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Final Thesis Report 2010, SEIT, UNSW@ADFA

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Modeling Aircraft Performance and Stability on X-Plane

Christopher W. S. Thong1

University of New South Wales at the Australian Defence Force Academy

Commercial flight simulator software has been long used by the public to hone their

piloting skills. X-Plane is the first commercially available flight simulator program

which directly outputs mathematical flight data without the need for programming

knowledge. This allows the public to readily simulate flight tests on a computer and also

acquire flight test data. This thesis models the F-15E in X-Plane and compares its

performance and handling characteristics to those predicted by theory and flight

manual data. These comparisons will be used to determine X-Plane’s usefulness as a

teaching and analytical tool in the demonstration of how forces and moments affect an

aircraft’s flight path in flight.

Nomenclature

Terms

CAM - Civil Aeronautics Manual

CFD - Computational Fluid Dynamics

CFT - Conformal Fuel Tanks

CG - Centre of Gravity

CPU - Central Processing Unit

DATCOM - DATa COMpendium

FADEC - Full Authority Digital Engine Control

FAR - Federal Aviation Regulation

FDM - Flight Dynamics Modules

FSX - Microsoft Flight Simulator X

GB - Gigabyte

Ghz - Gigahertz

GUI - Graphic User Interface

HUD - Heads-Up-Display

KIAS - Knots Indicated Air Speed

KTAS - Knots True Air Speed

NACA - National Advisory Committee for Aeronautics

NASA - National Aeronautics and Space Administration

RAM - Random Access Memory

RDS - Raymer Design Software

SFC - Specific Fuel Consumption

TR-824 - NACA Technical Report 824

USAF - United States Air Force

Variables

- Body frontal area

- Coefficient of Drag, consisting of skin friction, interference and pressure drag.

- Average aircraft wing chord

- Airfoil coefficient of lift

- Coefficient of drag on the body

- Maximum aircraft coefficient of lift

- Drag on body

- Wing Element Span

- Frequency

- Lift on wing element

1 Aeronautical Engineering Project, Thesis & Practical Experience ZEIT 4500


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- Pitching moment

- Dynamic pressure at flight condition

- Reference wing area

- Required Thrust

- Wing element velocity

- Stall speed

- Aircraft weight

-

- Angle of bank

ξ - Damping ratio

- Air density

- Natural frequency

I. Introduction

Computer flight simulation software has for decades been used extensively across the aerospace industry to

aid in the aircraft design. In this thesis, flight simulators will be taken to refer to computer software which

allows the user to pilot an aircraft with a visual representation of the cockpit and surroundings on the computer

monitor. It is also necessary to make the distinction between flight simulators and computer games which make

use of a similar cockpit GUI for the user to interact with. Thus, there is the additional constraint that flight

simulators must have a flight dynamics engine which sufficiently mimics real world physics. This is hard to

quantify so this thesis only considers software to be considered as a flight simulator if it focuses on the flight

dynamics and flying experience. While there are multiple benefits of flight simulation in relation to pilot

training (1 pp. 15-50), there are also numerous benefits for engineering applications. These include but are not

limited to:

time and cost savings as the aircraft can be simulated on the computer to determine its handling

characteristics and performance;

decreased personnel risk due to less actual test flights being flown ; and

the ability to test the effect of certain variables (such as the boundary layer effect or gravitational force)

on the aircraft which may be impossible to test in real life.

However, flight simulators built for engineering applications are usually expensive proprietary software,

built by major aircraft manufacturers to analyze aircraft before production. This thesis will use X-Plane, a

cheap, commercially available flight simulator, to model the F-15E aircraft.

Limitations of computer simulation are mainly based in the fundamental assumptions of the mathematical

model which drives internal calculations. Limitations may be exacerbated by the processing speed of the

computers used and accuracy required. Due to the usefulness of flight simulators, new software is constantly

being developed.

The thesis planning documents are contained in Appendices A, B and C whiles the essential and desirable

objectives of this thesis are listed below. Also, please note that due to the fact that numerous figures presented

in this thesis are in multiple colours, this report is best viewed in colour.

Essential Objectives

Collect dimensions, engine parameters and other required open source information on the F-15E

aircraft which will enable the creation of a model with maximum possible accuracy.

Build a model of the F-15E on X-Plane which can act as a teaching and building tool.

Obtain usable data relating to performance and handling qualities of the F-15E from public sources to

compare to X-Plane outputs.

Predict performance data and handling qualities of the F-15E by theoretical, non flight simulator means

to which the outputs obtained from X-Plane can be compared.

Compare the flight test outputs to predicted performance and stability data to assess the accuracy of the

simulator as well as the F-15E model.

Desirable Objectives

Develop as accurately as possible a working flight simulator model of the F-15E to assess the

possibility of making use of X-Plane to show the effect of changes on an aircraft.


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II. Methods of Predicting Aircraft Performance and Stability

There is a multitude of non-flight-simulator software which can provide estimates for aerodynamic

parameters, aerodynamic forces as well as stability and control characteristics of aircraft. These estimates will

be compared to certain X-Plane outputs so that the accuracy of using X-Plane can be established. The programs

elaborated on below are the more widely used software, each using different computational methods. It is also

possible to calculate certain parameters directly with the use of methods described by Raymer (2) and Roskam

(3) (4). Both these authors explain the method used to determine performance and stability characteristics and

provide necessary equations, graphs and historical data. They also explain the methodology as well as the

reasoning behind it and equation derivation in their books. However, their approaches are not covered in depth

in this section due to their relative simplicity.

A. USAF Stability and Control Digital DATCOM

DATCOM refers to a set of official USAF manuals which give guidance on how to calculate aerodynamic

coefficients, static and dynamic stability as well as control derivatives of fixed wing aircraft (5) while Digital

DATCOM refers to a USAF computer program written in FORTRAN which achieves the same task.

DATCOM requires the basic geometric properties, flight conditions and propulsion elements of the aircraft

under study in order to provide coefficients which approximate the performance and stability of the aircraft at

the stated flight conditions. It makes use of methods elaborated in the USAF Stability and Control DATCOM

volumes (6 p. 1) to compute 21000 different outputs from 125 inputs (7). The equations used by DATCOM are

stated in the official USAF Stability and Control DATCOM manual (8). DATCOM was developed on a

modular basis, with each module being a basic building block of an aircraft (6 p. 1). Examples of modules are:

body dimensions, synthesis parameters, wing plan form parameters and propeller/jet propulsion parameters (5).

Both Holy Cows, Inc. and the Open Aerospace Software Community have developed more user friendly

versions of DATCOM which are called DATCOM+ (9) and OpenDATCOM (10) respectively. While the only

difference between Digital DATCOM and DATCOM+ is some front end and back end adjustments to the

coding to increase user friendliness (7), Open DATCOM has a much easier to use GUI which was first released

as an alpha version in November 2009 (11). It is thus intended to use OpenDATCOM to predict the

performance and stability characteristics of the F-15E as this thesis author is unfamiliar with FORTRAN. .

Some limitations of DATCOM include not being able to calculate the effect of adding external stores or

inlets because DATCOM takes the fuselage to be a body of revolution as well as the fact that it is not possible to

attach two vertical tails to the aircraft. Possible remedies to these problems are increasing the cross section of

the fuselage such that the frontal cross section area of the enlarged fuselage is the same as that of the two inlets

in addition to the original fuselage and using a vertical tail with twice the area of the originals.

B. Raymer Design Software

RDS (12) primarily makes use of the aircraft design method outlined by Daniel P. Raymer Ph.D. in his book

―Aircraft Design: A Conceptual Approach‖ (13). RDS has multiple input parameters such as dimensions for

components including but not limited to the wings, fuselage, nacelles, seats and canopies. A component is

selected and the software then prompts the user for the required input data. RDS provides an extremely large

number of outputs and the ones most relevant to this thesis are performance outputs. These include takeoff and

landing speeds, rate of climb, turn rate and acceleration, which RDS can produce in graphical form.

While it was originally thought possible to use this software to predict the performance and handling

qualities of the F-15E, actual use of the software proved that it would be impractical to do so. One problem is

that the software requires aerodynamic inputs such as the aircrafts maximum, stall, climb and takeoff velocities,

as well as coefficients of lift and drag for the aircraft. This is because for aircraft design, the designer is

working towards designing an aircraft with certain characteristics in mind. Thus, this program cannot be used

for this thesis as most required RDS inputs are unknown.

C. Computational Fluid Dynamics

There are numerous different commercially developed computer programs which use CFD to solve fluid

flow problems including FLUENT, FLOW-3D and cfdesign. Due to the availability of FLUENT in the

university computer laboratories, it was initially planned make use of CFD by concentrating research on

FLUENT as well as learning how to use the software by enrolling in the CFD course. However, further work

on the subject proved overly time-consuming and CFD prediction was thus abandoned.

CFD is in essence fluid mechanic analysis of a situation making use of numerical methods and algorithms to

solve and analyze problems involving fluid flow. CFD makes use of three fundamental principles: conservation

of mass, conservation of energy and Newton’s second law (14 p. 5). These three principles lead to the Navier-

Stokes equations, as well as a variety of other equations necessary for modeling fluid flow. These mathematic

equations are usually partial differential equations in their most general form and CFD is the art of substituting

said equations for numbers and using the values along the boundaries to determine the fluid flow within the


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stated boundaries. CFD software does that by making use of

discretization methods such as the finite volume method, finite

element method, finite different method and the boundary

element method.

There are numerous ways of determining the fluid flow

within the boundaries. One could look at it as a two

dimensional situation or a three dimensional one. The user can

define a mesh which determines the number and position of grid

points at which the fluid flow must be determined.

FLUENT is extremely flexible and capable, with the ability

to model both laminar and turbulent flows, eddy currents and

vortices with a variety of different user defined methods. It can calculate the force, moment and pressure

distributions on objects in a flow based on the test piece’s geometry. FLUENT also presents data in a variety of

pictorial forms, one of which is shown in Fig. 1.

While it is fairly straightforward to develop simple models and meshes for use in FLUENT, it is a much

more complex task to model an aircraft in dynamic flight and was thus impractical to attempt considering the

scope of this thesis. This method can be very accurate in determining the forces on an aircraft but it would be

extremely time consuming to construct the model and complete the simulation. Even making use of a small

section of the aircraft (such as half the vertical tail) would require much calculation and modeling time.

Furthermore, the use of this extremely exact prediction method means that input data such as dimensions and

airfoils used would have to be much more accurate than those obtained for this thesis.

D. Comments

Due to the unavailability of the necessary specifications required to model the F-15E in RDS and the

resource intensity of CFD, these programs were not used to predict the performance of handling qualities of the

aircraft. However, OpenDATCOM appears to be a feasible method of predicting the required outputs. Of

utmost importance is the ability to validate our results. With the above stated software, the computer completes

all calculations and returns the requested outputs. This means that users are unable to obtain intermediate

calculations unless one writes new software to extract this data. Thus, certain calculations as described by

Roskam will be completed to validate a sample of OpenDATCOM outputs. The reason why Roskam’s

textbooks will be used instead of Raymer’s is due to the fact that Roskam is much more comprehensive and

detailed.

III. Existing Flight Simulators

This section reviews some of the best known flight simulators on the commercial market. All flight

simulators reviewed in this section appear to have adequate internal computations to determine aircraft flight

performance and handling characteristics. Unfortunately, they do not have a built in method to enable the user

to easily extract performance or handling data from the program without the need for programming knowledge.

While a large number of software tagged with the name ―flight simulator‖ exist commercially, most are either

computer games or have inadequate FDMs which do not calculate aircraft motion accurately enough to be

considered a flight simulator comparable to X-Plane. Thus, only the following two simulators were chosen to be

discussed in detail so that X-Plane’s greater suitability for this thesis can be appreciated.

A. FlightGear

FlightGear (15) is a free flight simulator maintained by Curt Olson which can be readily hacked to allow

users to tailor the program to their specific need. There are multiple different usable FDMs which make use of

different methods to model aerodynamic forces and moments to predict aircraft flight paths (16).

The most commonly used FDM is JSBSim (16) – an open source FDM in C++ which makes use of the

coefficient buildup method (17 pp. 5,16). JSBSim requires knowledge of the aerodynamic specifications such

as force and moment coefficients as well as stability and control derivatives (18 pp. 18 - 24). JSBSim also

requires data on graphs such as coefficient of lift versus angle of attack graphs. Due to its open source nature,

JSBSim is an extremely well developed FDM as an extensive range of users have contributed ideas for its

continual improvement (18 p. Preface).

Another notable FDM is YASim which, like X-Plane, takes primarily physical dimensions of the aircraft

into consideration for flight modeling (15 p. YASim Readme). The main difference between the two in terms of

data input is that YASim requires data such as cruise and approach information (15 p. YASim Readme) while

X-Plane takes airfoil data (19) instead. Thus, YASim, as with JSBSim, requires one to know to an extent the

abilities of the aircraft being modeled. There is a YASim helicopter FDM which makes use of blade element

theory (20) but throughout the process of literature review, no airplane FDMs were found which make use of

blade element theory.

Figure 1: A Hybrid Grid around an F-15

(55)


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While calculations are performed to determine the aircraft’s flight path in simulation, there are no prebuilt

options in the FlightGear simulation GUI or command line prompts for the user to automatically extract any

data to a spreadsheet or text file (15), (16). Thus, the user would have to write a program to interface with

FlightGear if he wanted to use this software to determine certain data values such as maximum thrust or lift to

drag ratio. One could even take the simulator out of the loop and feed data straight into JSBSim (17) or YASim

and extract data from there. However, these possibilities would require programming knowledge beyond that of

this thesis’ author.

B. Microsoft Flight Simulator X

FSX is one of the most popular flight simulation software products in the world (21). FSX makes use of an

FDM which consists of an ―*.air‖ file and an ―aircraft.cfg‖ file. The airfile contains hundreds of parameters

which define the aircraft’s flight characteristics but these parameters usually cannot be freely accessed and

altered due to copyright restrictions outlined by the aircraft manufacturers and the aircraft model designers (22).

Fortunately, the online community has developed hacking programs which allow the user to edit the .air file,

two of which being available at Mudpond (23) and Flight Simulator Aircraft Dynamics (24). The cfg-file is

made up of parameters such as joystick force feedback, elevator effectiveness, roll stability, CG location, engine

performance, aircraft geometry, stall speed etc. Most of the parameters contained in the cfg-file are related to

altering the user’s flight simulator cockpit experience and do not affect the flight characteristics of the aircraft.

The FDM largely depends on stability derivatives to determine an aircraft’s flight path. This flight simulator

does not provide any data output for users to graph or view and unfortunately for the flight simulator world,

Microsoft has laid off the entire Microsoft Flight Simulator team in order to ―align Microsoft’s resources with

(its) strategic priorities‖ (25).

C. Comments

The discussed flight simulation programs have very different backgrounds but similar outcomes – a usable

flight simulator which can be used for pilot training but no built in method of easily extracting flight data from

the simulator. This is largely due to the fact that most commercially available flight simulators make use of

stability derivatives to determine an aircraft’s flight path. Eq. 1 (2 p. 470) shows the yaw stability derivative.

(1)

Not only is stability derivative information kept confidential by aircraft manufacturers and their clients, the

above equation indicates that stability derivatives change with aircraft weight, payload positioning and aircraft

damage. Thus, if one was to simulate an aircraft in one of the above flight simulators, he would usually have to

predict the stability derivative required to achieve certain handling qualities in flight. Thus, it is possible to

have a visual model of a Boeing-747 which actually flies like an F-15 due to the fact that the model’s flight

characteristics are determined by stability derivatives as opposed to the actual simulation model. As a result,

these flight simulators cannot predict aircraft motion like X-Plane does. However, it is possible for one to use

an FDM in FlightGear which does not make use of stability derivatives. However, information on this was

sparse and thus not elaborated on.

IV. The X – Plane Software Package

X-Plane is a commercially available flight simulator which revolutionized the flight simulator industry by

using blade element theory in its FDM as opposed to the more traditional methods explained above (26). It is

not just a flight simulator used for pilot training and leisure; it can also be used to determine the forces on an

aircraft in flight and readily outputs flight data to the user without the need to do any programming. Numerous

companies and American government departments have purchased X-Plane in bulk to be used as an engineering

tool, including Cessna, Cirrus, Boeing, Lockheed Martin, NASA and the USAF (27). The software provided by

X-Plane consists of two relevant design programs with multiple inbuilt modules to enable its users to create

aircraft and airfoils as easily as possible.

The two programs are Plane Maker and Airfoil Maker. These two components, as their names suggest, are

used for designing aircraft and airfoils respectively. Due to the existence of an official X-Plane forum (28) and

the lack of specific details regarding X-Plane calculations in the user manual, this forum was engaged at

multiple times through the literature review stage so as to determine exactly how X-Plane completes

calculations and makes use of data for flight path prediction. Austin Meyer, the creator of X-Plane, was also

emailed a number of times for answers to more in-depth questions.

A. Mathematic Mechanics behind X-Plane


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Blade element theory is the method used by X-Plane to calculate an estimate of the forces acting on an

aircraft in flight. The aircraft’s lifting surfaces are divided into multiple longitudinal strips and the calculated

forces on each strip are then added together. This gives an estimate for the total force due to lifting surface such

as the wings and empennage on the aircraft. As an example, the lift equation shown in Eq. 2 (29) with dr, the

element span, being depicted in Fig. 2. The velocity used is the trigonometric sum of the longitudinal and

transverse component of flow over the wing. This allows X-Plane to consider the effect of sideslip on the forces

on the aircraft. The same method is used to determine the lift, drag and moment on all lifting surfaces made up

of an airfoil.

(2)

Laminar Research claims that

using blade element theory to

compute the forces on the aircraft is

more accurate than the stability

derivative method (26). Stability

derivatives indicate how quickly an

aircraft returns to straight and level

flight for each degree it is offset.

While this method is acceptable in

most civil aviation flight conditions, it

does not take into account effects

such as engine failures, turbulence,

stalls, spins, sonic effects and spiraling slipstream to name a few (26). Furthermore, the stability derivative

method is not able to predict how a new aircraft prototype will fly in a given flight condition. The aircraft

model creator has to have full knowledge of the aircrafts performance and stability characteristics as the

software is unable to determine them.

On the other hand, using blade element theory, X-Plane determines an aircraft’s flight characteristics with

the aircraft’s geometry as well as engine and airfoil data (26). The cycle of calculations determining the flight

path of the aircraft is contained in Appendix D, as stated on X-Plane’s official website (26).

Inspection of the data and calculation output from X-Plane gives some insight into the intricate details

regarding calculations involved. For example, it can be determined from the cycle dump file that the three

dimensional drag forces and moments on each modeled component is taken into account in each cycle. These

components include the fuselage, external stores and landing gear (if extended).

B. Plane Maker

Plane Maker (30) has numerous functions which allow the user to create nearly any possible aircraft

geometry. While Plane Maker creates the visual model used for simulation, it must be noted that unlike most

other commercial flight simulators, the dimensions of this model are directly taken into consideration for flight

modeling.

The modules contained within Plane Maker are used for designing the fuselage, wings, empennage,

undercarriage as well as miscellaneous bodies and wings such as wing pylons, speed brakes and CFTs. Due to

the fact that not all wings have wings of steady taper and airfoil, it will be necessary to model the aircraft with

multiple wing sections. Since the F-15E makes use of a NACA64A006.6 airfoil at the wing root and a

NACA64A203 airfoil at the wing tip, it is also necessary to model this in X-Plane with the right airfoil data. X-

Plane can interpolate between wing root and tip to obtain a smooth transition between the two airfoils (31)

which meets the above stated requirement.

In most of the modules, the user simply enters values into boxes for each stated parameter. However, for the

fuselage and miscellaneous bodies, it is possible to load a bitmap image onto the background of the GUI. A

bitmap image of the left side view and top view can be loaded. Plane Maker allows one to edit the fuselage

cross section at a maximum of 20 locations along the fuselage length, with up to nine nodes at each cross

section. This allows for much more accurate modeling of the fuselage than simply stating the radius and length,

as is the case in most software which can only model simple bodies of revolution.

When the designer is required to input the body coefficient of drag, the designer must include interference,

skin friction and pressure drag in this body coefficient of drag value (32). The drag on each body (such as the

fuselage) is then calculated with use of Eq. 3.

(3)

Figure 2: Depiction of how dr is determined on an F-15 wing (59)


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Other Plane Maker inputs include engine parameters and locations, forward, default and aft centers of

gravity and coefficient of friction between the wheels and the ground. Plane Maker can also blend parts of the

aircraft together, leading to the ability to smoothly join the fuselage and wings together like on the F-16 aircraft.

If necessary, Plane Maker has a GUI to program artificial stability and autopilot systems into the aircraft.

A notable characteristic of X-Plane is that it is compatible with numerous other well-known software

platforms such as Blender, SketchUp and FSX. Blender and Sketchup are drawing programs which allow one

to create objects. Aircraft models can be loaded from Blender into Plane Maker while scenery objects from all

three of the mentioned programs can be uploaded into X-Plane (33).

C. Airfoil Maker

Airfoil Maker is used to set the characteristics of the airfoils used by an aircraft. General airfoil information

required includes the Reynolds number at which the airfoil data is entered, the thickness to chord ratio and drag

divergence mach number at zero lift. Since a wing’s coefficients of lift, drag and moment vary with Reynolds

number, it is possible for one to insert data for the wing at multiple different Reynolds numbers and X-Plane

will interpolate between the data to determine the most realistic coefficients at the flight Reynolds number. If

data at only one Reynolds

number is input, X-Plane

will approximate for other

Reynolds numbers.

Next, the coefficient to

angle of attack graphs

must be set. The graph

shown in Fig. 3 depicts

the plot for the NACA

64A006.6 airfoil. The

graph shows the

coefficients between an

angle of attack of -200 and

200. Notable points would

include the fact that

minimum drag appears to

occur at zero angle of

attack, there exists a

maximum and minimum

lift coefficient which indicates the stall condition and that the

wing has a predominately pitch-down moment, as indicated by

the coefficient which is negative for most angles of attack.

Numerous controls are available which enable the user to

produce these graphs.

Airfoil Maker also presents the coefficient versus angle of

attack graphs from -1800 to 180

0 for the users’ information. The

user thus modifies the graphs for the -200 and 20

0 region and

determines the shape of the graphs over the remaining angles of

attack. The user can then check his airfoil data by calculating

the airfoil lift on drag ratio by inserting the aspect ratio and

Oswald’s efficiency factor of the wing.

There are a number of airfoils already built in X-Plane.

These are mainly standard NACA airfoils. The F-15E uses the

NACA 64A006.6 and 64A203 airfoils (34) and the only NACA

64 airfoil available in Airfoil Maker is the NACA 64-208 airfoil.

Thus, appropriate airfoils need to be created for an accurate

F-15E model. Two sources will be consulted for this – the

NACA Technical Report 824 (TR-824) and Javafoil. TR-824

contains airfoil data for numerous different airfoils and the ones

most similar to the F-15E’s are the NACA 64-006 and NACA

64-206. Data includes mean line data, the coordinates for upper

and lower surfaces, predicted critical Mach numbers and

aerodynamic characteristics such as the coefficients of lift, drag

and moment. These coefficients are necessary for modeling the

airfoil in Airfoil Maker but TR-824 only consists of data from -

Figure 3: Coefficient of Lift versus Angle of Attack (57) for NACA 64A006.6. Each

graduation on the x and y-axes indicates 10 angle of attack and 0.1 coefficient value

respectively.

Figure 4: Graphs of Coefficient of Drag

against Angle of Attack at multiple

Reynolds Numbers for NACA 64A006

(60 p. 177)


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120 to 16

0, as shown in Fig. 4. There were even less data points in some other graphs. Javafoil (35), a free

airfoil analysis program was used to approximate the coefficients over the rest of the required -200 to 20

0 range.

Javafoil outputs are contained in Appendix I.

Javafoil results are highly agreeable (36) with University of Illinois Urbana-Champaign (UIUC) wind tunnel

tests which is indicative of Javafoil’s accuracy. The UIUC experiments’ airfoil data were published in three

volumes (37) (38) (39) between 1995 and 1998 but unfortunately do not contain any data relevant to the airfoils

used in the F-15E (40). TR-824 was completed in 1945 and thus, the accuracy of the UIUC experiments can be

expected to be superior. Furthermore, the X-Plane stock airfoil data was compared to both TR-824 and Javafoil

data and was found to be more convergent to Javafoil data. Thus, when there was a deviation between Javafoil

and TR-824 coefficient values, the Javafoil value was favoured.

D. X-Plane Flight Simulator

The X-Plane Flight Simulator

program allows one to fly an aircraft

provided with the X-Plane software,

downloaded from the internet or

created by the user. There are many

features which increase X-Plane’s

realism. For example, if the payload

was changed, the new aircraft weight

and CG would be automatically

determined. As with other flight

simulators, system failures can be

programmed to occur as preset or

randomly. Also, airports from

around the world can be selected in

X-Plane Version 9.

The weather of the simulation

environment can be set which is

extremely useful when conducting

flight tests as the wind, cloud, precipitation and visibility can be set to optimum levels. Temperature and

pressure at sea level can be set to mimic the conditions at which the F-15E performance and handling data was

obtained. Turbulence and slipstream effects are also modeled in X-Plane (26).

The Flight Simulator has a Data Input & Output tab which is extremely useful for this thesis. The entire

flight’s data for up to 131 different parameter sets can be output into a text document for graphing or manual

interpolation. The table of all the possible data outputs is included in Appendix E. The 131 data sets provide

606 different parameters for the designed F-15E. The total number of data types would change dependent on

the number of components modeled in an aircraft. Up to 16 of these parameter sets can be displayed in real

time during flight. The user can set the disc rate, i.e. number of data points per second, to be between

0.1/second and 99.9/second. A disk rate of 15.0/second will be used since it is the default setting.

Structural limits can be set such that flying surfaces are removed in over-speed and over-G conditions, flaps

and gear doors are removed when they are extended beyond their stated never-exceed speed. This improves

realism for pilot training.

X-Plane also has the ability to pictorially present information about the aircraft’s flight path so far, the forces

acting on each object and wing, the velocity vectors of the flow field around the aircraft as well as angle of

attack vectors. This information is displayed on the aircraft model and an example of forces on the aircraft is

shown above in Fig. 5. In order not to clutter the pictorial display, only forces on the wings, empennage and

engines are displayed. One point which deserves explanation is that the element where the wing joins the

fuselage contributes the most lift to the F-15E. This is because the leading edge extension increases the lift at

this point.

E. Data and Cycle Dump Text Files

These two files are output by X-Plane and can be used for further analysis. The data text file is made up of

up to 131 different parameter sets as indicated in the output parameter selection tab is shown in Appendix E.

The data test file output after the completion of each flight contained data which was used to graph and

determine the F-15E model’s flight characteristics.

The cycle dump file on the other hand, is an entire cycle’s worth of calculations output into a data file. A

cycle is as described in Appendix E. It shows the calculations for force buildup on each element, engine,

miscellaneous object and payload item. Downwash and finite wing loss calculations are also taken into account,

Figure 5: A Screenshot from X-Plane of the Forces Acting on the

designed F-15E Model (27)


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as described in Appendix D. Cycle dump also gives the resultant radius of gyration in each of the three axes for

the simulated aircraft and the aircraft’s static margin.

F. Limitations

Online forums indicate what users think of X-Plane and how it compares to other commercially available

flight simulator software. However, most forum members are interested in the simulation experience such as

memory usage and the smoothness of graphics. Other than the inability to model fuselage lift, technical

limitations discussed by forum members include the inaccuracy of X-Plane in modeling separated flow over

surfaces as well as the lack of vortex analysis and inaccuracy of transonic and supersonic modeling. Another

real world effect which is not simulated in X-Plane is the wing flex.

Of importance to this thesis is the issue of X-Plane’s transonic and supersonic modeling (26). While

compressible flow effects are considered using Prandtl-Glauert, transonic effects are only simulated by an

empirical Mach-divergent drag increase. This is the Mach number at which compressibility effects start to

become apparent. The only GUI in which the Mach-divergent drag can be input is Airfoil Maker. In

supersonic flight, the aircraft airfoils are assumed to have a diamond shape with the same thickness ratio as the

input airfoils (26). Pressures behind the shock waves are then calculated on each of the plates on the diamond

airfoil and summed to give the total pressures on each airfoil element. This would enable the determination of

lift and drag on each airfoil element. Additional drag on each component due to supersonic effects is calculated

by determining the compression shock on each component. This compression shock is based on the angular

difference between neighbouring components and the local flow.

One interesting limitation of X-Plane is that if display options are set too high for the computer being used,

the cycle rate for completing calculations will decrease and the aircraft will suffer from abnormal oscillations.

Thus, in flight tests, graphics options were set to a minimum.

There are also some technical limitations discussed by online magazines. One such discussed limitation is

the inaccuracy of secondary aileron effect modeling. In reality, if a step aileron input acts on an aircraft, the

aircraft first rolls about its longitudinal axis and yaws in the opposite direction. After the turn is established, the

aircraft should yaw in the direction of the turn and if the turn is continued, the nose should drop and the aircraft

should enter a spiral descent. Sim Pilot Magazine writer looked at how a Cessna 172 in X-Plane reacted to an

aileron input (41). It eventually rolled in the opposite direction due to an increase in airspeed and a pitch up

moment developed after the initial roll. Thus, the spiral dive never developed, emphasizing the differences

between X-Plane’s mathematical modeling and reality. This scenario was recreated in X-Plane a number of

times to confirm the article’s claim and it was validated. This indicates that the authors other claims are also

likely valid. Due to time constraints, no attempt was made to determine the exact deficiency in the X-Plane

modeling.

V. F-15E Overview

In order to accurately model the F-15E in X-Plane, accurate dimensions and engine parameters were

required. The F-15E makes use of the Pratt & Whitney F100-PW-220 or F100-PW-229 engines (42), (42).

Since the only performance charts obtainable were those of an F-15E equipped with two F100-PW-220 engines,

the F-15E was modeled as such. Information on the F-15E was limited to aircraft dimensions, some engine data

and CG locations.

A. Dimensions

Externally, the F-15A and F-15E base airframes are identical, with the largest visible differences being the

addition of CFTs and a tandem cockpit on the F-15E (43 p. 55). The most specific F-15 schematic found is

included in Appendix F and was used to base the F-15E model on. Actual photographs of the F-15E were used

to accurately model the canopy and CFTs.

B. Performance

Basic engine data can be seen in Table 1.

Performance charts and data included in the F-15E flight

manual includes stall speeds, one engine inoperable

engine rate of climb, all engines operable rate of climb,

fuel required to climb, combat ceiling, optimum long

range cruise, long range cruise, level flight envelope,

maximum speed at level flight, dive recovery, level flight acceleration and sustained level turns. Most charts

are available for a variety of different aircraft configurations.

Usage of X-Plane indicates that the most easily replicated results would be those for stall speeds, level flight

envelope, maximum speed at level flight as well as sustained level turns.

Table 1: Data related to the F100-PW-220 (47)


10

An example of the data contained in the flight manual is shown in Appendix G (42 pp. A1-14) which

indicates the stall speed with gear and flaps up or down and provides a myriad of data which can be compared

with X-Plane outputs to test its ability to replicate real lift data.

C. Stability

Gross weight and CG locations for different payload combinations are contained in the F-15E flight manual

(42 pp. A1-8,9, A5-9). The aircraft has a 10 anhedral which has a slight destabilizing effect. This counters the

stabilizing effect of the high wing configuration, thus increasing the F-15E’s maneuverability.

VI. Creation of the X-Plane Model in Plane Maker and Airfoil Maker

In order to create a working model of the F-15E for use in X-Plane, it was necessary to study freely available

flight simulation models of the F-15E to fine-tune the method used to create the model. Unfortunately, all F-15

X-Plane models were found to be based on the model initially developed by Anthony Booher which meant that

there was only one original F-15 model available. This model was deconstructed piece by piece and numerous

errors, inefficiencies and points for improvement were found. One such inaccuracy with Anthony Booher’s F-

15E model is that it did not adhere to the official stall speeds.

Deconstruction and analysis of Anthony Booher’s F-15 model and other X-Plane fighter aircraft models

produced the following framework for producing the F-15E X-Plane Model. Numerous different components

were used to model the complex F-15E shape accurately.

A. Fuselage

The F-15E fuselage was relatively simple to

model. The cross section of the aircraft was

defined at 20 stations along the fuselage length

with the maximum of nine nodes selected at each

station. A bitmap image was loaded into Plane

Maker and each of the nine points can be dragged

into position. Accurate 3-view diagrams of the F-

15A were used to build the fuselage. Fig 6 shows

the top and side view of the model, with the top

view bitmap loaded. The body coefficient of drag

must also be defined in this section. This was

defined to be equal to 0.03, as indicated by

Hoerner’s estimations of drag numerous different

body shapes (44 pp. 3-9 to 3-22). Interference

drag was neglected at this stage and would be

taken into consideration if total aircraft drag was lower than expected.

B. Airfoils

Six different airfoils were used on this aircraft, with two being

airfoils provided in the X-Plane package and four being created during

this thesis. The two stock airfoil files used were the flat_plate(very

thin).afl and NACA0009(symmetrical).afl which were used for the

horizontal and vertical tails as well as the connection of the

empennage to the fuselage. The specially created

NACA64A006.6R9.afl, NACA64A203R9.afl and MidptR9.afl airfoil

files were used on the wings and leading edge extension while

eagle_fuse.afl was used within the F-15E fuselage to mimic the F-

15E’s ability to create lift with its fuselage.

The horizontal and vertical tails were modeled as very thin flat

plates as indicated by observation of photographs. This airfoil did not

produce any moment between angle of attack of -200 and 20

0 and

produced no lift when the angle of attack was 00. In reality, however,

aircraft typically use an airfoil which generates a force opposing wing

lift (2 p. 471). The use of very thin plat plates was deduced to be a

reasonable assumption this is standard practice in the X-Plane

community. Many comparable aircraft provided in the X-Plane

package as well as those produced by the online community make use

of flat_plate(very thin).afl for the horizontal and vertical tails.

Figure 6: The top and side view of the fuselage design GUI

(30), with a top view bitmap loaded to show how the

definition points line up.

Figure 7: Side view of the F-15E

Empennage


11

The empennage connection to the fuselage and wings was

modeled by making use of the NACA0009(symmetrical).afl

airfoil file. Being a symmetrical airfoil, it did not produce lift at

00 angle of attack. Also, as seen in Fig. 7 and 8, the airfoil is a

very similar shape to the actual empennage connection.

The NACA64A006.6R9.afl and NACA64A203R9.afl airfoil

files were designed by making use of two sources – TR824 and

the Javafoil program. The relevant TR 824 and Javafoil charts

are included in Appendix H and I respectively which can be

compared to the X-Plane airfoil files shown in Appendix J.

MidptR9.afl was designed by setting each of its input parameters

to be the mean between those of NACA64A006.6R9.afl and

NACA64203R9.afl. This is because MidptR9.afl was used to

ensure that the airfoil at the midpoint between wing root and

wingtip was such that there would be a smooth transition in

airfoil shape from root to tip.

Eagle_fuse.afl was used to simulate the fuselage lift of the F-

15E. Due to the fact that X-Plane does not reduce the drag or

moment on overlapping components, the coefficient of drag and moment of this airfoil were set to be zero so

that the internal airfoil would not cause additional drag or moments.

C. Wings and Empennage

The wings and miscellaneous wings functions were used to

create five different symmetrical wing sections, as well as the

horizontal and vertical tail planes. Each wing section is defined

by several factors. The factors are the wing section span, root

chord, tip chord, wing sweep, dihedral and wing location.

In order to determine these dimensions for each wing

section, measurements of three-view diagrams were taken for

each wing section. A bitmap can also be loaded onto the main

background of the GUI and the aircraft model can be rotated

such that it lines up with the bitmap. This was used to ensure

that the dimensions and location of each wing section was

correct.

Each wing section can also have a different wing incidence at 20 points

along its length. The wing incidence was estimated by observation of

different photographs of F-15s such as those in Appendix K. Due to a lack

of data, the wing incidence was estimated.

The wing airfoil can be set either to be a single airfoil or linearly

changing from one airfoil to another. This function was used such that the

airfoil could be selected to be a NACA 64A006.6 airfoil at the root and a

NACA 64A203 airfoil at the tip with the midpoint airfoil in between.

One wing section is set to be within the aircraft fuselage and engine

inlets to simulate the lift generated by the F-15E body. This section made

use of eagle_fuse.afl.

One wing section was designed as the leading edge extension up to the

engine inlet. Again, precise measurements were not available so the shape

was approximated with the NACA64A006.6R9.afl airfoil file.

The remaining three wing sections were used to model the F-15E main wing. Three separate wing sections

were required for accurate modeling due to the differing trailing edge sweep angles, as can be seen in Fig. 9.

The wing root was modeled as a NACA 64A006.6 airfoil and the tip was a NACA 64A203 airfoil. The wing

airfoil appears to vary linearly from root to tip and this was modeled by manually interpolating and creating an

additional airfoil as stated in the above airfoil section.

The empennage was designed by using three wing sections – one for each of the vertical tails and one for the

horizontal tail. Two wing sections initially used for the horizontal tail because of its unconventional stepped

shape, as shown in Fig. 10. Unfortunately, the more complex shape caused some issues as described in the

below discrepancies section. Thus, a simple unstepped horizontal stabilizer was used instead.

One unusual feature of the F-15 is that its fuselage creates enough lift to keep it airborne with only one wing.

This was demonstrated when an F-15I pilot was involved in a training accident which resulted in one entire

wing being ripped off from the wing root. (45 p. 420). Unfortunately, X-Plane is unable to determine if the

Figure 9: Four wing sections used to model

the F-15 leading edge extension (1) and the

main wing (2).

Figure 10: The sections

initially used to design the

horizontal tail

Figure 8: Bottom view of the F-15E

Empennage


12

fuselage will be able to generate lift. This was determined by reducing the coefficient of lift of all airfoils on the

aircraft to zero. The way around this was to insert a dragless wing within the model’s fuselage and X-Plane will

calculate the lift on that wing while still adding the drag of the fuselage to the model.

D. Engines

The engines modeled in X-Plane were F100-PW-220s. Their location and shape was determined by the

three view diagrams. The NASA Glenn EngineSim Program (46) was used to determine additional engine

parameters which were unavailable in the F100-PW-220 information sheet (47). The engines were set to have

specific fuel consumptions of 0.01/hr so as to have minimal effect on aircraft weight as the test flights

progressed. This meant that special test flights would not need to be designed to factor in changing aircraft

weight. Engines are only simulated to have drag if the engines are idling or flamed out.

E. Control Surfaces

The size and shape of ailerons, flaps and the rudders were determined from the three view diagrams. The

entire horizontal tail plane deflected to act as an elevator. The deflection angles were determined by observing

the deflection angles used to create similar X-Plane models. The ailerons were set to deflect 250 upwards and

150 downwards, the elevators were set to deflect 30

0 upwards and 18

0 downwards while the rudders were set to

deflect 300 in each direction. The flaps were plain flaps and set to deflect 30

0 downwards at full deflection.

F. Systems

Plane Maker has the ability for a designer to select properties in the aircraft’s electrical, bus, pressurization,

hydraulics, starter, warning, radio altimeter, instrument arc limits, external light, internal light and spring

bouncer systems. Due to the fact that these systems did not alter the X-Plane models flight characteristics and

were not required for accurate flight modeling, this section of modeling was not considered.

G. Artificial Stability

The artificial stability GUI allows one to specify the artificial stability and autopilot characteristics of the

model. The artificial stability system aims to maintain the model’s angle of attack, sideslip and roll-rate.

Without the appropriate artificial stability system, the model suffers from unwanted oscillations. During test

flights to confirm the artificial stability settings, inappropriate settings occasionally caused the model to oscillate

at such a rate that the airframe exceeded its g-limit. Autopilot settings also needed to be entered and fine-tuned.

Again, inappropriate settings caused excessive oscillations which made accurate test flights impossible.

H. Landing Gear and Speed Brake

The only tests requiring the landing gear to be down were the stall tests with flaps and gear deployed. The

X-Plane software does internal calculations to determine drag due to landing gear. The landing gear and speed

brake were sized with the aid of three view diagrams and photographs of the F-15E. This was a useful piece of

equipment during test flights as it enabled rapid deceleration of the model to the required test velocity. Neither

the landing gear nor speed brake contribute any drag while stowed.

I. Engine Intakes and Conformal Fuel Tanks

The engine intakes and CFTs were modeled with six different miscellaneous bodies so as maximize the

accuracy of the model’s shape, with three bodies on each side of the fuselage. One body was required to model

the air intake, one for the shaft from the air intake to the engine and one for the CFT. Due to the fact that X-

Plane does not reduce the drag for overlapping components, no more bodies were used. As with the fuselage

design, the miscellaneous bodies GUI allows each body to have up to 20 stations, each with 9 definition points.

The coefficient of drag also needed to be selected for these components. Due to the fact that air flows straight

through the engine intakes, the coefficient of drag was set to be minimal. However, if the aircraft were meeting

the air at an angle to the engine intakes, the intakes would still contribute drag based on its frontal area to the

angle of attack. This is in line with real world physics.

J. Other Miscellaneous Bodies

Miscellaneous bodies were also used to design the underbelly of the model, the cockpit and the boom

located in between the engine nozzles. The underbelly was shaped by comparison to photographs of F-15E

aircraft. The cockpit was shaped by use of the 3 view diagram. The cockpit’s coefficient of drag was again

obtained by comparison to similar bodies in Hoerner (44 pp. 3-9 to 3-22). The boom was also included for

accurate portrayal of the F-15E. Accurate portrayal of all parts of the aircraft was necessary for X-Plane to

determine the model’s frontal area when calculating drag.


13

K. Payload

The payloads used on the designed X-Plane

model were stock stores provided with the X-

Plane software. Table 2 provides information

on the stores used and their respective

asymmetric effects. Payload of differing

weights and location were tested to determine

if there was any measurable effect on the

model’s flight characteristics. Actual flight

tests or CFD would be useful to quantify the

effect of the tested payloads.

L. Cockpit Layout

Due to the fact that the cockpit layout of model is insignificant to the flight dynamics of the aircraft, the

cockpit layout of an existing model (48) which already had the essential autopilot switches and HUD was used.

This was to facilitate easier conduct of flight tests.

M. Aircraft Paint Scheme

The aircraft paint schemes only purpose is to improve the model’s image. It is possible to alter the physical

look of the aircraft with the paint scheme. This is undesirable but is hard to prevent due to the fact that the paint

scheme is designed by making use of photographs of the actual aircraft which leads to obvious differences

between the actual aircraft and the model. While this does not affect flight simulation and flying characteristics,

it may confuse users who are not familiar with the software. Thus, the model was left unpainted as this would

enable one to see the models actual geometry during flight.

N. Discrepancies between Model and Reality

One of the discrepancies between the model and the actual

aircraft is the lack of a step in the horizontal stabilizer. If the step

is modeled, each horizontal stabilizer is made up of two wing

sections. Each wing section would have a different root and

average chord. Since the horizontal stabilizers automatically

rotate about the quarter chord point, each wing section rotates

about a different axis and the horizontal stabilizer resultantly

separates during deflection. This effect is shown in Fig. 11. This

leads to the moment about the CG of the model being slightly

incorrect as the forces on the outboard section of the horizontal

stabilizer act on a different plane. It will also cause concern to

users of the X-Plane model who are unaware of this issue. In

order to correct this, the F-15E was modeled with non-stepped

horizontal stabilizer. The surface area of the horizontal stabilizer

was kept the same so as to maximize accuracy of forces and

moments simulated.

One more physical difference between the model and real

aircraft is the fuselage to empennage connection region. The

difference is shown is Fig. 12. The difference exists due to

miscellaneous bodies in X-Planes requiring an axis of symmetry.

It would be possible to use another few miscellaneous bodies to

increase the visual accuracy of the model but this would not lead to significant improvements in simulation.

This is because X-Plane does not factor in the effect of fluid flow around miscellaneous body on another (49).

Thus, additional modeling would only lead to overly increased drag since X-Plane doesn’t take into account the

overlapping of components.

Another difference is that the F-15E was modeled with an SFC of 0.01/hr. This meant that a negligible

amount of fuel was consumed in flight and that test flights need not be designed to factor in weight loss. Fuel

consumption is the only parameter affected by SFC so this does not alter the models flight characteristics at all.

The rationale behind being able to neglect weight loss in flight is explained in Appendix L. There is some

discrepancy in that the real F-15E has a rounded wing tip but the X-Plane model has a straight wing tip, this has

been decided to be acceptable as the wing area was kept the same.

Table 2: Comparison of Payload Asymmetric Effects

Figure 11: Separation of horizontal

stabiliser due to use of two wing sections

Figure 12: Slight shape discrepancy to

prevent overlapping of components


14

VII. Prediction of F-15E Performance and Stability by Methods other than X-Plane

As stated above, this thesis aims to compare X-Plane flight test results to theoretical predictions as well as

flight manual data. This section will analyse the predictions and determine if they can be used as a baseline to

which flight test results can be compared.

A. OpenDATCOM

Unfortunately, through use of the program, it was discovered that there are some errors present in the

OpenDATCOM GUI. Thus, no outputs were able to be extracted from OpenDATCOM. However, it would be

possible to use the determined inputs in DATCOM+ or the original Digital Datcom program. This would only

be possible if the user has experience in using FORTRAN, which this thesis author does not. Thus, while not

used in comparison of X-plane outputs, DATCOM inputs are attached in Appendix M while explanations to the

terms are contained in (50) so that future work can be readily initiated with regards to the use of DATCOM to

further refine the F-15E model.

B. Flight Manual Data

The F-15E flight manual contains data and charts which

have aided in the design of the F-15 X-Plane model. The

charts with which the experimental data are compared to are

contained in Appendix G and N. The charts in Appendix G

indicate the F-15’s stall speed at 00, 15

0, 30

0, 45

0 and 60

0

angle of bank at a range of aircraft weights between 30000lbs

and 80000lbs while the charts in Appendix N shows the level

flight acceleration on the F-15 at set weights between

42800lbs and 66900lbs. The level flight acceleration graphs

taper off to the maximum speed for the thrust setting

(maximum or military) at 10000ft and 40000ft which is the

value we can compare the F-15 model’s maximum level flight

speed to. Maximum thrust is the aircraft’s maximum thrust

with afterburners while military thrust is the aircraft’s

maximum thrust without afterburners.

There is also an uncertainty associated

with the flight manual data. This is due to

the flight manual’s method of data

presentation. The data is all presented on

graphs and it is necessary to read the data

from the graphs. Thus, the uncertainty in the

flight manual data at each point would be

equal to half a division of the graph. Tables

3 and 4 show the percentage uncertainty

associated with each data point taken from

the flight manual. This analysis led to

suspicion that the flight manual data may

contain some anomalous results. This is

because the maximum level flight speed at

61500lbs did not conform to the trend of the

other data points. The maximum level flight

speed for all conditions was expected to decrease with increasing aircraft weight but the data at 61200lbs

appears to be an outlier. The data in the flight manual definitely has an associated uncertainty and this would

most likely be the cause of this discrepancy. Unfortunately, the uncertainty in flight manual data was not

included in the flight manual.

C. Theoretical Calculations

Since DATCOM could not be used to provide the bulk of prediction data, Roskam’s aircraft design manuals

were used to calculate the expected stall speed, maximum level flight speed as well as the phugoid and short

period characteristics.

The stall speed is simply obtained by making use of Eq. 4. The wing reference area was simply obtained

from (34), with air density being dependent on altitude while weight is the chosen variable. The maximum

aircraft coefficient of lift was obtained from flight manual stall speed data by making use of Eq. 4. The chosen

maximum aircraft coefficient of lift was the one which led to the least percentage deviation between

Table 4: Percentage Uncertainty in Flight Manual Maximum

Thrust Data

Table 3: Percentage Uncertainty in Flight

Manual Stall Speed Data


15

theoretically predicted stall speeds and flight manual stall speeds. This method was used as the exact required

data was unobtainable in open source sources.

√

(4)

The theoretical and official clean stall speed values are as stated in Table 5. Due to the lack of open source

information on the maximum aircraft coefficient of lift, this value was determined from the official stall speed.

The differences between the official and theoretical stall speeds for clean and flapped configurations for the full

range of aircraft weights were at their minimums with a clean maximum aircraft lift coefficient of 2.36 and

flapped maximum aircraft lift coefficient of 2.46. Raymer indicates that the flapped maximum aircraft lift

coefficient should be 0.9 more than the unflapped value due to the use of plain flaps (2 p. 326). This is not the

case in these calculations which may indicate that the F-15E’s flaps are not as effective as those on other

aircraft.

The theoretical stall

speed in KTAS was

determined from Eq.4

and subsequently

changed to KIAS. The

maximum percentage

difference as seen is -

3.64%. As can be seen,

the theoretical stall

speed is higher than

official values at lower

weights but is lower

than official values at

higher weights. This

would indicate that the

assumption that the

aircraft has a single value for the maximum aircraft coefficient of lift is incorrect. The trend indicates that as the

F-15E’s weight is increase, its maximum aircraft coefficient of lift actually decreases. This is contrary to what

Raymer’s equations suggest in (2 pp. 316 - 327).

The maximum level flight speed can be determined with Raymer (2 p. 518). However, the Raymer

calculations require knowledge of the aircraft’s coefficient of drag. In order to determine the coefficient of drag

theoretically, it is necessary to factor in the skin friction drag, pressure drag, induced drag, interference drag as

well as wave drag. While not impossible to calculate, it will be extremely tedious to consider all required

factors.

Calculated engine power output would not be an appropriate baseline which X-Plane outputs could be

compared to. This is due to the fact that the F100-PW-220s on the F-15E make use of a FADEC and wastegate

to control the power output at different heights for maximum efficiency. Thus, maximum level flight speed

calculations will not be done.

The F-15E flight manual does not contain any numerical data or charts relating to phugoid or short period

motion. Thus, it was necessary to determine these characteristics through theoretical calculations. The

equations used in the calculations are contained in Appendix O. 31 input parameters are required, with 5 of

them either requiring excessive amounts of calculations (such as drag value) or unavailable data (such as

)

and 4 parameters being dependent on flight test conditions. Those 5 parameters were thus determined through

flight tests. The rest of the input parameters were

simply obtained from measurements of three-view

diagrams or available F-15E data. The 31 input

parameters used in this set of calculations are listed and

valued in Appendix R. The phugoid and short period

and ξ for the F-15E were thus calculated at altitudes of

10000ft and 40000ft and weights of 32000lbs, 55000lbs

and 80000lbs. The reason only six tests were conducted

for the phugoid and short period motion flight tests is

that much time is required for each test as well as its subsequent calculations.

Calculations were completed so as to determine the uncertainty associated with the short period and phugoid

and ξ due to measurements taken. The uncertainty is only due to measurements taken and does not include

Table 5: Comparison of Theoretical and Official Stall Speeds

Table 6: Uncertainty in Dynamic Longitudinal

Stability Theoretical Calculations


16

the uncertainty associated with

and

. This is because those two parameters were extremely hard to

measure accurately due to the fact that the aircraft suffers from slight oscillations. The oscillations can be seen

in all the X-Plane output graphs contained within the Appendices. The uncertainty associated with

and

could not be measured due to this fact. Thus, a certain amount of trial and error was required to determine

and

values which were generally correct. Further testing would enable more accurate predictions of

. This is because the is the only prediction which requires those two parameters as inputs.

Thus, since the uncertainty associated with

and

was not included in the measurements, the uncertainty

for ζ and is actually slightly more than as stated in Table 6.

The uncertainties in Table 6 also do not take into account the fact that Roskam’s equations are

approximations of real world effects. Assumptions are made so approximate an aircraft’s motion to the

equations. This is an avenue for uncertainty but cannot be measured.

One fact which can be deduced from Table 6 is that there is much more uncertainty associated with short

period motion characteristics than phugoid ones.

D. Summary of Results

The data from the official F-15E flight manual was originally expected to be perfect. However, the above

analysis indicated that certain data (such as the maximum speeds at 61500lbs) could be anomalous.

Furthermore, there would definitely be an uncertainty associated with the data which was not stated in the flight

manual. There were no anomalous data points in the stall speed charts. The uncertainty associated with reading

the flight manual charts was between 0.42% and 1.18% for maximum level flight speeds and between 0.56%

and 0.91% for stall speeds. Thus, the F-15E model would be expected to achieve a maximum level flight within

1.2% of flight manual data and stall speeds less than 1.0% different to flight manual data.

Theoretical stall speeds show close compliance with an uncertainty of only 3.7% to flight manual data. This

would indicate that it is unlikely that the flight manual stall speed charts would contain significant errors.

However, analysis indicates that the aircraft coefficient of lift would be a changing value. Due to the lack of

any definitive data on the aircraft coefficient of lift, this parameter will be taken as a constant.

Phugoid and short period and ξ cannot be compared to any real world data. Thus, the theoretical data

cannot be validated against anything. However, they can be expected to be fairly accurate in giving a general

estimate of the actual aircraft and ξ. This is because the and ξ align with expected values. As expected,

is very close to unity, while is closer to zero. The are also significantly

shorter that .

All considered, the predictions are expected to be fairly accurate baselines to which flight test data can be

compared.

VIII. Flight Test Methods

The model’s stall speed, level flight acceleration and maximum speed as well as dynamic longitudinal

stability are examined in this section. The reason these four performance and stability characteristics were

chosen is that they can be verified by methods mentioned in previous section as well as the fact that they test

different flight dynamics characteristics.

Stall speed (51 pp. 53, 54) is an indication of the aircraft’s lift while level flight acceleration and maximum

speed is an indication of thrust and drag. Dynamic longitudinal stability is dependent on a multitude of aircraft

parameters, as indicated in Appendices O and P.

In order to accurately conduct the test flights and compare data extracted from the simulated flights to flight

manual data, the simulated test flights must conform to the required test standard. The different test procedures

are clearly stated below, with certain alterations made due to simplifications made possible by the use of a flight

simulator to conduct the test flights.

A. Stall Speeds

The following method was considered for stall speed testing. It is the method stated by both CAM3 and

FAR Part 23 and summarized in (52 pp. 47-52). The aircraft should first be trimmed at approximately 1.5 times

the stall speed. Following that, the throttle should be brought back to idle and the deceleration rate to stall be

kept at 1 kn/s. The first two conditions could be met easily but there was no easy way of measuring and

controlling the deceleration. Thus, this method was altered slightly such that the test pilot simply keeps the

aircraft flying straight and level till the aircraft stalls.


17

The stall is defined to be the point at which the aircraft pitches nose down uncontrollably in level flight.

This point can be confirmed by using X-Plane’s data output function. The aircraft’s elevator deflection, altitude

and calibrated airspeed can be displayed as a function of time.

The aircraft had no external payload, as stated in the official flight manual. The flight manual contains stall

graphs for the aircraft in the clean condition as well as stall graphs for the aircraft with flaps and gear down.

Thus, flight tests were conducted for the F-15E in both configurations. Appendix L shows the calculations

which indicate that the weight change in each flight test is negligible. While this is completely unrealistic in

mimicking real world physics, it is an advantage of making use of flight simulators and keeps the CG position

as well as the aircraft weight basically constant throughout the test flight.

In order to accurately measure the stall speed of an aircraft at a given altitude and weight, each test point was

tested three times. This is to ensure validity of data. Any anomalous data points would be replaced by data

from another test. The resultant stall speed is the average of the three data points. Due to the fact that official

stall speeds were determined to the closest whole number, flight test results shall also be presented to the closest

whole number.

Two main test groups were conducted – one for the F-15E in the clean configuration and one in the flaps and

gears down configuration. The model’s stall speed was determined at 32000lbs, 45000lbs, 55000lbs, 65000lbs,

75000lbs and 80000lbs as well as at angles of bank of 00, 15

0, 30

0, 45

0 and 60

0 for both F-15 configurations. All

stall tests were conducted at 10000ft.

B. Level Flight Acceleration and Maximum Level Flight Speed Flight Test Procedure

The actual flight test technique for the speed power test of a jet aircraft is quite complex and it involves

many mathematical calculations, including the use of non-dimensionalisation to ensure accurate results. This is

because as fuel is burnt, the aircraft becomes lighter. In a real world flight test, the aircraft would be flown

while varying test altitude in order to keep a constant

(52 pp. 99, 100). This would require a large amount of

preflight planning as well as a great amount of pilot skill as it would be imperative to fly exactly the correct

flight path. However, as explained in Appendix L, the aircraft’s change in weight for these flight tests is

negligible. Thus, the method used would be to simply reach the required test altitude, stabilize at the test

altitude, engage the altitude hold autopilot, reach the initial test flight velocity then increase the throttle to its

appropriate maximum or military thrust setting and wait for the aircraft to reach its maximum speed.

The maximum level flight speed at maximum thrust was taken to be when the throttle was at maximum

thrust with afterburners engaged, altitude is constant and the aircraft was unable to accelerate anymore. The

maximum level flight speed at military thrust was the same but without afterburners.

The aircraft payload and weight were as stated for the stall speeds. The test flights were conducted with a

clean airframe. Due to the continuous nature of this flight test, only one test needs to be conducted at each

altitude and weight.

The tests were carried out at 10000ft and 40000ft, at 9 different aircraft weights between 42800lbs and

66900lbs. This is such that each available flight manual graph can be compared against. The tests at 10000ft

were conducted both at maximum thrust as well as at military thrust while those at 40000ft were conducted at

maximum thrust. This is due to limitations in flight manual data.

C. Dynamic Longitudinal Stability Flight Test Procedure –

Phugoid Motion

(52 p. 248) indicates that the aircraft should first trimmed to

the test trim speed at the predetermined test altitude. Once these

conditions are met, the aircraft is then displaced by 10 to 15

knots from the trim by elevator deflection. The control column

is then released and the resultant aircraft oscillation is recorded.

The airspeed can be either increased or decreased and normal

procedure is to observe phugoid motion from both cases. Once

the control column is released to its trim position, the control

column can be left free or held steady. Again, both possibilities

are usually tested as differences between stick-fixed and stick-

free cases normally exist. However, due to the lack of feedback

in the joystick used to interface with the flight simulator

program, the stick-fixed case cannot be simulated. This was the

exact method used to conduct these flight tests.

The method for calculating of the from flight test

data is shown in Fig. 13 while the calculations required for

are shown in Eq. 5 and Eq. 6.

Figure 13: Chart used to determine the

Phugoid Damping Ratio (52 p. 250)


18

√ (5)

Where

(6)

The phugoid motion is a large amplitude variation of aircraft airspeed, pitch angle and altitude. From a side-

on perspective, the aircraft would appear to be travelling in a sinusoidal motion. The important values

determined by this flight test are and the . The of an aircraft is it’s resonant frequency, the

frequency at which oscillations will increase amplitude with increased oscillations. ξ is related to the ratio of an

oscillatory amplitude to the following amplitude. If the ξ is positive, it is a measure of how quickly an

oscillation converges. If the ξ is negative, it is a measure of how quickly an oscillation diverges.

The aircraft payload was as stated for the stall speeds. Due to the substantial time taken for each test and

their consequent required calculations, only three weights were considered for the phugoid motion tests. These

weights were 32000lbs, 50000lbs and 80000lbs. CG location and weight changes were not considered as

indicated by Appendix L.

Two flight tests were conducted at each flight condition so as to obtain results from both possible flight test

methods. The aircraft was allowed to undergo at least five full oscillations in each flight test so that an average

and can be obtained.

The flight tests were conducted at altitudes of 10000ft and 40000ft, meaning a total of twelve different flight

tests.

D. Dynamic Longitudinal Stability Flight Test Procedure – Short Period Motion

There are three possible methods to conduct the short period motion flight test – the pulse input, doublet

input and 2-g pull up method. The method used in this thesis was the doublet input due to its ability to suppress

the phugoid motion as well as the lower required pilot ability. The doublet method requires the aircraft to first

be in a trimmed, unaccelerated level flight. Once the test begins, the pilot rapidly moves control column

forward (or backward), then backward (or forward), then back to trim. Again, due to the joystick used, it was

not possible to hold the control column at the trim position so the stick-free scenario was considered.

An aircraft’s short period motion is usually a heavily damped oscillation with a maximum period of a few

seconds. The motion is a rapid pitching of

the aircraft about its CG. Due to the rapidity

of oscillations, it is important for an

aircraft’s short period motion to be heavily

damped as the pilot would be unable to

correct the motion easily. Again, the short

period oscillations have an and ξ with

the same definitions as those for the phugoid

motion, with the method of determination

contained in Fig. 14.

The aircraft payload and weight will be

as stated for the phugoid motion tests.

As with the stall tests, each flight test

was conducted three times. Ideally, the

aircraft would have the same airspeed and

altitude at the start of each test. The doublet

method will be varied alternatively, i.e. if on

the first test the aircraft is displaced upwards

then downwards, in the following test it will

be varied downwards then upwards.

The flight tests were conducted at

altitudes of 10000ft and 40000ft for a total

of six different flight tests.

IX. Quantitative Analysis and Verification of X-Plane Outputs

This section will focus on analyzing and verifying the results of the X-Plane flight tests. The analysis

section will consider the results of each set of flight tests and confirm if they conform to an expected trend. It

will indicate X-Plane’s ability to mimic real world physics. This is determined by whether each set of flight test

results conforms to the expected trend.

Figure 14: Method to determine short period natural frequency

from flight test data (52 p. 252)


19

The verification section will indicate the accuracy of X-Plane’s flight characteristic prediction. Verification

will be done in two ways - one will be to simply compare the obtained flight test results to the official and

theoretical values while the other will be to take into

account the change in tested flight characteristic with

the flight test variable. The second form of

verification is called the delta method as it simply

considers the delta, or change, of a variable. This

would enable any inaccuracies in modeling the F-15E

to be neglected. The verification section will also

determine the source of inconsistencies between flight

test, theoretical and official values and look at

possible ways to improve the F-15E model if it is

determined that further improvements are required.

It should be noted that in this section, any

reference to flight testing would be specifically to

flight tests conducted in X-Plane with the F-15E

model designed by this thesis author.

A. Clean and Flapped Stall Speed Test Analysis

As an aircraft’s weight increases, so does its stall

speed, as indicated in Eq. 4. The stall speed also

increases with aircraft angle of bank. This is because

roll decreases the lift force working against aircraft

weight, as depicted in Fig. 15. These trends are visibly

present in the Fig. 16 and Fig. 17 plot. As angle of

bank and aircraft weight increases, so does stall speed.

It can also be seen that at two points in each graph, the

plots for stall speeds at 00 and 15

0 angle of bank

overlap. This can be attributed to pilot error.

Furthermore, the official clean stall speeds for

unbanked flight is114kts at 32000lbs and 174kts at

75000lbs while those for 150 banked flight is 116kts at

32000lbs and 177kts at 75000lbs. These values are

extremely close and a slight deviation in data may lead

to the plots overlapping. Similarly, the flapped stall

speed values are very close together for 00 and 15

0

angle of bank. Thus, apart from the infrequent

overlapping, the trend behaves as expected. This would

indicate that the X-Plane software simulates stall speeds

correctly. The following section will quantitatively

consider the ability of X-Plane’s simulation software to

accurately model stall.

B. Clean and Flapped Stall Speed Verification

The comparison plot and table of X-Plane

flight test to flight manual clean stall speeds

against aircraft weight at 00 angle of bank are

shown in Fig. 16 and Table 7 respectively. The

complete set of the clean stall speed comparison

plots are contained in Appendix Q. The difference

between X-Plane clean stall speed test results and

official values for the entire range of aircraft

weight and angle of bank is less than 4.7%, as

indicated by Table 7.

The comparison plot and table of flapped stall

speeds against aircraft weight at 00 angle of bank

are shown in Fig. 17 and Table. 8 respectively. The

rest of the flapped stall speed comparison plots are

contained in Appendix R. The difference between

Figure 15: Depiction of Lift and Weight Forces on a

Banked Aircraft (58)

Figure 16: Flight Test Clean Stall Speeds

Table 7: Percentage Difference between Flight Test and

Official Clean Stall Speeds

Figure 17: Flight Test Flapped Stall Speeds

Table 8: Percentage Difference between Flight Test and

Official Flapped Stall Speeds


20

X-Plane flapped stall speed test results and official values for the entire range of aircraft weight and angle of

bank is less than 3.4%, as indicated by Table 8.

The clean and flapped stall speeds indicate both a high degree of accuracy of the X-Plane F-15E model in

terms of its stall characteristics as well as a high degree of accuracy of the X-Plane software in modeling the

stall condition.

C. Level Flight Acceleration and Maximum Speed Analysis

It was initially planned to only consider the maximum level flight speed. However, upon conducting initial

flight tests to refine the F-15E model’s accuracy, it was discovered that the F-15E model had substantial issues

with reaching its appropriate maximum level flight velocities. At 10000ft and maximum thrust, the aircraft

accelerates to a maximum speed of Mach 1 instead of the official value of Mach 1.35 while at 40000ft, 42800lbs

and maximum thrust, the aircraft only reaches Mach 1.4 as opposed to the official value of Mach 2.4. Thus, it

was determined to also consider the acceleration from 250KTAS such that it can also be compared to the charts

from the F-15E flight manual. 250 KTAS is approximately equivalent to Mach 0.39 at 10000ft and Mach 0.83

at 40000ft.

Figs 18, 19 and 20 are graphs of time taken to accelerate from 250 KTAS to its maximum speed with the F-

15E’s simulated acceleration compared to the official values by putting them on the same graph. Flight manual

graphs were loaded onto the plot background with flight test results superimposed over them. The rest of the

comparison plots are shown in Appendix S.

D. Level Flight Acceleration and Maximum Speed Verification

The maximum test speed

at all altitudes and thrust

levels differ significantly

from the official values. At

10000ft, for both maximum

and military thrust, flight tests

indicated that the F-15E

model accelerates to Mach 1

for all weights. At 40000ft,

the aircraft obtains a

maximum speed of

approximately Mach 1.35.

The flight manual

indicates that at 10000ft and

maximum thrust, the F-15E should accelerate to Mach

1.35 at 42800lbs and 1.06 at 66900lbs. At military

thrust, the aircraft be able to reach Mach 1 at the

minimum tested weight of 42800lbs but would be at

lower speeds at higher weights. At 40000ft, the

aircraft at minimum and maximum test weights should

accelerate to Mach 2.4 and Mach 1.6 respectively.

However, as can be seen from Fig 18, 19 and 20

the F-15E model accelerates much faster than stated in

the flight manual. This trend is consistent in all level

flight acceleration flight tests. These graphs may

prove hard to read in black and white.

The lower maximum speed at maximum thrust

indicates that X-Plane simulates too little thrust to

drag in supersonic flight, while the higher maximum

speed at military thrust and greater acceleration

indicates that X-Plane simulates too much thrust to

drag in subsonic flight. There are two possibilities for

the significant differences between simulated and real

world data – either the X-Plane model could be

imperfectly built or the simulator could be incorrectly

modeling real world physics.

The X-Plane model may be inaccurate in two

aspects – the thrust at 10000ft and 40000ft may have

been set too high or the total drag on the aircraft could

Figure 18: Comparison Chart of X-Plane Outputs to Flight Manual Chart (42)

Figure 19: Comparison Chart of X-Plane Outputs to

Flight Manual Chart (42)

Figure 20: Comparison Chart of X-Plane Outputs to

Flight Manual Chart (42)


21

be too low. This was deduced by the previous analysis.

The thrust at altitude was determined by the X-Plane software, with the only way to change this parameter

being to change the baseline thrust at 100% low compressor speed at sea level, the critical altitude at which the

engine can put out its maximum allowable thrust, and whether the FADEC or waste-gate system is engaged.

The FADEC controls the operating parameters of the engine such that it operates at its maximum efficiency for

all flight conditions while the waste-gate prevents the engine from exceeding its maximum allowable thrust.

The critical altitude and FADEC settings were chosen after consulting the official X-Plane forum and Anthony

Booher, the designer of the other available X-Plane F-15 models. This may be an avenue for error but the lack

of other open source information on these parameters led this thesis author to make use of values recommended

by the X-Plane forum. Another source of error may be that Janes rates the F100-PW-220 in terms of dry thrust

and maximum takeoff thrust instead of thrust at 100% low compressor speed (47). This refers to the thrust

when the stage 1 low pressure compressor is at its maximum speed. This dry thrust value was assumed to be

equal to the 100% low compressor speed, with the difference between maximum takeoff thrust and dry thrust to

be equal to the additional thrust provided by afterburners. This assumption may be found to be invalid with

more data but open source information does not state the 100% low compressor speed thrust.

The total drag on the aircraft could be overly low due to a number of factors. The drag coefficient on each

component could have been set too low or the software could be incorrectly determining skin friction,

interference and wave drag. The only possible way of altering the drag on the aircraft would be to change the

drag coefficient on each component.

At 10000ft and military thrust, the F-15E model flies faster than expected while at 40000ft and maximum

thrust, the F-15 model flies slower than expected. While increasing weight was appropriately simulated by a

resultant decreased maximum speed, the delta in decreased speed did not match up to that of official values.

The model appears to suffer from excessive drag once it reaches transonic and supersonic speeds. In order

to test the theory that X-Plane was modeling supersonic flight incorrectly, a simple level flight deceleration

flight test was conducted.

E. Troubleshooting Flight Tests

It was initially thought that a level

flight acceleration flight test would be

more appropriate but this led to

extreme oscillations at velocities

above Mach 1. In order to show the

trend of drag coefficient to Mach

number at 10000ft, the X-Plane model

was edited such that it had enough

thrust to accelerate well beyond Mach

1.4 and Mach 2.4 at 10000ft and

40000ft respectively. The aircraft

would then be allowed to decelerate

in level flight to near stall velocity.

The resultant trend of drag coefficient

against Mach number would then be

plotted. The aircraft would be in a

clean configuration and with a weight

of 32000lbs.

As can be seen in Fig. 21, the drag

coefficient remains constant from Mach 0.5 to about Mach 0.8 before increasing slightly in a parabolic curve.

The drag instantly increases at Mach 1. The drag coefficient then increases to peak at about Mach 1.1 before

generally decreasing with increasing Mach number. A sketch of how the coefficient of drag versus Mach

number plot should look is superimposed over the plot in Fig. 21. Aircraft in Fig. 21 which are comparable to

the F-15E are the F104, F14, F4, F105 and the RA5C. Pictures of these aircraft and the F-15E are contained in

Appendix T.

As can be seen, all of them have a peak in drag coefficient at between Mach 1 and Mach 1.1. This is

accurately simulated in X-Plane. However, all of the drag coefficient peaks of about 0.04, except the F104 with

a peak at 0.05. This is very different from the F-15E X-Plane model’s peak drag coefficient of about 0.12.

However, the drag coefficients between Mach 0.5 to the critical Mach number are between 0.015 and 0.02 for

both the F-15E model at 10000ft and the comparable aircraft. It can be deduced that the X-Plane F-15E model’s

drag is thus modeled relatively accurately in the subsonic zone but is excessive in the transonic and supersonic

zone. This would seem to suggest an issue with the X-Plane software’s internal calculations as the aircraft

Figure 21: Comparison of Flight Test Zero Lift Drag Coefficient to

Known Zero Lift Drag Coefficient Graphs (2 p. 346)


22

designer only inputs one set of drag coefficient data without distinction between subsonic and supersonic

speeds.

Another difference is that the drag suddenly increases at Mach 1 instead of increasing from the critical Mach

number to a peak at around Mach 1. The drag coefficient obtained from flight tests then remains at nearly the

same level before further increasing and peaking at about Mach 1.1. This indicates that the mathematical

modeling involved in mimicking transonic and supersonic drag has significant room for improvement. The

imperfect transonic and supersonic drag modeling may be the reason for the F-15E aircraft to be unable to reach

its appropriate maximum velocities.

As indicated by the above analysis, the drag coefficient is accurately modeled at subsonic speeds. This

indicates that the drag coefficient of individual components is modeled correctly. At transonic and supersonic

speeds however, total drag coefficient is excessively high, more than twice the value of expected results. This

likely indicates that drag coefficient is overestimated by X-Plane. However, excessive acceleration in the

subsonic zone indicates that the X-Plane F-15E model has too much thrust at both tested altitudes.

Unfortunately, due to the lack of definitive thrust at 100% low compressor speed and the critical altitude of the

engines, accurate results would only be obtainable by trial and error. The correct thrust and drag settings will

improve and the method will be described in a later section.

F. Phugoid Motion Analysis

The F-15E aircraft underwent

phugoid motion as predicted, as

shown in Fig 22. The first

downward trough is the second

pulse of the doublet input. The

oscillations lasted for many

minutes with gradually decreasing

amplitude. Using the test method

described above, the graph of

indicated airspeed against time

was plotted and from which the

and were

determined. Each test was

conducted until the aircraft’s

altitude and airspeed was

changing minimally from the initial test altitude and airspeed.

As stated in the above flight test method description, it was planned to do two flight tests for each test point.

One flight test was initiated by pitching upwards while the other was initiated by pitching downwards.

However, difficulties in obtaining the exact same altitude and starting test speed meant that it was not feasible to

accurately compare data from one flight test to another. Thus, while two flight tests were completed in each

condition only one would be used as the comparison to theoretical data. This also meant that statistical analysis

was not done for phugoid motion flight test data. The flight test which was compared to theoretical data was the

one with the most similar and ξ.

Theoretical predictions indicated that the at both altitudes should remain fairly constant. Any

deviation from a constant value should be a slight decrease in as weight increases. This trend was upheld by

flight test results, with the flight test remaining fairly constant with an increase in aircraft weight. The

test results at 40000ft were extremely compliant to the expected horizontal trend line.

The was also expected to have a slight decrease, with the theoretical at 55000lbs and

80000lbs being approximately 0.60 and 0.40 times the value of the theoretical at 32000lbs. This trend

was not represented in the data obtained from flight testing. The obtained from flight tests at 10000ft

was basically constant while the values obtained at 40000ft indicated an increase with aircraft weight. Analysis

of the method used to determine

led to a possibility as to

why the values obtained

were trending differently from

theoretical values.

As can be seen in Fig 13, the

amplitude of each peak and

trough must be obtained and

then the can be obtained from

the ratio of a peak to its

Table 9: Value of Theoretical Dynamic Longitudinal Stability Characteristics

Figure 22: Plot showing the F-15E Phugoid Motion obtained from X-Plane


23

subsequent trough or vice versa. In order to increase accuracy, a minimum of five full oscillations were

conducted for each flight test. Multiple ratios of peak amplitude to trough amplitude were thus obtained and the

average value was determined for subsequent use. The peak to trough ratio was thus a fluctuating value

throughout the experiments. This led to a slight uncertainty in the obtained . Furthermore, the method used for

presenting the correlation between peak to trough ratio and was extremely coarse as shown in Fig 13. More

accurate graphs or data could be found so it would be expected that small changes in would not be detectable.

G. Phugoid Motion Verification

The calculated flight test

and are

compared to theoretical predictions

in Tables 9, 10 and 11. As can be

seen in Table 11, the

obtained from flight tests are within

30% of theoretical predictions.

Considering the uncertainty

associated with the theoretical

calculation, the flight test

values show significant correlation

to theory. The obtained

from flight tests were mostly within

84% deviation from the theoretical

predictions. Considering the small

absolute value of the difference

between those flight test results and

theoretical predictions, they can be

accepted as fairly accurate. Only

the at 10000ft and

80000lbs had a higher difference of

567%. This may possibly be due to

incorrect

and

values as

well as the coarse method of

determining from flight tests. Unfortunately, further testing did not result in an improved .

This is because of a short coming of the X-Plane trim function. It was found to be extremely difficult to trim the

aircraft to exact straight and level flight. In most cases, the aircraft would ascend or descend at a slow rate.

This affected the repeatability of the flight tests, as well as the accuracy of flight test outputs. The phugoid

characteristics appear to correlate to theoretical predictions much better than the short period values. This is

likely due to the significantly lower uncertainty due to the fewer number of inputs and equations involved.

H. Short Period Motion Analysis

As with phugoid motion flight tests, it was not feasible to compare data between multiple similar flight tests.

This was due to the slightly different starting altitudes and aircraft velocities. Furthermore, only a few points in

the flight test were used for calculations. Thus, statistical analysis was not conducted on the short period motion

flight test data. Due to the quantity and uncertainty of different variables and equations used to determine the

short period motion characteristics, there was much more uncertainty associated with it. The actual uncertainty

cannot actually be calculated due to the fact that uncertainty also lies in the use of equations. This is because

empirical equations used make underlying assumptions which cannot be quantified. This is a possibility as to

why the calculated seems to be overly low at 40000ft.

Even though there are no values to which the short period characteristics can be compared, we know that the

F-15E must satisfy the military safety regulations. The MIL-F-8785C for Class IV aircraft (fighter) category B

flight phase (cruise) specifies that the for an aircraft of this class is to between 0.2 and 2.00 (53 p.

13). Also, FAR part 23.181 (a) states that the short period motion is to be heavily damped, meaning having not

more than two cycles.

Taking into consideration both these regulations, it can be determined that theoretical predictions at 10000ft

80000lbs, 40000ft 55000lbs and 40000ft 80000lbs do not adhere to these guidelines. The simulated aircraft at

these three conditions undergoes more than two cycles of oscillations before reaching a steady state. Thus, it

would indicate that either the uncertainties are excessive or the simplifying assumptions invalid for these flight

conditions. Thus, these theoretical predictions will not be used to as the baseline for flight test results. It must

Table 11: Value of Dynamic Longitudinal Stability Characteristics obtained

from Flight Tests

Table 10: Comparison of Flight Test Dynamic Longitudinal Stability Results

to Theoretical Values


24

be noted that this analysis does not indicate accuracy of the calculated theoretical predictions, merely the

possibility that they are correct based on these references.

I. Short Period Motion Verification

Table 6 indicates the uncertainty associated with the dynamic longitudinal stability characteristic prediction.

There is a much larger uncertainty associated with the aircraft’s short period motion than phugoid. Thus, it is

within expectations that the obtained from flight tests has a larger difference than other results

when compared to theoretical results. However, the average difference is about 5000%, as indicated in Table

11. This is far too large for results to be considered comparable. Furthermore, the are significantly

different from theoretical predictions. This would indicate that either the F-15E model is inaccurately modeled

with respect to short period motion or that X-Plane is inaccurately determining the aircraft motion in this region

of flight. Further testing would be required to pinpoint the exact reason for the deviation of short period motion

from expected results.

X. X-Plane Repeatability and Comparison Flight Tests with Payload

It is a desired outcome of this thesis to develop as accurately as possible a working flight simulator model of

the F-15E which can show the effect of changes to the aircraft. For ease of modeling, these changes were

chosen to be the addition of an asymmetrical payload. However, due to the lack of a method to which flight test

results can be compared, the effect of changes to the aircraft cannot be discussed quantitatively, only

qualitatively. It is also necessary to determine whether differences between each flight test are significant. By

choosing a flight test which can be easily replicated for multiple different payloads, systematic error between

flight tests can be made negligible. The optimum aircraft weight, altitude and speed for the flight tests should

also be determined for maximum accuracy in results and thus significance when comparing to results of other

flight tests.

A. Determination of Optimum Flight Test Method

Multiple experiments were conducted to compare X-Plane outputs with expected trends. Due to the lack of

quantitative information in the flight manual regarding the F-15E under different payload conditions, a simple

flight plan was determined for the following flight tests. The aircraft would simply be allowed to decelerate

under conditions of no thrust from one flight velocity to another. Thus, it would be necessary to determine at

which altitude, weight and velocity the tests would face the least uncertainty. This was due to the fact that the

inbuilt autopilot led to slight oscillations in autopilot-controlled flight, it was necessary to determine the best

flight condition for minimum oscillations.

1. Determination of the Optimum Aircraft Altitude and Weight for X-Plane Payload Flight Tests

Experiments were conducted to determine the normal spread of results between

identical flight tests. Nine flight tests were performed in each flight condition and the

standard deviation of the test results in each flight condition was determined as shown

in Appendix U.

For a normal distribution, approximately 68% of measurements will lie within one

standard deviation of their mean (54 p. 34) and about 95% of measurements within two

standard deviations. Thus, the smaller the standard deviation, the lower the spread of

test results and the more accurate a comparison between different flight conditions.

Table 12 indicates the number of test flights required for a certain percentage

uncertainty in standard deviation. It was decided to conduct nine test flights such that a

low percentage uncertainty would be obtained while minimizing the amount of time

spent conducting test flights.

Once the optimum flight condition has been determined, the standard deviation will

be determined. This standard deviation would be such that there is a 95% probability that the flight parameter

would be within two standard deviations of the population mean and the uncertainty associated with this

standard deviation would be 25%.

The F-15E model was tested in the following conditions:

1. Clean, 10000ft, 32000lbs aircraft weight



4. 2 x AIM-54 asymmetrical payload, 10000ft, 34028lbs aircraft weight

5. 2 x AIM-54 asymmetrical payload, 40000ft, 34028lbs aircraft weight

Table 12: Percentage

Uncertainty in

Standard Deviation


25

Nine flights were conducted for the F-15E model in each of the above five flight conditions, with conditions

[1] and [4] being used as controls. The flight tests were conducted to determine the aircraft’s thrust, lift, drag,

side force, lift to drag ratio, total coefficient of lift, total coefficient of drag as well as the aileron, elevator and

rudder deflections. These parameters will be the only ones discussed as other parameters are either dependent

on the above parameters or are not meaningful to this analysis.

The standard deviation of the analyzed parameters for the above flight conditions were compared with the

control flights. A sample of the calculated standard deviations for the above set of flight tests is included in

Appendix U. Due to the large amount of data involved in each flight test, only a sample of standard deviations

for each flight condition is included in the Appendix. The data in Appendix U indicates that the standard

deviation of parameters was inversely proportionate to both altitude and aircraft weight. Thus, it would be

advantageous for the aircraft to have a lower altitude and weight. However, if the aircraft were flying too low,

X-Plane would take into consideration wing in ground effect which would increase the lift on the aircraft (19) ,

leading to errors in results. Ground effect affects aircraft when the aircraft is at a distance from the ground less

than half its wing span (13 p. 354). Thus, while excessive, the aircraft test altitude was chosen to be at 10000ft

such that it would be out of ground effect and would be at the same altitude as several other tests.

2. Determination of the Optimum Aircraft Speed Range for X-Plane Payload Flight Tests

The graphs of the above stated parameters against

true airspeed in flight conditions [1] and [4] are

contained in Appendix V and W respectively. These

graphs indicate that the F-15E model will suffer from

oscillations in lift, drag and side force which increase

with velocity. This trend is steady for the F-15E model

in both the clean and asymmetrical payload condition.

These oscillations are reflected in the graphs of aileron,

elevator and rudder deflections, also contained in

Appendices V and W. However, the control surface

deflection graphs for the clean aircraft indicate

abnormal aileron deflections between velocities of

260KTAS and 300KTAS as well as abnormal elevator

and rudder deflections between speeds of 340KTAS

and 370KTAS. The control surface deflection graphs

for the F-15E under payload shows similar trends.

Also, for the F-15E in a clean condition, the rudder

deflection graphs indicate that the rudder undergoes slight oscillations at velocities below 360KTAS.

As can be seen in Table 13, the speed range with the lowest oscillation amplitudes for the clean and

asymmetrical payload condition would be between 200KTAS and 250KTAS.

Thus, considering all the above factors, the optimum test speed range was determined to be 250KTAS to

200KTAS. This would minimize unwanted oscillations in aircraft forces and control surfaces, abnormal control

surface deflections as well as ensure the aircraft is well out of the transonic and supersonic zone.

As shown in Appendix V and W, the oscillations in aircraft lift follow a horizontal trend line. These

oscillation amplitudes can thus be determined easily. The lift was not exactly equal to weight because the

aircraft pitch varies with velocity and the resultant force which acts against aircraft weight would be a

trigonometric sum of aircraft thrust and total wing lift. The average total wing lift for all the clean flight tests at

10000ft was thus approximately 32030lbs, while that of the 2 x AIM-54 asymmetric payload tests was

34040lbs. Both these total wing lift values are slightly higher than the aircraft weight in those conditions. This

is because of two factors. Firstly, the actual force acting against gravity is a trigonometric sum of aircraft lift

and thrust, due to the fact that the aircraft is not flying at exactly 00 pitch. Secondly, the aircraft is undergoing

slight oscillations in pitch which causes the wing lift, total lift and resultant lift forces to vary.

B. Repeatability Flight Tests

1. Calculation of Standard Deviation

The optimum test flights were chosen to be conducted at 10000ft, 32000lbs aircraft weight (excluding

payload) and between 250KTAS and 200KTAS. Thus, the average standard deviations for the flight test output

parameters were calculated for the two extreme conditions of the flight tests – no payload and maximum

asymmetrical payload. These results are tabulated in Table 14.

As can be seen, two standard deviations is less than 2% of the mean for most measured parameters. The

standard deviation for thrust is 2.18% of the mean thrust for the F-15E with 2 x AIM-54 missiles. It was

assumed that the clean and 2 x AIM-54 payload would be extreme cases in terms of oscillations in output

Table 13: Comparison of the Oscillation Amplitudes

for Various Speed Ranges


26

parameters. Thus, other payloads would have standard deviations lower than those determined for the

aforementioned two aircraft configurations. The reason why the 2 x AIM-54 payload is considered an extreme

is not just that it’s weight exceeds that of a other payloads but also because it provides the greatest lateral

asymmetry (in ft-lbs).

One output parameter which needs explanation is the thrust. This is because the thrust is a negative value.

This is because the minimum possible aircraft weight was chosen – 32000lbs. This is only possible with nil

fuel. Thus, the engines are not operating so are producing drag, not thrust. This leads to the negative thrust

values. This is how X-Plane calculates drag on aircraft engines – it is factored into the thrust calculations.

2. Conclusion

The combination of all the above calculations indicates that the above parameter results from a single test

would be within 2.2% or population mean 95% of the time, with an associated uncertainty of 25%.

This leads to numerous possible deductions about the mathematical modeling involved in X-Plane. One

possible deduction is that there are very few possibilities or random errors occurring which may distort

experimental results. The likely reason for the uncertainty in the repeatability flight tests is that the autopilot

does not act in exactly the same manner in each flight test, leading to slight differences. Another conclusion

which can be made is that flight tests a very repeatable as long as the flight path and initial conditions are

readily controllable.

C. Payload Comparison Flight Tests

1. Expected Trends

It is expected that as lateral asymmetry increases, so

would aileron and rudder deflection. This would be

because increased lateral asymmetry would cause the

aircraft’s autopilot to increase aileron and rudder

deflection to as to maintain straight and level flight.

It is also expected that lift and drag would increase

with payload. This is because increased payload means

that total lift would have to increase to maintain straight

and level flight. However, total lift would be a

trigonometric addition of wing and horizontal stabilizer

lift and thrust. Since the aircraft is in straight and level

flight, drag would be acting purely horizontally.

Fortunately, this total lift value is the value provided in

the X-Plane data output file so the total lift can be easily

charted.

2. Analysis of Flight Test Results

The obtained trends for the different payload flight

tests were generally as expected. The plots of the

obtained results are contained in Appendix X. Aileron

and rudder deflection generally increases with lateral

asymmetry as shown in Fig 23 and 24 respectively.

Only the tests making use of the 2xAIM-54, 2xAIM-7,

1xAIM-54 and 1xAIM7 have a significantly different

trend to the others. As expected, the above four stated payloads are the payloads which result in the largest

lateral asymmetry, as indicated in Table 2. The same four stated payloads are also the only ones significantly

Table 14: Calculations for the Percentage Uncertainties for the Stated Flight Parameters.

Figure 24: Indication of Lateral Asymmetry Effects



27

different from the rest in terms of rudder deflection. However, the 2xAIM-7 payload is the one with the largest

rudder deflection instead of the 2xAIM-54 payload. This is unexpected because the 2xAIM-54 payload has a

larger lateral asymmetry than the 2xAIM-7 payload. The reason for the aircrafts deviation from the expected

trend is unknown and retests indicate similar results. This could be due to a postulated complex relationship

between lift, drag, pitch and control surface deflection and would be able to be pinpointed by use of further

testing.

The side force on the F-15E did not show any sort of discernible trend. This is contrary to what was

expected. However, since the rudder deflection is so minimal, it is possible that the effect of payload on side

force cannot be detected.

Lift and drag showed mixed trends. As expected,

aircraft lift increases with payload weight. This can

be seen in Fig. 25. Aircraft drag also increases with

payload weight and size. The 2xAIM-54

configuration clearly has more drag than the 1xAIM-

54 configuration. This is to be expected as X-Plane

does drag calculations on the payloads.

As velocity increases, pitch decreases and thus

drag decreases due to the decrease in frontal area and

induced drag. However, when landing gear is

extended, aircraft drag increases with velocity. This

is because when landing gear is extended, the

increase of drag on the landing gear far outweighs

the decrease in drag due to decrease pitch and is

visually represented in Fig. 26.

The GUI for creating payloads has a body

coefficient of lift input. As with other bodies, the

designer must include interference, skin friction and

pressure drag in this value before the total drag force

is calculated by Eq. 3. This is the only way X-Plane

determines the interference effect of the payload on

the lift over the wing directly above it.

It can be seen that X-Plane does simulate

changes in the F-15E aircraft rather well in terms of

trending correctly. Unfortunately, quantitative analysis could not be completed for these flight tests in this

thesis due to the lack of data to which results could be compared.

D. Conclusion

The flight tests conducted for this section of the thesis have shed light on numerous aspects of X-Plane.

With the right flight conditions and number of test flights, the uncertainty in a result can be reduced to a

minimal value. The best flight condition to conduct flight tests in was determined to be a simple level flight

deceleration test between the velocities of 250KTAS and 200KTAS.

The desired aim of this thesis was to produce an F-15E X-Plane model which could show the effect of

changes to an aircraft. This change was modeled as increasing lateral asymmetry. The above analysis proves

that lateral asymmetry on the aircraft model does indeed produce expected trends. The effect of an alteration to

the F-15E airframe can also be tested. This would likely have to be conducted by adding a miscellaneous body

to the F-15E aircraft, taking note that an accurate coefficient of drag must be known beforehand. Only then can

accurate results be obtained.

One important point to note is that the X-Plane model suffers from slight oscillations at all flight conditions.

This is because of the time required to complete one cycle of calculations. Once one cycle is completed, the

flight parameters would have changed slightly, leading to the need for the autopilot to recorrect the aircraft’s

flight path. Even if a supercomputer were used, oscillations would still exist. The only difference would be that

the magnitude of oscillations would be tiny in comparison. The oscillations can be seen in the flight output data

charts contained in this thesis paper as well as in the appendices. In order to improve the precision of output

data, this issue can be addressed with the use of a more powerful computer. The computer used for these flight

tests has an Intel Core i3 CPU processor, clocked at 3.07Ghz with 3.87 GB of usable RAM.




28

XI. Final Comments

The above described flight tests gave valuable insight as to the accuracy of the F-15E model as well as the

ability of the X-Plane software to correctly mimic real world physics. Any inaccuracies with regards to the

tested flight characteristics have been determined. These are summarized below and the results of further

improvements have been explained too. However, there are still many possibilities to improve on the designed

F-15E model. Numerous other flight tests can also be conducted so as to analyse the model’s characteristics in

other modes of flight, such as the spiral spin or sustained level flight turn.

A. Issues with F-15E Model

There were numerous issues discovered with the designed F-15E model. These issues included excessive

thrust, excessive supersonic drag, and substantial differences between obtained short period characteristics to

expected values. Alterations were made to the F-15E model to attempt to lessen the issues and the results of

these improvements are contained in the following section.

B. Method to Improve the F-15E Model after Analysis of Test Results

Much consideration needed to be taken into account before attempting to improve the F-15E model. Firstly,

the obtained stall speeds were already extremely compliant with flight manual data, indicating that wing and

empennage dimensions, as well as airfoil lift curve slopes were fairly accurate. Thus, it would be important not

to change those parameters as that would cause the stall speeds to deviate from official values.

The following method was decided upon to improve the aircraft’s maximum level speed and acceleration

characteristics. The drag settings would be corrected first, followed by the thrust settings. This was because the

aircraft’s thrust settings would be altered by observing aircraft acceleration which is dependent on drag but drag

settings would be corrected by observing level flight deceleration.

It was hypothesized that the F-15E X-Plane model had two components which had excessive drag – the

connection of the empennage to the fuselage and the wings. Thus, an altered X-Plane model would be created

which had the minimum drag setting on each of those components. If this led to a large decrease in drag

coefficient, it would most likely be the incorrectly modeled component. If a large decrease in drag coefficient

was not obtained, other components would be tested. If the nullification of each single component’s drag did

not lead to any components contributing excessive drag to the aircraft in the supersonic region of flight, then all

components’ coefficients of drag would be lowered and the aircraft would be tested again.

The X-Plane model’s thrust settings could then be corrected. For speedy testing, only the lightest and

heaviest aircraft weights would be tested. The aircraft (with corrected drag characteristics) would be accelerated

at 10000ft, military thrust and the thrust at 100% low compressor speed would be altered such that the correct

acceleration at 10000ft would be obtained. Once this is completed, the aircraft would be accelerated at 10000ft,

maximum thrust and its additional afterburner thrust would be edited so that it’s maximum thrust at 10000ft was

correct. Finally, the aircraft would be accelerated at 40000ft, maximum thrust and its critical altitude would be

altered so as to achieve the correct accelerations.

Once the above testing and corrections are completed, the aircraft’s maximum level flight speeds would be

checked and the aircraft component’s drag values would be finely adjusted so that the maximum level flight

speeds would be correct.

C. Results of Attempt to Improve F-15E Model

Unfortunately, attempts to improve the drag characteristics of the aircraft were unsuccessful. The above

method was used and even with the minimum drag setting for every single aircraft component in the F-15E

model, the aircraft could neither exceed Mach 1 at 10000ft nor reach Mach 2.4 at 40000ft and 42800lbs aircraft

weight. The airfoils on the wings were even changed to have near zero drag for angles of attack between -200

and 200 but even this did not allow the aircraft to pass the speed of sound at 10000ft. The airfoil’s Mach

divergent drag number was also increased to no avail.

Thus, it can be seen that with even minimal drag settings chosen on every single component in the aircraft,

the X-Plane software still determines that the aircraft is unable to fly supersonic. This would indicate that the

X-Plane software’s transonic and supersonic drag calculations are rather inaccurate as the simulated aircraft

drag is far too high in these regions of flight. As stated in Section IV. F, X-Plane’s transonic and supersonic

modeling is makes a number of simplifying assumptions and approximations. This is likely the cause of the

inaccuracies of transonic and supersonic modeling.

Due to the fact that the issue of aircraft drag could not be reconciled, the aircraft thrust was not altered.

D. Future Work

Further work can be conducted on the F-15E model to further improve the aircraft’s accuracy. This can be

facilitated by the conduct of additional flight tests which would indicate the necessary edits required on the F-

15E model. Additional flight tests to determine the F-15E’s takeoff distances, rotation speeds, single engine


29

rates of climb, climb performance, descent performance and sustained level flight turn performance would be

ideal. While the flight manual contains data on other flight characteristics, the above stated characteristics are

the easiest to compare flight test results to.

Flight characteristics not mentioned in the flight manual can also be tested with the use of theoretical

predictions. The aircraft’s static longitudinal stability, dynamic lateral-directional stability and maneuvering

stability are a few characteristics which can be predicted by the use of (4). The directions for the correct

conduct of all the above mentioned flight tests are contained in (52).

Use of DATCOM will provide another avenue to which stability characteristics can be compared.

Knowledge of FORTRAN would enable one to use the DATCOM source code. Since slight alterations need to

be made to the aircraft before DATCOM can be used, such as the use of a single vertical tail as opposed to two,

an aircraft should be designed in X-Plane making use of the exact dimensions used in DATCOM. This would

ensure that the DATCOM outputs are valid for the F-15E.

With enough resources, CFD analysis of the F-15E could be conducted for more accurate determination of

forces and moments on the aircraft. This would provide a benchmark to which the payload comparison

deceleration test results can be compared such that those flight test results can be verified. The reason why it is

preferable to use X-Plane over CFD to determine the forces, moments and other characteristics of the F-15E in

flight is that X-Plane takes a much shorter time to do the essential calculations. CFD can be used to ensure that

the input parameters are correct and X-Plane can then be used to do the bulk of the calculations. However, if

CFD were to be used, it would be imperative to obtain much more accurate measurements of the F-15E. This

would be so as to achieve the best possible correlation between the X-Plane and CFD models and the real

aircraft.

Further study into possible flight conditions for precise measurements should be taken. This would enable

the F-15E model to be suffering from the least possible amount of oscillations. This would increase the

precision of data collected from X-Plane.

E. Conclusion

A large amount of research has been conducted thus far to ensure accuracy and validity of results. Future

work should focus on improvement of the F-15E model as well as verification of its abilities. The best possible

way to verify the F-15E model would be to make use of either CFD or actual F-15E flight test data. Even if the

X-Plane aircraft model is not extremely accurate, the delta method can be used to determine the effect of

changes to the aircraft. However, X-Plane has proven in this thesis to be a rather accurate tool in predicting the

flight characteristics of an aircraft if its input parameters are correct. This is seen in the very close correlation of

obtained flight test stall speeds to flight manual data, as well as the correlation of maximum level flight

acceleration and speeds to flight manual data once the aircraft was improved. This would lead to X-Plane being

a powerful prediction tool in determining the approximate result of a change to an aircraft, with more precise

analysis methods being used to focus on certain scenarios which may be been determined through use of X-

Plane.

Acknowledgements

This thesis would not have been possible without the help of my thesis supervisor – Andrew Neely.

Throughout this thesis, he has been a great help on this thesis and a source of many fantastic ideas for

improvement. I would also like to thank Anthony Booher, who not only provided me with privately designed

aircraft models which are unavailable online but also aided me in understanding X-Plane and Javafoil. Without

him, my aims would have been much harder to meet. Lastly, I would like to thank Austin Meyer. One would

not expect the creator of such a well selling piece of software to have the time to reply an endless stream of

emails about the mathematics behind X-Plane but Austin has proved to be an exception to this rule. To all

others who have helped me along the way – thank you.


30

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