Aerospace Engineering 2201
Lab #3: Flight Simulator Test of Aircraft Stability
Barrett Lowry, James Obloy, Colin Anderson
Witeof: Friday 800 A.M.
Introduction
The purpose of this lab is to utilize the physics-based flight simulator X-Plane (v.10) to
measure the longitudinal stability characteristics of a Cessna 172. The longitudinal stability
characteristics obtained from the flight simulator will then be compared to theoretical data based
on the C-172 data provided.
Theory
Important Equations
Procedure
For Elevator Trim Angle, the aircraft was set to a predetermined flight condition of 90 knots at a
pressure altitude of 5000ft, with the aircraft in trimmed flight and CG location of 0”. Then while
maintaining steady level flight, the aircraft needed to be accelerated to 100 knots. When at 100
knots, measure the elevator deflection angle. Then using both the throttle and trim wheel
determine the trim airspeed associated with zero elevator deflection.
For Stick-Fixed Static Longitudinal Stability, the aircraft was set to a predetermined flight
condition of 90 knots at a pressure altitude of 5000ft, with the aircraft in trimmed flight and CG
location of 0”. Then achieve steady level flight at three airspeeds of 80, 90, and 100 knots for
three different CG locations of -10”, 0”,10”. At each of these conditions, record elevator angle,
airspeed, aircraft weight, and angle of attack.
Results and Discussions
Analysis #1
The elevator trim angle associated with trimmed flight at 100 knots was found to be -13.56°.
This value is consisted with the value from #2 part a. The work for analysis #1 can be found in
Appendix B: Analysis Work.
Analysis #2
Part A)
In part a, using methods details described in Anderson’s Introduction to Flight Seventh Edition,
the theoretical value for the neutral point (hn) was found to be 0.673. The theoretical static
margin (hn-h) was found to be 0.610. In Appendix B: Analysis Work, the work for part A is
included. In Appendix C: Matlab Codes, the matlab code for part A is included. Below the graph
of theoretical variation of moment coefficient is shown.
Part B)
Utilizing the flight test theory detailed in the lab, the neutral point or hn was found to be 0.673.
The static margin or hn-h was found to be 0.611. The values for neutral point and static margin
match the test data almost exactly, static test=0.611 and the static analysis=0.610. The numbers
are close to exactly the same because static margin and neutral points are design features not
something that can be altered in flat (altered easily). Neutral point depends on aerodynamic
center (does not change), VH (tail volume ratio, also does not change), a and at (lift slope for
wing and tail, respectively, also do not change, and dɛ/dα (down wash gradient, also does not
change). The only variable that changes is h if the Cg is shifted, but this is unaffected by flight
conditions. Therefore, analytical and experimental neutral points are almost exactly the same.
Since static margin depends on h and hn, they too depend on Cg location so flight configuration
means nothing as long the Cg does not move in flight. The work for part B is included in
Appendix B: Analysis Work.
Part C)
In part a, CM,0 was found to be .174 for a Cg location of 0”. CMα was found to be .1724 which is
very close to the value found in part a. Our findings appear to be very accurate. This is an error
of .9%. The work for part C is included in Appendix B: Analysis Work.
Part D)
For part D, the absolute angle of attack was found to be 4.55°. Using this trim value of αa and the
value for CMα, the CM,0 was found to be 0.250. The calculations for part D can be found in
Appendix B: Analysis Work.
Part E)
Matlab codes for the following graph are located in Appendix C: Matlab Codes.
Conclusion
This lab proved the static longitudinal stability in the X-Plane (v.10) flight simulator. The
theoretical values calculated for the data given on the handout very closely matches the
experimental data obtained from the simulator.
Appendix A: Simulator Data Tables
Tables 1-4: Flight Simulator Data
2. Elevator Trim Angle
Elevator Position
Elevator Trim Angle
(angle/degree)
(degree)
-0.004
-2.184
0
0
Part
a.
b.
Condition
(knots)
80
90
100
Condition
(knots)
80
90
100
Condition
(knots)
80
90
100
Airspeed (knots)
100
93.05
Cg Location of 10 and Altitude of 5000 Feet
Indicated
Elevator
Elevator
True
Aircraft
Airspeed
Angle
Trim Angle
Airspeed
Weight
(knots)
(degrees)
(degrees)
(knots)
(lbs)
79.5
0
0.24
85.64
2063
89.5
0
-3.668
96.39
2064
100.6
0
-7.336
108.3
2066
Cg Location of 0 and Altitude of 5000 Feet
Indicated
Elevator
Elevator
True
Airspeed
Angle
Trim Angle
Airspeed
(knots)
(degrees)
(degrees)
(knots)
80.07
0
4.704
85.32
90.26
0
0.768
97.2
99.78
0
-2.576
107.5
Indicated
Airspeed
(knots)
81.04
90.82
98.67
Aircraft
Weight
(lbs)
2061
2059
2057
Cg Location of -10 and Altitude of 5000 Feet
Elevator
Elevator
True
Aircraft
Angle
Trim Angle
Airspeed
Weight
(degrees)
(degrees)
(knots)
(lbs)
0
8.616
87.35
2051
0
4.2
97.82
2054
0
1.464
106.3
2056
Alpha
(degrees)
1.588
0.315
-0.695
Alpha
(degrees)
1.828
0.421
-0.437
Alpha
(degrees)
1.913
0.619
-0.145
Appendix B: Analysis Work
Analysis #1
deltrim=(CM,0+(dCM,CG/dαa)αtrim)/(VH(dCL,t/ddele))
CM,0=.174
dCM,CG/dαa=-0.055
VH=.68
dCL,t/ddele=0.053
αtrim=9°(based off of Figure 1)
deltrim=-13.56°
Analysis #2
Part A)
VH=(lt*St)/(c*S)
c=MAC=4.76ft
at=.1/degree
a=.09/degree
hacwb=.25
VH=.68
lt=14.9ft
St=38ft2
S=174ft2
static margin=.610
Static Margin=hn-h
h=.063
Iac=3.6ft
XCGref=3.3ft
c=MAC=4.67ft
CM0=.174
CM0=CMacwb+VH*at*(it+ɛ0)
CMacwb=-.03
VH=.68
at=.1/degree
it=3°
ɛ0=0(assumed, no value was given)
a=.09/degree
h=.063
hacwb=.25
VH=.68
at=.1/degree
Part B)
Neutral Point
for 0”
h=.063
a=.09/degree
hn=.674
for -10”
h=-.112
a=.09/degree
hn=.677
for 10”
h=.24
a=.09/degree
hn=.673
Static margin for 0”
static margin=hn-h=.611
Part C)
dCM,cg/dDele=-.011
dCM,cg/dαa=-0.055
K=-29
CMα=(( dCM,cg/dαa)/( dCM,cg/dDele))/-K
CMα=.1724
Part D)
CG=0”
W=2080 lbf
S=174 ft2
q=0.09/degree
αa=4.55°
(Part 1)
CM,0=0.250
(Part 2)
Appendix C: Matlab Codes
Matlab Codes
2a)
clear
clc
Cmac=-.03;
awb=.09;
alphawb=-15:.1:15;
h=.063;
hacwb=.25;
VH=.68;
at=.1;
a=.09;
dEdA=.44;
it=3;
Cmcg=Cmac+awb*alphawb*[h-hacwb-VH*(at/a)*(1-dEdA)]+VH*at*it;
plot(alphawb,Cmcg)
xlabel('Absolute Alpha (Degrees)')
ylabel('Moment Coefficient about Center of Gravity')
title('Theoretical Variation of Moment Coefficient')
2e)
% lab3plot.m
%
Anderson Lowry Obloy
% Plotting code for AERO2201 Lab #3
clear
clc
Cmac=-.03;
awb=.09;
alphawb=-15:.1:15;
h=.063;
hacwb=.25;
VH=.68;
at=.1;
a=.09;
dEdA=.44;
it=3;
Cmcg=Cmac+aw*alphawb*[h-hacwb-VH*(at/a)*(1-dEdA)]+VH*at*it;
Cm0=0.25;
dCmda=-.055;
Cmcg_mod=dCmda*alphawb+Cm0;
hold
plot(alphawb,Cmcg,’r--‘)
plot(alphawb,Cmcg_mod,’b-‘)
xlabel(‘Absolute alpha (degrees)’)
ylabel(‘Moment coefficient about center of gravity’)
title(‘Variation of Moment Coeff. with Absolute Angle of Attack’)
legend(‘Ideal’,’Experimental’)
hold
clear
clc