Comparison of Measured and Simulated Flight of a Flap Controlled Closed Box in Atmospheric Flight

Andy Blatchford* Eric Beyer* Mark Costello†

Department of Mechanical Engineering Oregon State University

Corvallis, Oregon

Nomenclature zyx ,, : Components of position vector of mass center in an inertial reference frame. ψθφ ,, : Euler roll, pitch, and yaw angles of box.

3210 ,,, qqqq : Quaternion orientation parameters of box. wvu ,, : Components of velocity vector of mass center in body reference frame. rqp ,, : Components of angular velocity vector in body reference frame. ZYX ,, : Total applied force components in body reference frame. NML ,, : Total applied moment components about mass center in body reference frame.

AAA wvu ,, : Relative aerodynamic velocity components of mass center in body reference frame.

AV : Magnitude of relative aerodynamic velocity vector of mass center.

MWV : Magnitude of mean atmospheric wind.

MWψ : Azimuth angle of mean atmospheric wind. ρ : Air density.

4321 ,,, δδδδ : Flap deflection of flap 1, flap 2, flap 3, and flap 4. α : Aerodynamic angle of attack. γ : Aerodynamic roll orientation. S : Box reference area. D : Box reference diameter.

XC : Aerodynamic force coefficient along BI .

YC : Aerodynamic force coefficient along BJ .

ZC : Aerodynamic force coefficient along BK .

LC : Aerodynamic moment coefficient along BI .

MC : Aerodynamic moment coefficient along BJ .

NC : Aerodynamic moment coefficient along BK .

* Graduate Research Assistant. † Associate Professor, Member AIAA.

1

AIAA Atmospheric Flight Mechanics Conference and Exhibit15 - 18 August 2005, San Francisco, California

AIAA 2005-6325

Copyright © 2005 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

I. Introduction he emergence of small, rugged, and inexpensive sensors and microprocessors along with advances in flight control techniques has enabled creation of micro air vehicles designed to perform missions previously not possible. Extreme tailoring of the vehicle’s geometry to optimize system performance against a specific and narrowly defined task is now possible. This process is yielding new air vehicle configurations that lie well

outside the realm of conventional aircraft and projectiles. Consider, for example, unpowered controllable boxes envisioned for air delivery of cargo. The boxes are released from a parent aircraft at altitude. By deflecting the rear flaps, the box is controlled as it falls toward the ground. Using small onboard sensors and microprocessors, an active flight control system guides the box to a commanded ground position.

T

A great deal of literature has amassed on flight dynamic modeling of conventional airplanes, projectiles, and rotorcraft. Common modeling methods are well known and documented in many texts. For flight dynamic modeling purposes, it is clear that a flying box can be adequately modeled as a rigid body. However, it is less clear as to the level of sophistication required in the aerodynamic model and how well the model will match flight test measurements. To develop high performance flight control systems, it is generally advantageous to understand the dynamics of the air vehicle and possess reasonably accurate dynamics models. With this in mind, the work reported here describes an experimental program focused on flight dynamics and control authority of a flap controlled box in atmospheric flight. Emphasis is placed on comparing flight test results with results generated from a 6 degree-of-freedom dynamic simulation.

II. Box Dynamic Model The numerical simulation employed in this study consists of a rigid body six degree of freedom model

typically utilized in flight dynamic modeling of air vehicles. A schematic of a closed box configuration with major elements of the system identified is given in Figures 1 and 2. The degrees of freedom include three position components of the box mass center as well as four quaternion orientation parameters of the body. The resulting thirteen equations of motion describing the flight dynamics of an open box are given below.

⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

+−−+−−−+−++−−−+

=⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧

wvu

qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq

zyx

23

22

21

2010322031

103223

22

21

203021

2031302123

22

21

20

222222222222

(1)

⎪⎪⎭

⎪⎪⎬

⎫

⎪⎪⎩

⎪⎪⎨

⎧

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

−−

−−−−

=

⎪⎪⎭

⎪⎪⎬

⎫

⎪⎪⎩

⎪⎪⎨

⎧

3

2

1

0

3

2

1

0

00

00

21

qqqq

pqrprqqrprqp

qqqq

(2)

⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

−−

−−

⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧=

⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧

wvu

pqpr

qr

mZmYmX

wvu

00

0

///

(3)

[ ] [ ]⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

−−

−−

⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧=

⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧−

rqp

Ipq

prqr

NML

Irqp

00

01 (4)

where [I] is the mass moment of inertia matrix of the box evaluated at the mass center with respect to body frame coordinates. The applied loads above contain contributions from weight (W) and air loads (A).

2

⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧+

⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧=

⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧

A

A

A

W

W

W

ZYX

ZYX

ZYX

(5)

The weight contribution is given by the following.

⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧

+−−+−

=⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧

23

22

21

20

1032

2031

2222

qqqqqqqqqqqq

mgZYX

W

W

W

(6)

The air loads contribution is given by,

⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧=

⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧

Z

Y

X

A

A

A

A

CCC

SVZYX

2

21 ρ (7)

The aerodynamic forces are applied at the aerodynamic computation point which is not necessarily the

aerodynamic center. The applied moments about the box mass center contain contributions from two sources. Since the aerodynamic force given above is not located at the mass center, it produces a moment about the mass center. Also, since the computation point is not the aerodynamic center, an aerodynamic moment is also present. The applied moments about the box mass center is given by,

⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

−−

−+

⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧=

⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧

A

A

A

xy

xz

yz

N

M

L

A

A

A

A

ZYX

rrrr

rr

CCC

SDVNML

00

0

21 2ρ (8)

where rx, ry, and rz are the components of the position vector from the center of mass to the aerodynamic computation point expressed in body frame coordinates.

The aerodynamic force and moment coefficients are dependent on aerodynamic angle of attack, aerodynamic roll orientation, and flap deflection. The magnitude of the aerodynamic angle of attack is given as

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

++= −

222

1cosAAA

A

wvu

uα (9)

The angle of attack is defined as negative while vA is positive and positive while vA is negative. The aerodynamic roll orientation of the open box is defined as

⎟⎟⎠

⎞⎜⎜⎝

⎛= −

A

A

vw1tanγ (10)

The relative aerodynamic velocity components of the box mass center used in the equations above are influenced by the atmospher c winds. The mean atmospheric wind acts in the horizontal ground plane and is directed at an angle

i

MWψ from the II axis. Thus, the relative aerodynamic velocity components of the box mass center are,

3

( )( )

⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

+−−−++−+−−−+−−+

+⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧=

⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧

0sincos

222222222222

23

22

21

2010322031

103223

22

21

203021

2031302123

22

21

20

MWMW

MWMW

A

A

A

VV

qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq

wvu

wvu

ψψ

(11)

III. Aerodynamic Coefficient Determination Limited public domain information is available for aerodynamic force and moment coefficient data for box

shapes. Aerodynamic force and moment data for box shapes with deflected flaps was not found in existing literature. Thus, aerodynamic coefficient data was generated using computational fluid dynamics. The software package FloWORKS / SolidWORKS was employed. Aerodynamic force and moment data was generated for angles of attack and roll, along with different flap deflection angles (Figures 3-8).

Due to symmetry of the open box configuration with no flap deflection, a moderate set of angle variations covers all orientations. When a flap is deflected, aerodynamic symmetry of the box is largely lost and angle of attack and roll orientation must be varied through a larger set of angles. In order to generalize these aerodynamic coefficients to the situation where several flaps are simultaneously deflected, superposition is used. By subtracting the aerodynamic coefficients calculated for the box with one flap deflected by that associated with no flap deflection, the contribution from one flap can be determined and generalized to each flap resulting in a model that predicts aerodynamic loads of a box with each flap deflected by a different amount.

IV. Flight Test Apparatus

Two configurations of the air vehicle are employed. The air vehicle used for no flap deflection data collection, hereby referred to as box configuration A, is a standard (6in. x 6in. x 6 in.) 0.015875 m cardboard cube as shown in Figure 9. The total mass of the box is 0.454 kg and the mass center is located at a stationline of -0.06771 m, a buttline of 0.001 m, and a waterline of 0.0 m relative to the origin of the body reference frame. Mass moment of inertia matrix components relative the body axis shown in Figures 1 and 2 are Ixx= 0.00234 kg m^2, Iyy= 0.00300 kg m^2, and Izz= 0.00300 kg m^2. The major components on the aircraft include the cardboard box shell, ballast weights for mass center management, batteries to power all electronics, foam filler for shock loads mitigation, and an electronics board.

The air vehicle used for collecting data with flaps deflected, hereby referred to as box configuration B, is also a standard (6in. x 6in. x 6 in.) 0.015875 m cardboard cube as shown in Figure 10. The total mass of box B is 0.555 kg and the mass center is located at a stationline of -0.079 m, a buttline of 0 m and a waterline of 0.008 relative to the origin of the body reference frame. Mass moment of inertia matrix components relative to the body axis shown in Figures 1 and 2 are Ixx= 0.00183 kg m^2, Iyy= 0.00603 kg m^2, and Izz= 0.00556 kg m^2. The components of vehicle B include the cardboard box shell, ballast weights to mass center management, batteries to power the electronics, servos systems to control flap deflection angles, foam filler for shock load mitigation and all electronics.

The electronics board contains a host of MEMS sensors including a three axis accelerometer, a three axis gyroscope, a three axis magnetometer, and a barometric altimeter. The accelerometer, gyroscope, and magnetometer are contained within a unit produced by MicroStrain (Part Number 3DM-GX1). The MicroStrain unit also provides internal data processing for computation of orientation. Both Euler angles and quaternion parameters are output. Because the MicroStrain data processing uses accelerometers in orientation estimation, and implicitly assumes low acceleration of the platform, results during high acceleration maneuvering are least accurate. The data recorder collects readings from the various sensors at a rate of ~10 readings per second and stores them locally until they are uploaded onto a computer.

A schematic of a flight test event is shown in Figure 11. The box in initialized on the ground and subsequently hoisted to a specific drop altitude using a weather balloon. The balloon is a 2.44 m diameter latex weather balloon filled with approximately 7.1 m^3 of helium which provides approximately 6 N of lift. The balloon was tethered to the ground and retrieved for subsequent tests. The basket was suspended from the balloon and was equipped with a trap door which when commanded by radio, dropped the box out of the bottom. The trap door acted sufficiently fast such that it did not interact with the box.

V. Results

4

All testing was performed in Corvallis, Oregon. The boxes were dropped from an initial altitude of ~180 m above the ground which corresponded to approximately 260 m above sea level. Attempts were made to drop the box from a steady quiescent state; however, nonzero initial angular rates imparted to the box during release were collected by the sensors and used as the initial conditions for the math model.

Typical observations of air vehicle A with no flap deflections in flight is presented in Figures 12 through 14. During a typical trajectory, the box falls to the ground with significant coning motion and small perturbations in down range or cross range position. Coning angle is formally defined as the angle between the box axis of symmetry and the vertical. Figure 12 compares box coning angle from flight test measurements (Figure 12a) and 6 DOF simulation (Figure 12b). Coning of the box increases to an average of around 30 deg after 4 sec while experiencing peaks of 62 deg. The period of oscillations for coning is 0.5 sec at steady state for both the measured and simulated data. Notice that while the basic trends are about the same, the simulation results show lower average coning and the measured results are more erratic. This topic is explored in more detail below. Figure 13 compares measured and simulated roll, pitch and yaw rates of the box. Roll rate increases to 6.5 rad/s after 4.8 sec then decreases and experiences a roll reversal at 9.2 sec. Roll rate then increases to 5.5 rad/s in the opposite direction before performing another roll reversal at 14.1 sec. The pitch and yaw rates are characterized by oscillations at a frequency of about 1.5 Hz bounded by an amplitude of 7 rad/s. Similar to the coning comparison, the magnitude and period of the angular rates show the same trends, but detailed agreement is poor. Figure 14 shows the time history of the box altitude referenced from the ground during its descent. The box started at 264 m from the ground and upon release free fell for 16.5 sec before impact. The box reaches a steady state velocity of 17 m/s, 1.8 sec after release. Good correlation is observed between the measured and simulated results.

Measurements and simulation for air vehicle B with no flap deflected for the duration exhibit the same basic dynamic characteristics as discussed above. Flight tests were also run where the air vehicle was allowed to free fall with the flaps set to 0 deg, then at a particular altitude relative to the ground, the flaps flare to 90 deg as a means to arrest the rate of descent. Observations of this flight showed the same characteristics as the 0 degree flap deflection flight. The box started at an altitude of 175 m and fell to an altitude of 34 meter in 10.85 sec. Using altimeter readings, at an altitude of 34 m the flaps were deflected to 90 deg using the servo actuators which take approximately 0.2 sec to reach full deflection. From this altitude the box continues to descent for 2.1 sec before impact. The steady state rate of descent for the box prior to flap deflection was 16.8 m/s and 13.6 m/s after the flaps were deflected. This is a 19% reduction of the velocity of the box upon impact. The simulation results from deployment of the flaps prior to impact with the earth shows that the box exhibits the same deceleration effect due to the flaps as from testing. The box started from an altitude of 175 m about the earth and fell to 15.5 m in 10.85 sec. At 15.5 m above the ground the flaps are instantly deployed in the simulation, and impact with the earth occurs 1.1 seconds later. Prior to the flap deployment the box reaches a steady stead velocity in the vertical direction of 17.1 m/s the rate of descent of the box after the flaps were deployed was 13.8 m/s. This is a 19.3% decrease in the descent rate of the box due to flap deployment, which correlates well with measured results. When the flaps were deflected a large change in coning angle was predicted in the simulation, but not observed in testing.

A comparison between flight test measurements and 6 DOF simulation yields reasonably good agreement between the altitude and subsequently rate of decent with flaps deflected and not deflected. Basic trends in aircraft coning are in agreement between flight test measurements and simulated data. However, two major differences are noticed. First, flight test measurements often exhibit single or multiple roll rate reversals while simulation results do not exhibit this behavior. Moreover, pitch and yaw rate time histories do not match well. Secondly, flight test measurements of aircraft coning indicate erratic behavior. Both of these anomalies can be attributed to small gusts that excite the air vehicle during flight test that are not present in the nominal simulation results. To substantiate this claim, the two different gusts are inserted into the simulation to mimic the flight test environment. The first gust excitation consists of a slowly varying atmospheric mean wind beginning at 2.0 m/s and ramping to 2.4 m/s after 20 sec. The gust direction begins at an angle of just under 29 deg and reduces to 22 deg at 20 sec. Figures 15 through 18 show time simulation results of box angular rates, coning, and gust structure. Notice that multiple roll rate reversals are experienced by the aircraft and coning behavior is more erratic than the quiescent atmosphere of the nominal simulation. The second gust excitation consists of a random mean wind velocity bounded by 2.0 m/s and a sinusoidally varying atmospheric mean wind direction. As shown in Figures 19 through 22, this gust structure also creates multiple roll rate reversals and an erratic coning behavior. The third gust excitation consists of three discrete gusts impinging on the aircraft at an angle of 23.5 deg. As shown in Figures 23 through 26, the primary effect of the discrete gusts at a constant wind azimuth is to cause erratic peaks in the coning response. The roll rate response is not effected in a significant manner. Thus, it appears that the main cause of roll rate reversals is atmospheric winds that change direction as the aircraft flies through.

5

VI. Conclusions The flight dynamics of a flap controlled closed end box air vehicle has been explored by contrasting flight data with simulation results. Both dynamic model and flight test measurements exhibit the same gross behavior. The dynamic model has been shown to be capable of determining the descent rate of the box for both 0 and non-zero flap deflections. The box is very sensitive to wind disturbances which can greatly alter the coning angle and angular rates; however, the frequency of oscillation shows good correlation. Differences between flight data and simulation results are attributable to unknown wind gust, and imperfect in the aircraft used during testing.

References

1. S.F. Hoerner, Fluid – Dynamic Drag, Hoerner Fluid Dynamics, Bakersfield, CA, Library of Congress Catalog Card Number 64-19666, 1965.

2. S.F. Hoerner, H.V. Borst, Fluid – Dynamic Lift, Hoerner Fluid Dynamics, Bakersfield, CA, Library of Congress Catalog Card Number 75-17441, 1975.

Table 1 – Mass properties of the box configurations.

Box Configuration A B Mass (kg) 0.454 0.555

rCGx (m) -0.068 -0.079

rCGy (m) 0.001 0.000

rCGz (m) 0.000 0.008 Ixx (kg m2) 0.00234 0.00183 Iyy (kg m2) 0.00300 0.00603 Izz (kg m2) 0.00300 0.00556 Ixy (kg m2) 0.00000000 0.00000000 Ixz (kg m2) 0.00000000 0.00000000

Iyz (kg m2) 0.00000000 0.00000000

6

Figure 1 – Schematic of the Box Reference Frames.

Figure 2 – Orthographic View of Box with Controllable Flaps.

7

-90 -75 -60 -45 -30 -15 0 15 30 45 60 75 90-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

C X

Angle of Attack: α (deg)

γ = -90°γ = -75°γ = -60°γ = -45°γ = -30°γ = -15°γ = 0°γ = 15°γ = 30°γ = 45°γ = 60°γ = 75°γ = 90°

Figure 3 – Aerodynamic force coefficient along BI as a function of the aerodynamic angle of attack

and roll orientation ( 04321 ==== δδδδ degrees).

-90 -75 -60 -45 -30 -15 0 15 30 45 60 75 90-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

C Y

Angle of Attack: α (deg)

γ = -90°γ = -75°γ = -60°γ = -45°γ = -30°γ = -15°γ = 0°γ = 15°γ = 30°γ = 45°γ = 60°γ = 75°γ = 90°

Figure 4 – Aerodynamic force coefficient along BJ as a function of the aerodynamic angle of attack

and roll orientation ( 04321 ==== δδδδ degrees).

8

-90 -75 -60 -45 -30 -15 0 15 30 45 60 75 90-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

C Z

Angle of Attack: α (deg)

γ = -90°γ = -75°γ = -60°γ = -45°γ = -30°γ = -15°γ = 0°γ = 15°γ = 30°γ = 45°γ = 60°γ = 75°γ = 90°

Figure 5 – Aerodynamic force coefficient along BK as a function of the aerodynamic angle of attack

and roll orientation ( 04321 ==== δδδδ degrees).

-90 -75 -60 -45 -30 -15 0 15 30 45 60 75 90-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

C L

Angle of Attack: α (deg)

γ = -90°γ = -75°γ = -60°γ = -45°γ = -30°γ = -15°γ = 0°γ = 15°γ = 30°γ = 45°γ = 60°γ = 75°γ = 90°

Figure 6 – Aerodynamic moment coefficient along BI as a function of the aerodynamic angle of attack

and roll orientation ( 04321 ==== δδδδ degrees).

9

-90 -75 -60 -45 -30 -15 0 15 30 45 60 75 90-1.5

-1

-0.5

0

0.5

1

1.5

C M

Angle of Attack: α (deg)

γ = -90°γ = -75°γ = -60°γ = -45°γ = -30°γ = -15°γ = 0°γ = 15°γ = 30°γ = 45°γ = 60°γ = 75°γ = 90°

Figure 7 – Aerodynamic moment coefficient along BJ as a function of the aerodynamic angle of attack and roll

orientation ( 04321 ==== δδδδ degrees).

-90 -75 -60 -45 -30 -15 0 15 30 45 60 75 90-1.5

-1

-0.5

0

0.5

1

1.5

C N

Angle of Attack: α (deg)

γ = -90°γ = -75°γ = -60°γ = -45°γ = -30°γ = -15°γ = 0°γ = 15°γ = 30°γ = 45°γ = 60°γ = 75°γ = 90°

Figure 8 – Aerodynamic moment coefficient along BK as a function of the aerodynamic angle of attack and roll

orientation ( 04321 ==== δδδδ degrees).

10

Figure 9 – Flight Test Box Configuration A Ready Before Deployment.

Figure 10 - Flight Test Box Configuration B Ready Before Deployment.

11

Figure 11 – Schematic of Flight Test Operations.

12

a)

0 2 4 6 8 10 12 14 16 18 200

10

20

30

40

50

60

Coni

ng A

ngle

(de

g)

Time (s)

b)

0 2 4 6 8 10 12 14 16 18 200

5

10

15

20

25

30

35

40

Coni

ng A

ngle

(de

g)

Time (s)

Figure 12 – Coning Angle vs. Time from a)Testing Results and b)Simulated Results

(Box Configuration A , 04321 ==== δδδδ degrees)

13

a)

0 2 4 6 8 10 12 14 16 18 20

-5

0

5

P (r

ad/s

)

0 2 4 6 8 10 12 14 16 18 20

-5

0

5Q

(ra

d/s)

0 2 4 6 8 10 12 14 16 18 20

-5

0

5

R (r

ad/s

)

Time (s)

b)

0 2 4 6 8 10 12 14 16 18 20-5

0

5

P (r

ad/s

)

0 2 4 6 8 10 12 14 16 18 20

-5

0

5

Q (

rad/

s)

0 2 4 6 8 10 12 14 16 18 20

-5

0

5

R (r

ad/s

)

Time (s)

Figure 13 – Angular Rates with Respect to the Box vs. Time from a)Testing Results and b)Simulated Results

(Box Configuration A , 04321 ==== δδδδ degrees)

14

0 2 4 6 8 10 12 14 16 18 200

50

100

150

200

250

300

Alti

tude

(m

)

Time (s)

ModelTest

Figure 14 – Altitude vs. Time Comparison.

(Box Configuration A , 04321 ==== δδδδ degrees)

15

0 2 4 6 8 10 12 14 16 18 20

-2

0

2

P (r

ad/s

)

0 2 4 6 8 10 12 14 16 18 20

-5

0

5

Q (

rad/

s)

0 2 4 6 8 10 12 14 16 18 20

-5

0

5

R (r

ad/s

)

Time (s)

Figure 15 – Angular Rates vs. Time from Simulated Flight (Winds, Case I). (Box Configuration A , 04321 ==== δδδδ degrees)

0 2 4 6 8 10 12 14 16 18 200

5

10

15

20

25

30

35

40

Coni

ng A

ngle

(de

g)

Time (s)

Figure 16 – Coning Angle vs. Time from Simulated Flight (Winds, Case I).

(Box Configuration A , 04321 ==== δδδδ degrees)

16

0 2 4 6 8 10 12 14 16 18 200

0.5

1

1.5

2

2.5

3

Velo

city

(m

/s)

Time (s)

Figure 17 – Wind Amplitude vs. Time from Simulated Flight (Case I). (Box Configuration A , 04321 ==== δδδδ degrees)

0 2 4 6 8 10 12 14 16 18 20

18

20

22

24

26

28

30

Azim

uth

(deg

)

Time (s)

Figure 18 – Wind Azimuth Angle vs. Time from Simulated Flight (Case I). (Box Configuration A , 04321 ==== δδδδ degrees)

17

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

-1

0

1

2

P (r

ad/s

)

0 2 4 6 8 10 12 14 16 18 20

-5

0

5

Q (

rad/

s)

0 2 4 6 8 10 12 14 16 18 20

-5

0

5

R (r

ad/s

)

Time (s)

Figure 19 – Angular Rates vs. Time from Simulated Flight (Winds, Case II). (Box Configuration A , 04321 ==== δδδδ degrees)

0 2 4 6 8 10 12 14 16 18 200

5

10

15

20

25

30

35

40

Coni

ng A

ngle

(de

g)

Time (s)

Figure 20 – Coning Angle vs. Time from Simulated Flight (Winds, Case II). (Box Configuration A , 04321 ==== δδδδ degrees)

18

0 2 4 6 8 10 12 14 16 18 200

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Velo

city

(m

/s)

Time (s)

Figure 21 – Wind Amplitude vs. Time from Simulated Flight (Case II). (Box Configuration A , 04321 ==== δδδδ degrees)

0 2 4 6 8 10 12 14 16 18 2018

20

22

24

26

28

30

Azim

uth

(deg

)

Time (s)

Figure 22 – Wind Azimuth Angle vs. Time from Simulated Flight (CaseII). (Box Configuration A , 04321 ==== δδδδ degrees)

19

0 2 4 6 8 10 12 14 16 18 20-5

0

5

P (r

ad/s

)

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

-5

0

5

10

Q (

rad/

s)

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

-5

0

5

10

R (r

ad/s

)

Time (s)

Figure 23 – Angular Rates vs. Time from Simulated Flight (Winds, Case III). (Box Configuration A , 04321 ==== δδδδ degrees)

0 2 4 6 8 10 12 14 16 18 200

5

10

15

20

25

30

35

40

45

50

Coni

ng A

ngle

(de

g)

Time (s)

Figure 24 – Coning Angle vs. Time from Simulated Flight (Winds, Case III). (Box Configuration A , 04321 ==== δδδδ degrees)

20

0 2 4 6 8 10 12 14 16 18 200

0.5

1

1.5

2

2.5

3

Velo

city

(m

/s)

Time (s)

Figure 25 – Wind Amplitude vs. Time from Simulated Flight (Winds, Case III). (Box Configuration A , 04321 ==== δδδδ degrees)

0 2 4 6 8 10 12 14 16 18 2022

22.5

23

23.5

24

24.5

25

Azim

uth

(deg

)

Time (s)

Figure 26 – Wind Azimuth Angle vs. Time from Simulated Flight (Winds, Case III). (Box Configuration A , 04321 ==== δδδδ degrees)

21