Flight Lab: Calculation of C.

G
Group D

April 3, 2018

1 Aim of the Experiment

To find the center of Gravity of the Airplane and find the C.G of the airplane as passengers
are loaded.

2 Introduction
The Location of center of gravity has great influence on the stability and control of the
airplane. An airplane must be designed in such a manner that there is minimum variation of
C.G. In this Experiment We need to find out how C.G travels longitudinally when passengers
move in and out of airplane.The C.G is further used in determination of neutral point and
maneuvering point.
The center of gravity is calculated as follows.

x1 N + x2 L + x3 R
xc.g =
L+N +R
Where:
x1 is distance of Reference point from Nose wheel
x2 is distance of Reference point from Rear wheel
L is weight measured in Nose wheel
N is weight measured in left wheel
R is weight measured in Right wheel

For Piper Saragota Aircraft: x1 = 14.2 inches,x2 = 109.7 inches.

3 Procedure
1. Find Out Reactions at Nose Wheel, and main Wheels when 5 passengers are sitting.

2. One by one ask each passenger to move out of aircraft and Note down the reactions.

3. Note Down reading in Tabulated Form

1
 4. Plot a Graph Showing Variation of C.G and number of passengers

4 Record Chart : CG Location

No of Pas- Left Wheel Nose Wheel Right Total XC.G

sengers Reaction Reaction Wheel Weight (inches)
(L) (N) Reaction
(R)
P4 603 308 633 1544 90.649481865285
P3 564 338 581 1483 87.9339851652057
P2 500 355 535 1390 85.3097122302158
P1 467 366 487 1320 83.2204545454546
P0 441 343 442 1226 82.9818107667211
Empty 406 325 421 1152 82.7577256944445

Table 1: Observation table

5 Plot

2
6 Discussions
1) Why this graph look like this?
A)The position of cg is closer to the pilot seat so addition of pilot, co-pilot weights doesn’t
effect the position much but as the number passengers gets increased and as they sit farther
from the C.G the position of cg will shift away from the reference point.From the Graph
we can confirm that addition of pilot and co pilots weight change the C.G position little
compared to the addition of passengers which changed the C.G

2) What is Range of C.G position drastically.?

A) the position of cg moves away as the number of passengers gets increased with a range
of 9 inches (82.98-90.64 inches).

3)Why pilot prefers for having a co-pilot with heavier mass?

A)Heavier mass co-pilot will shift the cg towards the pilot (or will not shift too much away
from him) so that he can apply less amount of stick forces to control the aircraft.static
Stability is more when the cg is nearer.

Physical Significance

• The position of the C.G is important since it affects the static margin.

• The C.G position is important in case of disturbance to flight angle the stability is
affetced by position of C.G as the control to be applied depends on the posotion of
Center of gravity.

7 Conclusions
• The Center of Gravity of the Piper Saratoga aircraft is 82.7 inches from the Reference
point.

• variation of the C.G with addition of passengers is observed.

3
 Flight Lab: calibration of control surfaces
Group D

April 5, 2018

1 Aim of the Experiment

To Calibrate the Control Surfaces like ailerons and Elevators on airplane to construct a
Scale for measurement in flight

2 Introduction
Calibration is the process of configuring an instrument to provide a result for providing
sample within an acceptable range. Eliminating the factors that cause inaccuracies is the
fundamental aspect of instrumentation design.
In This experiment we will determine the relationship between the control surface deflection
angle and the output voltage. Calibration will be performed on Hansa-3 aircraft using
inclinometers and data acquisition system. Hansa-3 is manufactured by National Aerospace
laboratories, Banglore.The Calibration data is used in the other experiments like estimation
of neutral point and maneuvering point. since in these experiments we need to record
elevator deflection and aileron deflection.

3 Procedure
1. Fix the inclinometer on the control surface where we have to measure the output volt-
age of the control surface such as alierons on the wing and elevators on the horizontal
stabilizers for specific deflection angle.

2. Connect the Data Acquisition system.

3. Measure the Control surface Deflection using control stick.

4. Measure corresponding output Voltage.

5. Plot a Graph With voltage on X-axis and deflection on y-Axis.

6. Draw a straight line joining the points and measure deflection.

1
4 Observations Record

v θ
0.46 10.21
0.64 8.19
0.79 6059
1.01 4.13
1.18 2.28
1.37 0.3
1.59 -2.12
1.81 -4.26
2.01 -6.27
2.2 -8.14
2.42 -10.19
2.64 -12.28
2.83 -14.17
3.1 -16.62
3.28 -18.35
3.5 -20.38
3.65 -22.02
3.58 -21.05
3.7 -22.2
3.92 -24.16
4.16 -26.24
4.4 -28.45
4.49 -29.26

Table 1: Elevator Calibration Data

2
 v θ
0.85 25.26
0.99 22.89
1.17 20.15
1.34 17.5
1.49 15.12
1.6 12.56
1.87 9.49
1.99 7.76
2.15 5.46
2.36 2.57
2.53 0.31
2.71 -2.2
2.93 -5.11
3.08 -7.09
3.28 -9.72
3.48 -12.56
3.68 -14.98
3.86 -17.26
4.06 -19.83
4.27 -22.4
4.44 -24.66
4.64 -27.15
4.88 -30.17

Table 2: Alieron Calibration Data

3
5 Plot

4
6 Discussions
6.1 Importance of Calibration
• The calibration process generally involves using the instrument to test samples of one
or more known values called calibrators. The results are used to establish a relationship
between the measurement technique used by the instrument and the known values.

• Ideally a product would produce test results that exactly match the sample value, with
no error at any point within the calibrated range. This line has been labeled Ideal
Results. However, without calibration, an actual product may produce test results
different from the sample value, with a potentially large error.

• Calibrating the product can improve this situation significantly. During calibration,
the product is taught using the known values of Calibrators 1 and 2 what result
it should provide. The process eliminates the errors at these two points, in effect
moving the Before Calibration curve closer to the Ideal Results line shown by the
After Calibration curve. The Error At Any Point has been reduced to zero at the
calibration points, and the residual error at any other point within the operating range
is within the manufacturers published linearity or accuracy specification.

6.2 Precautions
• Calibrators should be well maintained in order to reduce the external influences.

• Calibration should take place in secured environment to ensure minimal impact of

external vibrations etc

• Random Errors produced can be reduced by producing large number of measurements

and taking mean of the experiment.

7 Conclusions
• The Slope of Elevator Deflection vs Voltage plot is -13.6200. intercept is 35.3413

• The Slope of Aleron Deflection vs Voltage plot is -9.73849. intercept is 13.80354

5
 Flight Lab: Drag Polar Estimation using Cessna-206H
Group D

April 10, 2018

1 Aim of the Experiment

To CalculateCD0 and k of the Cessna 206H using the Drag polar of the aircraft through
Flight testing.

2 Introduction
The purpose of this experiment is to estimate drag polar relationship for Cessna 206H
aircraft. The drag polar is the relationship between the lift on an aircraft and its drag,
expressed in terms of dependence of the lift coefficient on the drag coefficient. Many perfor-
mance parameters can be determined from the drag polar such as optimum rate of climb.
The drag polar equation may be written as

CD = CD0 + KCL2
where CD is total coefficient. CD0 is the drag coefficient.CL denotes coffieient of lift and
1
K = πARe where AR is aspect ration of the wing and e is oswald efficiency factor. KCL2
is the induced drag coefficient of a wing. and unavoidable companion of the Lift of Wing.
The other drag are parasite drag and wave drag are included in the CD0 .

3 Cruise mode
In this experiment we will take the readings at cruise mode. Cruise is the level portion of
the aircraft travel where flight is most fuel efficient. It occurs between ascent and descent
phases and is usually the majority of a journey, Technically. cruise consists of heading
changes only at a constant airspeed and altitude.for most commercial passenger aircraft.
the cruise phase consumes a lot of fuel consumes the majority of fuel, typical speed is
400-500 knots.Commercial aircraft is optimized for cruise phase.

3.1 Instruments for this Experiment

• Airspeed Indicator

1
 • Engine RPM Indicator
• Manifold pressure gauge
• Outside air temperature
• Altimeter
• Stopwatch

3.2 Calculation
Brake horse power Equation

BHP = D · V
ρV 2 SCD
D=
2
CD = CD0 + KCL2
ρV 2 S
BHP = (CD0 + KCL2 )
2
ρV 2 SCL
Now using L = 2 and also knowing L = W during cruise, we get:

ρSCD0 2KW 2
BHP = +
2 ρS
The Density correction is applied with the international standard ISA Table
Break Horse Power using Data
(rpm)(M P )(T s)(rHP )
BHP =
(rrpm)(rM P )(OAT )

3.3 Procedure
• Wait Until altitude is reached.
• Record airspeed indicator, Engine manifold pressure, outside air temperature, RPM
of engine during the cruise.
• Obtain Break Horse Power using the Recorded Data.
• Repeat for all Altitudes.
• Power required for the Steady level flight is given by
W2
1 1
ρV S
Preq = ρV 3 SCD0 + 2
2 πAReρS

2
 • The Above equation is modified as

1 2W 4
P V = ( ρSCD0 )V 4 +
2 πAReρS

• The above equation is a straight line Y = mX + c with

Y = PV
1
m = ρSCD0
2
2
e=
πAReρS
We can calculate the slope and intercept from data We can calculate the required
parameters using above equations

4 Climb Mode
Following Take off Airplane Has to climb to maintain safe and economic Flight. Climb may
be achieved by increasing angle of attack on the wing, or by increasing the thrust of the
engine to increasing speed in some cases both techniques are used.

As lift decreases with density a climb once initiated, ends when lift is equal to weight
at that point steady flight.

4.1 Calculations
Consider Equilibrium of Forces.

T − D − W sin γ = 0
L − W cos γ = 0

Now By rearranging terms we get that

VT −VD
= V sin γ
W
dh
RC = = V sin γ
dt
This can be evaluated at various speeds and the values of v corresponding to maximum rate
of climb can be obtained.

3
4.2 Rate of Climb
if the time to traverse the altitude band is also recorded then we can actually calculate tru
rate of climb of the aircraft.
Let observed temperature is T0 and the standard temperature at the altitude is Ts , Then
Pressure recorded since the pressure change is always the true pressure difference for alti-
tude change shown by the altimeter.

δp = −ρs g(δH)p

s:Standard altitude
p:Pressure altitude
δHT is true change in altitude, will have same temperature difference.

δp = −ρT g(δH)T
δHT ρs T0
= =
δHp ρT Ts
Therefore ,
T0
RCtrue = RCobserved ∗
Ts

4.3 Procedure
• Record the Take off Weight(WT ).

• Note the initial and final altitudes ( h1 h2 ) and time instants (t1 t2 ).

• Repeat for different climb speeds.

• Record the weight after the landing.and consider average weight for calculations.

• Find out the rate of climb for each velocity and corresponding angle of climb Γ using
following equations.
h2 − h 1 T0
RC ≈ · RCtrue = RCobserved ×
t2 − t1 Ts

• Plot rate of climb vs speed.

• Plot angle of climb vs speed

• From the plots find Maximum rate of climb and maximum angle of climb and the
corresponding velocities.

4
5 Observations Record
Cessna 206H parameters

Parameter Value
Rated RPM 2700
Manifold pressure 29.92 in Hg
Sea Level Tempeature 288.15K
Wing Area (S) 16.16 m2
Wing Span (b) 10.9728m
Rated Hp (rHP) 223.709 kW

V MP RPM OAT Altitude

93 19.5 2270 32 500
99 21.1 2260 30 1000
95 20.9 2310 28 1600
93 22.9 2300 28 2020
90 22 2440 26 2400
94 21.2 2380 24 3040

Table 1: Cruise Expreiment Data

V RPM MP OAT h1 h2 Time

97 2530 25.2 31 500 1000 77.91
95 2370 25.3 30 1000 1500 71.37
80 2550 24.6 28 1500 2000 107.36
87 2550 24.4 27 2000 2500 53.69
100 2540 24 25 2500 3000 78.1

Table 2: Climb Experiment Data

5
6 Plot
PV vs V4

1e+07
PV

9e+06

8e+06

1.0e+07 1.1e+07 1.2e+07 1.3e+07 1.4e+07

V4

Rate of climb vs Speed

3.0

2.5
rate of climb (m/s)

2.0

1.5

42.5 45.0 47.5 50.0

Speed (m/s)

6
 Angle of climb vs Speed

3.5
Angle of climb (degrees)

3.0

2.5

2.0
42.5 45.0 47.5 50.0
Speed (m/s)

7 Calculation
• The value of Aspect ratio is calculated as 7.456

• The line Equation of the Cruise equation for the graph is given by Y = .03220X +
5.059e + 06

• From the Formulas above we can calculate the CD0 = 0.0326 and e = 0.21565

• the value of k is equal to 0.20

8 Discussions
• The Drag Polar is the relationship between the lift on an aircraft and its drag, ex-
pressed in terms of the dependence of the lift coefficient on the drag coefficient.

• Drag Polar helps to determine many performance parameter such as the power re-
quired at different altitudes and speed, the optimum speed and altitude for cruise.
and optimum rate of climb.

• We can verify the rate of climb obtained from the altitude and time measurement
with help of temperature readings at the corresponding altitude.Since we know the

7
 standard atmosphere lapse rate, we can calculate the altitude from the difference
between temperature readings. Since we know the time, we can get the rate of climb
from the above mentioned. And hence verify the the rate of climb. Both the observed
and the rate of temperature changes should have a similar profile.

• Oswald’s efficiency factor is a generalized parameter connected with an aircraft’s

aerodynamic efficiency . Specifically, for a parabolic drag polar, there exists a de-
pendency.The Oswald efficiency factor e reflects the airplane lifting properties deteri-
oration caused by the distortion of an elliptical lift distribution and accounts for the
non-ellipticity of the lift distribution, the increase of profile drag of the wing, fuselage,
tail plane, nacelles and various interference effects with angle of attack

• There is a discrepancy between expected and actual value obtained because oswald
efficiency factor depends upon the area of fuselage and the wing leading edge cross-
sectional shape which can enforce the suction at the leading edge zone and decrease
drag due to lift.

• All the measurements are taken from FPS system is a system of units. Here all
our calculations are done in SI units the appropriate conversions are applied before
calculation procedure.

• The script used for the Generation of plots can be found here.

• The average weight of aircraft is used in the formulas which is average of take off and
landing weight.

9 Conclusions
• The coefficients CD0 and e are calculated.

• The Plots for the Angle of Climb and rate of climb with the variation of velocity are
plotted.

• The maximum rate of climb is found around 45.2m/s.

• the maximum angle of climb is also found around 45m/s.

8
Flight Lab: Determination of Neutral Point and Maneuvering
Point from Flight Tests

Group D

April 10, 2018

Aim of the Experiment

To ind Neutral Point and Maneuvering Point of NAL Hansa3 airrraft by performing fight
experiments.

Introdurtion
In this experiment our aim is to determine the stirk ixed (Elevator Fixed) neutral point from
fight test. Neutral Point is the renter of gravity position hhere the pitrhing moment is
independent of the angle of attark. It is ralled airplane aerodynamir renter, hhen the C.G. is at
this point the airplane is neutrally stable.
Estimation of the Neutral point (Stirk Fixed)

δ etrim =δ e0 +
( ∂δe
∂C L trim
)
∂ δ e −∂C m
=
∂C L Cm δ
trim e

N.P. is the C.G. loration hhere,

∂ δe
=0
∂C L trim

Instruments Used
1 Airspeed indirator

2 Elevator angle indirator

Altimeter

4 OAT gauge

5 Bank Angle Indirator

Proredure
1 Fly at diferent renter of gravity roniguration and exerute rruise.
2W /s
2 Estimate rorresponding C L = and rerord δ e.
0.5 ρ V 2
trim

3 Plotδ e vs C L
trim trim

4 Cross plot [ ]
∂ δe
∂ C L trim
vs x́ cg to get neutral point
Observations and Results

Take3of Total Weight

(Kg) 727
Landing Total Weight
(Kg) 72
Average Weight (Kg) 725
Pilot Weight (Kg) 85
Student Weight (Kg) 71

Weight Moment Arms

Label Mass (Kg) (mm) Moment (N3mm)
Plane Strurture 550 5401 1027.52 55496 5.52
Pilot+ Student 156 15 1.92 11 0 17 1069.60
Fuel (Average) 19 186.58 1800 5844.00

Total
Weight 7119.5 Total Moment 7616549.12
CG 1069.82

Velority (Knots) Velority(m/s) CL (Trim) Elevator Defertion (degrees)

70 6.01108 0.146 9 961 0.5788
75 8.58 0.127525406 0.960 7
80 41.15552 0.112082877 1.495
85 4 .72774 0.099284486 1.9529
 Chart Title
2.5

2
f(x) = − 29.38 x + 4.81

1.5

0.5

0
0.09 0.1 0.11 0.12 0.13 0.14 0.15

Elevator Defecton
2.5

2
f(x) = − 40.25 x + 5.98
1.5

0.5

0
0.09 0.1 0.11 0.12 0.13 0.14 0.15 0.16

All Groups graphs:

 Elevator Defecton V/S CL
2

1 f(x) = 140.81 x − 19.72

0
0.09 0.1 0.11 0.12 0.13 0.14 0.15 0.16
-1

-2

-3

-4

-5

-6

-7

Elevator Defecton V/S CL

2.5

f(x) = − 32.2 x + 5.02

1.5

0.5

0
0.09 0.1 0.11 0.12 0.13 0.14 0.15 0.16
 Elevator Defecton
2.5

2
f(x) = − 38.76 x + 5.68

1.5

0.5

0
0.09 0.1 0.11 0.12 0.13 0.14 0.15

Elevator Defecton
0
0.09 0.1 0.11 0.12 0.13 0.14 0.15
-1

-2

-3

-4

-5
f(x) = − 43.96 x − 0.97
-6

-7

-8

Elevator Defecton
2.5

2 f(x) = − 41.43 x + 6.06

1.5

0.5

0
0.09 0.1 0.11 0.12 0.13 0.14 0.15
 Chart Title
0
0.09 0.1 0.11 0.12 0.13 0.14 0.15 0.16
-1

-2

-3

-4

-5 f(x) = − 31.57 x − 1.42

-6

-7

Fig 1: Graph – δe vs CL (at trim)

0
1066.00 1067.00 1068.00 1069.00 1070.00 1071.00 1072.00
-5
-10
-15
-20

dδe/dCL -25
-30
-35
f(x) = 0.47 x − 539.25
-40
-45
-50

xcg

Fig 2: Graph – dδe/dCL vs diferent rg lorations

Equation of the straight line y=0.469 x−539.25

Neutral point is the x loration hhen y=0, thus Neutral point is at x=1148.8 mm.
Disrussions

1. Was there any inrident related to this experiment ?

The experiment has performed rarefully in NAL Hansa and therefore there has no
report of any arrident.

2. Why is V’ is used instead of V∞ for relative hind at tail ?

Tail aerodynamirs is infuenred by tho inferenre points. Due to the inite hing, the
airfoh at the tail has deferted dohnhards by the dohnhash.
Due to the retarding forre of skin frirtion and pressure drag over the inite hing, the
airfoh rearhing the tail got slohed.

3. What is the physiral relevanre of this experiment ?

For statir longitudinal stability, the neutral point and thus the statir margin are very
important fartors. If an airrraft in fight sufers a disturbanre in pitrh that rauses an
inrrease (or derrease) in angle of attark, it is desirable that the aerodynamir forres on
the airrraft rause a derrease (or inrrease) in angle of attark so that the disturbanre does
not rause a rontinuous inrrease (or derrease) in angle of attark. This is longitudinal
statir stability. Statir margin is a ronrept used to rhararterize the statir longitudinal
stability and rontrollability of airrraft.

4. What is the signiiranre of the experiment for rommerrial fying ?

The knohledge of statir margin and point of neutral stability is a must for any airrraft.
For the stirk ixed stability, elevator trim angle, Coefrient of Lift at trim etr are
required.