Preliminary Design Optimization of an Amphibious Aircraft  
 
by 
 
Jason W. Cary 
 
 
 
 
A thesis submitted to the Graduate Faculty of 
Auburn University 
in partial fulfillment of the  
requirements for the Degree of 
Master of Science 
 
Auburn, Alabama 
December 12, 2011 
 
 
 
 
Approved by 
 
Gilbert L. Crouse Jr., Chair, Associate Professor of Aerospace Engineering 
John E. Cochran Jr., Professor of Aerospace Engineering 
Winfred A. Foster Jr., Professor of Aerospace Engineering 
 
 
 
  
 ii 
 
 
Abstract 
 
An amphibious aircraft combines the speed and range benefits of a 
conventional aircraft with the ability to land and takeoff on open water.  There 
are other appealing factors to operating an amphibious aircraft including 
convenience, the ability to operate without a hard surface runway and additional 
safety for overwater operations.  These factors, however, all come at a cost and 
impact the design of the aircraft.  To examine these tradeoffs, common design 
and optimization methods were applied to the conceptual design of an 
amphibious aircraft and then compared to wind tunnel results of that design.  In 
this study, a hypothetical troop and cargo transport aircraft mission profile was 
selected.  
A sizing program was developed to create an aircraft geometry and evaluate 
its performance.  This code was written to account for many different aircraft 
criteria, including tail configuration, wing and fuselage geometry, and method of 
water operation (floats, hydrofoil, boat hull, etc.).  The sizing code was first 
validated on several classes of existing aircraft.  It was then run in conjunction 
with a hybrid, particle swarm-simplex optimizer to find a configuration for the 
hypothetical transport aircraft with minimum overall weight. 
The optimized design was tested in Auburn University?s subsonic,     3 ft. x 4 
ft. wind tunnel.  The model was run through a battery of tests including 
measuring the forces and moments, and surface flow visualization.  Runs were 
made at various angles of attack and sideslip angles.  The testing included cases 
with several different control surface deflections.  Analysis was also performed 
 iii 
on the aircraft using Athena Vortex Lattice and Orca3D to determine stability in 
flight and while on water.  Results of the testing were used to validate the 
performance parameters estimated by the design code.   
 iv 
 
 
 
Acknowledgments 
 
The author would like to thank Dr. Gilbert L. Crouse Jr. for the opportunity 
to work on this research as well as for his guidance and support throughout the 
course of this effort. Thanks are also due to Mr. Jason Welstead, Mr. Brian Reitz, 
Mr. David Wall, and Ms. Rachel Ottaway for all the assistance they offered over 
the course of this research. Many thanks go to Andy Weldon for the advice and 
work he put into every piece machined for this project. The author would also 
like to thank his father and mother for their help, support and encouragement.  
 
 
 
 
 
 
 
 
 
 
 v 
 
 
 
Table of Contents 
 
 
Abstract ........................................................................................................................ ii 
Acknowledgments ...................................................................................................... iv 
List of Figures ............................................................................................................. ix 
List of Tables .............................................................................................................. xv 
Chapter 1: Introduction ................................................................................................ 1 
1.1 Amphibious Aircraft Design ........................................................................ 1 
Chapter 2: Review of Literature .................................................................................. 5 
2.1 Aircraft Design .............................................................................................. 5 
2.2 Water Operations .......................................................................................... 8 
2.3 Optimization Models .................................................................................. 17 
2.4 Wind Tunnels .............................................................................................. 23 
Chapter 3: Sizing Code Development and Validation ............................................ 30 
3.1 Development ............................................................................................... 30 
3.1.1 Introduction ............................................................................................. 30 
 vi 
3.1.2 Lifting Surface Geometry Calculations ................................................. 32 
3.1.3 Water Operation Method Geometry Calculations ............................... 35 
3.1.3.1 Boat Hull Calculations ................................................................ 35 
3.1.3.2 Twin Float Calculations .............................................................. 38 
3.1.3.3 Wing Tip Float and Sponsons Calculations .............................. 40 
3.1.3.4 Hydrofoil Calculations ............................................................... 43 
3.1.4 Performance Estimation .......................................................................... 44 
3.1.4.1 Component Drag Estimation ..................................................... 44 
3.1.4.2 Mission Performance Estimation ............................................... 45 
3.1.5 Weight Buildup ....................................................................................... 48 
3.1.6 Center of Gravity and Neutral Point Calculation ................................. 50 
3.1.7 Sample Output......................................................................................... 54 
3.2 Validation..................................................................................................... 55 
3.2.1 Lockheed C-130-H ................................................................................... 56 
3.2.2 Cessna 172-R ............................................................................................ 58 
3.2.2.1 Wind Tunnel Model and Results ............................................... 61 
Chapter 4: Design Optimization................................................................................ 64 
 vii 
4.1 Optimizer Selection ..................................................................................... 64 
4.2 Optimization Methodology ........................................................................ 68 
4.2.1 Penalty Functions .................................................................................... 69 
4.3 Results .......................................................................................................... 73 
4.3.1 Parametric Studies ................................................................................... 75 
Chapter 5: Optimized Design Analysis and Testing ............................................... 78 
5.1 3-D CAD Model Development................................................................... 78 
5.2 Wind Tunnel Testing .................................................................................. 83 
5.2.1 Model Design and Construction ................................................................ 83 
5.2.2 Testing Setup ............................................................................................... 88 
5.2.3 Testing Results............................................................................................. 89 
5.3 Orca3D ....................................................................................................... 104 
5.3.1 Model...................................................................................................... 107 
5.3.2 Results .................................................................................................... 108 
5.4 Athena Vortex Lattice (AVL) ................................................................... 110 
5.4.1 Model...................................................................................................... 113 
5.4.2 Results .................................................................................................... 115 
 viii 
Chapter 6: Conclusions and Suggestions for Further Work ................................. 122 
6.1 Improvement of Sizing/Optimization Methods ..................................... 122 
6.1.1 Drag Estimation ..................................................................................... 123 
6.1.2 Stability During Water Operations ...................................................... 124 
6.1.3 Control Surface Sizing .......................................................................... 125 
Bibliography .............................................................................................................. 127 
Appendix A:  Sizing Code Text Output Sample .................................................... 132 
Appendix B: Final Optimized Design Sizing Code Output .................................. 137 
Appendix C: Cessna 172 Wind Tunnel Data and Results ..................................... 142 
Appendix D: Optimized Aircraft Wind Tunnel Data and Results ....................... 145 
Appendix E: AVL Input Files .................................................................................. 157 
 
  
 ix 
 
 
 
 
List of Figures 
 
 
Figure 1: Boat Hull Configuration [8] ......................................................................... 9 
Figure 2: Twin Float Configuration [8] ..................................................................... 10 
Figure 3: Grumman JRF-5 with Grunberg Hydrofoil System [15] ......................... 14 
Figure 4: Supercavitating Hydrofoil Shapes [17] ..................................................... 15 
Figure 5: Reynolds Number Correction Chart [29].................................................. 24 
Figure 6: Dye lines and Injection Ports in a Water Tunnel [33] .............................. 28 
Figure 7: Oil Visualization Technique [29] ............................................................... 29 
Figure 8: Sizing Code Flowchart ............................................................................... 32 
Figure 9: Effect of C? on?/R at Best Trim Angles *35+ ............................................. 37 
Figure 10: Transverse Metacentric Height [36] ........................................................ 40 
Figure 11: Wing Tip Floats [36] ................................................................................. 42 
Figure 12: Sponsons [36] ............................................................................................ 42 
Figure 13: Float Weight vs. Displacement ................................................................ 49 
Figure 14: Fuselage Moment Term [38] .................................................................... 52 
 x 
Figure 15: Upwash Estimation [3] ............................................................................. 53 
Figure 16: Sizing Code Sample Output .................................................................... 55 
Figure 17: Lockheed C-130-H [40] ............................................................................. 56 
Figure 18: Lockheed C-130-H Sizing Code Output ................................................. 57 
Figure 19: Cessna 172-R [41] ...................................................................................... 58 
Figure 20: Cessna 172-R Sizing Code Output........................................................... 59 
Figure 21: Cessna 172-R with Floats Sizing Code Output ....................................... 61 
Figure 22: Cessna 172 Wind Tunnel Model .............................................................. 62 
Figure 23: Optimization Program Flowchart ........................................................... 69 
Figure 24: Wing Structure Penalty Function ............................................................ 72 
Figure 25: Optimization Results ................................................................................ 74 
Figure 26: Final Optimized Design ........................................................................... 75 
Figure 27: Stall Speed Parametric Study ................................................................... 76 
Figure 28: Various Types of Boat Hull Bottoms [45] ............................................... 79 
Figure 29: Final Optimized Aircraft Design ............................................................. 81 
Figure 30: Right View of Optimized Design ............................................................ 82 
Figure 31: Front View of Optimized Design ............................................................ 82 
 xi 
Figure 32: Top View of Optimized Design ............................................................... 83 
Figure 33: Internal Structure and Pyramidal Balance Mounting Blade ................. 85 
Figure 34: Yaw Alignment Disc ................................................................................. 86 
Figure 35: Wind Tunnel Model and Mounting Blade in SolidWorks .................... 86 
Figure 36: Wind Tunnel Model, Mounting Blade and Shroud ............................... 87 
Figure 37: Model Installed in Wind Tunnel ............................................................. 87 
Figure 38: Baseline Wind Tunnel Results ................................................................. 90 
Figure 39: Drag Polar.................................................................................................. 92 
Figure 40: CM vs AoA for Elevator Deflection ........................................................ 94 
Figure 41: Elevator Deflection Results ...................................................................... 95 
Figure 42: Lateral Static Stability Plots ..................................................................... 97 
Figure 43: Rudder Deflection Results ....................................................................... 98 
Figure 44: Wind Tunnel Model with Transition Strip ........................................... 100 
Figure 45: Transition Strip Result Examples (1) ..................................................... 100 
Figure 46: Transition Strip Result Examples (2) ..................................................... 101 
Figure 47: Flow Visualization - 5 Degree AoA - No Strip ..................................... 102 
Figure 48: Flow Visualization - 5 Degree AoA - Strip ........................................... 102 
 xii 
Figure 49: Flow Visualization - 20 Degree AoA - No Strip ................................... 103 
Figure 50: Flow Visualization - 20 Degree AoA - Strip ......................................... 104 
Figure 51: Personal Watercraft Modeled as a NURBS and a T-Spline [46] .......... 107 
Figure 52: Rhinoceros Model ................................................................................... 108 
Figure 53: Orca3D Results with Virtual Waterline ................................................ 109 
Figure 54: Velocity Induced by a Finite Length Vortex Segment [47] .................. 111 
Figure 55: Control Surface Sizing Parametric Study ............................................. 119 
Figure 56: Cessna 172 Float Comparison, 0 Elevator Deflection .......................... 142 
Figure 57: 172 No Floats Results.............................................................................. 142 
Figure 58: 172 with Floats Results ........................................................................... 143 
Figure 59: 172 No Floats, Elevator Sweep............................................................... 143 
Figure 60: 172 with Floats, Elevator Sweep ............................................................ 144 
Figure 61: 0 Yaw, Rudder Comparison................................................................... 145 
Figure 62: 0 Yaw, Elevon Comparison .................................................................... 145 
Figure 63: 0 Yaw, Roll Comparison ......................................................................... 146 
Figure 64: -5 Yaw, Rudder Comparison ................................................................. 146 
Figure 65: -5 Yaw, Elevon Comparison .................................................................. 147 
 xiii 
Figure 66: -5 Yaw, Roll Comparison ....................................................................... 147 
Figure 67: -11.5 Yaw, Rudder Comparison ............................................................ 148 
Figure 68: -11.5 Yaw, Elevon Comparison .............................................................. 148 
Figure 69: -11.5 Yaw, Roll Comparison................................................................... 149 
Figure 70: +5 Yaw, Rudder Comparison ................................................................. 149 
Figure 71: +5 Yaw, Elevon Comparison .................................................................. 150 
Figure 72: +5 Yaw, Roll Comparison ....................................................................... 150 
Figure 73: Engine Comparison ................................................................................ 151 
Figure 74: 0 Rudder, 0 Elevon, Transition Strip Comparison ............................... 151 
Figure 75: -5 Rudder, 0 Elevon, Transition Strip Comparison .............................. 152 
Figure 76: +5 Rudder, 0 Elevon, Transition Strip Comparison ............................. 152 
Figure 77: -20 Rudder, 0 Elevon, Transition Strip Comparison ............................ 153 
Figure 78: +20 Rudder, 0 Elevon, Transition Strip Comparison ........................... 153 
Figure 79: 0 Rudder, -5 Elevon, Transition Strip Comparison .............................. 154 
Figure 80: 0 Rudder, +5 Elevon, Transition Strip Comparison ............................. 154 
Figure 81: 0 Rudder, -20 Elevon, Transition Strip Comparison ............................ 155 
Figure 82: 0 Rudder, +20 Elevon, Transition Strip Comparison ........................... 155 
 xiv 
Figure 83: 0 Rudder, Left Roll (5 Degrees), Transition Strip Comparison ........... 156 
Figure 84: 0 Rudder, Left Roll (20 Degrees), Transition Strip Comparison ......... 156 
 
  
 xv 
 
 
 
List of Tables 
 
 
Table 1: Lockheed C-130-H Validation Results [40] ................................................ 58 
Table 2: Cessna 172-R Validation Results [41].......................................................... 60 
Table 3: Float Sizing Comparison .............................................................................. 62 
Table 4: Drag Comparison for Cessna 172-R ............................................................ 62 
Table 5: Angle of Attack Calibration Data ................................................................ 88 
Table 6: Pyramidal Balance Calibration Data ........................................................... 89 
Table 7: Baseline Derivatives ..................................................................................... 91 
Table 8: Sizing Code and Wind Tunnel Drag Comparisons ................................... 92 
Table 9: Elevator Deflection Derivatives .................................................................. 95 
Table 10: Lateral Stability Derivatives ...................................................................... 97 
Table 11: Rudder Deflection Derivatives .................................................................. 98 
Table 12: AVL Run Cases ......................................................................................... 115 
Table 13: AVL Results - Control Surface Deflections for Trim ............................. 116 
Table 14: Eigenvalue Analysis Results for Optimized Aircraft ............................ 118 
 xvi 
Table 15: Modified Control Surface Deflections for Trim ..................................... 120 
Table 16: Eigenvalue Analysis Results for Modified Aircraft ............................... 120 
 1 
Chapter 1 
Introduction 
 An amphibious aircraft can be defined as an aircraft that can take off and 
land on either land or water.  There are historically two classes of amphibious 
aircraft: flying boats and floatplanes.  The earliest examples of amphibious 
aircraft were built in the 1920?s but they did not see widespread service until 
World War II.  The first amphibious aircraft in use by the United States military 
were a family of light-utility, amphibious aircraft produced by the Grumman 
Corporation: the Goose, the Widgeon, and the Mallard.  Initially produced for 
civilian use, the potential military applications of these aircraft were quickly 
recognized and large numbers were put into service in air-sea rescue and anti-
submarine patrol roles.  Following these successes, Supermarine Aircraft in the 
United Kingdom produced the Walrus and the Sea Otter, a family of single-
engine biplanes which were also used during World War II, performing 
observation and rescue duties.   Following the war, the demand for amphibious 
aircraft began to decrease due to the increased availability of hard surface 
landing strips in remote areas.  Today, the main roles of amphibious aircraft are 
in firefighting, search and rescue, as well as providing access to remote, 
unforgiving locations [1].   
 
1.1 Amphibious Aircraft Design 
 Unfortunately, designing an aircraft capable of landing and taking off on 
open waters will incur penalties on the aerodynamics and performance of the 
aircraft, generally in the form of additional weight and drag.  These penalties 
 2 
make it increasingly important that, for a given mission profile, an amphibious 
aircraft be properly sized during the preliminary design phase. 
 An amphibious aircraft must be designed to meet the conditions of both a 
boat and an aircraft.  For example, when on water, the seaplane should have 
good takeoff and landing characteristics, proper amounts of buoyancy, and 
adequate lateral and longitudinal stability for water operations.  When in the air, 
the primary concerns are the aircraft?s aerodynamic characteristics, which are 
generally hindered through meeting the water operations goals mentioned.   
 The initial thrust of this research centered on the creation of an amphibious 
aircraft sizing code that took a basic set of inputs and output the aircraft?s 
geometry and performance data.  To allow the designer maximum flexibility 
when deciding what configuration the aircraft will have, five different water 
operations methods, three different aircraft tail and wing configurations, two 
fuel locations, two aircraft types, and two engine types have been included. The 
designer is allowed to choose from twin floats, a boat hull, a hydrofoil, wing tip 
floats, sponsons, or any combination thereof for the method of water operations. 
The sizing code was designed to properly calculate the size of the water 
operations device and factor it into the drag calculations for the aircraft, which in 
turn impacts its performance characteristics.  The designer can choose between 
having the aircraft in a canard, conventional or flying wing configuration.  The 
fuel can be located in the wings of the aircraft or held at the center of gravity of 
the aircraft.  The aircraft can either be a cargo/transport aircraft or a general-
aviation aircraft, which are the two primary types of amphibious aircraft.  
Finally, the sizing code has separate models for jet and propeller engine types.    
The code will take the designer?s choices on all these configurations and properly 
analyze the affect those choices will have on the overall design of the aircraft. 
 3 
 With the sizing code modified to account for the addition of water 
operations devices, the next thrust of this research was directed toward 
integrating an optimization algorithm into the sizing code.  This allows a number 
of variables to be systematically varied by the sizing program to find the lightest 
weight aircraft configuration possible to meet a given mission profile.  Multiple 
optimizers were investigated, including: unconstrained nonlinear optimizers, a 
constrained linear optimizer, a pattern search optimizer, as well as a hybrid 
particle swarm-pattern search optimizer.  The unconstrained nonlinear 
optimizers used were the fminsearch and fminunc functions built into MATLAB.  
The constrained nonlinear optimizer used was the fmincon function built into 
MATLAB. In the case of this research, a hybrid particle swarm-simplex optimizer 
was employed as the optimization algorithm.  This hybrid optimization 
algorithm leverages the simplex technique?s ability to quickly and efficiently find 
a local optimum in a well defined solution space, while it uses the particle swarm 
as a transport mechanism for individual search particles [2]. To test the validity 
of this sizing code and optimizing algorithm, an aircraft was designed and 
optimized to meet a hypothetical mission profile.  In this case, the mission profile 
is that of a littoral transport aircraft, capable of carrying 50 soldiers and their 
equipment or an equal amount of cargo weight totaling 18,750 lb.  The aircraft 
will have range of approximately 1,000 nmi. at a cruise altitude of 20,000 ft.  For 
low altitude landing/approach and extraction, it will operate in ground effect for 
30 nmi., representing two, 15 nmi., near-water-level mission legs.  The 
optimization code was used to go through all the various aircraft configurations 
available to the sizing code, as well as a number of geometrical inputs, 
eventually resulting in what was the lightest possible configuration and 
geometry.   
 4 
 Finally, it is important to design an aircraft that is not only optimized for 
minimum weight, but also has adequate performance characteristics on the water 
and in the air.  To this end, the design of the hypothetical aircraft was run 
through a number of tests after optimization was complete.  This included the 
design and construction of a wind tunnel model, which was tested in Auburn 
University?s 3 ft. X 4 ft. subsonic wind tunnel to determine the accuracy of the 
drag and performance estimates given by the design code.  Second, the 
longitudinal and lateral water stability of the design was tested using Orca3D.  
This was useful in determining whether the sizing code was designing the water 
operations devices to be of adequate size to stabilize the aircraft while on the 
water?s surface.  Finally, Athena Vortex Lattice (AVL) was used to estimate the 
stability derivatives of the aircraft and assess whether the design had any 
unstable or divergent flight modes and determine if the tails and control surfaces 
were sized properly.  Together, this information will be useful in determining 
ways to improve the sizing code and optimization techniques used to make a 
better preliminary design of an amphibious aircraft.    
 5 
Chapter 2 
Review of Literature 
2.1  Aircraft Design 
 Aircraft design in general and seaplane design in particular have been a 
focus of study for many decades.  Raymer [3] and Roskam [4] have published a 
detailed breakdown of the steps involved in the conceptual design of aircraft.  
Their work details the processes involved in taking initial requirements for the 
aircraft and sizing the aircraft from those requirements.  ?Sizing? refers to the 
general size of the aircraft, with special focus on the airplane weight needed to 
fulfill its required mission objectives.  The Class I sizing process, which uses 
largely empirical methods, does a progressive build-up of the takeoff weight of 
the aircraft.  This build-up includes the weight of the crew, payload, fuel and 
empty-weight of the aircraft. Raymer performs the empty-weight estimation 
based on an empirical ratio of the takeoff weight of the aircraft to the empty 
weight of the aircraft.  This ratio can vary depending on the class of the aircraft 
being designed. The Class II sizing process uses a different method of calculating 
the empty weight of the aircraft, in which the individual component weights are 
calculated based on weight equations.  The equations are statistically based but 
they do allow the designer to account for very detailed configuration design 
parameters.  The drawback of this method of empty weight calculation is that the 
design of the aircraft has to have progressed significantly further than is required 
in the Class I method.  It is necessary to have the aircraft?s V-n loads diagram, a 
preliminary structure for the aircraft, and to have made decisions on all systems 
and equipment that will be necessary for the aircraft?s mission. Once estimates of 
fuel-fractions during different portions of the mission are made, empty weight 
 6 
calculations can proceed.  Some fuel-fractions (takeoff, climb, descent, landing) 
are based largely on historical data trends for different segments of the mission.  
Others, such as cruise, ground effect and reserve time, are calculated based on 
performance parameters during that mission segment.  Finally, an iterative 
approach is used to calculate an estimated takeoff weight using the estimated 
fuel-fractions and empty weight equation.  An initial takeoff weight guess is 
made, followed by a statistical empty weight calculation and an estimate of fuel 
fractions, which leads to an estimated takeoff gross weight.  Then, the initial 
guess is compared to the calculated takeoff gross weight.  If the results do not 
match, a value between the two is used as a next guess and the process is iterated 
until convergence is obtained.   
 The next step in the design process outlined by Raymer is to use the initial 
weight sizing of the aircraft to create a geometry for the aircraft.  This includes 
the selection of airfoil shape, main wing and tail geometries, engine sizing and 
fuselage sizing.  First, an airfoil is chosen based on its lift and drag characteristics 
during cruise, stall characteristics, pitching moment characteristics, and available 
thickness necessary to accommodate structure and fuel.  Next, the main wing 
geometry is designed.  This consists of determining the necessary planform area, 
S, of the wing based on its gross takeoff weight and lift coefficient.  The shape of 
the wing is determined by its aspect ratio, taper ratio and sweep angle and any 
twist in the wing.   
 The horizontal and vertical tails are designed by Raymer using the ?tail 
volume coefficient? method [3].  Since the force due to the lift produced by the 
tail is proportional to the area of the tail, the tail-effectiveness is proportional to 
the tail area multiplied by the length of the tail moment arm.  According to 
Raymer, for the vertical tail, wing yawing moments that must be countered are 
 7 
most directly related to the span of the wing (b), leading to the ?vertical tail 
volume coefficient? in Equation 2.1.   
                                                                  (2.1) 
In the same way, a horizontal tail or canard must counter the pitching moments 
caused by the main wing and can be most directly related to the wing mean 
chord (  ).   
                                                                (2.2) 
Raymer gives typical values of these volume coefficients for multiple classes of 
aircraft and from that data the planform area of the tails can be calculated.  Sizing 
of the control surfaces (elevator, ailerons, and rudder) is addressed primarily 
using historical guidelines and trends to determine the spanwise length and the 
ratio of control surface chord length to main wing chord length. 
 Raymer performs initial engine sizing using historical thrust-to-weight 
ratios (T/W) for jet-engine aircraft or power-to-weight ratios for propeller-
powered aircraft.  T/W is not constant as it varies with the changing weight of 
the aircraft as fuel is burned.  Engines also produce varying amounts of thrust 
depending on the altitude and velocity which the aircraft is being flown at.  In 
design, the thrust-to-weight ratio is generally referring to the T/W value during 
sea-level static, standard-day conditions at design takeoff weight and maximum 
throttle settings.  This historical T/W value is then used to calculate the required 
lift to drag ratio during different mission segments. 
Finally, Raymer presents his method of initial sizing of the fuselage.  Once 
again, his method uses a largely statistical method based on historical data 
trends.  The method presented is based solely on gross takeoff weight but has 
shown to have very good correlation to most existing aircraft.  Raymer [5] also 
 8 
performed a recent analytical optimization study which examined the effect of 
the fineness ratio in subsonic aircraft.  The fineness ratio is the ratio between the 
fuselage length and its maximum diameter.  If the aircraft being designed does 
not have a circular fuselage, an equivalent diameter is calculated from the cross-
sectional area.  It was found that the optimum fineness ratio for a subsonic 
aircraft with its interior volume held constant is generally between six and eight.  
Corke [6] also details a method for determining over-nose and over-side angles 
necessary for proper pilot visibility.  A majority of this method is based on the 
landing approach angle and landing velocity.  Corke goes on to give over-nose 
and over-side angles for different aircraft classes for use as a general guideline in 
the preliminary design phase.  
 
2.2 Water Operations 
 The primary problem with designing an amphibious aircraft is the large 
performance penalty incurred due to the adaptation of the airplane to water 
operations.  The addition of any water operations features, such as floats, a 
hydrofoil, or a boat-hull and sponsons, will negatively impact the aerodynamic 
characteristics of the aircraft.  Not only are there aerodynamic issues, but also 
stability issues, problems caused by loading due to wave slap, and problems 
with landing and taking off from anything other than a very calm sea state.   
 The two primary configurations that aircraft have used for water operations 
are the boat-hull (Figure 1) with wing-tip floats or sponsons design and twin-
float design (Figure 2).  Garner and Coombes [7] discuss that both of these design 
configurations suffer due to the difficulty in designing either configuration with 
both aerodynamic and hydrodynamic considerations in mind.  A compromise 
 9 
must be made, and this is usually to design the aircraft to be as minimally stable 
in the water as is necessary to be considered safe.   Float designs in particular 
have a tendency to be longitudinally unstable if pitched nose downwards at 
approximately one-third of its takeoff speed.  This is due to suction over the 
bottom of the region of greatest curvature, which is generally towards the front 
of the float.  Boat-hulled aircraft have fewer of these longitudinal stability 
problems, as there is a larger fore- and aft-body to reduce the tendency of the 
aircraft to pitch at speed. 
 
Figure 1: Boat Hull Configuration [8] 
 Even if a float is designed to be adequately stable longitudinally by having 
enough of a restoring moment when an angular displacement is introduced, both 
bodies are still susceptible to longitudinal instability due to insufficient damping, 
which results in oscillations known as porpoising. Porpoising was studied in 
detail by Klemin, Pierson and Storer [9].  They determined that there were two 
main classifications of porpoising.  One class can be counteracted by applying a 
 10 
steady load to the horizontal tail surface, which causes the aircraft to pass to 
another trim angle, ?getting through? the porpoising as quickly as possible.  The 
second class can only be counteracted through an alternative application of 
upward and downward loads on the tail surfaces, although even this is not 
always successful.   
 
Figure 2: Twin Float Configuration [8] 
 As shown by Garner and Coombes [7], lateral stability is also an issue with 
single-body float or boat-hull configurations.  This is due to the fact that the 
metacenter is below the center of gravity of the aircraft.  Nelson [8] defines the 
 11 
metacenter as being the point at which a vertical line from the heeled center of 
buoyancy crosses through the vertical line of the original center of buoyancy.  
 This lateral instability can be countered in multiple ways.  As the size of the 
aircraft increases, the center of gravity with respect to the metacenter moves 
down.  It was calculated that for an aircraft with greater than 100 tons of 
displacement, the center of gravity would be sufficiently low so that no 
additional lateral stabilizer would be necessary.  For small amphibious aircraft 
though, the issue of lateral stability has been handled primarily in two ways: the 
addition of a second float to the single float design, and the addition of wing-tip 
floats or sponsons to the single boat-hull design. 
 There have been strides made in studying methods of improving a float?s 
hydrodynamics and aerodynamics simultaneously.  Benson and Lina [10] 
performed a study on the use of a retractable planning flap in place of a fixed 
step on a float.  The step is the abrupt break in the bottom line of the float.  It is 
used to cause the water to separate from the float, which leads to a reduction in 
suction, assists in getting the float to plane, and improves longitudinal control. 
Performance improvements were gained by adjusting the depth of the retractable 
step during and after takeoff.  Improvements of eight percent in water resistance 
and two to three percent in total air drag were noted. 
 Efforts have also been made to decrease the aerodynamic drag of boat-hull 
designs.  A large portion of this work has come in studying the effects of varying 
the length-beam ratio of the hull of the aircraft, as is discussed by Carter [11].  
The length refers to the overall length of the hull while the beam refers to the 
maximum width of the hull.  Carter studied an increase in the length-beam ratio 
from 6 to 15 while keeping the length-beam product constant.  It was found 
through wind-tunnel tests that, for a length-beam ratio increase from 6 to 15, the 
 12 
minimum drag coefficient was reduced by 29 percent, while not significantly 
affecting the hydrodynamics of the hull.   
During takeoff in calm seas, it is often possible for a seaplane to operate at 
trim conditions that give maximum lift to drag ratios.  When the aircraft has to 
takeoff from seas with significant waves, departures from these usual takeoff 
trim conditions are made due to the uncontrollable pitching and heaving of the 
aircraft in the water.  The aircraft will experience increased water loads.  Drag 
will also increase due to having a larger wetted length to beam ratio.  Spray may 
also become more prevalent, which can lead to having wetted control surfaces 
that would be dry under nominal conditions.  These factors all increase the 
resistance of the aircraft which leads to a decrease in takeoff performance.  
Research was conducted by Mottard [12] to examine the effects of these factors 
on the takeoff resistance.  Tests were run on a boat-hulled seaplane with a length 
to beam ratio of 15 and a wing loading of 120 lb/ft2.  The high wing loading was 
used so as to have a range of water speeds corresponding to that of a high-speed 
amphibious aircraft.  Results showed that the maximum takeoff resistance 
increase occurred at around 70 percent of takeoff speed.  In 6 ft waves, the 
takeoff resistance of the aircraft increased 65 percent over nominal values during 
calm seas.  These results were very consistent over a range of dead-rise angles, 
which is the angle from the keel of the hull to its chine. 
More experimental methods of water interaction have been explored such as 
the use of hydro-skis or hydrofoils.  A supersonic amphibious aircraft, Seadart, 
was built using a pair of retractable hydro-skis by Convair San Diego for the 
United States Navy in 1951.  As is discussed by Long [13], a test pilot in the 
Seadart program, there were five Seadart hulls built, with three of those hulls 
being tested over the course of five years.  Tests of the first Seadart revealed 
 13 
serious vibrations and loading on the aircraft created by the blunt aft-body of the 
skis as it crossed waves.  In an attempt to reduce vibrations and loads, the twin 
skis were replaced by a single large ski but it was found to have unacceptable 
hydrodynamic stability and control characteristics.  This was remedied by 
changing the ski shape and increasing the lateral deflection of the elevons, which 
gave the aircraft excellent hydrodynamic stability and control characteristics. 
Research conducted by Fisher and Hoffman [14] looked at the calm- and 
rough-water landing and takeoff characteristics of a seaplane with a single 
retractable hydroski.  The initial results found that the ratio of gross weight to 
maximum ski resistance was 3.2 with loads of 8 to 10g?s in waves eight feet high.  
A yawing instability occurred just prior to the hydroski emerging from the 
water?s surface.  This was fixed by adding an afterbody extension to the ski, but 
this increased ski resistance and resulted in a reduced weight to resistance ratio 
of 2.9. 
A hydrofoil is a second type of experimental water operations method and 
refers to the wing-like structure that is mounted on struts below the hull of a 
boat.  It can be used to lift the boat partially or fully out of the water during 
forward motion.  As the speed of the craft increases, the amount of lift that the 
hydrofoil produces increases to raise the hull partially out of the water, which 
greatly reduces the amount of drag and thusly allows for an increase in speed.  
The hydrofoil concept has also been applied to a number of amphibious aircraft 
(Figure 3). 
 14 
 
Figure 3: Grumman JRF-5 with Grunberg Hydrofoil System [15] 
As discussed by McKann, Blanchard and Pearson [16], a subsonic airfoil 
section shape performs well as a hydrofoil at low forward speeds.  With a 
completely attached flow and while operating at equal Reynolds numbers, the 
forces and moments created in air and water are essentially identical for these 
foil types.  A foil that operates at these conditions is often referred to as a 
?subcavitating? hydrofoil.  At high speeds, the static pressure around the foil 
falls below the vapor pressure of water, which causes the water to evaporate 
around the foil and leads to the formation of water vapor bubbles. Ventilation 
can occur if the foil is surface-piercing, as air can be sucked down into the low 
pressure region.  This two phase (liquid and gas) flow phenomenon is termed 
?cavitation? and when the entire upper surface of the hydrofoil is free of an 
attached flow, it is said to be ?supercavitating?.  Supercavitating hydrofoil 
shapes have been developed for use at these high speeds where cavitation cannot 
be avoided.  These hydrofoils are characterized by a sharp leading edge, usually 
having an entrance angle of about six degrees.  The most common section shapes 
are: a plane faced wedge with a blunt trailing edge; an ogive shape, consisting of 
 15 
convex circular arc surfaces with sharp leading and trailing edges; and a circular 
arc concave lower surface with a contoured upper surface.  Examples of 
supercavitating hydrofoil shapes are shown in Figure 4. 
 
Figure 4: Supercavitating Hydrofoil Shapes [17] 
Vagianos and Thurston [17] detail many different hydrofoil configurations 
that have been used, on both airborne and maritime platforms.  The first and 
most common is the single hydrofoil system, which consists of one hydrofoil 
placed slightly ahead of the center of gravity of the aircraft.  The single hydrofoil 
supports a predetermined design percentage of the gross weight of the vehicle at 
unporting.  Unporting occurs when a hydrofoil breaks the water?s surface.  
Additional stability in this configuration must be provided in addition to the foil; 
 16 
such as the wing, tail or control surfaces of the airplane.  The Grunberg system 
uses one main hydrofoil positioned behind the center of gravity while two small 
floats or hydroskis are placed at the front of the aircraft to provide necessary 
stability.  In this configuration, the hydrofoil takes a majority of the design load, 
with the two smaller members being used primarily for stabilization.  A tandem 
hydrofoil system consists of using two foil arrangements, one at the bow and one 
at the stern of the aircraft.  At unporting, each hydrofoil array carries about 50 
percent of the load.  This arrangement is not practical for seaplane design due to 
the additional drag weight and cost compared to a single foil configuration.  This 
arrangement develops undesirable lateral and longitudinal stability problems 
during unporting in heavy seas.   
Some of the problems with the use of hydrofoils are detailed in Petrie?s [18] 
report on the developmental and operational experiences with the United States 
Navy?s first hydrofoil ship named ?High Point?.  During the testing of the ship in 
1961, it was found that there was cavitation damage in the aft propellers due to 
separation off the upper surface of the hydrofoil.  Ventilation of the forward foil 
of the aircraft was also a problem while in large, short-crested waves.  
Ventilation of a hydrofoil occurs when part of the foil pierces the surface of the 
water and air is sucked down the lifting surface of the foil.  This causes a drastic 
decrease in lift due to the density reduction from water to air.  This ventilation 
issue was fixed by lengthening the forward strut to get the hydrofoil deeper into 
the water.  This also led to an increased sea state capability for the craft. 
 
 
 
 17 
2.3 Optimization Models 
 As the computational capacity of computers and the understanding of the 
physics involved in aerospace design have increased, the modeling of aircraft 
through optimization methods has become a powerful tool to aid in the 
development of new aircraft.  As discussed by Jenkins and Hartfield [2], a variety 
of different algorithms have been proposed and used as optimizers and they can 
be broken down into two general categories: a stochastic and a direct 
methodology.  A stochastic optimizer is a process that uses a non-deterministic 
approach to finding its solution, following a predictable pattern but with an 
element of randomness introduced.  This allows for a greater chance of obtaining 
a globally optimized solution, as opposed to a solution that gets stuck on a local 
optimum.  Types of stochastic optimizers include genetic algorithms (GA?s) that 
are based on survival of the fittest principles, and particle swarm algorithms 
(PSO?s), which are based on principles of social behavior.  Direct solution 
techniques include pattern search algorithms (PS) and gradient-based 
optimizers, among others.  More recently, hybrid optimizers have been 
developed that utilize a combination of optimizing algorithms to improve 
optimization efficiency for a range of problems. 
 A genetic algorithm uses a probabilistic methodology for optimization, 
primarily based on survival of the fittest principles.  Genetic algorithms were 
initially developed based on principles from John Holland?s book, ?Adaptation 
in Natural and Artificial Systems? [19].  A population of potential solution 
candidates is created, with each candidate possessing a fitness and a 
chromosome.  The chromosomes are composed of genes which are GA variables 
set in the input file.   To create a new population, certain individual members are 
chosen according to their fitness to create an offspring based on a tournament 
 18 
style selection process.  The ?weaker? solutions are killed off, while the 
?stronger? solutions go on to ?reproduce? and ?mutate? using various crossover 
routines to produce new generations of offspring solutions. Genetic algorithms 
have been shown to be very effective and robust for a wide range of optimization 
problems.  For example, Obayashi, Yamaguchi and Nakamura [20] employed a 
genetic algorithm in designing a transonic wing planform shape; research 
conducted by Vicini and Quagliarella [21] utilized a genetic algorithm to 
optimize airfoil selection for a given aircraft; and Crossley and Laananen [22] 
preformed a conceptual design of a helicopter via the use of a genetic algorithm.  
The GA?s superior effectiveness stems from its ability to find optimums in a 
design space with a fairly large number of variables, and also its ability to 
operate in design spaces that are not necessarily smooth and continuous.  This 
makes the use of genetic algorithms ideal for complex engineering problems.  
The downside of the use of a GA is that it takes many more evaluations of the 
objective function than a direct search method, such as a gradient-based 
optimizer or pattern search. 
 Particle swarm optimization is a population-based, stochastic algorithm 
originally developed by Kennedy and Eberhard [23] in 1995.  PSO is based 
around a type of swarm intelligence modeled after human social interaction.  The 
algorithm begins by generating a population of randomly chosen members 
defined by a set of independent parameters.  Each particle moves through the 
possible solution space with some velocity, and seeks a globally optimized 
position by changing its given parameters in accordance with a specified set of 
rules.  The particles are allowed to interact with neighboring particles, mimicking 
the social behavior of a group of individuals collectively seeking a common goal.  
Each particle has two or three rudimentary reasoning capabilities: memory of its 
 19 
own best position, knowledge of its local neighborhood?s best position and/or 
knowledge of the entire population?s best position.  Individual particles 
communicate desirable positions on the solution space to each other and adjust 
their own position and velocity based on these good positions.  An objective 
function is usually set, which allows these desirable positions to be evaluated to 
determine which produces the most favorable performance characteristics.  
Repulsive Particle Swarm Optimization (RPSO) is a variation of the standard 
PSO in which a repulsive force is introduced between particles to attempt to 
ensure particles will not get caught in local minima or maxima.  This prevents 
premature convergence and increases the chance of finding a globally optimum 
solution. A modification was made by Mishra [24] to the RPSO which allowed 
each particle an opportunity to pause and search its immediate surroundings for 
a possible better solution before continuing on in the more generalized swarm 
search.  
 A pattern search algorithm is a direct optimizing technique proposed by 
Hooke and Jeeves [25] in 1961.  This algorithm works by first selecting an initial 
trial case.  Exploratory moves are made, varying each individual parameter in a 
systematic manner while holding all other parameters constant.  After each 
individual change the objective function is reevaluated but not changed.  For 
example, if, in a maximization problem, the change increases the objective 
function, then the value of the parameter is set to the modified value.  The other 
parameters are modified in turn.  If all the parameters have undergone 
exploratory moves and the objective function is increased, then the variables are 
changed simultaneously in a pattern move.  If the pattern move does not lead to 
an increase in the objective function, the sizes of the exploratory moves are 
reduced and the process is repeated.  One of the greatest strengths of the pattern 
 20 
search algorithm is that it is relatively efficient at finding local optimums if it is 
well positioned in the possible solution space.  One of the greatest weaknesses of 
the pattern search is that it requires a well chosen initial guess to be effective, 
particularly in a solution space that is computationally discontinuous. 
 The gradient method is a first order optimization algorithm.  Hasdorff [26] 
describes multiple methods of using gradient optimization to find a local 
minimum; with the most popular being the method of steepest descent and the 
method of conjugate descent. 
 The method of steepest descent is an algorithm for finding the nearest local 
minimum of a function.  This method presupposes that the gradient of the 
function can be computed.  The gradient of a function with n variables is 
        
 
       
 
                                         (2.3) 
An initial guess is made at point P0, and a sequence is then constructed P0, P1, 
P2,< such that:  
                                                               (2.4) 
This sequence is found by propagating the from Pi to Pi+1 along a line extending 
from Pi in the direction of        , which is the local downhill gradient and is 
recalculated at each step. The next point in the sequence is found using   
                                                            (2.5) 
where ? is the step size, which is allowed to change each iteration.  The search 
slides down the gradient until it converges on a solution, which is where the 
directional derivative is equal to 0.  One of the downsides of the use of the 
steepest descent method is that if the function has a long, narrow valley shape, 
the minimum can take a significant amount of iterations to find. 
 21 
 The drawbacks of the steepest descent method are addressed through the 
use of the conjugate descent method, which, instead of using the local gradient of 
a function to go downhill to a minimum, conjugate directions are used.  Two 
vectors, v and u, are said to be conjugate with respect to A if: 
                                                             (2.6) 
In other words, u and v are conjugates if they are orthogonal with respect to A.  
As with the steepest descent method, an initial guess P0 is made.  For each 
iteration of the conjugate descent method, a metric must be in place to determine 
if the search is converging toward a local minimum.  This metric comes about 
through the fact that P*, the unknown local minimum, is also the unique 
minimizer of the following quadratic function: 
                                                          (2.7) 
This means that if f(P) becomes smaller after an iteration, the search is 
converging toward P*.   Next, the first basis vector, v1, is taken to be the negative 
of the gradient of f at P0.  This gradient is equal to AP0-b.  The other vectors in the 
basis will be conjugate to the gradient.  Next, let rn be the residual at the nth step 
in the iteration. 
                                                            (2.8) 
Here, rn is the negative of the gradient at Pn, so if the gradient descent method 
was being used, the search would move in the direction of rn.  Instead, for the 
conjugate descent method, it is insisted that the directions, vn, be conjugate to 
each other.  The method also requires that the next search direction be found 
from a combination of the current residual and all the other previous search 
directions.  This gives the expression for the next search vector: 
 22 
                
     
                                            (2.9) 
Following this direction, the next optimal location is given by: 
                                                       (2.10) 
where 
             
         
                                             (2.11) 
This iterative process will continue until a local minimum value is reached.  The 
conjugate descent method is used at a slight cost in calculation time per iterative 
step when compared to the steepest descent method, but the number of iterations 
needed to converge on a minimum value is much less.            
 There have been a number of different combinations of optimizing methods 
employed together in the form of a hybrid optimizer in an effort to more quickly 
and efficiently arrive at a globally optimum solution to various engineering 
problems.  Jenkins and Hartfield [2] have made use of a hybrid particle swarm-
pattern search optimizer in rocket motor optimization problems.  The hybrid 
optimizer makes use of the pattern search technique?s ability to quickly find a 
local optimum in a limited solution space, while using the particle swarm as a 
transport mechanism for the pattern search particles.  A random population of 
particles is created, with initial particle velocities and positions being defined.  
The particle swarm calculations then determine new particle positions and 
fitness.  A pattern search is initiated, followed by a check to see if the swarm has 
been improved.  The particle swarm then calculates new particle positions and 
the cycle repeats itself.  Since the particle swarm is non-elitist, the combined 
hybrid optimizer can examine a very large number of possible solutions, leading 
to a greater chance of finding a globally optimum solution to a problem.  This 
 23 
method also, perhaps just as importantly, is capable of finding many near-
optimum solutions to a given problem, increasing its usefulness as a design tool.   
 
2.4 Wind Tunnels 
 While there have been large advances in theoretical and computational 
methods, low-speed wind tunnel testing is still essential for obtaining the full 
range of data necessary to guide design decisions for many practical engineering 
applications.  In aerospace applications, wind tunnel results provide 
experimental data on the lift and drag of a model, as well as roll, pitch and yaw 
moments, from which stability derivates, as well as the location of the neutral 
point, can be found. 
 One of the most important concepts for relating wind tunnel results to 
theoretical and computational models is that of similar flows.  Usually, it is not 
economically feasible to perform wind tunnel tests on a full size model, so 
scaling factors must be introduced.  The goal of the scaling process should be to 
produce a model that is dynamically similar to the unscaled aircraft.        
Anderson [27] describes two flows as being dynamically similar if: bodies in both 
flows are geometrically similar, and the similarity parameters, which in 
aerospace applications are Mach number and Reynolds number, for both flows 
are the same.  Having dynamically similar flows is important because lift, drag 
and moment coefficients will be identical for two geometrically similar bodies in 
these flows.  This means that the aerodynamic coefficients measured during 
wind tunnel testing will be the same as the aerodynamic coefficients for the full 
scale model at the same Mach and Reynolds numbers.  It is often not practical to 
obtain full scale Reynolds numbers on a scale model due to limitations of some 
 24 
wind tunnel?s operating speeds.  The Reynolds number can be matched by 
increasing speed, but the Mach number will now be incorrect.  This problem can 
be overcome through the use of a variable density tunnel (VDT), which was first 
developed by NACA [28] in 1929, and can be used to match Reynolds and Mach 
numbers through tunnel pressurization.  Unfortunately, most wind tunnels are 
not capable of pressurization and are therefore not capable of achieving a 
dynamically similar flow when scaling down from a full scale model.  In these 
instances, corrections can be applied through scaling corrections, as described by 
Barlow, Rae and Pope [29].  First, a plot of CD vs CL is made from the wind tunnel 
data.  Next, the induced drag coefficient is calculated using the following 
equation. 
                                                                 (2.13) 
The induced drag coefficient is then subtracted from total drag coefficient to give 
the profile drag coefficient, CD,0.  CD,0 is then corrected for the change in Reynolds 
number from model scale to full-scale using Figure 5.   
 
Figure 5: Reynolds Number Correction Chart [29] 
 25 
This step is considered to be relatively controversial, as some engineers believe 
that manufacturing defects on the actual aircraft can cause an increase in drag as 
great as the drag reduction due to Reynolds number scaling from model scale to 
full-scale.  For the purposes of this research, the correction was used as we are 
looking to see the theoretical accuracy of the sizing code compared to the wind 
tunnel results, and the sizing code does not take into account any manufacturing 
defects.   The correction factor is the difference in CD value between the tunnel 
Reynolds number and the Reynolds number for the wing of the full-scale aircraft.  
This correction factor is subtracted from the tunnel profile drag coefficient to 
bring it to full-scale.  The lift induced drag is then added back in to find the total 
drag at full-scale Reynolds number.  The zero lift drag coefficient, CD0 can then be 
used to find the drag area.  This scaling correction method allows wind tunnel 
drag results to be scaled up to flight condition Mach and Reynolds numbers. 
 There are a number of factors that lead to incorrect correlation between 
wind tunnel data and any flight test.  Collected tunnel data will suffer from an 
inexact or unknown Reynolds number, boundary layer effects, interference and 
wall effects, simulation of flow through engine nacelles, etc.  Flight test data will 
suffer from piloting irregularities, gust interference, and errors in the center of 
gravity location just to name a few.   
 The largest boundary layer effect that influences the accuracy of wind 
tunnel results is the improper transition location from a laminar to turbulent 
boundary layer.  Usually the transition is delayed due to the smaller lengths 
involved on the scale model.  Turbulent boundary layers have much greater 
associated skin friction than their laminar counterparts, so by delaying transition, 
drag estimations can be thrown off.  While there is a higher drag associated with 
turbulent flows, there is far less energy in laminar flows, which makes it more 
 26 
susceptible to roughness or corners and can lead to premature separation of the 
boundary layer.  This leads to a loss of lift and an increase in drag on the model.  
Both of these examples of boundary layer effects cause error between wind 
tunnel results and computational or flight test results.  One way of mitigating 
these effects, which is explored by Braslow, Hicks and Harris [30], is through the 
use of grit-type boundary layer transition trips.  When applied correctly, these 
are intended to fix the boundary layer transition location.  Incorrect application, 
such as the transition strip protruding too high above the surface of the model, 
can result in undesirable effects, which can include additional drag or possibly 
robbing the newly created turbulent boundary layer of energy and leading to 
premature separation.  Transition trip location can vary depending on the type of 
airfoil being used.  As documented by Holmes and Obara [31], on a NACA four 
or five digit airfoil, transition will occur at approximately 10% chord at cruise 
conditions.  Newer, laminar flow airfoils can transition much later, at nearly 60% 
chord.   
 Another issue is that of wall interference and blockage.  The presence of 
tunnel walls reduces the area through which the air must flow around the model 
compared to free-air conditions. This, in accordance with Bernoulli?s equation, 
means that the velocity of the air in the vicinity of the model will be increased in 
comparison to a free-air velocity, leading to errors in wind tunnel results.  Wake 
blockage is also a problem present in wind tunnel testing.  Any model without 
some type of suction-type boundary layer control will generate a wake that will 
have an average velocity that is lower than that of the free stream.  To maintain a 
constant volumetric flow rate, the velocity outside the wake in a closed tunnel 
must increase to make up for the decreased velocity inside the wake.  This higher 
velocity means a lower pressure by Bernoulli?s principle, and this lower pressure, 
 27 
which arises as the boundary layer (which later becomes the wake) grows on the 
model, puts the model in a pressure gradient.  Research conducted by Thom [32] 
shows viable mathematical methods for correcting velocities in wind tunnels due 
to blockage effects. 
 Flow visualization techniques are also a powerful tool for analyzing the 
flow over a model.  Using flow visualization, it is possible to see stagnation 
points as well as areas of separation on a model, and this information can be 
used to reduce drag by correcting any aerodynamically problematic areas of the 
design.  Many flow visualization techniques are in practice today, with each 
having specific pros and cons.  For the purposes of this research, dye, smoke, and 
oil visualization techniques are the primary methods considered.   
 The observation of fluid motion using smoke and dye is one of the oldest 
visualization techniques in fluid mechanics.  It is relatively inexpensive and easy 
to implement, while still giving great insight into the complex phenomena 
occurring in fluid flows.  Smits and Lim [33] describe multiple methods of using 
various dyes to perform flow visualization in a water tunnel.  Generally a 
suitable dye has to meet three requirements: neutrally buoyancy, high stability 
against mixing and good visibility.  The most popular dyes are conventional food 
dye, milk and fluorescent dye.  Most commonly, the dye of choice is introduced 
into the flow upstream of the model through a probe, usually constructed out of 
a hypodermic needle or stainless steel tube approximately 1.5 to 2 mm in 
diameter.  The greatest drawback of this method of injection is the disturbance 
this can cause to the flow field.  This is usually countered by placing the probe 
significantly upstream to minimize these effects.  Dye ports in the model are 
another common method of dye injection (Figure 6).  When using dye ports, it is 
 28 
important to keep the exit velocity to a minimum so as to disturb the flow as 
little as possible.   
 
Figure 6: Dye lines and Injection Ports in a Water Tunnel [33] 
 The principle of visualizing the flow over a model in a wind tunnel is the 
same, in principle, as the visualization in a water tunnel using a dye, as detailed 
by Merzkirch [34].  A number of different ?smokes? can be injected into the flow 
well upstream of the test section.  These ?smokes? can include steam, aerosols, 
and tracer gases, which leave a residue on the surface and become visible under 
special optical conditions.  The ?smoke? has to be of a gaseous nature in order to 
maintain neutral buoyancy in air, with only the tracer particles being 
significantly denser than air. The solid or liquid particles normally have a 
diameter less than 1 ?m, which makes the buoyancy effects practically negligible. 
Also, at the related low particle Reynolds numbers, the drag force, which acts in 
 29 
the vertical direction, is very high and almost balances the force of gravity which 
basically suspends the particles in the flow. 
 Lastly, oils can be used to visualize surface flows.  The oil is usually spread 
onto the areas of interest with a paint brush before the wind tunnel is turned on.  
It will then flow under the influence of shear stress from the airstream and 
gravity.  Because the surfaces of interest are usually inclined in some fashion, the 
oil mixture must have sufficient viscosity to sufficiently resist the influence of 
gravity.  The most common material for oil flow visualization is a petroleum 
based lubricating oil.  It is important to have the color of the oil mixture contrast 
with the color of the model surface.  One popular way of doing this is by adding 
fluorescent dye to the oil and using an ultraviolet light to illuminate flow (Figure 
7).  Oil can also be made white by mixing titanium dioxide into it.  This approach 
is best used on a black surface and removes the need to install and use black 
lights to illuminate the flow.  Photographs can be taken after the flow is turned 
off but the available time is relatively short because the oil will flow just under 
the influence of gravity [29]. 
 
Figure 7: Oil Visualization Technique [29]  
 30 
Chapter 3 
Sizing Code Development and Validation 
3.1 Development 
3.1.1 Introduction 
 A code was developed in MATLAB to size and predict performance 
characteristics for an amphibious aircraft.  When given required input 
parameters, such as a mission profile, wing aspect ratio, taper ratio, tail volume 
coefficients, fuselage fineness ratio, etc., the code outputs all major aircraft 
component geometries, fuel and component weight estimations, center of gravity 
and neutral point locations, component drag estimates, and mission performance 
characteristics.   
 The sizing code is set up to work with a number of different aircraft 
configurations.  The designer has the choice of using a conventional, canard or 
flying wing aircraft configuration.  Also, multiple methods of water operation 
can be used in the code, which lets the designer compare the impacts a specific 
type of water operation method will have on the performance and weight of the 
amphibious aircraft.  The code can be configured to analyze the aircraft using a 
boat hull, twin floats, a hydrofoil, sponsons, or wing-tip floats.  Often times, 
amphibious aircraft are designed with a combination of the above water 
operation methods, such as a boat hull being used with the addition of wing-tip 
floats or sponsons to increase lateral stability, or the addition of a hydrofoil to 
any configuration to decrease the load on the airplane as it approaches takeoff 
speed.  To increase the usefulness of the sizing code, as well as to obtain a more 
feasible final preliminary design, any combination of the various water 
operations methods may be used, which allows for testing as many 
 31 
configurations as possible.  Additionally, the code allows the designer a choice 
on where the aircraft?s fuel will be stored, either located at the center of gravity 
or stored in the wings, as well as the option for the use of strut-braced wings. 
 The sizing code functions by inputting an initial takeoff gross weight 
estimate for the aircraft, as well as certain geometry inputs. The code is then put 
into a while loop, where it compares the difference between the initial gross 
weight estimate and the gross weight calculated based on aircraft geometry and 
performance characteristics.  Initially, the gross weight estimate and geometric 
input parameters are used to size the major components of the aircraft (main 
wing, horizontal and vertical tails, water operations method).  With the 
components sized, the drag on individual components is calculated during 
different mission legs, such as cruise in and out as well as time spent in ground 
effect.  These drag estimates are then used to determine fuel consumption which 
leads to a component-by-component weight build up of the vehicle.  The code 
then checks to see if the calculated gross weight is within a specified difference 
margin to the initially estimated gross weight, in the case of this paper 0.1 lb.  If 
the calculated value is within this margin, the aircraft sizing is considered to be 
at a converged solution and the while loop terminates.  If the difference between 
the estimated and calculated value is greater than the difference threshold, the 
initial gross weight estimate is overwritten by the calculated gross weight 
estimate and the sizing code iterates until a converged solution is found. 
 32 
 
Figure 8: Sizing Code Flowchart 
 With the aircraft sized, individual component weights are sent to functions 
which calculate the center of gravity and neutral point of the aircraft.  With these 
parameters, a static margin can be calculated.  Aircraft geometry and 
performance characteristics are then output into a text file and a picture showing 
the basic geometry is drawn. 
 
3.1.2 Lifting Surface Geometry Calculations 
 With an initial gross takeoff weight estimation, as well as various input 
parameters, the next step in the sizing process is to size the major components of 
the aircraft.  First, the wing loading of the aircraft is calculated using an initial 
estimate of the maximum lift coefficient, CLmax, and the stall speed. 
 33 
 
   
 
           
                                                (3.1) 
Now the required planform area of the main wing, S, can be calculated using the 
estimated gross takeoff weight and wing loading. 
                                                                      (3.2) 
The total wing span, b, of the main wing can be found using Equation 3.3, 
                                                             (3.3) 
where AR is the aspect ratio of the main wing.   
 The main wing is divided into an inboard and outboard section to allow for 
maximum flexibility in determining the shape of the wing.  Both sections are 
allowed to have distinct sweep angles and taper ratios. Also, the width of the 
inboard wing segment, to be called the wing segment width (WSW) for the 
remainder of this paper, is not permanently fixed.  As the sizing code iterates 
through in an attempt to converge on a correct gross takeoff weight, the WSW is 
driven by with the volume of fuel the aircraft requires, as it is to be carried only 
in the inboard section between 30% and 65% of the local chord length.  The root 
chord length for conventional and canard configurations is calculated using 
Equation 3.4, 
                      
                                         
            (3.4) 
where ? is the taper ratio for the inboard and outboard wing section, which are 
both inputs, as noted in the subscript.  With the inboard chord length now 
known along with the inboard and outboard taper ratios, the chord length at the 
separation between wing segments as well as at the tip of the wing can be found. 
                                                               (3.5) 
 34 
The final geometric calculation for the main wing is to determine sweep angles at 
the leading and trailing edge.  There is an input for the sizing code that allows 
the designer to choose a sweep angle at a specific percentage of the wing chord 
length, but to find the sweep angle for various locations on the wing Equation 3.6 
must be used, 
                                              
   
                         (3.6) 
where x1 is the input sweep angle position, x2 is the position along the chord 
where the sweep angle is being calculated, ? is the sweep angle of x1 and x2 as 
noted. bwsw is the semi-span of the inboard wing section length and Cr and Ct are 
the root and tip chord lengths of the inboard or outboard section, depending on 
what portion of the wing the sweep angle is being calculated for. 
 The planform areas for the vertical and horizontal tails are calculated using 
the following equations referenced from Raymer [3], 
          
  
                                                     (3.7) 
          
  
                                                     (3.8) 
where, CVT and CHT are tail volume coefficients for the vertical and horizontal tail 
respectively, LVT and LHT are moment arms for the vertical and horizontal tail 
respectively, which can be approximated as the distance between the tail quarter-
chord to the quarter-chord of the main wing.  The mean chord length is given by 
  . The span and root chord length of the tails are found using Equations 3.7 and 
3.8 using terms for the respective tail instead of the main wing. 
 
 
 
 35 
3.1.3 Water Operation Method Geometry Calculations 
 The sizing code allows for the design of an amphibious aircraft using a wide 
variety of water operation methods.  It can calculate the geometry and resulting 
effects on the performance of the aircraft due to a boat hull, twin floats, wing tip 
floats, sponsons or a hydrofoil.  In order to maintain maximum flexibility in the 
code, it was designed to allow multiple methods to be chosen simultaneously.  
For example, most amphibious aircraft that make use of the boat hull 
configuration also use either wing-tip floats or sponsons to increase the stability 
of the vehicle during its time on the surface of the water at the expense of 
aerodynamic performance.  Each method of water operation is sized and 
analyzed separately to properly capture the performance impact on the aircraft. 
 
3.1.3.1 Boat Hull Calculations 
 The primary factors that affect the shape of any float or hull on an aircraft 
are those that concern how it behaves in the water, with aerodynamic 
considerations, to a large extent, being secondary.  For instance, early examples 
of floats had difficulty taking-off from the surface of the water.  This problem 
was fixed through the addition of a step on the float, which causes water to 
separate from the aft end of the float and significantly reduce resistance through 
the water, although it negatively impacts performance in the air.  
 The primary functions of any float or hull is to give the amphibious aircraft 
buoyancy, and to provide longitudinal and transverse stability on the water and 
when underway to takeoff speeds.  The float must provide reasonable resistance 
while in the water so that the aircraft is capable of taking-off with the power it 
has available.  It must also be designed in such a way so as to hold landing 
 36 
impact pressures to reasonable levels.  All of these factors can drastically change 
the form of floats, but for the purpose of this study, many of the design details 
are out of scope for a preliminary design and will be omitted until the sizing of 
the aircraft is complete.  The floats can then be designed in more detail, taking 
into account the specific characteristics of the resulting aircraft and how those 
characteristics will drive the design of the float. 
 For the purpose of this sizing code, the guidelines for the design of a boat 
hull set out by Shoemaker and Parkinson [35] were used for initial sizing 
calculations.  Initially, a load coefficient, C?, for the hull is given.  This coefficient 
will determine the beam, b, of the hull.   A seaplane experiences the greatest 
amount of water resistance at hump speed, which is the speed just before it 
begins to plane on the step of its float structure.  In Figure 9, hump speed 
corresponds to the velocity coefficient of 2.3.  For this study, the load coefficient 
was taken to be 0.425, which corresponds to the highest load coefficient on the 
CV=2.3 curve.  The negative slope of this curve indicates that decreasing the beam 
of the float will lead to an increase in resistance.  Alternatively, the curves for CV 
values of 4.5 and 6.0 show that reducing the beam will reduce the water 
resistance of the aircraft. According to Langley [36], the practical range of load 
coefficients for boat hulls is between 0.35 and 0.5. 
 37 
 
Figure 9: Effect of C? on?/R at Best Trim Angles [35] 
 Next, the beam of the hull is calculated based on the load coefficient and 
weight of the aircraft. 
            
       
                                                 (3.9) 
For the analysis performed in this study, the hull height was assumed to be equal 
to the hull beam.  The necessary displacement of the hull was then calculated, 
 38 
with a 100% reserve factor, meaning that the hull will displace twice its weight in 
water.  A length-to-beam ratio, which varies between 3.5 for aircraft below 5,000 
lb. to 4.5 for aircraft above 20,000 lb. is then input, and interpolation is used to 
find values in between.  Generally, a lower length-to-beam ratio will result in a 
lower water resistance in the high speed range as well as a lower structural 
weight.  Often times, however, the shorter beam can lead to excessive spray [35] 
and reduce the transversal stability of the aircraft on water.  The length of the 
boat hull is calculated using Equation 3.10. 
               
    
                                                (3.10) 
Where RLB is the length-to-beam ratio and Dhull is the displacement of the boat 
hull.  The length of the boat hull is then compared to the minimum fuselage 
length set by the designer and the program continues. A hull of this length, 
width and height will now be used when doing drag calculations to determine 
the performance of a boat-hulled aircraft.   
 
3.1.3.2 Twin Float Calculations 
 The design of floats for a twin float aircraft is very similar to the design of an 
amphibious aircraft that makes use of a boat hull.  Once again buoyancy, 
stability, clean running and good takeoff properties are desirable hydrodynamic 
features, but these features are largely incompatible with desirable aerodynamic 
features, such as having a low drag shape, and the minimum size and weight 
possible.  Unlike the boat hull, the twin float configuration must have 80% 
reserve buoyancy [37], meaning that the water displacement of each float must 
be equal to 90% of the gross takeoff weight of the aircraft.  In the case of twin 
floats, having a wide cross section is not as important as with a boat hull 
 39 
configuration, as having two floats with a wide base track will increase 
transverse stability. 
 The sizing code first calculates the required individual float displacement, 
which by regulation must be equal to 90% of the fully loaded takeoff weight.   
               
     
                                               (3.11) 
Next the proportions and dimensions of the float can be found since the total 
submerged float displacement has been fixed.  A block coefficient for the float is 
assumed to be 0.5. The block coefficient is the ratio of the volume the float to the 
volume of a rectangular block with the same length, depth and breadth.  For 
most Vee-bottom floats, which is the standard configuration used on most 
amphibious aircraft, the block coefficient is between 0.48 and 0.52.  The breadth 
of a float can be found using Equation 3.12. 
                
     
                                                  (3.12) 
Cblock is the float?s block coefficient, bfloat is the breadth of the float, and Dfloat is the 
float displacement and has units of ft3.  Langley also offers guidelines for finding 
the length and depth of the float as a function of breadth based on historical 
ratios to obtain a float that has sufficient longitudinal stability.  The length of the 
float should be eight times the breadth while the depth should be 1.125 times the 
breadth [36].  These factors are then used by the sizing code to find the 
appropriate length and depth of the float based on the gross takeoff weight.  Two 
floats are then used by the performance section of the sizing code for drag 
calculations. 
 
 
 40 
3.1.3.3 Wing Tip Float and Sponsons Calculations 
 Most amphibious aircraft that use a boat hull as their primary water 
operation method must augment their transverse stability through auxiliary 
means.  To properly understand the reason for this lack of transverse stability, it 
is necessary to explain the concept of the transverse metacenter.  
 
Figure 10: Transverse Metacentric Height [36] 
In this figure, the center of gravity of the hull is located at point G.  The center of 
buoyancy is located at point B.  The center of buoyancy of a hull is located at the 
center of gravity of the water a hull displaces.  The hull is heeled through a small 
 41 
angle, ?, so that the water line moves from WL to W?L?.  This causes the center of 
buoyancy to move from point B to point B? while the center of gravity stays at 
point G.  If a vertical line is drawn through point B?, the transverse metacenter is 
located at the intersection point between that line and the centerline of the hull.  
The transverse metacentric height is the distance between the center of gravity 
and the transverse metacenter.  If the metacenter is above the center of gravity, 
the aircraft is stable.  If the metacenter coincides with the CG, the aircraft is in 
neutral stability.  If the metacenter is below the CG, the aircraft is unstable. 
 The reason that a flying boat?s hull is normally augmented for transverse 
stability is because, in practice, it is basically impossible to achieve positive 
transverse stability due to the center of gravity almost always being above the 
transverse metacenter.  Since the majority of the structure of a flying boat is 
above the load water line, the center of gravity will be significantly higher than 
the load water line.  Furthermore, the metacenter is normally relatively low 
because of the limits to the value of the transverse moment of inertia, I, of the 
boat hull at the load water line.  I is a function of the beam of the hull, which 
could be increased to give the aircraft sufficient transverse stability by lifting the 
metacenter above the center of gravity, but this would lead to very undesirable 
effects while on the water, namely a large increase in water resistance, making it 
increasingly difficult to takeoff. 
 Two methods are normally used to increase the transverse stability of a boat 
plane without the drastic measure of greatly increasing the beam.  There will 
usually be either outboard wing-tip floats mounted on either side of the fuselage 
(Figure 11) or sponsons (Figure 12) built off the side of the hull. 
 42 
 
Figure 11: Wing-Tip Floats [36] 
 
Figure 12: Sponsons [36] 
Both methods provide lateral stability to the aircraft in the event of any heeling 
rotations. 
 Wing-tip floats and sponsons are designed by the same method.  The 
Federal Aviation Administration [37] has specified a required buoyancy for any 
lateral stabilizing floats by mandating that the righting moment provided by a 
float when fully submerged be greater than, 
                                                          (3.13) 
where M is the righting moment of the lateral float in lb-ft, R is a coefficient 
based on the weight of the aircraft, h is the negative metacentric height of the 
hull in feet and ? is the angle of heel required to completely submerge a lateral 
float.  The buoyancy required is found by dividing the righting moment by the 
distance from the center of gravity of the lateral stabilizing float to the center of 
 43 
the fuselage.  This is the only major difference between the sizing of the wing-tip 
floats and sponsons.  The sizing code then calculates the breadth of the 
stabilizing floats, bstabs, 
                                                                   (3.14) 
where Dstabs  is the displacement of one stabilizing float.  The ratios for the length 
and depth to the breadth are given by Langley [36], with the length being 4 times 
the breadth and the depth being 0.5 times the breadth.  Two stabilizing floats of 
these dimensions are then used to calculate drag and performance parameters. 
 
3.1.3.4 Hydrofoil Calculations 
 A hydrofoil is an experimental method of water operation when applied to 
amphibious aircraft.  A hydrofoil refers to a wing structure, usually mounted on 
a strut below the hull, which is used to lift the hull out of the water during 
forward motion.  As the aircraft gains speed, the hydrofoil generates more lift, 
and begins to push the hull out of the water.  This greatly reduces the amount of 
drag on the aircraft and allows for an increase in speed.  The hydrofoil is usually 
configured in a Vee-shape, so as it comes out of the water, also known as 
unporting, it gradually looses lift until an equilibrium is achieved between the 
hydrofoil generated lift and the weight of the aircraft.  In a single-hydrofoil 
configuration the hydrofoil is usually slightly in front of the center of gravity of 
the aircraft.  
 The design and weight analysis of the hydrofoil in the sizing code takes 
place after the weight buildup of the aircraft.  It is assumed that the lift the 
hydrofoil is generating is equal to the weight of the aircraft minus the lift 
 44 
generated by the wing.  Next, the lift coefficient of the hydrofoil, as well as the 
aspect and taper ratios must be assumed.  Knowing these variables allows for the 
calculation of the planform area and span of the hydrofoil.  It is assumed that the 
hydrofoil will unport at the stall speed of the aircraft. 
        
        
                                                   (3.15) 
                                                          (3.16) 
 
3.1.4 Performance Estimation 
3.1.4.1 Component Drag Estimation 
 With all the components (lifting surfaces, fuselage, water operation 
methods) of the aircraft now sized, the sizing code performs a drag buildup on 
the individual components during cruise and while in ground effect.  The code 
calculates the parasitic (skin friction) drag of each component to approximate the 
drag for the entire aircraft.   
 The first step is to calculate the Reynolds number of each component using 
Equation 3.17, 
                                                            (3.17) 
where ? is the air density, V is the velocity, L is the characteristic length of the 
component and ? is the viscosity.  The Reynolds number gives a measure of the 
ratio of inertial forces to viscous forces and expresses the relative importance 
between the two types of forces.  Next, the flow over the component is assumed 
to be fully turbulent and the friction coefficient is estimated using a power law fit 
based on the component?s Reynolds number with Equation 3.18 [3]. 
 45 
            
                        
                                       (3.18) 
Finally, with the friction coefficient found, a component parasitic drag coefficient 
can be estimated using the Equation 3.19 [3], 
                        
   
                                             (3.19) 
where FF is a form factor used to account for pressure drag and higher-than-
freestream velocities along the surface of the component, Swet is the wetted area 
of the component, and Sref is a reference area used to normalize the drag 
coefficients of the various components.  The drag coefficients are then summed 
to find an estimated zero lift drag coefficient CD,0. 
 
3.1.4.2 Mission Performance Estimation 
 With estimates for component drag coefficients, the sizing code now 
calculates performance parameters, such as lift-to-drag ratios during various 
mission segments, maximum-range speed, required sea-level thrust and weight 
fractions.  These weight factions are then used to determine the amount of fuel 
necessary for the aircraft to fly its mission profile. 
 First, a lift coefficient is found using Equation 3.20.  This lift coefficient is 
then used to calculate the induced drag coefficient in Equation 3.21. 
         
   
                                                   (3.20) 
                                                             (3.21) 
In Equations 3.20 and 3.21, q is the dynamic pressure and e is Oswald efficiency 
factor, which is a ratio between the drag due to lift of a 3-D wing and a wing 
 46 
having an equivalent aspect ratio and an elliptical lift distribution.  The overall 
drag coefficient of the aircraft is then calculated using Equation 3.22. 
                                                         (3.22) 
CD is calculated during cruise, flight in ground effect and alternate-airport-
diversion mission legs and used to find the drag force generated by the aircraft, 
followed by the estimated weight being divided by the drag to find lift-to-drag 
ratios of the aircraft throughout its mission.   
 The sizing code is set up to accommodate both jet and propeller engines, 
with the maximum-range speed being calculated using Equations 3.23 and 3.24 
respectively. 
            
                 
                                         (3.23) 
            
                 
                                         (3.24) 
 
The maximum-range speeds are then used to find the thrust specific fuel 
consumption [3].   
                                                           (3.25) 
                                                             (3.26) 
Equations 3.25 and 3.26 are the equations for power specific fuel consumption 
and thrust specific fuel consumption respectively.  Power is found from Equation 
3.27. 
      
 
                                                        (3.27) 
 47 
Finally, Equations 3.25, 3.26 and 3.27 are combined and solved for Ct.  
                
 
                                              (3.28) 
The engine?s required sea-level thrust is found using the total drag of the aircraft 
during the cruise segment of the flight profile multiplied by the ratio of density 
at sea-level to the density at cruise altitude.  The weight fraction (WF) during the 
various mission legs (cruise, in ground effect, during IFR reserves), is then found 
using the max-range speed, thrust coefficient, lift-to-drag ratio, and the range (R) 
of the mission leg in Equation 3.29. 
    
    
 
                                                          (3.29) 
The weight fractions for all the mission legs are then used to calculate the fuel 
weight fraction (FWF) which corresponds to the amount of fuel the aircraft will 
require to complete its mission using Equation 3.30. 
                                                                 (3.30) 
The weight fraction during take-off, climb, descent and landing are given by 
Raymer [3] and are hardcoded into the sizing program.  The fuel weight fraction 
can then be multiplied by the estimated weight to find the weight of fuel needed 
by the aircraft to complete its mission. 
 The aerodynamic center of the main wing and tails as well as the Oswald 
efficiency factor is calculated using a vortex lattice subroutine inside of the sizing 
code.  The vortex lattice routine is fed the geometry of the wings and tails and 
models these surfaces as an infinitely thin sheet of discrete horseshoe vortices, 
which are then used to calculate the lift and induced drag of the lifting surface.  
These results are used to determine the location of the aerodynamic centers of 
 48 
the main wing and horizontal tail, which are then output back into the sizing 
code and used in subsequent calculations. 
 
3.1.5 Weight Buildup 
 Next, the sizing code performs a detailed weight build up of the amphibious 
aircraft.  Much of the procedure for the weight build up is taken from        
Raymer [3], who uses a predominately empirical method for determining the 
weights of the individual aircraft components based on the weight breakdowns 
of existing aircraft.  The code is set up to perform the weight build up of both 
general aviation and cargo aircraft.  These two aircraft configurations use 
different sets of empirical equations because of the great differences in both their 
size and utility. 
 The sizing code also calculates the additional weight due to the aircraft?s 
chosen method of water operation.  The weight of the floats is calculated using 
two methods and the average of these weights is used for the empty weight 
analysis.  The first method plots the weight of various production floats against 
their displacement.  A linear trendline is then applied to the data and is used to 
find the weight of the float being designed based on its necessary displacement. 
 49 
 
Figure 13: Float Weight vs. Displacement 
The second method of finding the float weight, taken from Langley [36], uses the 
empirical relationship shown in Equation 3.31. 
                                                            (3.31) 
Both of these empirical relationships have units of lbs.  The weight of the struts 
used to connect the floats to the fuselage/wings of the aircraft is also given 
through the use of an empirical formula taken from Langley [36], with the struts 
weighing approximately 3% of the total weight of the aircraft.   
 The weight of the wing-tip floats, which are used to augment the transverse 
stability of the amphibious aircraft, is calculated through the use of an empirical 
relationship, with the weight of the wing-tip floats being 1.2% of the total weight 
of the aircraft.  The weight of the stabilizing sponsons is calculated by assuming 
the sponson has a wall thickness of ? in. and is made of fiberglass with a density 
y  =  0 . 1 3 4 x
0 . 9 7 7 8
R ?  =  0 . 7 0 1
y  =  0 . 1 3 5 8 x  +  1 2 8 . 6 5
R ?  =  0 . 9 9 1 2
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
0 5000 10000 15000 20000 25000 30000 35000
W
e
i
g
h
t
 
(
l
b
s
)
D i s p l a c e m e n t  ( l b s )
F l o a t  W e i g h t  v s  Di s p l a c e me n t
S tr ai g ht
A m phi b
P owe r  ( S tr ai g ht)
L i ne ar  ( A m phi b)
 50 
of 96.768 lb/ft3.  The weight of the hydrofoil and attaching strut is calculated by 
multiplying the volume of the hydrofoil, which is determined during its sizing, 
by the density of aluminum.   
 Finally, the weight of the fuel is calculated by multiplying the fuel weight 
fraction by the estimated gross takeoff weight of the aircraft.  The weights of the 
individual aircraft components, the chosen method of water operation, fuel and 
payload are then sent to the center of gravity (CG) and neutral point calculation 
functions. 
 
3.1.6 Center of Gravity and Neutral Point Calculation 
 The CG function assumes that the weight of the water operation device is 
located at the center of gravity.  The location of the center of gravity is found by 
adding the moment caused by the weight of each component, with the reference 
location at the nose of the fuselage, together and dividing by the total weight of 
the aircraft minus the weights of components located at the CG.  This results in 
the CG location as a distance back from the nose of the fuselage. 
 The weight of all the lifting surfaces is assumed to be concentrated at the 
quarterchord of those surfaces.  Placement of those surfaces is dependent on the 
aircraft configuration (flying wing, canard, or conventional).  For example, the 
leading edge of the horizontal tail in the canard configuration is located at the 
nose of the fuselage, while the trailing edge of the horizontal tail in the 
conventional configuration is located at the aft end of the fuselage.  There is no 
horizontal tail in the flying wing configuration.  The vertical tail placement in the 
conventional configuration is dependent on the LVT parameter, which is the 
distance from the vertical tail quarterchord to the quarterchord of the main wing.  
 51 
In the flying wing and canard configurations, due to the shorter moment arm 
available because of the placement of the main wing, the vertical tail is moved 
out to the separation point between the inboard and outboard wing segments.  
This allows for a reduction in the vertical tail planform area necessary to give 
sufficient control of the aircraft.  Fuel placement is based on whether the code is 
sizing an aircraft with fuel at the CG or in the wings.  If the fuel is in the wings, it 
is placed in the inboard wing section between the 35% and 60% chord-line. The 
other components, such as engines, landing gear, hydraulics, anti-ice gear, etc. 
are placed based on the location of the main wing and fuselage and rely largely 
on the designer to place them in a realistic position. 
 With the center of gravity position located, the sizing code then moves on to 
neutral point calculation.  First, the locations of the aerodynamic centers of the 
main wing and horizontal tails are located with their reference point at the nose 
of the fuselage to put it in the same reference frame as the CG location.   
 To simplify the equations for calculating the neutral point, the positions of 
the center of gravity and aerodynamic centers of the main wing and horizontal 
tail are all expressed as fractions of the mean chord of the main wing. 
 The position of the aircraft?s neutral point is calculated using Equation 3.32, 
         
                  
     
   
       
                   
                             (3.32) 
where    and      are the lift curve slope for the main wing and horizontal tail 
and are calculated by the vortex lattice code.        and       are the locations of 
the aerodynamic centers of the wing and horizontal tail respectively.      is a 
coefficient representing the ratio between the dynamic pressure at the tail and 
the freestream dynamic pressure.  For a canard, this coefficient is 1.0, while for a 
 52 
conventional aircraft it ranges from about 0.85 to 0.95 and is taken to be 0.9 for 
these calculations.         is the pitching moment contribution from the fuselage 
and was calculated using Equation 3.33. 
                 
 
                                                       (3.33) 
Wf is the maximum width of the fuselage and Lf is the length. Kf is an empirical 
pitching moment factor found from Figure 14. 
 
Figure 14: Fuselage Moment Term [38] 
Finally, the       term is a downwash derivative that describes the flow 
interaction between the main wing and horizontal stabilizers and changes the 
local angle of attack.  For a canard configuration, there is no downwash from the 
 53 
wing on the horizontal stabilizer, but the downwash from the canard will affect 
the wing.  The estimation of the canard effect on the wing is difficult because the 
downwash varies across the canard span and, outboard of the canard, the wing 
tip vortices actually create an upwash on the wing. In a canard configuration, the 
effect of upwash from the wing onto the canard is calculated using Equation 3.34, 
   
     
   
                                                    (3.34) 
where       is interpolated from Figure 15. 
 
Figure 15: Upwash Estimation [3] 
For a conventional tail configuration, the downwash derivative is found using 
Equation 3.35, 
   
     
  
                                                      (3.35) 
 54 
where      is found using an Equation 3.36 from Pamadi [39]. 
  
   
    
                                                         (3.36) 
For an aircraft with a flying wing configuration, there is no downwash derivative 
and the equation for the neutral point simplifies down to Equation 3.37. 
                      
  
                                           (3.37) 
It can be seen from this equation that there is no stabilizing term for a tailless 
aircraft (flying wing), which means that the aerodynamic center of the main wing 
must be behind the center of gravity of the aircraft to make the aircraft statically 
stable. 
 With the position of the neutral point and center of gravity now known, the 
longitudinal static margin of the aircraft can be calculated using Equation 3.38. 
                                                           (3.38) 
If the CG of the aircraft is ahead of the neutral point, the static margin is positive, 
so the aircraft is statically stable.  At the CG?s aft most position, the static margin 
of a typical transport aircraft is usually between 5-10%. 
 
3.1.7 Sample Output 
 When the previously described calculations are complete, the sizing code 
has determined the size and geometry of the aircraft wing surfaces, fuselage, and 
water operation device.  It has also performed a drag build up on a component-
by-component basis and used it to determine the performance characteristics of 
the aircraft.  Additionally, it has created an empty weight build up of the aircraft 
based on each individual component and used those weights to determine the 
 55 
location of the center of gravity.  Finally, the sizing code has found neutral points 
of the lifting surfaces and calculated the static margin of the aircraft.  To properly 
convey this information to the designer, the code has been designed to output 
both a drawing of the aircraft (Figure 16), which shows the placement of major 
components, as well as a text file, which has a more detailed breakdown of the 
aircraft, showing the geometric parameters, placement and weights of 
components and performance parameters.  An example of the output text file can 
be found in Appendix A. 
 
Figure 16: Sizing Code Sample Output 
 
 
3.2 Validation 
 The sizing code was validated by using a Lockheed C-130-H and a Cessna 
172-R to ensure that the sizing algorithms used in the code were working 
 56 
properly over a large range of aircraft gross weights as well as aircraft types.  
Geometries of the two aircraft were run through the code to determine how well 
the coded algorithms predicted the takeoff weight and performance parameters. 
 
3.2.1 Lockheed C-130-H 
 The Lockheed C-130-H is a turboprop, four-engine, military transport 
aircraft in use by the United States military and many other countries around the 
world.  It was primarily designed for troop and cargo transport but has seen 
duty in a number of other roles, including as a gunship (AC-130), aerial 
refueling, search and rescue, and aerial firefighting.   
 
Figure 17: Lockheed C-130-H [40]  
 The C-130-H was used in this validation effort as an example of a large, 
cargo aircraft. Figure 18, below, shows the Lockheed C-130-H geometry from the 
 57 
sizing program and Table 1 presents a comparison of the weight calculations and 
geometric parameters from the program and from the actual aircraft.  The weight 
calculations are within 7.5% and the largest geometrical deviation is the 
horizontal tail root chord length, which reflects a difference in the assumed taper 
ratio. 
 
Figure 18: Lockheed C-130-H Sizing Code Output 
 
 
 
 
 
 
 
 58 
Table 1: Lockheed C-130-H Validation Results [40] 
 
Sizing Code Actual % Error 
Gross Take-off Weight (lb) 155,401.3 155,000.0 0.3% 
Empty Weight (lb) 73,629.1 75,745.0 2.8% 
Fuel Weight (lb) 36,772.1 34,255.0 7.3% 
Planform Area (ft2) 1,752.3 1,745.0 0.4% 
Span (ft) 132.8 132.6 0.2% 
Root Chord (ft) 15.6 15.1 3.5% 
Wingloading (lb/ft2) 88.7 88.8 0.2% 
Planform Area, Horizontal Tail (ft2) 491.3 536.0 8.3% 
Span, Horizontal Tail (ft) 50.4 52.7 4.3% 
Root Chord, Horizontal Tail (ft) 14.9 17.2 13.7% 
Planform Area, Vertical Tail (ft2) 307.0 300.0 2.3% 
Span, Vertical Tail (ft) 24.9 24.6 1.1% 
Root Chord, Vertical Tail (ft) 19.2 21.5 10.7% 
Cruise Speed (knots) 267.6 292.0 8.3% 
 
3.2.2 Cessna 172-R 
 The Cessna 172-R Skyhawk is a four-seat, single piston-propeller engine, 
general aviation aircraft.  More Cessna 172 variants have been built than any 
other aircraft in history.  The 172-R variant was introduced in 1996 and is the first 
Skyhawk to have a fuel-injected engine from the factory. 
 
Figure 19: Cessna 172-R [41] 
 59 
The Cessna 172-R was included in this validation effort as an example of a small, 
light-weight, general aviation aircraft.   
 Figure 20 shows the geometry for the 172-R and Table 2 shows a comparison 
of the various weight and geometric parameters.  The weight estimates are 
captured quite reasonably, with the greatest error being a 5.6% difference in 
estimated fuel weight.  As with the C-130-H, the largest geometric error was in 
the root chord length estimates for the horizontal and vertical stabilizers. 
 
Figure 20: Cessna 172-R Sizing Code Output 
 
 
 
 
 60 
Table 2: Cessna 172-R Validation Results [41] 
  Sizing Code Actual % Error 
Gross Take-off Weight (lb) 2,492.1 2,550.0 2.3% 
Empty Weight (lb) 1,562.2 1,639.0 4.7% 
Fuel Weight (lb) 354.9 336.0 5.6% 
Planform Area (ft2) 174.1 174.0 0.1% 
Span (ft) 36.1 36.1 0.0% 
Root Chord (ft) 5.3 5.3 0.0% 
Wingloading (lb/ft2) 14.3 14.7 2.3% 
Planform Area, Horizontal Tail (ft2) 29.4 30.0 2.1% 
Span, Horizontal Tail (ft) 10.8 11.3 4.8% 
Root Chord, Horizontal Tail (ft) 3.5 4.0 13.5% 
Planform Area, Vertical Tail (ft2) 14.9 14.9 0.3% 
Span, Vertical Tail (ft) 4.1 4.0 2.0% 
Root Chord, Vertical Tail (ft) 5.1 5.3 2.3% 
Cruise Speed (knots) 82.9 94.0 11.8% 
 
 To assess the accuracy of the drag impact due to the inclusion of water 
operations in the sizing code, the Cessna 172-R geometry was run again, this 
time with the addition of twin floats, a modification regularly seen to Cessna 
172?s.  Figure 21 shows the resulting geometry.  Adding a set of Baumann floats 
to a Cessna 172-R increases the gross weight of the aircraft by approximately 275 
lb [42], which yields a gross weight of 2825 lb.  The gross weight of the 172-R 
with floats predicted by the sizing code was 2779.49 lb.  This results in a 1.61% 
error. 
 61 
 
Figure 21: Cessna 172-R with Floats Sizing Code Output 
 
 
3.2.2.1 Wind Tunnel Model and Results 
 A wind tunnel model was built to assess the floats? impact on the 
performance of the 172-R as well as to validate the performance data the sizing 
code had output for the modified 172-R.  The floats were modeled off of the 
Baumann BF2550 Floats [42], which are regularly used for Cessna 172 
conversions.  The model was tested in Auburn University?s 3 ft. X 4 ft. subsonic 
wind tunnel.  Full results from these wind tunnel tests can be found in Appendix 
C. 
 62 
 
Figure 22: Cessna 172 Wind Tunnel Model 
 
Table 3: Float Sizing Comparison 
  Sizing Code BF22250 % Error 
Breadth (ft) 2.06 2.17 5.3% 
Length (ft) 16.44 16.92 2.8% 
Depth (ft) 2.31 2.17 6.7% 
Displacement (ft3) 39.09 39.58 1.3% 
 
Table 4: Drag Comparison for Cessna 172-R 
 
CD0 Drag Area (ft2) 
 
No Floats Floats No Floats Floats 
Actual Aircraft 0.03207 - 5.58 - 
Sizing Code 0.03265 0.04594 5.68 8.00 
Wind Tunnel 0.0480 0.0641 8.35 11.15 
Adjusted Wind Tunnel 0.0340 0.0506 5.91 8.79 
% Error (Sizing Code vs 
Adjusted Wind Tunnel) 4.1% 10.1% 4.0% 9.9% 
 
 From Table 3, it can be seen that the sizing code very accurately predicted 
the necessary size of the floats, with less than 7% error in any dimension.  Also,  
Table 4 shows that the sizing code accurately predicts the zero-lift drag 
coefficient as well as the equivalent parasitic drag area for the case with no floats 
when compared to the actual drag values from a 172-R.  Also, results from the 
 63 
wind tunnel tests of the 172-R model (once corrected to the full-scale Reynolds 
number) with and without floats were very encouraging.  The tunnel tests were 
consistently predicting conservative drag numbers, which is logical, as there are 
blockage effects and wall interactions as well as surface imperfections and 
manufacturing defects, which will all increase the measured drag of the model.  
 The Reynolds number correction methodology used in this research was 
described by Barlow, Rae and Pope [29], and detailed in Section 2.4 of this report.   
 
  
 64 
Chapter 4 
Design Optimization 
4.1 Optimizer Selection 
 As has been discussed previously, there are many different optimization 
methods and algorithms that could be applied to the problem of amphibious 
aircraft preliminary design.  Each optimizer has its pros and cons, with some 
meeting the requirements of this research better than others.  Aircraft design 
optimization requires the variation of a large number of variables, which means 
that the chosen optimization algorithm will have to operate in a large design 
space.  To be effective and useful, the optimizer must converge fairly quickly yet 
still process a large enough sample of possible candidates to reasonably ensure 
that the final design is a global optimum. 
 As the sizing code was written in MATLAB, the first optimizer selected for 
use was fminsearch, which is built into MATLAB.  Fminsearch is a nonlinear 
numerical optimization method that uses a Nelder-Mead simplex algorithm, as 
described in Lagarias [43], to minimize a function.  Initially, for an n-dimensional 
vector x and initial guess x0, the algorithm adds 5% of each component variable, 
x0(i), to x0, and uses these n vectors in addition to x0 to create a n+1 simplex 
around x0.  Then, the algorithm modifies the simplex repeatedly according to the 
following procedure. 
1. Let x(i) be all the points in the current simplex, where i=1, 2,<, n, n+1. 
2. The points in the simplex are then ordered from the lowest function value, 
f(x(1)), to the highest function value, f(x(n+1)).  For each iteration step, the 
algorithm throws away the worst point, x(n+1), and accepts another point 
into the simplex. 
 65 
 
3. A reflected point, r, is generated using the following equation,  
                                                           (4.1) 
where 
                                                                  (4.2) 
and f(r) is then calculated. 
4. If f(x(1)) ? f(r) < f(x(n)), r is accepted into the simplex and this iteration of 
the minimization algorithm is terminated. 
5. If f(r) < f(x(1)), calculate the expansion point, s, 
                                                       (4.3) 
and calculate f(s). 
a. If f(s) < f(r), accept s into the simplex and terminate the iteration. 
b. If not, accept r into the simplex and terminate the iteration. 
6. If f(r) ? f(x(n)), a contraction is performed between m and the lower value 
of x(n+1) and r. 
a. If f(r) < f(x(n+1)), calculate c using 
                                                            (4.4) 
and then find f(c).  If f(c) < f(r), accept c into the simplex and 
terminate the iteration. 
b. If f(r) ? f(x(n+1)), calculate cc using 
                                                             (4.5) 
 66 
and then find f(cc).  If f(cc) < f(x(n+1)), accept cc into the simplex 
and terminate the iteration. 
7. Finally, calculate the n points 
                                                                 (4.6) 
and calculate f(v(i)), for i=2, 3,<, n, n+1.  The simplex at the next iteration 
will be x(1), v(2),<, v(n), v(n+1). 
Fminsearch will continue using this Nelder-Mead simplex algorithm to return 
local minimizers of the target function until a stopping criterion is met.  
MATLAB allows for a number of different stopping criteria: maximum number 
of function evaluations reached, maximum number of iterations reached, 
tolerance on the function value reached, and tolerance on x value reached.  One 
of the drawbacks of using fminsearch is that the optimizer generally tends to 
become stuck on local optima, as it is very reliant on the initial guess, x0. 
 To counter this reliance on having a very accurate initial guess and to 
increase the chances of find a globally optimized solution, a particle swarm 
technique was integrated with the fminsearch simplex optimizer.  This hybrid 
optimization algorithm uses the particle swarm as the global optimizer and 
transport mechanism.  Fminsearch is used as the local simplex optimizer.   If the 
allowed design space is compared to an area full of hills, with the top of each hill 
being a locally optimized solution, then it could be said that the particle swarm 
moves the particles, which represent possible answers, from one hill to another 
while the simplex optimizer finds the top of the hill it is on.  In this way, the 
hybrid optimizer is much more likely to find a globally optimized solution to a 
given problem. 
 67 
 Initially, when using the hybrid particle swarm/simplex algorithm, a 
random population sample must be generated.  All variables that are to be 
optimized (in the case of this research there are 10) will be randomized for each 
particle to give the particle a position on the available design space [44]. 
                                                            (4.7) 
where i=1,<,population size, j=1,<,number of variables, and R is a randomly 
chosen number. 
 With an initial random sample of particles in place, the simplex optimizer 
runs to find the local optimum position of each particle.  With that completed the 
particle swarm then gives each particle a new velocity and position [2]. 
                                                      (4.8) 
                                                              (4.9) 
where ?, ?, and ? are constants; ? is an inertial constant which gives relative 
weights to the local and global particle bests; R1, R2, and R3 are random numbers; 
xi is the current particle position; and    and     are the best position the 
individual particle and whole swarm have seen, respectively.  The algorithm 
then runs the local simplex optimizer again, and this process repeats itself 
through a given number of generations.  The individual particles have basic 
knowledge of both their own best position and the best position that the swarm 
has seen.  Over multiple generations, this knowledge is used to adjust their 
velocity and position to keep the particles moving toward the globally optimized 
solution.  The effect of the particle?s best position on its velocity is the first term 
in the velocity equation.  The effect of the swarm?s best position on velocity is the 
second term of the velocity equation.  The last two terms in the velocity equation 
are repulsive terms.  They are designed to keep the particles away from each 
 68 
other to prevent the overall solution from becoming trapped on local optima.  
These repulsive forces make the hybrid optimization algorithm more effective at 
finding globally optimized solutions, but at the expense of computation time. 
          
4.2 Optimization Methodology 
 With the optimizer determined, the next step was to integrate it into the 
existing sizing code.  To do this, first a new execution file was made and the 
current sizing program was changed into a function.  This allowed the sizing 
code to be looped through the optimization program, which is necessary as the 
optimization program was used to call the particle swarm optimizer, which 
globally optimized the particles, as well as fminsearch, the simplex optimizer 
which found local minima around each particle.   
 It was decided that the amphibious aircraft would be optimized for 
minimum weight, because, in general, the lower the weight of the aircraft, the 
less expensive the aircraft is to design and manufacture.  With an objective 
function chosen, 10 optimization variables were selected: aspect ratio, inboard 
and outboard taper ratios, inboard and outboard sweep angles, tail moment arm 
length, fineness ratio, canard fraction, engine position, and cabin position.  By 
choosing to use these parameters, the optimizer was given as much freedom as 
possible to completely change the geometry of the aircraft.  Minimum and 
maximum bounds were set on the variables to keep the geometry from becoming 
unrealistic.  The hybrid optimizer was set to run for 10 generations. 
 To increase the usefulness of the optimizer even further, another program 
was set up to loop the optimization program through multiple configurations of 
aircraft.  The program controlled both the aircraft tail configuration (flying wing, 
 69 
canard, or conventional), as well as the method of water operation.  It allowed a 
loop to be constructed that would optimize the design for every allowable 
aircraft configuration without requiring user input.     
 
Figure 23: Optimization Program Flowchart 
 
 
4.2.1 Penalty Functions 
 Three penalty functions were used to make it less likely that the optimizer 
would change the geometric variables in such a way that the resulting airplane 
would be in an infeasible configuration.  The penalty functions cause an increase 
to the objective function, in this case the aircraft gross weight, if they are 
violated.  They increase the weight in an exponential fashion; the further away 
from the limits set by the penalty functions, the greater the penalty.  Ideally, this 
forces the optimizer to stay in the bounds set down by the penalty functions. 
 The first penalty function set bounds on the static margin of the aircraft.  
The static margin, as stated previously, is the difference between the location of 
the neutral point and center of gravity of the aircraft, expressed as a percentage 
 
T a i l  Co n f i g u r a t i o n  
W a t er O p e r a t i o n  
Co n f i g u r a t i o n  
I n i t i a l  G eo m e t r y  
G u es s  
O p ti mi z e r  S i z i n g  Co d e  
10
th
 
G en erat i o n ?  
N o                             Y e s  
 70 
of fuselage length.  If the center of gravity of the aircraft is more forward than the 
neutral point, the aircraft is longitudinally statically stable in flight.  To ensure 
that the aircraft will be sufficiently stable, the lower bound set by the penalty 
function was a static margin of 8%.  Excessive stability also is not a wanted, as 
too much stability will result in an aircraft that is difficult to trim and maneuver.  
The upper bound set by the penalty function was a static margin of 15%.  The 
functions chosen were: 
                                                         (4.10) 
                                                         (4.11) 
                                                            (4.12) 
where c = 106 and a = 4.  The values of c and a are constant though all three 
penalty functions.  If the static margin lies between 8% and 15%, the value of 
penalty function is 0. 
 The second penalty function influences the spacing between the horizontal 
tail and main wing of the aircraft, dependent on configuration.   For a 
conventional configuration, the penalty function requires that there must be at 
least one root chord length of the main wing between the horizontal tail leading 
edge and main wing trailing edge.   
                                                            (4.13) 
For a conventional aircraft, the penalty function also states that the main wing 
must be at or behind the nose of the aircraft. 
                                                           (4.14) 
 71 
 For a canard, the penalty function says that there must be at least 1.5 canard root 
chords between the trailing edge of the canard and the leading edge of the main 
wing.   
                                                              (4.15) 
The penalty function also states that the canard must be at or aft of the nose of 
the aircraft.   
                                                            (4.16) 
If the required conditions are not met, the penalty function then chooses the 
smaller of dx1 and dx2 to perform the penalty on. 
                                                            (4.17) 
                                                           (4.18) 
                                                            (4.19) 
 Finally, the third penalty function aims to ensure that a straight spar can be 
installed over the full span of the wing, between the 20% and 30% chord 
locations at the wing root and wing tip.   
 72 
 
Figure 24: Wing Structure Penalty Function 
To accomplish this, the penalty function locates the position of Points A, B, C, 
and D.  These points lie on the intersection between straight lines connecting the 
20 and 30% chord locations on the root and tip of the wing and the split between 
the inboard and outboard section of the wing.  In order for the spar to be straight, 
Point A must always lie forward of Point B, and Point D must always lie aft of 
Point C.   
                                                          (4.20) 
                                                          (4.21) 
If either dx1 or dx2 is less than 0, then the structural requirement of keeping a 
straight spar for the wing is not being met, and the penalty function will choose 
the greater of the absolute value of dx1 and dx2 to perform its penalty on. 
                                                             (4.22) 
                                                             (4.23) 
 73 
                                                             (4.24) 
If dx1 and dx2 are greater than 0, then a straight spar can be maintained from 
wing root to wing tip, and no penalty is applied to the objective function. 
  
4.3 Results 
 With the optimizer now integrated with the sizing code and penalty 
functions in place to steer the aircraft toward a realistic geometry, a mission 
profile was input as well as basic geometrical characteristics.  The mission profile 
was chosen to be that of a littoral troop transport aircraft.  This aircraft would 
replace the current method of deploying to beaches, which is generally 
performed with by transport ship or hovercraft, both of which are quite slow and 
lacking in range without the support of a larger ship.  This littoral transport 
aircraft is designed to deploy from a distant base, land near the shore of its target 
location, offload its cargo, and return to its base of origin.  It will have a mission 
cruise radius of 1,000 nmi. at 20,000 ft., descend to near sea level for a 15 nmi. 
approach leg, land and extract in the reverse order.   The mission duration totals 
2,000 nmi. at 20,000 ft. and 30 nmi. in ground effect.  The aircraft will also have 45 
minutes of IFR reserve fuel.  The aircraft has a payload capacity of 18,750 lb., 
which is the equivalent of 50 soldiers and their gear. 
 The optimizer was run for 30 different aircraft configurations.  Three 
different tail configurations (conventional, flying wing, and canard), with two 
different fuel placement locations (fuel at the center of gravity and fuel in the 
wings), were run for five different water operation configurations: twin floats, 
boat hull with hydrofoil and sponsons, boat hull with hydrofoil and tip-floats, 
 74 
boat hull with sponsons, and boat hull with tip-floats.  The results of this 
optimization run are shown in Figure 25. 
 
Figure 25: Optimization Results 
0 . 0 0
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1 0 0 . 0 0
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2 0 0 . 0 0
2 5 0 . 0 0
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 75 
The lowest weight configuration, 93,900.30 lb., found by the optimizer was a 
flying wing, with a boat hull and sponsons as the method of water operation, 
and fuel located in the wings. 
 
Figure 26: Final Optimized Design 
A full breakdown of the final optimized aircraft, including its geometry, 
component weight breakdown, drag analysis, and performance data is provided 
in Appendix B. 
       
4.3.1 Parametric Studies 
 A parametric study was conducted to examine how the changing of the stall 
speed of the aircraft would impact the aircraft?s gross takeoff weight.  The stall 
speed is important, especially for an amphibious aircraft, because it is indicative 
 76 
of the takeoff and landing speeds of the aircraft.  For example, Raymer [3] states 
that, for military applications, an aircraft must have an approach speed that is 1.2 
times the stall speed. Having a low takeoff speed is especially important for an 
amphibious aircraft as the lower its takeoff speed, the less impact loads the 
aircraft will experience.  As the aircraft accelerates to takeoff speed, the impact 
loads that are caused by wave slamming increase, especially on the forebody of 
the hull.  Having a lower stall speed, and thus a lower load on the fuselage, will 
allow the aircraft to operate in rougher seas. 
 
Figure 27: Stall Speed Parametric Study 
 The final aircraft in this optimization study was designed with a stall speed 
of 85 knots.  The parametric study was done using the same input parameters as 
the final design, except the stall speed was varied from 80 knots to 110 knots in 
increments of 5 knots.  The results of this study are shown in Figure 27.  It can be 
seen that the stall speed and gross weight of the aircraft are inversely 
y  =  - 2 8 3 . 9 2 x  +  1 1 8 5 3 3
86000
87000
88000
89000
90000
91000
92000
93000
94000
95000
96000
97000
70 75 80 85 90 95 100 105 110 115
G
T
O
W
 (l
b)
S t a l l  S pe e d ( k t s )
 77 
proportional; as the stall speed decreases, the aircraft weight increases.  This is 
because a decrease in an aircraft?s stall speed requires an increase in wing area, 
and the larger wing area means an increased gross weight. 
 
  
 
        
                                                   (4.25) 
This means that a tradeoff must be made, a lower stall speed, which gives the 
aircraft lower takeoff and landing speeds at the expense of a higher gross takeoff 
weight, or a higher stall speed, which decreases the gross takeoff weight but 
leads to increases in the speed at which the aircraft must takeoff and land.  These 
increases in landing and takeoff speeds also correspond to increased difficulty 
for the pilot, as well as increased loads for the aircraft.  As mentioned previously, 
for an amphibious aircraft to be able to operate at increased sea states, a low 
takeoff speed is required to decrease the loading on the hull due to wave slap.  
Most amphibious aircraft have stall speeds in the range of 55-100 knots.  The 
Hughes H-4, the largest amphibious aircraft to fly, had a stall speed of 75.6 knots.  
It was felt that the 85 knot stall speed of the final optimized aircraft was a good 
balance between weight and takeoff and landing speeds.  Lowering the stall 
speed further would have increased the gross takeoff weight an inacceptable 
mount, as the purpose of the optimization was to keep the aircraft weight low.  
At the same time, further increasing the stall speed would have significantly 
lowered the weight, but aircraft takeoff and landing performance would have 
suffered greatly as a result.  
  
  
 78 
Chapter 5 
Optimized Design Analysis and Testing 
5.1 3-D CAD Model Development 
 With the preliminary design of the amphibious aircraft finalized, a 3-D 
model was constructed using SolidWorks.  This model was used to construct a 
wind tunnel model as well as run Orca3D test cases.  To obtain valid 
comparisons between the various analysis programs that were used to validate 
and improve the optimization code, it was very important to keep the 3-D model 
as true as possible to the final optimized design that was output by the sizing 
code. 
 While the output file specifies the exact geometry of all the lifting surfaces 
and engine nacelle, it only provides general dimensions for the fuselage and 
sponsons, although the code does have relative positions for all the components.  
This means that these last two components must undergo detailed design not 
specified by the optimization code. 
 The sizing code output specifies the length, width and height of the boat 
hull fuselage of the aircraft, but does not specify any further details, such as the 
shape of the bottom of the fore- and aftbody and the location of the step of the 
hull.  Both of these design factors will affect the performance of the amphibious 
aircraft while it is on the water, especially in respect to its takeoff performance.   
 79 
 
Figure 28: Various Types of Boat Hull Bottoms [45] 
Figure 28 shows a variety of different bottom shapes for a boat hull or float 
aircraft.  The bottom chosen will always be a compromise between quick takeoff 
and seaworthiness.  According to Brimm [45], the flatter the bottom, the quicker 
an aircraft will takeoff in calm seas. But, in rougher seas, the flatter bottom will 
cause severe pounding due wave slam, which will likely make the aircraft 
takeoff slower than if it had a sharp bottom, which cuts through waves instead of 
going over them.  This tendency to slam in rough water makes having a flat 
bottom hull a poor choice for an amphibious aircraft that is to operate littorally. 
 The double concave is desirable because it combines the advantages of the 
sharp and blunt ?Vee?. It has a sharp edge for entry into the water and cutting 
through waves yet still has a comparatively flat surface on which to plane.  
Another benefit of the double concave is that it deflects spray down and away 
from the fuselage and wings of the aircraft, which decreases loads and reduces 
the threat of water spray into the engines.  The best overall compromise is the 
 80 
double scalloped bottom.  Not only does it share the advantages of the double 
concave, but as the aircraft increases speed and begins to plane, it begins to rise 
up out of the water, and is supported on successively lower scallops, reducing 
the water resistance as the speed increases.  The forebody of the boat hull was 
chosen to have a double scalloped bottom, for its combination of reduced drag 
and spray characteristics as well as its ability to cut through the water, while the 
aftbody was designed to be a double concave because of its behavior during 
planing. 
 When water moves over the convex surface of the bottom of a seaplane, it 
creates suction in a normal direction to the surface.  This means that as an 
amphibious aircraft accelerates through the water, the downward suction would 
increase with increasing speed.  Takeoff performance would be greatly 
hampered by this.  To prevent this from happening, a sharp step is placed into 
the hull to separate the water from the skin of the seaplane.  The step is 
?ventilated,? in that an air pocket generally forms behind it.  As the speed of the 
aircraft increases, more air is drawn into this pocket and begins to extend back 
toward the stern, eventually completely separating the aft end of the hull from 
the water, which is called planing.  The location of the step can vary, but is 
generally placed approximately 1/16 of the length of the hull behind the center of 
buoyancy.  Langley [36] recommends that the depth of the step be approximately 
5-8% of the breadth of the hull.  For the 3-D model, the step was made to be 12 in. 
deep, or 6.5% of the breadth of the hull. 
 Sponsons are used to increase the transverse stability of the amphibious 
aircraft.  The length, breadth and height of the sponsons, as well as their vertical 
placement on the fuselage, are specified by the sizing code.  The sponsons are 
generally an airfoil shape, often with a blunt trailing edge.  This is important 
 81 
because if the aircraft happens to drift backwards there should be no tendency 
for the sponsons to be pulled under the water.  Generally, the sponson is set at a 
slight incidence angle to present more bottom area than is necessary, which can 
lead to a quicker takeoff.  It is also general practice to have the sponson extend 
beyond the step, but not interfere with the lines of the aftbody.  
 The sizing of rudders and elevons is specified by the sizing code, and 
follows historical trends.  The rudders were sized to be 32% of the vertical tail 
chord length and span 90% of the vertical tail.  The elevons were sized to be 30% 
of the wing chord and span 40% of the wingspan.  The size and longitudinal 
position of the engines was specified by the sizing code, but their vertical 
placement was not.  The engines were placed on the upper surface of the wing to 
protect them as much as possible from water spray. 
 
Figure 29: Final Optimized Aircraft Design 
 82 
 
Figure 30: Right View of Optimized Design 
 
Figure 31: Front View of Optimized Design 
 83 
 
Figure 32: Top View of Optimized Design 
        
5.2 Wind Tunnel Testing 
 Scale model testing was performed in Auburn University?s 3 ft. X 4 ft. 
subsonic wind tunnel.  This testing was used primarily to determine the accuracy 
of the drag estimates predicted by the sizing code, as well as to obtain data on 
the aerodynamic performance characteristics of the amphibious aircraft. 
 
5.2.1 Model Design and Construction 
 A scaled down model was derived from the full scale 3-D model that had 
been constructed in SolidWorks.  The model was scaled about its centroid to 
have a wingspan of 30 in.  The factor used to scale the solid model from full size 
to having a 30 in. wingspan was .0169987081.  This size resulted in acceptable 
model blockage, with a ratio of model frontal area to test section cross-sectional 
area of 2.1%.  According to Barlow, Rae, and Pope [29], the maximum blockage 
factor of the tunnel should be less than 7.5% to obtain accurate results.  The total 
 84 
solid and wake blockage correction factor, also provided by Barlow, Rae and 
Pope [29], for an irregular shape is given by the following equation. 
                                                                                        (5.1) 
The total blockage correction factor for these tests was found to be .00524. 
  The wind tunnel model was constructed by Laser Reproductions using an 
additive manufacturing process known as stereolithography.  Stereolithography 
uses a vat of resin that cures under ultraviolet (UV) light and a UV laser to build 
parts one layer at a time.  For each layer, the beam traces the cross section of the 
part being built.  The beam is controlled by a computer, which reads from a 3-D 
model of the part.  Exposure to the UV light cures and solidifies the pattern 
traced into the resin and causes it to adhere to the layer below.  The platform the 
model is being built on then descends the thickness of one layer and a fresh coat 
of the liquid resin is laid on top and the process repeats itself.  Stereolithography 
allows for rapid, accurate prototyping of parts. 
 In order to prepare the model for the rapid prototyping process, the model 
fuselage/wing was divided into four sections: the right wing, left wing, forward 
fuselage and rear fuselage.  The elevons and rudders were cut out of the wing 
and vertical tails, respectively.  A cavity was made inside the parts to make room 
for an aluminum internal structure, which provides rigidity to the model during 
the testing as well as allows for a mating point to the pyramidal balance being 
used. 
 85 
 
Figure 33: Internal Structure and Pyramidal Balance Mounting Blade 
As shown in Figure 33, an aluminum blade was designed and fabricated to 
attach the model to the pyramidal balance.  To reduce interference to the airflow 
over the model as well as drag created by exposed sections, the blade mount has 
the shape of a NACA 0016 symmetric airfoil.  Also, the pyramidal balance is 
exposed inside the of the test section.  To reduce the drag created by the mating 
of the blade mount to the pyramidal balance, a shroud was built, which was also 
in the shape of a symmetric airfoil. 
 So that yaw cases could be run, a metal disc (Figure 34) was made which 
had alignment holes for yaw angles of 2, 5, 10, and 11.5 degrees in the positive 
and negative directions.  This disc was mounted to the model.  Another disc was 
mounted to the top of the blade to align the yawing holes. 
 86 
 
Figure 34: Yaw Alignment Disc 
 It was important to be able to test control surface deflection to determine if 
they had been properly sized during the optimization process.  To accomplish 
this, steel brackets were made to hold the control surfaces at 0, 5, and 20 degrees 
in the positive and negative directions.  These fit into matching slots in the 
control surfaces and wing surfaces. 
 
Figure 35: Wind Tunnel Model and Mounting Blade in SolidWorks 
 87 
 
Figure 36: Wind Tunnel Model, Mounting Blade and Shroud 
 
Figure 37: Model Installed in Wind Tunnel 
 88 
             
5.2.2 Testing Setup 
 All of the test runs were conducted in the 3 ft. X 4 ft. closed circuit subsonic 
wind tunnel at Auburn University.  The tunnel is capable of producing velocities 
up to 180 ft/s, although all test runs for this research were run at 100 ft/s.  A pitot 
tube attached to a port in the test section is used to calculate the freestream 
velocity.  Force and moment data were collected from a six component 
pyramidal balance, which reads normal, axial, and side forces as well as pitch, 
roll and yaw moments.  This data was then processed using Labview data 
acquisition software.  An accelerometer attached to the mounting blade was used 
to determine and control the model?s angle of attack.  Table 5 shows results of a 
calibration test of the accelerometer.  
Table 5: Angle of Attack Calibration Data 
 
 The pyramidal balance was calibrated using a series of weights.  A 
?calibration tree? was fabricated to assist in the calibration of the balance.  The 
tree has five branches: one fore, one aft, one port, one starboard, and a vertical 
branch.  The branches are marked with notches every inch, which allows 
accurate hanging of weights to ensure the induced moments are being calculated 
I n p u t A n g l e  ( d e g ) M e a s u r e d  A n g l e  ( d e g )
- 1 4 - 1 3 . 8
- 1 2 - 1 1 . 9
- 1 0 - 9 . 9
-8 - 7 . 9
-4 - 3 . 9
0 - 0 . 2
4 3 . 9
8 8
12 1 1 . 9
16 1 5 . 8
20 1 9 . 9
 89 
correctly.  The top branch allows weight to be placed directly over the pyramidal 
balance to calibrate the normal force.  Table 6 shows the results from the initial 
calibration test performed on the balance.  Raw data from the calibration run can 
be found in Table 6.  No data point had greater than 4% error. 
Table 6: Pyramidal Balance Calibration Data 
 
 
5.2.3 Testing Results 
 A series of wind tunnel tests were run to determine the drag and 
performance characteristics of the optimized aircraft.  Tests were run at sideslip 
angles of -5, 0, +5, and +11.5 degrees.  For each of these sideslip angles, the 
N o r ma l  F o r c e  O n l y
0 . 5 0 - 0 .5 1 0 . 0 2 0 . 0 0 0 . 0 0 0 . 0 1 0 . 0 0
1 . 0 0 - 1 .0 0 0 . 0 0 0 . 0 0 0 . 0 1 0 . 0 1 0 . 0 0
2 . 0 0 - 2 .0 1 0 . 0 1 0 . 0 0 0 . 0 3 0 . 0 2 0 . 0 0
N o r ma l  F o r c e   a n d  P i tc h i n g  M o me n t ( F o r e  B r a n c h  a t 6  i n . )
0 . 5 0 - 0 .5 0 0 . 0 0 0 . 0 0 - 0 .2 5 0 . 0 1 0 . 0 1
1 . 0 0 - 1 .0 0 0 . 0 0 0 . 0 0 - 0 .5 0 - 0 . 0 1 0 . 0 0
2 . 0 0 - 1 .9 9 - 0 . 0 1 0 . 0 0 - 1 .0 0 - 0 . 0 2 0 . 0 0
N o r ma l  F o r c e   a n d  P i tc h i n g  M o me n t ( A f t B r a n c h  a t 6  i n . )
0 . 5 0 - 0 .5 0 0 . 0 1 0 . 0 0 0 .2 5 0 . 0 1 0 . 0 0
1 . 0 0 - 1 .0 0 0 . 0 1 0 . 0 0 0 .5 1 0 . 0 2 0 . 0 1
2 . 0 0 - 2 .0 0 0 . 0 2 0 . 0 0 1 .0 2 0 . 0 4 0 . 0 2
N o r ma l  F o r c e   a n d  R o l l i n g  M o me n t ( P o r t B r a n c h  a t 6  i n . )
0 . 5 0 - 0 .5 0 0 . 0 0 0 . 0 0 0 . 0 1 0 .2 6 0 . 0 0
1 . 0 0 - 1 .0 0 0 . 0 0 - 0 . 0 1 - 0 . 0 1 0 .5 2 0 . 0 0
2 . 0 0 - 2 .0 0 0 . 0 0 - 0 . 0 1 0 . 0 2 1 .0 4 0 . 0 0
0 . 5 0 - 0 .5 0 0 . 0 0 - 0 . 0 1 0 . 0 1 - 0 .2 6 0 . 0 0
1 . 0 0 - 1 .0 0 0 . 0 1 0 . 0 0 0 . 0 1 - 0 .5 0 0 . 0 0
2 . 0 0 - 2 .0 1 0 . 0 1 0 . 0 1 0 . 0 3 - 1 .0 0 0 . 0 0
Co l l e c te d  D a ta
W e i g h t 
A p p l i e d  ( l b )
N o r ma l  
F o r c e  ( l b )
A x i a l  F o r c e  
( l b )
S i d e  F o r c e  
( l b )
P i tc h i n g  
M o me n t ( l b - i n . )
R o l l i n g  M o me n t 
( l b - i n . )
Y a w i n g  M o me n t 
( l b - i n . )
N o r ma l  F o r c e   a n d  R o l l i n g  M o me n t ( S ta r b o a r d  B r a n c h  a t 6  i n . )
 90 
rudders and elevons were deflected at angles of -20, -5, 0, +5, and +20 degrees to 
test rudder and elevator effectiveness.  To test aileron effectiveness in roll, tests 
were also run with the elevons deflected in opposite directions, at 5 and 20 
degrees.  All of the tests were run at a test section velocity of 100 ft/s, and each 
test went through an angle of attack sweep from -14 to +20 degrees. 
 The baseline test was performed with no control surface deflections or 
sideslip angle and the results of this test are shown in Figure 38. 
 
 
Figure 38: Baseline Wind Tunnel Results 
From these baseline results, it is possible to determine if the aircraft has 
longitudinal static stability as well as find the change in lift, drag and pitching 
moment with respect to the change in angle of attack (                 , respectively).  
For an aircraft to have longitudinal static stability, the induced pitching moment 
due to a disturbance at a given angle of attack (e.g., due to vertical gusts, air 
turbulence, etc.) must be nose down as that will tend to restore the aircraft to its 
0
0 . 0 5
0 . 1
0 . 1 5
0 . 2
0 . 2 5
0 . 3
- 20 - 15 - 10 - 5 0 5 10 15 20 25
C
D
.t
o
ta
l
? (d e g )
- 0 . 4 5
- 0 . 4
- 0 . 3 5
- 0 . 3
- 0 . 2 5
- 0 . 2
- 0 . 1 5
- 0 . 1
- 0 . 0 5
0
0 . 0 5
- 20 - 10 0 10 20
C
M
? (d e g )
- 0 . 8
- 0 . 6
- 0 . 4
- 0 . 2
0
0 . 2
0 . 4
0 . 6
0 . 8
1
- 20 - 15 - 10 - 5 0 5 10 15 20 25
C
L
? (d e g )
 91 
original angle of attack.  Using the sign convention of +x out the nose and +y out 
the right wing, a nose down pitching moment is assumed to be negative while a 
nose up pitching moment is assumed to be positive.  Thus, for an aircraft to have 
longitudinal static stability in flight: 
   
                                                              (5.2) 
where         , q is the dynamic pressure, S is the model reference area, and   is 
the model reference length.  The wing area and mean aerodynamic chord of the 
model were used as the reference area and length, 159.732 in2 and 7 in. 
respectively.   
Table 7: Baseline Derivatives 
   
   4.1600 1/rad 
   
   1.0256 1/rad 
   
   -1.5126 1/rad 
 
The results of this test show that the optimized aircraft is longitudinally statically 
stable since CM? < 0.   These results also allow for the calculation of the lift curve 
slope, CL?, as well as CD?, the slope of the drag curve, which demonstrate how 
angle of attack effect lift and drag characteristics of the aircraft.  The values for 
drag were adjusted for the Reynolds number scaling effects using the same 
process as was used for the Cessna 172 wind tunnel data.    
 92 
 A drag polar of this data can be used to find the minimum drag coefficient, 
CDmin, as well as the lift coefficient that corresponds to the minimum drag 
coefficient, CLmin drag.   
 
Figure 39: Drag Polar 
The minimum drag coefficient of the aircraft is 0.02618 which corresponds to a 
lift coefficient of 0.1284. 
 The zero lift drag coefficient, CD0, can also be found from the drag polar.  For 
the optimized aircraft, CD0 is 0.02625.  The drag area can be found by multiplying 
CD0 by the planform area of the full-size aircraft.  Table 8 shows the drag 
comparison between the sizing code output and wind tunnel results. 
Table 8: Sizing Code and Wind Tunnel Drag Comparisons 
 
Much of this error is due to the lack of component detail in the sizing code drag 
estimations.  For example, the sizing code analyzes the fuselage as though it were 
a cylinder.  In order to make the wind tunnel model, an actual fuselage shape 
- 0 . 8
- 0 . 6
- 0 . 4
- 0 . 2
0
0 . 2
0 . 4
0 . 6
0 . 8
1
0 0 . 0 5 0 . 1 0 . 1 5 0 . 2 0 . 2 5 0 . 3
C
L
C D
C D0 D r a g  A r e a  ( f t 2 )
S i zi n g  Co d e 0 . 0 1 3 2 4 5 0 . 8 4
W i n d  T u n n e l 0 . 0 2 6 2 5 1 0 0 . 7 9
 93 
had to be designed, and with that extra design detail comes additional drag.  For 
instance, the step in the fuselage that is designed to reduce the fuselage?s drag 
through the water is not accounted for in the sizing code, but it will cause 
boundary layer separation while in flight and result in an increase in drag.  Other 
examples of additional drag due to detailed component design after the initial 
sizing optimization would be the scallops in the fore- and aft-body of the 
fuselage, as well as the blunt trailing edge of the sponsons which allows them to 
follow the lines of the aft fuselage.  The sizing code also does not take into 
account flow interaction between the different components.  For example, the 
fuselage and sponsons both contribute to ?dirtying? the flow along the underside 
of the main wing to a width of approximately half the wingspan or more.  This 
will lead to an increase in the measured drag and a decrease in the measured lift.  
Early boundary layer separation due to the low Reynolds numbers at which the 
wind tunnel tests were conducted may produce additional drag.  This is 
primarily due to the improper transition from a laminar to a turbulent boundary 
layer.  Laminar to turbulent transition occurs much earlier as a percentage of 
chord length on a full scale airplane than a scale model.  While a laminar 
boundary layer may produce less drag than a turbulent boundary layer, the 
laminar boundary layer also has less energy, which makes it far more likely to 
separate when encountering corners or excessive roughness.  Because of this, 
there may be separation occurring near the highly curved leading edge of the 
wing, which would lead to the formation of a laminar separation bubble over a 
large portion of the wing, which in turn increases drag.     
 Another important design point of the aircraft that can be pulled from the 
wind tunnel data is its trim characteristics.  When an aircraft is trimmed, it is in a 
state of equilibrium where the pitching moment around the center of gravity of 
 94 
the aircraft is zero.  If the aircraft cannot be trimmed, then the aircraft cannot be 
flown.  The trim criterion of an aircraft is: 
                                                               (5.3) 
where CM,0 is the pitching moment coefficient at an angle of attack of 0 degrees.  
To determine if the aircraft can be trimmed, CM vs. AoA curves are plotted for 
various elevon deflections, seen in Figure 40.     
 
Figure 40: CM vs AoA for Elevator Deflection 
These results show that the aircraft can meet the trim criterion.  When the 
elevons are both deflected -20 degrees, which is an upward deflection in the 
standard axis orientation, the aircraft can be trimmed at approximately 2 degrees 
angle of attack. 
 To analyze the elevons? effectiveness as elevators, the change in lift, drag 
and pitching moment were plotted against the change in elevon deflection at 
multiple angles of attack.   
- 0 . 5
- 0 . 4
- 0 . 3
- 0 . 2
- 0 . 1
0
0 . 1
- 20 - 10 0 10 20 30
C
M
? (d e g )
- 2 0  E le v o n
+ 2 0  E le v o n
0  E le v o n
 95 
 
 
Figure 41: Elevator Deflection Results 
As can be seen in Figure 41, the slopes of curves at different angles of attack are 
very consistent, which means that the aircraft will have consistent elevator 
effectiveness throughout most of it the angles of attack it will operating in.  Table 
9 shows the elevator deflection derivative values. 
Table 9: Elevator Deflection Derivatives 
   
    0.2808 1/rad 
   
    -0.02864 1/rad 
   
    -0.1260 1/rad 
 
While the curves for the lift and moment coefficients vs. elevator deflection 
follow a basically linear trend, the drag curve slope transitions from negative to 
0
0 . 0 1
0 . 0 2
0 . 0 3
0 . 0 4
0 . 0 5
0 . 0 6
0 . 0 7
0 . 0 8
0 . 0 9
0 . 1
- 30 - 20 - 10 0 10 20 30
C
D
d e
- 6  A o A
0  A o A
6  A o A
- 0 . 2 5
- 0 . 2
- 0 . 1 5
- 0 . 1
- 0 . 0 5
0
0 . 0 5
- 30 - 20 - 10 0 10 20 30
C
M
d e
- 6  A o A
0  A o A
6  A o A
- 0 . 6
- 0 . 4
- 0 . 2
0
0 . 2
0 . 4
0 . 6
0 . 8
- 30 - 20 - 10 0 10 20 30
C
L
d e
- 6  A o A
0  A o A
6  A o A
 96 
positive at 0 elevator deflection.  The drag derivative is taken from the negative 
elevator deflection angle data, as this shows the effectiveness of the elevators 
during trim conditions. 
 Longitudinal stability takes into consideration disturbances to the aircraft?s 
angle of attack, and is assumed to only be in the vertical plane.  Conversely, 
lateral stability is concerned with disturbances to the aircraft?s sideslip angle, 
which is completely contained in the horizontal plane.  While longitudinal 
stability is primarily concerned with the pitching moment, sideslip will always 
couple rolling and yawing motions.   
 For an aircraft to be laterally statically stable it must have an inherent 
capability to realign its flight path into a resultant wind if it is disturbed from 
steady, level flight.  This is expressed mathematically as:  
   
                                                              (5.4) 
where Cn is the yawing moment coefficient and ? is the sideslip angle.  Wind 
tunnel tests were run at sideslip angles of 11.5, 5, 0, and -5 degrees.  The plots in 
Figure 42 show the optimized aircraft?s yaw moment, n, rolling moment, l, and 
side force, y, for the range of sideslip angles tested.  All data in the following 
plots was taken with the aircraft at 0 AoA.  
 97 
   
 
Figure 42: Lateral Static Stability Plots 
The lateral stability derivatives are then calculated by finding the slope of the 
linear portions of the plots.  Lateral stability derivatives are shown in Table 10. 
Table 10: Lateral Stability Derivatives 
Cn? 0.3437 1/rad 
Cl? -0.2864 1/rad 
CY? 0.5730 1/rad 
 
The optimized aircraft meets the criterion for being statically stable with respect 
to disturbances in sideslip angle since it has a positive value for Cn?. 
 Rudder effectiveness was evaluated by plotting the yawing moment, rolling 
moment and side force against rudder deflection at a range of angles of attack, 
shown in Figure 43. 
- 0 . 0 2
0
0 . 0 2
0 . 0 4
0 . 0 6
0 . 0 8
0 . 1
- 10 - 5 0 5 10 15
C
n
?
- 0 . 0 9
- 0 . 0 8
- 0 . 0 7
- 0 . 0 6
- 0 . 0 5
- 0 . 0 4
- 0 . 0 3
- 0 . 0 2
- 0 . 0 1
0
- 10 - 5 0 5 10 15
C
l
?
- 0 . 0 4
- 0 . 0 2
0
0 . 0 2
0 . 0 4
0 . 0 6
0 . 0 8
0 . 1
0 . 1 2
0 . 1 4
- 10 - 5 0 5 10 15
C
y
?
 98 
   
 
Figure 43: Rudder Deflection Results 
As with elevon deflections, Figure 43, the slopes of curves at different angles of 
attack are very consistent, which means that the aircraft will have consistent 
rudder effectiveness throughout most of it the angles of attack it will operating 
in.  Table 11 shows the rudder deflection derivative values. 
Table 11: Rudder Deflection Derivatives 
   
    0.6417 1/rad 
   
    -0.3610 1/rad 
   
    -0.7563 1/rad 
 
The derivatives are taken from the slopes of the linear portions of the rudder 
deflection curves, between -5 and +5 degrees of deflection. 
- 0 . 1
- 0 . 0 8
- 0 . 0 6
- 0 . 0 4
- 0 . 0 2
0
0 . 0 2
0 . 0 4
0 . 0 6
0 . 0 8
- 6 - 4 - 2 0 2 4 6C
n
d r
- 6  A o A
0  A o A
6  A o A
- 0 . 0 8
- 0 . 0 6
- 0 . 0 4
- 0 . 0 2
0
0 . 0 2
0 . 0 4
- 6 - 4 - 2 0 2 4 6
C
l
d r
- 6  A o A
0  A o A
6  A o A
- 0 . 1 2
- 0 . 1
- 0 . 0 8
- 0 . 0 6
- 0 . 0 4
- 0 . 0 2
0
0 . 0 2
0 . 0 4
0 . 0 6
0 . 0 8
- 6 - 4 - 2 0 2 4 6C Y
d r
- 6  A o A
0  A o A
6  A o A
 99 
 To address the issue of early separation due to the low Reynolds numbers 
the wind tunnel tests are being conducted at, a round of further tests were 
conducted with a boundary layer transition strip.  The purpose of the strip is to 
trigger the boundary layer to transition from laminar to turbulent flow by 
increasing the energy in the boundary layer, which will reduce drag and make 
the flow over the scale model more similar to a full scale test.  Barlow, Rae and 
Pope [29] suggest multiple methods for implementing a transition strip.  The 
method chosen for these wind tunnel tests was to use a layer of tape cut using 
pinking shears, leaving the edges in 90 degree triangles, which are placed 
pointing forward on the model.  Layers of tape were added to reach the required 
transition strip height.  The necessary height of the transition strip is given by: 
                                                                 (5.5) 
where K is based on the model Reynolds number (600 for Re>100,000, 1000 for 
Re<100,000).  With an average Reynolds number of approximately 300,000, K had 
a value of 600 for these tests.  The total required height of the transition strip was 
found to be .025 inches.  The tape had an approximate thickness of .012 inches, so 
two layers were used in the construction of the transition strip.  At the 
suggestion of Barlow, Ray and Pope [29], the strip was placed at the 10% chord 
position on all lifting surfaces and engine nacelles.  It was placed at the 20% 
length position on the fuselage.  The full range of control surface deflections were 
rerun with the transition strip at 0 degree sideslip angle. 
 100 
 
Figure 44: Wind Tunnel Model with Transition Strip 
 
Figure 45: Transition Strip Result Examples (1) 
 101 
 
Figure 46: Transition Strip Result Examples (2) 
Figure 45 and Figure 46 show two examples of the wind tunnel runs with 
transition strips compared to the same run without the strip.  All the results 
found that the effect of the transition strip was negligible, with all tests showing 
a very slight increase in drag as opposed to the expected reduction. 
 To better understand the airflow over the plane, as well as to further assess 
the effectiveness of the transition strip, a flow visualization technique was 
employed.  Fluorescent dye was mixed with S.A.E. 10W-30 motor oil and applied 
to the upper surface of the model.  The model was then run in the wind tunnel at 
angles of attack of -5, 0, +5, +10, +15, and +20 degrees under an ultraviolet light.  
The purpose of these flow visualization runs was to find areas of flow separation 
and stagnation.  In areas of separation, the oil will pool, as the local velocity of 
the air is very low.  The oil will be blown off areas of the model where the flow is 
attached due to the high velocity of the local air, leaving a clean surface.  These 
 102 
tests were performed with and without the transition strip to visualize any 
effects it was having on the airflow over the model.  All tests were run at a 
velocity of 100 ft/s. 
 
Figure 47: Flow Visualization - 5 Degree AoA - No Strip 
 
Figure 48: Flow Visualization - 5 Degree AoA - Strip 
 103 
 Figure 47 and Figure 48 show flow visualization results at 5 degrees AoA.  It 
is apparent that the flow over the wing is separating prematurely in the run with 
no transition strip, as there is a large area just behind the leading edge of pooled 
oil.  This is evidence of a laminar transition bubble, with the flow being detached 
until immediately before the elevon.  In contrast, the run with the transition strip 
shows a clean flow over the whole chord length of the wing.  This indicates that 
the transition strip was effective, even though it is not drastically influencing the 
data collected during the wind tunnel tests.  The transition strip is putting energy 
into the boundary layer and causing it to stay properly attached over the whole 
wing. 
 
Figure 49: Flow Visualization - 20 Degree AoA - No Strip 
 104 
 
Figure 50: Flow Visualization - 20 Degree AoA - Strip 
 Figure 49 and Figure 50 illustrate the flow visualization results with the 
model at 20 degrees angle of attack, well into its stall regime. In this instance, 
with the flow over the wing completely stalled in both instances, there are no 
major differences between the visual results of the two model configurations, as 
would be expected.  All results of the wind tunnel tests can be found in 
Appendix D. 
 
5.3 Orca3D 
 Orca3D is a suite of tools used for naval architectural design and analysis 
that were written as a plug-in for the Rhinoceros 3-D modeling software.  For 
this research, Orca3D was used to determine if the amphibious aircraft that was 
output by the sizing code had satisfactory longitudinal and transverse stability in 
the water.  The stability of the aircraft in water is determined by the finding the 
location of the longitudinal and transverse metacenters.  In order for a craft to be 
 105 
considered stable, the metacenter must lie above the center of gravity.  Nelson [8] 
has provided an empirical equation to determine if the aircraft will be 
sufficiently stable.  The transverse and longitudinal metacenters should be 
approximately equal and have a minimum value of   
                                                           (5.6) 
where, GM is the distance from the metacenter to the center of gravity, W is the 
displacement of the aircraft in pounds, and K is a constant depending on the type 
of water operations employed by the aircraft.  For a twin float plane, K=1.4, for a 
boat hull aircraft with wing tip floats, K=1, and for a boat hull aircraft with 
sponsons, K=0.75.  For the optimized aircraft, with a weight of 93,900 lb. and a K 
value of 0.75, the required transverse and longitudinal metacentric heights are 
409.07 in. 
 Classically, Simpson?s Rule was the primary tool used in designing boat 
hulls.  Simpson?s Rule is a method of numerical integration and is governed by 
the following approximation: 
                                                               (5.7) 
Using this approximation, a designer could calculate the location of the 
longitudinal and transverse metacenters, as well as the center of buoyancy and 
center of floatation, of a boat hull he or she was designing.     
   Computer aided hull design has been becoming more and more prominent 
in recent years, as it offers advantages over traditional design methods. A 
majority of CAD representations of a boat hull are curve-surfaces.  Orca3D 
generates a mesh from this surface to calculate most of its hydrostatic and 
stability parameters.  With a mesh created, Orca3D then uses Simpson?s Rule to 
numerically integrate between the mesh nodes.  This method of computer aided 
 106 
mesh generation and numerical analysis leads to more accurate results, as it 
doesn?t rely on a manually calculated station model, which has a tendency to 
miss local hull features, such as discontinuities and curvature changes. 
 According to Sederberg [46], the de-facto CAD standard for representing 
curved surfaces since the 1970?s has been the non-uniform rational B-splines 
(NURBS).  NURBS are the only free-form surface type supported in the IGES file 
format, which is the most popular format for transferring data between CAD 
software.  Unfortunately, NURBS have two weaknesses that impact hull design 
and analysis.  First, to make hull optimization and analysis easier, it is helpful to 
have the entire hull represented with a single surface.  Unfortunately, due to 
NURBS needing rectangular topography when making its mesh, a complicated 
hull cannot always be represented by a single surface.  Secondly, control node 
points for a NURBS surface must lie in a rectangular grid, which leads to there 
being a large number of control points that carry no significant geometric 
information and only serve to increase calculation time.  Figure 51 illustrates the 
drawbacks of the NURBS model.  The personal watercraft depicted is divided 
into 13 surfaces in order to maintain the required rectangular topography.  Also, 
many of the nodal points are unnecessary and are merely included to satisfy 
rectangular shape constraints. 
 To address the limitations of using NURBS to model complex boat hulls, T-
Splines were introduced.  T-Splines are not limited to a rectangular geometry, 
which significantly reduces the number of superfluous points needed to 
complete the mesh as well as make the modeling of a complex body with a single 
surface possible.  In the NURBS mesh, all the interior control points have a 
valence of four, which means that all the interior control points touch four edges.  
A T-Spline mesh (T-Mesh) allows control points to have valence other than four.  
 107 
These points are shown in Figure 51 as yellow dots.  The ability to have nodal 
points with different valence values gives T-Splines the ability to model any 
surface using a single T-Mesh.  T-Splines were integrated into Orca3D to 
decrease calculation time as well as increase the accuracy of the calculations by 
removing discontinuities between surface meshes.     
 
Figure 51: Personal Watercraft Modeled as a NURBS and a T-Spline [46] 
   
5.3.1 Model 
 The 3-D model of the full scale optimized design was transferred from 
SolidWorks to Rhinoceros in the form of an IGES file.  While Rhinoceros only 
accepts NURBS meshes, the Orca3D addon allows for the creation of a single 
surface T-Spline mesh when performing stability and hydrostatic parameter 
calculations. 
 108 
 
Figure 52: Rhinoceros Model 
    
5.3.2 Results 
 Orca3D requires a number of parameters in order to output meaningful 
hydrostatic and stability data.  The hull was designed so that the load water line 
(LWL) would have the aircraft sitting at a 1.5 degree trim angle in the water.  
During the design of the hull shape, the load water line was specified and the 
hull shaped to provide that attitude while in the water.  Considerations were 
taken to keep the vertical tails out of the water during water operations.  Next, 
Orca3D needs an input weight (GTOW = 93,900 lb.) and heel angle.  The heel 
angle was set to 0 degrees.  Finally, a vertical center of gravity position was 
needed, which directly affects the metacentric height of the craft, as that is the 
distance from the metacenter to the center of gravity.  From this data and given 
aircraft geometry, Orca3D outputs the location of the center of buoyancy and 
center of floatation.  It also gives the lateral and longitudinal metacentric heights, 
and draws in a waterline on the model to give a visual representation of its 
attitude in the water (Figure 53).   
 109 
 
 
Figure 53: Orca3D Results with Virtual Waterline 
 The longitudinal and transverse metacentric heights were calculated to be 299.03 
and 168.89 in. respectively.  While these results do indicate positive stability of 
the aircraft in the water at this attitude, these values do not meet the metacentric 
height value of 409.07 in. that has been found to provide the best results 
historically.  In order to address stability in the longitudinal direction, the shape 
or the dimensions of the fuselage must change.  The nose of the fuselage would 
need to be blunter, which would provide an increase in surface area that is in 
contact with the water.  Reducing the slope of the fuselage aft of the step to the 
trailing edge of the wing would also make the aircraft sit deeper in the water, 
which would lead to an increase in longitudinal stability.  Unfortunately, there is 
little room to move the step forward, which would decrease the aft slope, and the 
height of the fuselage is set by the optimization code, so that cannot be reduced 
to provide more sink to the aircraft.  In the transverse direction, the width of the 
sponsons will have to be increased to increase the lateral stability of the aircraft.  
Accordingly, they may be able to be made thinner to keep the volume constant, 
 110 
which could lead to a reduction in airflow interference on the lower surface of 
the wing.  Possible methods of implementing changes and improvements to the 
sizing code to attempt to correct these problems will be discussed further in 
Chapter 6.  
          
5.4 Athena Vortex Lattice (AVL) 
 An estimate of the aerodynamic characteristics of the optimized amphibious 
aircraft was obtained through the use of the Athena Vortex Lattice 
aeroprediction code, which is a vortex-lattice method.  For this research, AVL 
was used primarily to test for any unstable dynamic modes as well as to verify 
that the vertical tails and various control surfaces were properly sized.  AVL only 
considers the wing and tail surfaces of the aircraft to predict vehicle 
aerodynamics.  No contributions from the fuselage are considered.  Because of 
this a drag correction must be added into the .avl file.  A zero-lift drag correction 
of 0.01324 was added to the drag data corresponding to the zero-lift drag 
coefficient output by the sizing code. 
 AVL employs an extended vortex lattice model for lifting surfaces and can 
use a slender body model for fuselages and nacelles.  The vortex lattice method 
(VLM) is a numerical method which models lifting surfaces as an infinitely thin 
sheet of discrete vortices to compute lift and induced drag.  The influence of 
wing thickness and fluid viscosity is neglected. 
 The VLM models the wing segments as a finite number of panels.  A 
horseshoe vortex is placed at the quarter chord of each panel and consists of a 
bound vortex on the panel and two semi-infinite trailing vortices extending from 
the ends of the bound vortex to infinity aft of the panel.  Each panel has a control 
 111 
point placed at the three quarter chord and centered between the two trailing 
vortices. 
 
Figure 54: Velocity Induced by a Finite Length Vortex Segment [47] 
 If a horseshoe vortex has a strength of ?n with a length of dl, then the 
velocity induced by the vortex is found using the Law of Biot and Savart. 
                                                                              (5.8) 
Referring to Figure 54, the magnitude of the induced velocity is then found to be: 
                                                                   (5.9) 
Integrating this equation results in the total induced velocity produced by the 
vortex filament: 
                    
 
                                             (5.10) 
 Next, to obtain the strength of the vortex at the surface of the wing, a 
boundary condition is applied.  This condition states that the flow does not pass 
 112 
through the wing but maintains tangency with the wing surface.  Bertin [47] 
suggests using the following approximation for the tangency condition if the 
wing has a modestly sloped camber line: 
                     
 
                                 (5.11) 
A 2-D, planar approximation can be further applied if the wing is of modest 
thickness 
                                                        (5.12) 
or, when dealing with only small angles of attack: 
                                                          (5.13) 
As derived by Bertin [47], the downwash at collocation point i on panel j can be 
summed to find the total downwash at i, wmi. 
                                                              (5.14) 
Substituting this into the tangency condition for small angles of attack to find 
equations for the vortex strengths: 
 
        
                                                    (5.15) 
The definition of the lift coefficient, using the Kutta-Joukowski theorem [27] is: 
                                                         (5.16) 
Solving for CL and substituting in the equation for ?: 
                                                          (5.17) 
Finally, solving for the effective angle of incidence, ?e 
        
  
                                                    (5.18) 
 113 
This equation provides a relationship between the effective angle of incidence of 
each segment and the aerodynamic angle of attack of the segment, which 
includes the influence of one segment on another.  The effective angle of attack 
can then be used to find the total lift and moment of each segment. 
 
5.4.1 Model 
 AVL requires a .avl file and a .mass file to run.  The .avl file specifies the 
geometry of the lifting surfaces and the .mass file specifies masses and inertias as 
well as sets the units for the run cases. 
 The .avl file requires an operating Mach number, as well as wing area, mean 
aerodynamic chord length and wingspan.  The user is required to choose a 
reference position, which is important for properly placing the lifting surfaces.  
In the case of this research, it was simplest to make the reference point at global 
coordinates of (0, 0, 0), which coincides with the nose of the aircraft. The .avl file 
also requires the location of the center of gravity as measured from the reference 
point. 
 Next, wing surfaces are constructed in sections.  The .avl file is set up so that 
you initially divide the surface into panels in the spanwise and chordwise 
directions, which influence the speed and accuracy of the AVL results.  The 
location of the leading edge of the root chord of the wing surface is input next 
with respect to the reference point.  The surface is divided into sections which 
define the chord length at some spanwise location along the surface.  At least two 
sections are necessary to complete a surface, a root and tip section.  The position 
of the leading edge of the section chord as well as the length of the section chord 
is input into the .avl file.  AVL then interpolates between the two sections to 
 114 
build a surface.  Due to this interpolation, a new section must be created at each 
change in sweep angle of the surface, as well as a section where a control surface 
begins or ends.  AVL also allows the user to input the shape of the airfoil camber 
line, which by default is a flat plate, by creating a .DAT file with coordinates for a 
unit airfoil shape.  This input can be used to introduce twist to the wing, by 
having different camber profiles at different wing sections and having AVL 
interpolate between the two shapes.  Control surfaces may also be designed into 
wing surfaces by placing a hinge deflection on section planes.  First, a control 
variable, such as aileron, elevator, rudder, etc., must be defined. Next, the 
location of the hinge as a percentage of section chord length must be input, as 
well as a gain variable, which determines the sensitivity of the control surface.  
This gain variable allows for the contribution of more than one control variable 
at a section.  For example, if an aileron and flap are put into a section, with gains 
of 1.0 and 0.3 respectively, the overall deflection will be: 
                                                            (5.19) 
 The .mass file defines many aircraft parameters, such as mass and moments 
of inertia, as well as simulation parameters, such as the units of length, mass and 
time as well as the value of gravitational acceleration and a baseline operational 
density.  
 Two .mass files and three .avl files were made for this research.  Each one 
contained surfaces representing the main wing and two vertical tails, as well as 
elevons and rudders.  The fuselage was not modeled, as it cannot be accurately 
drawn in AVL. One of each file type was made for baseline run cases, which 
were cruise, stall, cruise into a crosswind and stall into a crosswind.  A separate 
.mass and .avl file had to be made for the run cases where the aircraft was 
cruising in ground effect.  The third .avl file was made to demonstrate the effects 
 115 
of modifications to the control surfaces on trim and stability characteristics.  Full 
.avl and .mass files can be found in Appendix E. 
    
5.4.2 Results 
 A total of five cases were run for the optimized aircraft.  Table 12 shows the 
details of the cases that were run. 
Table 12: AVL Run Cases 
 
To simulate flying into a crosswind, the sideslip angle ? was set to 11.5 degrees.  
The stall cases were run at takeoff speed, with is 10 percent greater than stall 
speed.  The constraint put on all the models was to trim the aircraft at the given 
speed and flight conditions, which meant setting the roll, pitch and yaw 
moments to 0.  When run, AVL would calculate necessary control surface 
deflection angles to trim the aircraft as well as identify any dynamic 
maneuvering flight modes the aircraft may have.   
 Table 13 shows the results of the AVL trim scenarios.  The elevons function 
as both ailerons and elevators for the purpose of this analysis.  Roskam [48] states 
that acceptable control surface deflections must be within the stall limits of the 
control surface, which is approximately 25 degrees. 
V e l oc i t y  
( f t / s )
A l t i t ud e  
(ft)
D e ns i t y  
( s l ug / f t ^ 3 ) ?  ( de g)
S t a l l 1 5 7 . 8 5 0 0 . 0 0 2 3 7 7 0
C r ui s e 2 8 0 . 0 0 2 0 , 0 0 0 0 . 0 0 1 2 6 7 0
G r ou nd  E f f e c t 2 5 5 . 2 0 0 0 . 0 0 2 3 7 7 0
C r os s w i nd  S t a l l 1 5 7 . 8 5 0 0 . 0 0 2 3 7 7 1 1 . 5
C r os s w i nd 2 8 0 . 0 0 2 0 , 0 0 0 0 . 0 0 1 2 6 7 1 1 . 5
 116 
Table 13: AVL Results - Control Surface Deflections for Trim 
 
The results of these runs show that there are unacceptable amounts of elevon and 
rudder deflection needed to trim the aircraft.  The elevon is under-sized for 
functioning as an elevator in all cases, and the rudder not effective enough for 
the case of stalling in a crosswind.  The elevons are adequately sized to trim the 
rolling moment though. 
 In addition to a trim analysis, AVL also conducted an eigenvalue analysis to 
identify unstable maneuvering modes, such as Dutch roll, short period, phugoid, 
and spiral modes.   
 Dutch roll is one of the basic flight dynamic modes, and is the result of a 
yaw-roll coupling moment.  It is usually excited by use of the ailerons and 
rudder.  Dutch roll tendencies, which coincide with increases in an aircraft?s 
restoring rolling moment, can be increased by: the placement of wings above the 
center of gravity, increasing wing sweep, and increasing wing dihedral.  Often 
times, Dutch roll modes will experience decreased damping when an aircraft 
increases altitude.  To counteract the Dutch roll mode, many aircraft employ yaw 
dampers to artificially increase Dutch roll stability [39].  
 Short period modes describe the rapid pitching of an aircraft around its 
center of gravity.  The mode is generally very quickly damped out, with a period 
lasting only a few seconds.  The period is short enough that the airspeed of the 
aircraft does not have time to change, and instead functions as just a variance in 
angle of attack. 
A i l e r o n E l e v a t o r R u d d e r
S t a l l 0 . 0 0 0 6 6 . 0 4 5 0 . 0 0 0
C r ui s e 0 . 0 0 0 3 6 . 9 1 9 0 . 0 0 0
G r ound E f f e c t 0 . 0 0 0 2 5 . 1 2 8 0 . 0 0 0
C r os s w i nd S t a l l 1 0 . 1 2 9 6 9 . 0 5 6 3 1 . 2 6 3
C r os s w i nd 6 . 0 3 8 3 9 . 9 6 1 2 1 . 6 3 7
 117 
 The phugoid mode is a long period mode that consists of an aircraft pitching 
up and down as well as gaining and losing altitude, but experiencing very little 
change in angle of attack.  This mode can last for minutes in large aircraft, such 
as the optimized amphibious aircraft being used in this research.  While the 
damping of phugoid modes is normally weak, the period is long enough that the 
pilot usually can correct for this motion without problem. 
 The spiral mode is a lateral-directional mode involving roll-yaw coupling 
with a very long period.  A divergent spiral mode may be excited by a gust, 
which applies a small initial roll angle, which produces a small sideslip.  This 
sideslip then causes a yawing moment.  If the aircraft lacks sufficient dihedral 
stability and yaw damping, the spiral mode will be unstable and the aircraft will 
continue to turn while maintaining its sideslip and yaw angle.  This spiral will 
get continuously steeper and if left unchecked, a high speed spiral dive will 
result.  Usually, this mode happens relatively slowly, allowing for pilot 
correction.  In order to be spirally stable, an aircraft must have sufficient 
dihedral, which will increase roll stability, and a sufficiently long vertical tail 
moment arm, which will increase yaw damping. 
 Results of the eigenvalue analysis for the optimized aircraft are in Table 14.  
They show level 1 and level 2 damping and frequency requirements for a cargo 
aircraft [49].           
 118 
Table 14: Eigenvalue Analysis Results for Optimized Aircraft 
 
 The results of the eigenvalue analysis show that the aircraft achieves level 1 
stability for all dynamic flight modes except for Dutch roll during cruise, where 
falls in the high range of level 2 stability.  Level 1 stability refers to an aircraft 
having flying qualities that are clearly adequate for the required mission while 
level 2 stability refers to an aircraft having flying qualities are adequate to 
accomplish the mission but may require additional pilot workload or may cause 
degradation in mission effectiveness.  Neither level requires exceptional pilot 
skill or technique to return the aircraft to level, steady flight [49].  The level 2 
Dutch roll stability requirement encountered during cruise could be corrected 
with the addition of an artificial yaw damper, which would increase yaw 
stability and provide level 1 stability for the aircraft in all dynamic flight modes. 
   Analysis through AVL shows that the primary problem of the optimized 
aircraft configuration is the large control surface deflections necessary to trim the 
aircraft under stall and crosswind flight conditions.  To assist in finding an 
optimal size for the control surfaces, a parametric study was conducted varying 
what percent of the wing chord the control surfaces would occupy.  The tests 
Fl i gh t N a t ura l Ti m e  t o
C on di t i on R e a l I m a g Fre q. D a m pi ng D ou bl e ?? M od e
- 1 . 6 4 2 . 7 6 3 . 2 1 0 . 5 1 1 . 6 4 S h o r t  P e r i o d 0 . 3  ?  ?  ?  2 . 0 0 . 2  ?  ?  ?  2 . 1
- 0 . 1 5 1 . 4 1 1 . 4 1 0 . 1 1 0 . 1 5 D u t c h  R o l l ? ? 0 . 0 8 ? ?  ?  0 . 1 5 ?  ?  0 . 4 ?  ?  0 . 0 2 ? ?  ?  0 . 0 5 ?  ?  0 . 4
- 1 . 7 9 0 . 0 0
0 . 0 0 0 . 0 0
- 0 . 0 4 0 . 2 1 0 . 2 1 0 . 1 7 0 . 0 4 P h u g o i d ?  ?  0 . 0 4 ?  ?  0
- 1 . 6 9 0 . 0 0
- 0 . 1 4 1 . 4 8 1 . 4 9 0 . 0 9 0 . 1 4 D u t c h  R o l l ?  ?  0 . 0 8 ? ?  ?  0 . 1 5 ?  ?  0 . 4 ?  ?  0 . 0 2 ? ?  ?  0 . 0 5 ?  ?  0 . 4
- 1 . 1 3 2 . 8 6 3 . 0 8 0 . 3 7 1 . 1 3 S h o r t  P e r i o d 0 . 3  ?  ?  ?  2 . 0 0 . 2  ?  ?  ?  2 . 0
0 . 0 0 0 . 0 0
- 0 . 0 1 0 . 1 1 0 . 1 1 0 . 1 1 0 . 0 1 P h u g o i d ?  ?  0 . 0 4 ?  ?  0
- 3 . 4 0 0 . 0 0
- 0 . 2 9 1 . 7 3 1 . 7 5 0 . 1 7 0 . 2 9 D u t c h  R o l l ?  ?  0 . 0 8 ? ?  ?  0 . 1 5 ?  ?  0 . 4 ?  ?  0 . 0 2 ? ?  ?  0 . 0 5 ?  ?  0 . 4
- 2 . 2 2 3 . 6 0 4 . 2 3 0 . 5 2 2 . 2 2 S h o r t  P e r i o d 0 . 3  ?  ?  ?  2 . 0 0 . 2  ?  ?  ?  2 . 1
0 . 0 0 0 . 0 0
- 0 . 0 1 0 . 1 1 0 . 1 1 0 . 0 9 0 . 0 1 P h u g o i d ?  ?  0 . 0 4 ?  ?  0
- 1 . 5 8 2 . 6 7 3 . 1 0 0 . 5 1 1 . 5 8 S h o r t  P e r i o d 0 . 3  ?  ?  ?  2 . 0 0 . 2  ?  ?  ?  2 . 1
- 1 . 7 6 0 . 0 0
- 0 . 1 6 1 . 4 1 1 . 4 2 0 . 1 1 0 . 1 6 D u t c h  R o l l ? ? 0 . 0 8 ? ?  ?  0 . 1 5 ?  ?  0 . 4 ?  ?  0 . 0 2 ? ?  ?  0 . 0 5 ?  ?  0 . 4
- 0 . 0 4 0 . 2 0 0 . 2 0 0 . 1 8 0 . 0 4 P h u g o i d ?  ?  0 . 0 4 ?  ?  0
0 . 0 0 0 . 0 0
- 1 . 5 5 3 . 6 1 3 . 9 2 0 . 3 9 1 . 5 5 S h o r t  P e r i o d 0 . 3  ?  ?  ?  2 . 0 0 . 2  ?  ?  ?  2 . 1
- 1 . 7 4 0 . 0 0
- 0 . 1 5 1 . 4 7 1 . 4 8 0 . 1 0 0 . 1 5 D u t c h  R o l l ? ? 0 . 0 8 ? ?  ?  0 . 1 5 ?  ?  0 . 4 ?  ?  0 . 0 2 ? ?  ?  0 . 0 5 ?  ?  0 . 4
- 0 . 0 1 0 . 1 1 0 . 1 1 0 . 1 3 0 . 0 1 P h u g o i d ?  ?  0 . 0 4 ?  ?  0
0 . 0 0 0 . 0 0 4 9 6 . 5 2 S p i r a l T 2 s  >  1 2 T 2 s  >  8
Le v e l  1  R e q. Le v e l  2  R e q.
E i ge nv a l ue s
C r os s w i nd
C r os s w i nd  S t a l l
G r ou nd  E f f e c t
C r ui s e
S t a l l
 119 
were performed using the crosswind at stall speed test scenario, which yielded 
the worst results overall. The results of that study are shown in Figure 55. 
 
Figure 55: Control Surface Sizing Parametric Study 
 The results of this parametric study show that the elevator is most effective 
when it is approximately 27 percent of the total chord while the aileron?s 
performance continually increased with an increase in its size.  The rudder 
performance sees a steady increase as the percentage of chord increases until it is 
approximately 50 percent of the chord length of the wing, where the added 
benefits of more rudder become negligible.  In accordance with the findings of 
the parametric study, the elevons were resized to be 27% of the local chord, a 
decrease in size, and the rudder was increased in size to 50% of the local chord.  
Also, having to deflect the elevons almost 37 degrees to trim during steady cruise 
flight indicates that the elevons alone do not have enough size to control the 
0
5
10
15
20
25
30
10 20 30 40 50 60
D
e
f
l
e
c
t
i
on
 
A
ng
l
e
 
(de
g
)
%  C hor d
E le v a t o r
A il e r o n
R u d d e r
 120 
aircraft properly.  To compensate for this, a dedicated elevator was added 
between the vertical tails to assist the elevons in controlling the pitch of the 
aircraft.  Like the elevons, the elevator was sized at 27% chord.  Table 15 shows 
the results of the aircraft with revised control surface sizing. 
Table 15: Modified Control Surface Deflections for Trim 
 
With the increase in size of the rudder, slight decrease in size of the elevons and 
addition of a dedicated elevator, the control surface deflections for all run cases 
have been brought under the stall threshold of 25 degrees. 
 To ensure that the change in control surface sizing, along with the addition 
of an elevator, had not caused the aircraft to develop an unacceptable dynamic 
stability mode, an eigenvalue analysis was run again.  Results of this analysis are 
in Table 16. 
Table 16: Eigenvalue Analysis Results for Modified Aircraft 
 
A i l e r on E l e v a t or R udde r
S t a l l 0 . 0 0 0 1 8 . 9 4 2 0 . 0 0 0
C r ui s e 0 . 0 0 0 1 0 . 5 8 5 0 . 0 0 0
G r ound E f f e c t 0 . 0 0 0 6 . 9 1 5 0 . 0 0 0
C r os s w i nd S t a l l 9 . 5 8 6 2 0 . 2 2 3 2 1 . 7 4 2
C r os s w i nd 5 . 4 3 1 1 1 . 4 9 8 1 6 . 7 9 4
Fl i gh t N a t ura l Ti m e  t o
C on di t i on R e a l I m a g Fre q. D a m pi ng D ou bl e ?? M od e
- 0 . 2 1 1 . 4 3 1 . 4 5 0 . 1 5 0 . 2 1 D u t c h  R o l l ? ? 0 . 0 8 ? ?  ?  0 . 1 5 ?  ?  0 . 4 ?  ?  0 . 0 2 ? ?  ?  0 . 0 5 ?  ?  0 . 4
- 1 . 6 7 0 . 0 0
- 1 . 6 3 2 . 7 6 3 . 2 1 0 . 5 1 1 . 6 3 S h o r t  P e r i o d 0 . 3  ?  ?  ?  2 . 0 0 . 2  ?  ?  ?  2 . 1
0 . 0 2 0 . 0 0 3 9 . 8 4 S p i r a l T 2 s  >  1 2 T 2 s  >  8
- 0 . 0 4 0 . 2 1 0 . 2 1 0 . 1 8 0 . 0 4 P h u g o i d ?  ?  0 . 0 4 ?  ?  0
- 0 . 1 6 1 . 5 3 1 . 5 4 0 . 1 0 0 . 1 6 D u t c h  R o l l ?  ?  0 . 0 8 ? ?  ?  0 . 1 5 ?  ?  0 . 4 ?  ?  0 . 0 2 ? ?  ?  0 . 0 5 ?  ?  0 . 4
- 1 . 7 3 0 . 0 0
- 1 . 5 9 3 . 7 2 4 . 0 5 0 . 3 9 1 . 5 9 S h o r t  P e r i o d 0 . 3  ?  ?  ?  2 . 0 0 . 2  ?  ?  ?  2 . 0
0 . 0 1 0 . 0 0 7 6 . 9 2 S p i r a l T 2 s  >  1 2 T 2 s  >  8
- 0 . 0 1 0 . 1 1 0 . 1 1 0 . 1 2 0 . 0 1 P h u g o i d ?  ?  0 . 0 4 ?  ?  0
- 0 . 3 1 1 . 7 8 1 . 8 1 0 . 1 7 0 . 3 1 D u t c h  R o l l ?  ?  0 . 0 8 ? ?  ?  0 . 1 5 ?  ?  0 . 4 ?  ?  0 . 0 2 ? ?  ?  0 . 0 5 ?  ?  0 . 4
- 2 . 9 1 0 . 0 0
- 2 . 7 4 4 . 3 7 5 . 1 5 0 . 5 3 2 . 7 4 S h o r t  P e r i o d 0 . 3  ?  ?  ?  2 . 0 0 . 2  ?  ?  ?  2 . 1
0 . 0 1 0 . 0 0 8 3 . 7 0 S p i r a l T 2 s  >  1 2 T 2 s  >  8
- 0 . 0 1 0 . 1 1 0 . 1 1 0 . 1 1 0 . 0 1 P h u g o i d ?  ?  0 . 0 4 ?  ?  0
- 1 . 5 7 2 . 6 6 3 . 0 9 0 . 5 1 1 . 5 7 S h o r t  P e r i o d 0 . 3  ?  ?  ?  2 . 0 0 . 2  ?  ?  ?  2 . 1
- 1 . 6 2 0 . 0 0
- 0 . 2 3 1 . 4 3 1 . 4 4 0 . 1 6 0 . 2 3 D u t c h  R o l l ? ? 0 . 0 8 ? ?  ?  0 . 1 5 ?  ?  0 . 4 ?  ?  0 . 0 2 ? ?  ?  0 . 0 5 ?  ?  0 . 4
- 0 . 0 4 0 . 2 0 0 . 2 1 0 . 1 9 0 . 0 4 P h u g o i d ?  ?  0 . 0 4 ?  ?  0
0 . 0 2 0 . 0 0 3 2 . 3 2 S p i r a l T 2 s  >  1 2 T 2 s  >  8
- 1 . 5 4 3 . 6 1 3 . 9 2 0 . 3 9 1 . 5 4 S h o r t  P e r i o d 0 . 3  ?  ?  ?  2 . 0 0 . 2  ?  ?  ?  2 . 1
- 1 . 7 0 0 . 0 0
- 0 . 1 7 1 . 4 9 1 . 5 0 0 . 1 1 0 . 1 7 D u t c h  R o l l ? ? 0 . 0 8 ? ?  ?  0 . 1 5 ?  ?  0 . 4 ?  ?  0 . 0 2 ? ?  ?  0 . 0 5 ?  ?  0 . 4
- 0 . 0 2 0 . 1 1 0 . 1 1 0 . 1 4 0 . 0 2 P h u g o i d ?  ?  0 . 0 4 ?  ?  0
0 . 0 1 0 . 0 0 5 7 . 6 3 S p i r a l T 2 s  >  1 2 T 2 s  >  8
C r os s w i nd  S t a l l
C r os s w i nd
E i ge nv a l ue s
Le v e l  1  R e q. Le v e l  2  R e q.
S t a l l
C r ui s e
G r ou nd  E f f e c t
 121 
The control surface changes resulted in large improvements of Dutch roll 
stability.  All dynamic flight modes now comply with level 1 requirements for 
military cargo aircraft.  While all modes are now compliant, the changes to the 
control surface have resulted in the addition of a spiral mode to every run case.  
Fortunately, the time to double is very slow in all cases and is easily corrected 
through pilot input. 
  
  
 122 
Chapter 6 
Conclusions and Suggestions for Further Work 
6.1 Improvement of Sizing/Optimization Methods 
 The purpose of this research effort was to analyze the optimization and 
sizing methodology used in the creation of a preliminary design for an 
amphibious aircraft and to make suggestions about ways it can be improved.  It 
is very difficult, if not impossible, to create an aircraft that will function perfectly 
after the first design iteration.  This is why it is called a preliminary design.  A 
preliminary design aims to address as many design issues as possible in an 
expedient manner before beginning detailed design work on the remaining 
problems.  A good preliminary design process can save a company vast amounts 
of money because design problems are caught early.  The further into the design 
and manufacturing process a product is when a major problem is found in its 
design, generally the more expensive that problem is to correct.  If weaknesses 
can be found in the sizing and optimization process used in the preliminary 
design of an amphibious aircraft, efforts can be made to address these issues, and 
develop a more accurate and efficient preliminary design process in the future. 
 While the main focus of this paper was the suggestion of possible 
improvements that could be made to the sizing and optimization methods used, 
there were many positive results found throughout the course of this research 
work.     
 First, the results of the validation work done on the sizing code were very 
promising.  The geometric parameters predicted by the sizing code for Lockheed 
C-130-H and Cessna 172-R validation cases were very accurate.  The drag 
 123 
predicted for Cessna 172 with and without floats was also quite accurate, with 
the percent error for the two cases being approximately 4% and 10%, 
respectively.  The sizing code reasonably predicted the size of floats necessary for 
a Cessna 172, with the largest error in the predicted float geometry being the 
depth of the float with 6.7% error. 
 Also, the optimized aircraft was found to be statically stable in flight in both 
the longitudinal and lateral directions through the analysis of wind tunnel test 
results.  This demonstrates the effectiveness of the penalty functions put in place 
to produce a stable aircraft.  Also, there were no unacceptable dynamic 
maneuvering modes found through analysis using AVL.  The damping of all 
maneuvering modes was found satisfy the level 1 flying quality requirements, 
except for a Dutch roll mode during cruise conditions which just missed 
qualification for level 1 stability.  Both level 1 and 2 flight quality requirements 
are acceptable for aircraft, requiring no exceptional piloting ability to return the 
craft to level and steady flight.  If needed, the stability in the cruise Dutch roll 
mode could be increased to meet level one requirements through the addition of 
a yaw augmentation device.          
 
6.1.1 Drag Estimation 
 Drag estimation in the sizing code seemed to be quite inconsistent.  When 
the Cessna 172 was used for validation with and without floats, the percent error 
without floats was within 4%, and the percent error with floats was within 10%.  
In contrast, when the optimized model was tested in the wind tunnel, the results 
showed almost a 50% error between the wind tunnel and sizing code results.  
The method of drag calculation used by the sizing code is imperfect.  It doesn?t 
 124 
take into account interference from one component to another.  There is also the 
issue of the shape of the individual components.  The sizing code does not have a 
detailed model of components such as the fuselage and sponsons.  It does not 
account for drag due to flow separation at the step of the fuselage.  It does not 
consider the blunt trailing edge of the sponsons that was put in place to allow 
them to follow the contour lines of the aft part of the fuselage.  It also does not 
include the additional drag due to the scalloped cut outs in the fore and aft 
sections of the fuselage.  One method of improving aerodynamic prediction 
could be the inclusion of a vortex panel code into the design code.  This would 
completely replace the current aerodynamic calculations made in the sizing code 
and could hopefully help improve drag predictions [50].    
 
6.1.2 Stability During Water Operations 
 A second issue that arose with the sizing code was found during the 
analysis of its lateral and longitudinal stability on the water using Orca3D.  
While the aircraft was found to be stable in both the lateral and longitudinal 
directions, it did not have the levels of metacentric heights that have been 
recommended through the gathering of empirical data from existing amphibious 
aircraft.  
 This is a difficult problem to solve, as it requires the designer to know the 
shape of the fuselage in order to calculate its center of buoyancy and metacentric 
heights.  This requires a more detailed design than is currently being used and 
may not be feasible with the current approach.  On the other hand, if a panel 
method could be implemented that could handle the complex geometries 
involved in detailed boat hull design, then it is possible that that geometry could 
 125 
have a sectioning method performed on it inside the sizing code to predict its on-
water performance.  Alternatively, if a panel method or something similar 
enables the creation of a 3-D hull geometry inside the sizing code, it could be 
exported into Orca3D through a subroutine built into the sizing code to analyze 
its stability during water operations.  Once Orca3D has analyzed the model, the 
output data could be fed back into the sizing code and checked for appropriate 
levels of stability and the geometry could be adjusted from there.  The option of 
exporting to an outside program would seem to be very time intensive though, 
and may not be feasible when going through the many design iterations 
necessary during the optimization process.   
 If an panel method was used that was allowed to change many of the 
geometrical parameters of the fuselage and other components, the smart use of 
penalty functions would be necessary to make sure that the geometry maintains 
a level of feasibility.  This includes parameters such as length-to-beam ratio, 
which is currently user input.  Care would need to be taken that it could not be 
made too large or too small, as either extreme is not feasible.   
 
6.1.3 Control Surface Sizing 
 Proper control surface sizing is very important to having an aircraft that is 
capable of being trimmed.  Initially in the sizing code, the chord and span factors 
of the ailerons, elevators, and rudders were determined from guidelines based 
on existing aircraft.  When the aircraft was analyzed in AVL with control 
surfaces at the sizes suggested by these guidelines, the aircraft could not be 
trimmed.  A parametric study was performed that looked at finding the control 
surface size that would result in the minimum deflection angle needed to trim 
 126 
the aircraft.  A flying wing aircraft normally gets rid of the use of a dedicated 
elevator and instead uses elevons to fill the rolls of both the elevator and ailerons.  
AVL results showed that the addition of a dedicated elevator as well as some 
slight resizing of the elevons and rudders would result in an aircraft that 
trimmed within acceptable limits of control surface deflection.   
 Presently, the sizing code treats the span and chord factors for the control 
surfaces as inputs and does not vary them or analyze their effectiveness.  In order 
to properly size them during the preliminary design and optimization process, 
an analysis tool must be integrated with the code.  One possible method would 
be to create a subroutine in the sizing code that writes an AVL input file then 
runs AVL for a worst-case scenario to determine if the control surfaces are of 
proper size.  Since AVL can return the results in a text file format, the results 
could be read back into the sizing code and checked to see if the current size is 
acceptable.   
 
 
  
 127 
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 132 
Appendix A:  Sizing Code Text Output Sample 
 
CONVERGENCE TEST 
Weight Estimate                   117169 lbs 
Excess Weight                          0 lbs 
 
FLIGHT PLAN 
Time Airborne                     11.13 hrs 
 
AIRCRAFT SPECIFICATIONS 
Main Wing 
   Planform Area                 3090.39 ft^2 
   W/S                             37.91 lb/ft^2 
   Total Span                     179.82 ft 
   Inner Wing Segment Half-Span     4.83 ft 
   Root Chord                      23.57 ft 
   Aspect Ratio                    10.46  
   e                                0.76  
   Mean Aerodynamic Chord          17.56 ft 
   Inboard Taper Ratio              0.89  
   Outboard Taper Ratio             0.62  
   Inboard Sweep Angle (LE)        17.65 deg 
   Outboard Sweep Angle (LE)        4.95 deg 
   Inboard Sweep Angle (TE)       -13.48 deg 
   Outboard Sweep Angle (TE)       -0.39 deg 
   Location of c/4 Behind Nose     15.53 ft 
Horizontal Tail 
   Planform Area                  994.76 ft^2 
   Span                            73.13 ft 
   Root Chord                      20.73 ft 
   Aspect Ratio                     5.38  
   Taper Ratio                      0.31  
   Sweep Angle (LE)                13.00 deg 
 133 
   Location of c/4 Behind Nose     62.17 ft 
Vertical Tail 
   Planform Area                  647.67 ft^2 
   Span                            36.81 ft 
   Root Chord                      27.36 ft 
   Aspect Ratio                     2.09  
   Taper Ratio                      0.29  
   Sweep Angle (LE)                27.96 deg 
   Location of c/4 Behind Nose     57.20 ft 
 
BUOYANCY CHARACTERISTICS 
Total Displacement               2349.43 ft^3 
   Wing                           109.01 ft^3 
   Fuselage                       228.16 ft^3 
   Cabin                         1785.00 ft^3 
   Tail                            51.16 ft^3 
   Floats                          82.38 ft^3 
   Systems                         43.70 ft^3 
   Batteries                        0.00 ft^3 
   Fuel (Submerged)                50.01 ft^3 
 
FLIGHT CHARACTERISTICS 
L/D Cruise                       20.2594 
L/D Ground Effect                21.0098 
Speed Cruise                      184.12 kts 
Speed Ground Effect               167.66 kts 
Cruise Thrust (Sea Level)       10850.21 lbs 
 
FUSELAGE DIMENSIONS 
Fuselage Width                      9.67 ft 
Fuselage Height                     9.67 ft 
Fuselage Length                    77.72 ft 
 
 134 
WEIGHT BREAKDOWN 
Gross Weight                   117169.01 lb     22.08 ft 
   Empty Weight                 73600.04 lb 
   Fuel Weight                  24818.97 lb     22.08 ft 
   Payload                      18750.00 lb     19.50 ft 
       Cargo Weight             18750.00 lb 
       Pilot Weight                 0.00 lb 
   
Component Weight Breakdown 
   Wing                            18223 lb     20.95 ft 
   HT                               3112 lb     65.55 ft 
   VT                               1403 lb     62.75 ft 
   Fuselage                        15422 lb     17.10 ft 
   Cabin                            6212 lb     19.50 ft 
   Main LG                             0 lb     20.95 ft 
   Nose LG                             0 lb     15.54 ft 
   Nacelle Group                    1958 lb     20.95 ft 
   Engine                           1938 lb     20.95 ft 
   Engine Controls                    51 lb     20.95 ft 
   Starter                            70 lb     20.95 ft 
   Fuel System                       173 lb     20.95 ft 
   Flight Controls                  1431 lb     20.95 ft 
   Instruments                       548 lb     19.50 ft 
   Hydraulics                        340 lb     31.09 ft 
   Electrical                        532 lb     19.50 ft 
   Avionics                         5392 lb     19.50 ft 
   Furnishings                      1097 lb     19.50 ft 
   A/C                               957 lb     19.50 ft 
   Anti-Ice                          234 lb     20.95 ft 
   Handling Gear                      35 lb     19.50 ft 
   Cargo Handling Sys                467 lb     19.50 ft 
   Struts                           3515 lb     20.95 ft 
   Floats                          10489 lb     22.08 ft 
 135 
 
CENTER OF GRAVITY CALCULATIONS 
C.G. Location (From Nose)          22.08 ft 
C.G. Percent of Fuselage           28.41 %  
 
NEUTRAL POINT CALCULATIONS 
N.P. Location (From Nose)          23.52 ft 
N.P. Percent of Fuselage           30.26 % 
Static Margin                       8.20 % 
 
Component Drag Breakdown 
                   Cruise     In GE   
   Wing           0.00755   0.00702   
   Fuselage       0.00163   0.00151    
   H Tail         0.00305   0.00284   
   V Tail         0.00188   0.00175   
   Nacelle        0.00020   0.00019   
   Floats         0.00225   0.00209   
   Struts         0.00042   0.00040   
   Misc          -0.00170  -0.00158   
   TOTAL Cd0      0.01529   0.01422   
   Drag Area        47.27     43.95 ft^2 
Reynolds Numbers 
                   Cruise     In GE   
   Wing          21574637  31037475   
   Fuselage      95480151 137358636   
   H Tail         6944615   9990588    
   V Tail         9042993  13009334    
   Nacelle       11706502  16841083   
   Floats        70309984 101148598   
   Struts         1228494   1767322    
Friction Coefficients 
                   Cruise     In GE   
 136 
   Wing           0.00253   0.00235   
   Fuselage       0.00188   0.00174   
   H Tail         0.00317   0.00295   
   V Tail         0.00301   0.00279   
   Nacelle        0.00285   0.00265   
   Floats         0.00199   0.00185  
   Struts         0.00448   0.00417   
Flight Parameters 
                   Cruise     In GE   
   Speed           184.12    167.66 kts 
   Mach Number       0.30      0.25      
   Dyn Pressure     61.18     95.17 lbs/ft^2 
   Cl               0.620     0.398    
   Cd              0.0306    0.0205    
   Cdi             0.0153    0.0047    
   L/D              20.26     21.01    
  
 137 
Appendix B: Final Optimized Design Sizing Code Output 
 
CONVERGENCE TEST 
Weight Estimate                    93900 lbs 
Excess Weight                          0 lbs 
 
SUBMERGED PROPULSION TYPE 
Battery Powered When Submerged. 
 
FLIGHT PLAN 
Time Enroute to Dropoff            12.14 hrs 
   Time Airborne                   12.14 hrs 
   Conversion Time                  0.00 hrs 
   Time Submerged                   0.00 hrs 
 
AIRCRAFT SPECIFICATIONS 
Main Wing 
   Planform Area                 3838.83 ft^2 
   W/S                             24.46 lb/ft^2 
   Total Span                     147.07 ft 
   Inner Wing Segment Half-Span    10.18 ft 
   Root Chord                      57.45 ft 
   Aspect Ratio                     5.63  
   e                                0.83  
   Mean Aerodynamic Chord          34.32 ft 
   Inboard Taper Ratio              0.74  
   Outboard Taper Ratio             0.10  
   Inboard Sweep Angle (LE)        56.75 deg 
   Outboard Sweep Angle (LE)       23.94 deg 
   Inboard Sweep Angle (TE)         4.92 deg 
   Outboard Sweep Angle (TE)       -9.32 deg 
   Location of c/4 Behind Nose     14.36 ft 
Vertical Tail 
 138 
   Number of Vertical Tails            2 
   Planform Area Per Tail         455.54 ft^2 
   Span                            30.41 ft 
   Root Chord                      19.97 ft 
   Aspect Ratio                     1.40  
   Taper Ratio                      0.50  
   Sweep Angle (LE)                23.70 deg 
   Location of c/4 Behind Nose     47.30 ft 
 
BUOYANCY CHARACTERISTICS 
Total Displacement               2519.89 ft^3 
   Wing                           205.67 ft^3 
   Fuselage                       414.84 ft^3 
   Cabin                         1785.00 ft^3 
   Tail                            28.01 ft^3 
   Floats                           0.00 ft^3 
   Systems                         43.70 ft^3 
   Batteries                        0.00 ft^3 
   Fuel (Submerged)                42.67 ft^3 
Downforce Required              86989.40 ft^3 
Dry Volume for Neutral Buoyancy   732.30 ft^3 
 
FLIGHT CHARACTERISTICS 
L/D Cruise                       18.5401 
L/D Ground Effect                19.2081 
L/D Submerged                    17.2394 
Speed Cruise                      166.14 kts 
Speed Ground Effect               151.21 kts 
Speed Submerged                     3.89 kts 
Cruise Thrust (Sea Level)        9501.85 lbs 
Power Submerged                    60.29 HP 
 
FUSELAGE DIMENSIONS 
 139 
Fuselage Width                     15.16 ft 
Fuselage Height                    15.16 ft 
Fuselage Length                    57.45 ft 
 
WEIGHT BREAKDOWN 
Gross Weight                    93900.30 lb     26.82 ft 
   Empty Weight                 54253.13 lb 
   Fuel Weight                  20897.17 lb     33.79 ft 
   Payload                      18750.00 lb     19.50 ft 
       Cargo Weight             18750.00 lb 
       Pilot Weight                 0.00 lb 
       Underwater Equipment         0.00 lb 
   Submerged Prop. Batt. Weight     0.00 lb     17.63 ft 
   Submerged Prop. Motor Weight     0.00 lb     34.47 ft 
Component Weight Breakdown 
   Wing                            14116 lb     29.02 ft 
   HT                                  0 lb     51.70 ft 
   VT                               1199 lb     51.51 ft 
   Fuselage                        15582 lb     28.72 ft 
   Cabin                            6212 lb     19.50 ft 
   Main LG                          1005 lb     29.02 ft 
   Nose LG                           579 lb     11.49 ft 
   Nacelle Group                    1706 lb     29.02 ft 
   Engine                           1675 lb     29.02 ft 
   Engine Controls                    43 lb     29.02 ft 
   Starter                            65 lb     29.02 ft 
   Fuel System                       156 lb     33.79 ft 
   Flight Controls                  1288 lb     29.02 ft 
   Instruments                       489 lb     19.50 ft 
   Hydraulics                        274 lb     45.96 ft 
   Electrical                        479 lb     19.50 ft 
   Avionics                         5392 lb     19.50 ft 
   Furnishings                      1225 lb     19.50 ft 
 140 
   A/C                               830 lb     19.50 ft 
   Anti-Ice                          188 lb     29.02 ft 
   Handling Gear                      28 lb     19.50 ft 
   Cargo Handling Sys                292 lb     19.50 ft 
   Sponsons                         1429 lb     26.82 ft 
 
CENTER OF GRAVITY CALCULATIONS 
C.G. Location (From Nose)          26.82 ft 
C.G. Percent of Fuselage           46.68 %  
 
NEUTRAL POINT CALCULATIONS 
N.P. Location (From Nose)          31.13 ft 
N.P. Percent of Fuselage           54.18 % 
Static Margin                      12.56 % 
 
Component Drag Breakdown 
                   Cruise     In GE   
   Wing           0.00673   0.00627    
   Fuselage       0.00459   0.00427    
   H Tail         0.00000   0.00000    
   V Tail         0.00185   0.00173    
   Nacelle        0.00015   0.00014    
   Sponsons       0.00140   0.00130    
   Misc          -0.00147  -0.00137   
   TOTAL Cd0      0.01324   0.01234    
   Drag Area        50.84     47.36      
Reynolds Numbers 
                   Cruise     In GE   
   Wing          38414066  54730444   
   Fuselage      64301475  91613533   
   H Tail               0         0          
   V Tail        18233917  25978775    
   Nacelle        9935922  14156206    
 141 
   Sponsons      23776693  33875846   
Friction Coefficients 
                   Cruise     In GE   
   Wing           0.00225   0.00210    
   Fuselage       0.00203   0.00189    
   H Tail         0.00000   0.00000    
   V Tail         0.00261   0.00243    
   Nacelle        0.00295   0.00275    
   Sponsons       0.00248   0.00231    
Flight Parameters 
                   Cruise     In GE   
   Speed           166.14    151.21 kts 
   Mach Number       0.27      0.23       
   Dyn Pressure     49.81     77.41 lbs/ft^2 
   Cl               0.491     0.316      
   Cd              0.0265    0.0178     
   Cdi             0.0132    0.0041     
   L/D              18.54     19.21      
 
 
 
  
 142 
Appendix C: Cessna 172 Wind Tunnel Data and Results 
 
Figure 56: Cessna 172 Float Comparison, 0 Elevator Deflection 
  
Figure 57: 172 No Floats Results 
 143 
 
Figure 58: 172 with Floats Results 
  
Figure 59: 172 No Floats, Elevator Sweep 
 144 
 
Figure 60: 172 with Floats, Elevator Sweep 
  
 145 
Appendix D: Optimized Aircraft Wind Tunnel Data and Results 
 
Figure 61: 0 Yaw, Rudder Comparison 
 
Figure 62: 0 Yaw, Elevon Comparison 
 146 
 
Figure 63: 0 Yaw, Roll Comparison 
 
Figure 64: -5 Yaw, Rudder Comparison 
 147 
 
Figure 65: -5 Yaw, Elevon Comparison 
 
Figure 66: -5 Yaw, Roll Comparison 
 
 148 
 
Figure 67: -11.5 Yaw, Rudder Comparison 
 
Figure 68: -11.5 Yaw, Elevon Comparison 
 149 
 
Figure 69: -11.5 Yaw, Roll Comparison 
 
Figure 70: +5 Yaw, Rudder Comparison 
 150 
 
Figure 71: +5 Yaw, Elevon Comparison 
 
Figure 72: +5 Yaw, Roll Comparison 
 151 
 
Figure 73: Engine Comparison 
 
Figure 74: 0 Rudder, 0 Elevon, Transition Strip Comparison 
 152 
 
Figure 75: -5 Rudder, 0 Elevon, Transition Strip Comparison 
 
Figure 76: +5 Rudder, 0 Elevon, Transition Strip Comparison 
 153 
 
Figure 77: -20 Rudder, 0 Elevon, Transition Strip Comparison 
 
Figure 78: +20 Rudder, 0 Elevon, Transition Strip Comparison 
 154 
 
Figure 79: 0 Rudder, -5 Elevon, Transition Strip Comparison 
 
Figure 80: 0 Rudder, +5 Elevon, Transition Strip Comparison 
 155 
 
Figure 81: 0 Rudder, -20 Elevon, Transition Strip Comparison 
 
Figure 82: 0 Rudder, +20 Elevon, Transition Strip Comparison 
 156 
 
Figure 83: 0 Rudder, Left Roll (5 Degrees), Transition Strip Comparison 
 
Figure 84: 0 Rudder, Left Roll (20 Degrees), Transition Strip Comparison 
  
 157 
Appendix E: AVL Input Files 
 
-Baseline AVL Input File 
Amphibious_Flying_Wing 
0.27 
0    0    0 !out of ground effect 
!0    1    -9.62  ! Ground effect: Ground at -9.618 feet 
3838.83    34.32    147.07 !Reference area  
26.82     0    0  !CG location for most aft position 5% SM  
0.01324 
 
SURFACE                              
Main Wing                              
6    1    20    -2                  
YDUPLICATE                              
    0                          
ANGLE                              
    0                          
TRANSLATE                              
0    0    0                      
SECTION                              
    0    0    0    57.45    0          
AFILE 
hsnlf213_smooth.dat                          
SECTION                              
    15.5271    10.18    0    42.513    0          
AFILE 
hsnlf213_smooth.dat                          
SECTION                              
    30.5960    44.121    0    22.0152    0          
AFILE 
hsnlf213_smooth.dat                          
CONTROL                              
    Aileron    1    0.7    0    0    0     -1 
CONTROL                              
    Elevator   0.75    0.7    0    0    0     1 
SECTION                                            
    43.6551    73.535    0    4.2513    0          
AFILE 
hsnlf213_smooth.dat                          
CONTROL                              
    Aileron    1    0.7    0    0    0     -1 
CONTROL                              
    Elevator   0.75    0.7    0    0    0     1                        
 
 
 158 
 
 
SURFACE                              
VS Upper                               
6    1    20    -2                  
YDUPLICATE                              
    0                          
ANGLE                              
    0                          
TRANSLATE                              
42.30728 36.7675 0 
SECTION                              
    1.829    0    -4.1667    9.985    0          
NACA                              
    0012  
CONTROL                              
    Rudder    1    0.68    0    0    0     -1 
SECTION                                             
    0    0    0    19.97    0          
NACA 
   0012                                                                        
CONTROL                              
    Rudder    1    0.77    0    0    0     -1     
SECTION       
    10.1851   0    23.2023    11.142    0          
NACA                              
    0012                          
CONTROL                              
    Rudder    1    0.68    0    0    0     -1                        
SECTION                              
    11.52    0    26.2433    9.985    0          
NACA                              
    0012 
 
  
 159 
-Modified Control Surfaces AVL Input File 
Amphibious_Flying_Wing_Modified 
0.27 
0    0    0 !out of ground effect 
!0    1    -9.62  ! Ground effect: Ground at -9.618 feet 
3838.83    34.32    147.07 !Reference area  
26.82     0    0  !CG location for most aft position 5% SM  
0.01324 
 
SURFACE                              
Main Wing                              
6    1    20    -2                  
YDUPLICATE                              
    0                          
ANGLE                              
    0                          
TRANSLATE                              
0    0    0                      
SECTION                              
    0    0    0    57.45    0          
AFILE 
hsnlf213_smooth.dat 
CONTROL                              
    Elevator   0.75    0.73    0    0    0     1                          
SECTION                              
    15.5271    10.18    0    42.513    0          
AFILE 
hsnlf213_smooth.dat 
CONTROL                              
    Elevator   0.75    0.73    0    0    0     1                          
SECTION                              
    30.5960    44.121    0    22.0152    0          
AFILE 
hsnlf213_smooth.dat                          
CONTROL                              
    Aileron    1    0.73    0    0    0     -1 
CONTROL                              
    Elevator   0.75    0.73    0    0    0     1 
SECTION                                            
    43.6551    73.535    0    4.2513    0          
AFILE 
hsnlf213_smooth.dat                          
CONTROL                              
    Aileron    1    0.73    0    0    0     -1 
CONTROL                              
    Elevator   0.75    0.73    0    0    0     1                        
 
 160 
SURFACE                              
VS Upper                               
6    1    20    -2                  
YDUPLICATE                              
    0                          
ANGLE                              
    0                          
TRANSLATE                              
42.30728 36.7675 0 
SECTION                              
    1.829    0    -4.1667    9.985    0          
NACA                              
    0012  
CONTROL                              
    Rudder    1    0.5    0    0    0     -1 
 
SECTION                                             
    0    0    0    19.97    0          
NACA 
   0012                                                                        
CONTROL                              
    Rudder    1    0.6714    0    0    0     -1     
SECTION       
    10.1851   0    23.2023    11.142    0          
NACA                              
    0012                          
CONTROL                              
    Rudder    1    0.5484    0    0    0     -1                        
SECTION                              
    11.52    0    26.2433    9.985    0          
NACA                              
    0012                         
CONTROL                              
    Rudder    1    0.5149    0    0    0     -1                   
  
 161 
-AVL Mass File 
#  Amphibious Flying Wing 
# 
#  Dimensional unit and parameter data. 
#  Mass & Inertia breakdown. 
 
#  Names and scalings for units to be used for trim and eigenmode calculations. 
#  The Lunit and Munit values scale the mass, xyz, and inertia table data below. 
#  Lunit value will also scale all lengths and areas in the AVL input file. 
Lunit = 1 ft 
Munit = 1 slug 
Tunit = 1 s 
 
#-------------------------  
#  Gravity and density to be used as default values in trim setup (saves runtime 
typing). 
#  Must be in the unit names given above (i.e. m,kg,s). 
g   = 32.2 
rho = 0.001267 
 
#------------------------- 
#  Mass & Inertia breakdown. 
#  x y z  is location of item's own CG. 
#  Ixx... are item's inertias about item's own CG. 
# 
#  x,y,z system here must be exactly the same one used in the .avl input file 
#     (same orientation, same origin location, same length units) 
# 
#  mass     x      y     z      Ixx       Iyy         Izz   [  Ixy   Ixz   Iyz ] 
*   1.      1.     1.    1.     1.        1.          1.       1.    1.    1. 
+   0.      0.     0.    0.     0.        0.          0.       0.    0.    0. 
2916.149  26.82   0     -2.5    1515379.13 262034.017  1543783.282     ! entire 
aircraft