as it could have picked up or resulted better values if it was placed in the centre of the aircraft

model. Another hypothesis for this result could be the density of air within the wind tunnel

might have been different in our presumptions; it could also be due to wrong assumptions

like the y-axis moment might have been negative in respect to our assumption of what the

positive moment rotation is. Also, the force balance was connected in the rod instead of the

model plane; this can create a different pitch moment that the plane experiences and a

different drag force when compared to what the model is undergoing.

DISCUSSION

50


The values of Cmα had an error of 88.6395% and was a factor of 10 out when compared and

plotted with the experimental values of the lab test, the outcome of CmδE

was completely

different to the experimental values that were taken from the lab. Even though the same

procedures were used to obtain the theoretical values, the trend relationship that came out

showed instability in the pitching moment coefficient due to the elevator angle. As stated

before, certain factors could have affected the entirety of the report ranging from the

ineffectiveness of the apparatus and procedures up to the possibility of wrong assumptions in

the theoretical calculations. The data also shows that there is a moment about the X-axis

(rolling moment) in one direction for all tests. This suggests that there is more lift or drag on

one of the wings, a reason for this occurrence may be due to the trip wires not being set up

symmetrically resulting in higher turbulent flow over one wing resulting in increased drag

and decreased lift. This occurrence may also be a significant contributor to the measured

moment about the Z-axis (yaw moment).

In theory, the effects of Reynold’s number to the pitch moment diminishes the faster the

aircraft moves (>0.6) and is practically eliminated at Mach 0.9. In the experiment, there was a

noticeable effect of Reynold's number on the pitching moment in and beyond the stall region

but this effect diminishes as the angle of attack increases. The most important effect that

Reynold's number has on pitch moment is its effect on the boundary layer thickness and thus

the displacement thickness. It is also important for determining laminar and turbulent flows

over the model as it expresses the ratio of inertial forces to viscous forces.

CONCLUSION

51


The P-51D model aircraft was thoroughly examined under strict test conditions. It's

background shows that it's the perfect aircraft to be used in these circumstances as it performs

superbly in terms of stability during pitching moments. The lab test was performed under a

constrained and closed loop test section in an attempt to derive force and balance

measurements; through this, we were able evaluate the three different pitch moment

coefficients (pitch due to angle of attack, pitch rate and deflection) and compare the results of

the experiment to our theoretical values. As stated in the discussion and comparison of

theoretical and experimental, the pitch moment due to the angle of attack, Cmα, already had a

large error difference and just from looking at the graphs of Cm_del.E (pitch moment

coefficient due to the elevator deflection) it 's obvious that it yields a completely different

result with the results from the lab even when the same method and procedure were

implemented. This could probably be smoothened quite a bit if the test conditions and other

distinct factors were altered such as the fact that the force balance placement was on the rod

which creates its own drag and pitch moment. Another factor that affected the overall

accuracy was the laminar flow quality inside the wind tunnel, our data showed that there is a

moment in the roll axis when the purpose of the lab was to measure the pitch; this indicates

that there is some sort of drag or lift in one side of the model and the reason this was picked

up could have been due to the apparatus being asymmetrical. In terms of data similarity and

differences, the different angles still resulted the same output but just with a different

magnitude. In our circumstances of calculating the theoretical values of Cm_del.E,it

should've been correct as the steps and procedure were checked several times, unless, we

assume that the positive moment rotation is actually supposed to be a negative y-axis moment

then this might transform the results a bit.

Further improvements within the apparatus and its positioning could definitely result a

different experimental data. Seeing as most of the calculations and procedures were followed

thoroughly and correctly, the only conclusion or assumption possible would be that there

might have been something wrong with the way the lab test was done, because most of the

theoretical explanation that could've resulted this were only due to the wrong assumptions of

positive and negative moments and nothing else.

REFERENCES

52


N.a(n.d) What Are Wind Tunnels? | NASA. Retrieved April 24, 2013, from

http://www.nasa.gov/audience/forstudents/5-8/features/what-are-wind-tunnels-

58.html#.U1ijI_mSySo

N.a (n.d.). Boeing: P-51 Mustang. Retrieved April 24, 2014, from

http://www.boeing.com/boeing/history/bna/p51.page

Kinzey, Bert. P-51 Mustang in Detail & Scale: Part 1; Prototype through P-51C.

Carrollton, Texas: Detail & Scale Inc., 1996. ISBN 1-888974-02-8

Kinzey, Bert. P-51 Mustang in Detail & Scale: Part 2; P-51D thu P-82H. Carrollton,

Texas: Detail & Scale Inc., 1997. ISBN 1-888974-03-6

Advanced thermal solutions. (2012, 07 17). Some basic principles of wind tunnel design. Retrieved 04 15, 2014, from Advanced themal solutions Inc: http://www.qats.com/cms/2012/07/17/some-basic-principles-of-wind-tunnel-design

ATI Industrial Automation. (2014, 01 01). F/T Sensor: Nano17 Titanium. Retrieved 04 16, 2014, from ATI Industrial Automation, Inc: http://www.ati-ia.com/products/ft/ft_models.aspx?id=Nano17+Titanium

Pandiripalli, B. (2010). Repeatability and Reproducibility studies: A comparison of techniques. Wichita State University. Kansas: Unpublished.

Rona, A., & Soueid, H. (2010). Boundary Layer Trips for Low Reynold's Number Wind Tunnel Tests. Orlando: American Institute of Aeronautics and Astronautics, Inc.

53

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advanced aerodynamics lab report

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