A Preliminary Design Analysis for an Uninhabited Long Range Supersonic Strike Vehicle Instructors: Neil Weston and Carl Johnson By Michael Lopez December 5, 2014 I certify that I have abided by the honor code of the Georgia Institute of Technology and followed the collaboration guidelines as specified in the project description for this assignment
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A Preliminary Design for a Unmanned Long Range Strike Vehicle
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A Preliminary Design Analysis for an Uninhabited Long Range Supersonic Strike Vehicle
Instructors: Neil Weston and Carl Johnson
By Michael Lopez
December 5, 2014
I certify that I have abided by the honor code of the Georgia Institute of Technology and followed the collaboration guidelines as specified in the project description for this assignment
Abstract
This document is a preliminary design for the creation of an uninhabited long range strike
vehicle. The design process used for the creation of this vehicle was primarily taken from Dr.
Jan Roskam’s series of aircraft design books. A figure of merits analysis was performed to
determine to best component configuration. Using these configuration choices, a weight
sizing analysis was performed based on the mission profile, mission fuel fractions, and the
class I drag polar to produce a takeoff weight for the vehicle. Subsequently, a constraint
analysis was performed on each segment of flight in order to produce an optimal thrust to
weight ratio at sea level takeoff and an optimal wing loading at takeoff. These ratios
produced preliminary values for thrust and wing area. Using all of this information, a
preliminary component design of the fuselage, wing, tail, high lift devices, and control
surfaces was performed. Finally, landing gear were attached to the aircraft and the entire
configuration was weighed and balanced to produce a finalized initial aircraft design. In
addition to this design process, trade studies were performed on key assumptions and design
decisions throughout the process to provide justification of various choices and demonstrate
the impact that changing these values would have on important design parameters.
Nomenclature
α = thrust lapse
β = vehicle weight over vehicle takeoff weight
Λ = quarter chord sweep angle
Γ = dihedral angle
λ = taper ratio
ρ = density
μ = turn bank angle
μto = ground friction coefficient
AR = main wing aspect ratio
b = wing span
c = chord
CD,o = coefficient of zero lift drag
CD = coefficient of drag
Cf = coefficient of skin friction
CL = coefficient of lift
d = diameter
e = Oswald’s efficiency factor
2
g0 = gravitational acceleration
h = altitude
KΛ = sweep coefficient
K1 = 1st order drag polar coefficient
K2 = 2nd order drag polar coefficient
kL = approach speed safety factor
kTO = takeoff speed safety factor
M = vehicle Mach number
n = load factor
q = dynamic pressure
R = vehicle range
RC = vehicle rate of climb
S = component area
SG = takeoff distance
Swet = vehicle wetted area
Tmax = maximum engine thrust
TSL = thrust at sea level
TSFC = thrust specific fuel consumption
t/c = thickness to chord ratio
T/W = thrust to weight ratio
v = vehicle speed
V = volumetric coefficient
WE = empty weight
WF = maximum fuel weight
WP = payload weight
WTO = maximum takeoff weight
W/S = wing loading
List of Figures
Figure 1: Final Vehicle Configuration..........................................................................................................................10
Figure 16: Fuselage Top View......................................................................................................................................36
Figure 17: Fuselage Side View.....................................................................................................................................36
Figure 18: Fuselage Front View
Figure 19: Coefficient of Lift versus Angle of Attack for NACA 64-204
Figure 20: Coefficient of Drag versus Angle of Attack for NACA 64-204
Figure 21: Coefficient of Moment about the Leading Edge versus Angle of Attack for NACA 64-204.....................39
Figure 22: 2-D Drag Polar for NACA 64-204..............................................................................................................40
Figure 23: Main Wing Top View..................................................................................................................................43
Figure 24: Main Wing Side View.................................................................................................................................43
Figure 25: Main Wing Front View
Figure 26: Tail Top View
Figure 27: Tail Side View
Figure 28: Tail Front View...........................................................................................................................................47
Figure 29: Vehicle Top View.......................................................................................................................................48
Figure 30: Vehicle Subsonic Leading Edge..................................................................................................................49
Figure 31: Neutral Point Location................................................................................................................................50
Figure 32: Center of Gravity Range
Figure 33: Weight-C.G. Excursion Diagram
Figure 34: Landing Gear Side View
4
Figure 35: Final Design Top View
Figure 36: Final Design Side View
Figure 37: Final Design Front View
List of Tables
Table 1: Analysis of Alternatives...................................................................................................................................7
Table 4: Number of Fuselages Selection........................................................................................................................9
Table 5: Tail Type Selection...........................................................................................................................................9
Table 7: Number of Engines Selection.........................................................................................................................10
feet per minute. For this analysis, the desired ceiling has been defined to be 60,000 feet and the Mach number for
this ceiling has been given as Mach 2.0. At that altitude and Mach number, the velocity is calculated to be 1,147
knots. The values used for this analysis are shown in Table 26.
Table 27: Service Ceiling Analysis Values
α β v (ft/s) rho (slugs/ft3) dh/dt (ft/s) q (lbs/ft2)
.175 .945 1936.15 .000224 1.67 419.44
Using these values, the resultant thrust to weight values required to reach this service ceiling range from .95
down to .57 as wing loading is increased. Therefore, the given service ceiling requirement is not a factor when
considering the overall design point.
H. Design Point
The purpose of this entire constraint sizing analysis was to determine a point on the graph of wing loading vs
thrust to weight ratio that satisfied all the individual mission segment requirements. This design point would
minimize the thrust to weight ratio necessary while maximizing the wing loading. This point is the most design point
because a minimized thrust to weight ratio expands the range of possible engines that can provide the necessary
thrust. The less thrust that is required, the lighter the engine can be. In addition, a maximized wing loading
minimizes the necessary wing area required for the vehicle and reduces the structural load placed on the fuselage as
well as the inner spars and ribs needed. After doing the energy based constraint analysis on all of the segments of
flight, the two segments that define this design point are shown to be the acceleration and the delivery of the
payload. The intersection of these two curves defines the location with the minimum thrust to weight ratio while still
attempting to maximize the wing loading. Therefore, for this constraint analysis, the resultant thrust to weight ratio
was determined to be 1.06 with a wing loading of 98 lbs per square ft. Using these values as well as the initially
determined takeoff weight value of 36,711 lbs, the sea level thrust necessary and the wing area of the vehicle were
calculated to be 39,031 lbs and 375.7 ft2 respectively. All of the different thrust to weight ratio curves as well as the
design point can be seen below in Fig. 11.
30
Figure 11: Constraint Analysis
VI. Constraint Analysis Sensitivity Studies
Now that a design point has been determined for the vehicle, the requirements of the design call for sensitivity
studies in order to determine the impact of both performance requirements as well as the assumptions made
throughout the analysis.
A. Descent Rate Trade Study
The first performance parameter that was analyzed was the descent rate during the accelerated dive of the
vehicle. The acceleration segment of the flight was one of the determining factors of the design point. Therefore, the
descent rate was chosen in order to determine how relaxing or increasing the dive performed would affect the
overall design of the vehicle. The result of this trade study is shown below in Fig. 12.
31
50 70 90 110 130 150 170
-1.5
-1
-0.5
0
0.5
1
1.5
2Simple Takeoff
Friction Takeoff
Climb
Supercruise
Dash 1
Zoom
Delivery
Acceleration
Dash 2
Descent 1
Subcruise
Descent 2
Landing
Service Ceiling
Design PointWing Loading at Takeoff (lbs/ft2)
Thru
st to
Wei
ght a
t Sea
Lev
el T
akeo
ff (~
)
50 70 90 110 130 150 170
-1.5
-1
-0.5
0
0.5
1
1.5
2
150 ft/s
175 ft/s
200 ft/s
225 ft/s
250 ft/s
Wing Loading at Takeoff (lbs/ft2)
Thru
st to
Wei
ght a
t Sea
Lev
el T
akeo
ff (~
)
Figure 12: Descent Rate Trade Study
The results of this sensitivity study show the strong impact that the descent rate has on the overall thrust to
weight value of the acceleration segment. The steeper the dive, the greater the acceleration due to gravity and the
less acceleration that the engines themselves are required to put out. Therefore, from a performance perspective, it is
always desireable to dive as steeply as possible in order to both reduce the time necessary for the desired
acceleration as well as reduce the necessary output of the engines of the vehicle.
B. Load Factor Trade Study
The other mission segment that defined the design point for this vehicle was the delivery of the payload modeled
as a constant speed and constant altitude turn. The driving factor in the thrust to weight ratio of this analysis was the
load factor of the vehicle. The greater the load factor, the steeper the turn being performed and the greater the load
on the vehicle itself. The sensitivity study with respect to the load factor is shown in Fig. 13 below.
32
50 70 90 110 130 150 170
-2
-1
0
1
2
3
4
0.8
1.2
1.6
2
2.4
Wing Loading at Takeoff (lbs/ft2)
Thru
st to
Wei
ght a
t Sea
Lev
el T
akeo
ff (~
)
Figure 13: Load Factor Trade Study
This sensitivity study shows just how large an impact the load factor has on the resulting thrust to weight values.
For the initially suggested load factor of two, the maximum wing loading of the vehicle would be very small in order
to maintain the desired maximum of 1.2 on the thrust to weight ratio. Increasing the load factor to 2.4 results in a
very steep curve with thrust to weight ratios well beyond the acceptable range. Therefore, for this design, the load
factor was decreased to 1.6 in order to expand the range of possible wing loading values that would meet the
specified requirements.
C. Maximum Lift Coefficient on Approach Trade Study
One of the most important assumptions in this analysis was the assumption regarding the maximum lift
coefficient during the final approach and landing of the vehicle. This assumption is important because the approach
segment of flight determines the maximum wing loading possible for the vehicle. The values of the lift coefficient
vary depending on the amount of extra surfaces and wing area that are added by the use of devices such as flaps and
slats. The greater the wing area that is increased during landing, the larger the resulting maximum lift coefficient
will be. A sensitivity study was performed on this lift coefficient in order to determine the magnitude of its effect on
the resulting wing loading value. The results of this sensitivity study are shown below in Fig. 14.
33
50 70 90 110 130 150 170 190 210 230
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
1.6
1.9
2.2
2.5
2.8
Wing Loading at Takeoff (lbs/ft2)
Thru
st to
Wei
ght a
t Sea
Lev
el T
akeo
ff (~
)
Figure 14: Maximum Lift Coefficient on Approach Trade Study
The results of this sensitivity confirm that the lift coefficient on approach has a strong impact on the maximum
wing loading possible for the vehicle. An increase in the lift coefficient of .3 results in an increase in the maximum
wing loading by approximately 23. For this design analysis, a lift coefficient of 2.2 was chosen due to data shown in
Roskam detailing the lift coefficient due to flaps at landing.
D. Takeoff Distance Trade Study
The final design assumption that was analyzed for a sensitivity study was the requirement for takeoff distance.
While the takeoff segment did not have an impact on the design point chosen for the vehicle, the length of takeoff is
still a very important parameter as it defines the set of possible runways this vehicle is capable of using. The shorter
the necessary distance for takeoff, the greater possible takeoff and landing locations the vehicle can use. This can be
highly desirable for possible uses on an aircraft carrier or rapidly assembled bases near military front lines. The
results of this sensitivity study are shown below in Fig. 15.
Figure 15: Takeoff Distance Trade Study
The results of this sensitivity study show that the required distance for takeoff does have a strong impact on the
thrust to weight ratio necessary for the vehicle. The shorter the allowable takeoff distance, the greater the slope of
the relationship between wing loading and thrust to weight ratio. Should the takeoff distance be reduced even
34
further, it could become a design point consideration. However, for the purposes of this design analysis, the takeoff
performance was not a priority and so a distance of 10,000 feet was used to ensure that the takeoff performance did
not affect the overall design choices.
VII. Component Design
After performing the constraint analysis on the desired vehicle, the next step in the design process is to begin
designing individuals components of the overall vehicle. Each component was designed using a specific process
detailed in Roskam’s Part II design book. Previous analysis and configuration choices resulted in a vehicle with one
fuselage, a conventional, mid mounted wing, and a v-tail. This paper will explain the design choices made and show
their impact on the final design of each component. Throughout the report, many of the design choices made were
taken from Roskam’s data regarding the F-16 military fighter. This is due to the fact that the F-16 shares a similar
speed and capability and overall size to that of the vehicle designed for this long range strike mission.
VIII. Fuselage Design
The primary component of this supersonic vehicle that must be designed first is the fuselage. The preliminary
configuration choices resulted in a single fuselage aircraft. This fuselage would contain the weapons payload, the
avionics, and as much of the necessary mission fuel as possible.
35
50 70 90 110 130 150 170
-1.5
-1
-0.5
0
0.5
1
1.5
2
5,000 ft
7,500 ft
10000 ft
12,500 ft
15,000 ft
Wing Loading at Takeoff (lbs/ft2)
Thru
st to
Wei
ght a
t Sea
Lev
el T
akeo
ff (~
)
A. Weight
The first step in the design process of the fuselage involved compiling a list of all the various components that
would be placed inside the fuselage. The fuselage must be sized in order account for all the weights and volumes of
these components. In order to determine the weight of the avionics equipment necessary in the aircraft, a simple
relationship shown in Eqn. 26 is used. The density of the avionic equipment is assumed to be 30 lbs per square feet.
The list of these weights and sizes is shown in Table 27 below.
W avionics
W E
=.03 (26)
Table 28: Fuselage Component Weight and Volume
Weight (lbs) Volume (ft3)
Avionics 395 13.2
Military Payload 4,000 42.9
Mission Fuel 19,657 408.8
As can be seen from the table, the mission fuel requirement easily dominates both the weight and the volume
requirements. The avionics weight and volume were taken from simple relations from Raymer’s design book based
on the empty weight of a fighter aircraft which can be used for preliminary design purposes. The weight of the
avionics was taken to be 3% of the empty weight of the aircraft and the density of the avionics was taken to be 30
lbs/ft3.6 The military payload weight was given by the requirements in the early design phase of the aircraft while the
volume was taken from the known dimensions of a GBU-32 smart bomb7. Finally, the fuel volume needed for the
aircraft was calculated using the previously known fuel weight of 19,657 lbs and the density of JP-8 military fuel
taken to be .775 kg/L8.
B. Design Choices
Using the known volumes of the various components inside the fuselage, the fuselage cross section and length
can be considered. The most important parameter in the design of the fuselage itself is fineness ratio. This ratio is
defined as the length of the fuselage divided by the diameter. Using Roskam’s table of values for fineness ratio
found in Table 4.1 of Part II of his design book series, a fineness ratio of 10 was selected for this aircraft9. Due to the
supersonic requirements of the vehicle’s mission, a longer, thinner fuselage section is desired because it will
6Raymer, Daniel P. Aircraft Design: A Conceptual Approach. Reston, VA: American Institute of Aeronautics and Astronautics, 1999. Print.7 "Joint Direct Attack Munition (JDAM) GBU-29, GBU-30, GBU-31, GBU-32."Joint Direct Attack Munition (JDAM) GBU-31. N.p., n.d. Web. 6 Nov. 2014. http://fas.org/man/dod-101/sys/smart/jdam.htm. 8 Schmigital, Joel, and Jill Tebbe. JP-8 and Other Military Fuels. Rep. N.p., 12 Jan. 2011. Web. 8 Nov. 2014. www.dtic.mil%2Fcgi-bin%2FGetTRDoc%3FAD%3DADA554221. 9 Roskam, Jan. Preliminary Configuration Design and Integration of the Propulsion System. Lawrence, Kan.: DARcorporation, 2004. Print.
The properties such as the wing area, aspect ratio, span of the wing, and thickness to chord ratio come from
previous weight sizing and constraint sizing analysis. The incidence angle and dihedral angle of the wing are chosen
to be zero in order to optimize performance and control of the aircraft during high speed flight. Finally, the sweep
41
angle and taper ratio of the wing were chosen based on the F-16 data displayed in Roskam’s Table 6.9 in Part II of
his design series.12
D. Flap Design
Before the full wing can be designed and modeled, the control surfaces that will be placed on the wing must be
sized and located. The first of these control surfaces that must be designed is the flaps on the wing. During takeoff
and landing, the vehicle requires a large cL,max than can be produced by a plain wing. Therefore, flaps are needed to
increase the lift on the vehicle and either help it get in the air on takeoff or help it slow down upon landing. In order
to decide which flaps to use and how to size these flaps, a process was used to determine the change in C l,max that
each flap would produce. First, the change in cL at takeoff and landing was calculated using Eqn. 27. The values of
CL,max for takeoff and landing were taken from the previously assumed values during the constraint analysis.
Table 30: Maximum Lift Coefficients
CL,max,TO CL,max,L
1.8 2.2
ΔC Lmax ¿ /L
=1.05(CLmax¿ / L
−CLmax) (27)
Then, the required increase in cl,max due to the flaps being lowered was calculated using Eqn. 28.
Δcl max=
ΔC Lmax∗S
Swf
K Λ
(28)
The value KΛ accounts for the effect of sweep angle when the flaps are down and can be calculated using Eqn. 29.
K Λ=(1−.08 cos Λ c4
2)cos Λc /43/4
(29)
The ratio of the main wing area to the flap area can be estimated using multiple values between zero and one and
running the calculations multiple times. The necessary increase in c l due to flap deflection can be calculated by Eqn.
30.
Δcl=1K
Δclmax(30)
12 Roskam, Jan. Preliminary Configuration Design and Integration of the Propulsion System. Lawrence, Kan.: DARcorporation, 2004. Print.
42
The factor K can be found for each type of flap using Fig. 7.4 in Roskam’s Part II13. Finally, the increase in cl due to
the flaps can be calculated using Eqn. 31.
Δcl=c l∝∝δ f
δ f (31)
The value of αδ,f is the section lift effectiveness parameter and can be found using Fig. 7.8 in Roskam 14. The δf
represents the flap deflection. For this aircraft, Swf/S of .84 and a flap chord to main wing chord ratio, c f/c, of .30
were chosen. Due to the high change in lift needed, Fowler flaps were chosen to be placed on the wing. The result of
these calculations is shown in Table 30 below.
Table 31: Flap Sizing Values
KΛ Swf/S bf/b K αδ,f δf (°)
Takeoff .74 .4 .75 .92 .53 25
Landing .74 .4 .75 .92 .46 40
The result of these calculations was a Fowler flap covering 75% of the span and 40% of the wing area. The flap
would be deflected 25° at takeoff and 40° at landing.
E. Aileron Design
The other necessary control surface to place on the wing is the ailerons. Unlike the flaps, for this initial design,
the aileron sizing was taken from historical data provided by Roskam for fighter aircraft in Table 8.9b in his Part
II.15 Using the values in this table as a base point, the aileron was chosen to be at the tip of the wing. The size is
shown in the final 2D modeling.
F. Wing Mode
With the flaps and the ailerons designed, the wing was then designed and modeled in three different views. One
half of the wing is shown with the other half being symmetrical with respect to the midline of the aircraft. The three
views of the main wing are shown in Figs. 23, 24, and 25.
13 Roskam, Jan. Preliminary Configuration Design and Integration of the Propulsion System. Lawrence, Kan.: DARcorporation, 2004. Print.
14 Roskam, Jan. Preliminary Configuration Design and Integration of the Propulsion System. Lawrence, Kan.: DARcorporation, 2004. Print.
15 Roskam, Jan. Preliminary Configuration Design and Integration of the Propulsion System. Lawrence, Kan.: DARcorporation, 2004. Print.
43
Figure 23: Main Wing Top View
Figure 24: Main Wing Side View
Figure 25: Main Wing Front View
G. Final Wing Design Summary
The result of this wing analysis and design was a wing of span 30.6 ft, area of 374 ft 2, 45° quarter chord sweep,
with Fowler flaps along 75% of the span and ailerons near the wing tips. Two spars were added into the wing as can
44
be seen in the top view of the wing. The leading edge spar is placed at .5% of the chord while the second spar is
placed just before the control surfaces.16 In many aircraft, fuel is stored in the wings but for this design, all the
mission fuel necessary was placed inside the fuselage. This design choice was made in order to minimize the weight
and thickness of the wing with the goal of maximizing supersonic performance. In the future, this wing may need to
be altered slightly to account for the position and weight of the vehicle’s engines. However, at this time, the wing
meets all requirements and design choices and can be used for a preliminary modeling layout.
X. Tail Design
The final vehicle component that must be designed during this stage is the vehicle’s tail. This part of the vehicle
is critical for its contribution to stability and control, future weight and balance of the vehicle, as well as a lesser
contribution to lift. In the preliminary configuration analysis, a v-tail was chosen for its high velocity performance
and minimal drag.
A. Tail Configuration
The process by which the tail was designed was the volume coefficient method. Assumptions were made about
the moment arm of the horizontal and vertical tail as well as the volume coefficient of the horizontal and vertical tail
in order to determine the area of the tail required. The area of the horizontal and vertical tail can be calculated
separately using Eqns. 32 and 33.
Sh=V h S c
xh
(32)
Sv=V v Sb
xv
(33)
Because the tail is a v-tail, the horizontal and vertical surface areas must then be combined into one surface with a
dihedral angle that can be calculated easily using Eqn. 34.
Γh=tan−1 Sv
Sh
` (34)
The final values from these calculations are shown in Table 31.
Table 32: Volumetric Coefficient Method
x V S dihedral (°)
Horizontal 20 0.3 68.60 38.1
16 Roskam, Jan. Preliminary Configuration Design and Integration of the Propulsion System. Lawrence, Kan.: DARcorporation, 2004. Print.
45
Vertical 20 0.094 53.74 38.1
B. Tail Geometry Specifications
After the surface areas and dihedral angle for the tail have been calculated, the next step in the process was to
choose the geometric parameters which would define the shape of the tail. These parameters include the incidence
angle, the aspect ratio, the sweep angle, the thickness ratio, the airfoil, and the taper ratio. These choices were made
based on the previously designed main wing as well as values taken from Roskam’s Tables 8.13 and 8.14 in Part II. 17The final values chosen for the tail geometry are shown in Table 32.
Table 33: Tail Sizing Values
AR Sweep (°) taper t/c airfoil incidence (°)
3 40 .3 .04 NACA 64-204 0
C. Tail Control Surfaces
Similarly to the design of the main wing, before the tail can be fully designed and modeled, the control surfaces
that will be placed on the tail must be sized and located. Due to the designed tail being a v-tail, the two control
surfaces normally on the horizontal and vertical tail of an airplane, the elevators and the rudder, were combined into
one control surface which controlled both pitch and yaw motion. The basis for the these sizing and locating
decisions was the data provided in Roskam’s Table 8.9a and 8.9b in Part II18. The v-tail control surfaces for this
aircraft were based on the control surfaces of similar style fighter aircraft. By this reasoning, the entire length of the
span of the v-tail was used for the ruddervator. The final control surface design and placement can be seen in the
design model of the tail.
D. Tail Model
With finalized values for the tail and control surface sizing, the final tail can be designed and modeled. Only one
tail is shown in these models with the other tail being a reflection across the center of the aircraft. The three views of
the tails are shown in Figs. 26, 27, and 28.
17 Roskam, Jan. Preliminary Configuration Design and Integration of the Propulsion System. Lawrence, Kan.: DARcorporation, 2004. Print.18 Roskam, Jan. Preliminary Configuration Design and Integration of the Propulsion System. Lawrence, Kan.: DARcorporation, 2004. Print.
46
Figure 26: Tail Top View
Figure 27: Tail Side View
47
Figure 28: Tail Front View
E. Final Tail Design Summary
The result of the tail design process is a v-tail on each side of the midline of the aircraft with a height of 4.31 ft, a
width of 5.50 ft, and a length of 5.86 feet. The ruddervator is located at the back of this v-tail and will be used to
control both pitch and yaw of the vehicle. While this may require a more complicated feedback response controller
and sensors, the v-tail gives much better performance in the conditions required for this mission. This tail will likely
be moved and resized in the weight and balance process but for this preliminary design, the v-tail meets all
requirements and chosen parameters and can be used to model the first stage of the design.
XI. Final Design Summary
Once all three major vehicle components had been sized, designed, and modeled, they could be combined to
create the first working visual model of the full aircraft. This aircraft will need much more analysis and repetitive
iteration through all steps of the design but with this model, the design can proceed into more detailed design work.
F. Final Model
The final model of the preliminary design for the uninhabited long range strike vehicle is shown in Fig. 29.
48
Figure 29: Vehicle Top View
The result of combining the three components designed in this initial design phase is a vehicle that somewhat
resembles a large missile. This is realistic because at the high supersonic speeds this vehicle is designed for, the
vehicle shape needs to be streamlined and narrow to reduce the impact of the wave drag. One important parameter
that must be analyzed with the final configuration is the supersonic or subsonic leading edge of the vehicle. A
supersonic leading edge results in shocks forming on the surface of the wing. In order to greatly reduce the
disturbances across the wing, the leading edge must be contained within the Mach cone that the vehicle creates in
flight. All flow within this cone is initially subsonic so the leading edge of the vehicle wing will interact with
subsonic flow. The relationship to calculate the Mach cone of the vehicle is shown in Eqn. 35.
μ=sin−1 1M
(35)
At Mach 2, this cone is 30° on either side of the line of symmetry of the aircraft. The angle between the nose of
the aircraft and the leading edge of the tip chord is shown in Fig. 30.
49
Figure 30: Vehicle Subsonic Leading Edge
G. Neutral Point
One crucial point on the aircraft to determine from this initial design is the neutral point. The neutral point is the
point on the aircraft which defines the location of the center of gravity which would be statically neutral. The neutral
point is a critical factor in computing the longitudinal static stability of the entire aircraft. The distance between the
center of gravity and the neutral point is called the static margin and is a measure of this stability. If the neutral point
is not behind the center of gravity, then the vehicle is unstable. In order to find the neutral point for this
configuration, the coefficients of lift, coefficients of moment, and other geometric factor were used. The
relationships used to find the neutral point are shown below in Eqns. 36, 37, 38 and 39.
CL ,α , w=C l , α , w
1+Cl , α ,w
π ARw
(36)
CL ,α ,t=Cl , α ,t
1+C l ,α , t
π AR t
(37)
dεdα
=2CL, α ,w
π ARw
(38)
xNP
c=
x AC
c+η V H
cL ,α ,t
cL ,α , w
(1− dεdα
) (39)
50
The values used in these calculations are shown in Table 33. The results of the neutral point calculations are
shown in Table 34.
Table 34: Neutral Point Analysis Values
c xac/c CM,α,f Cl,α,w Cl,α,t η VH ARw ARt
12.2 .25 -.24 6.11 6.11 1 .3 2.5 3
Table 35: Neutral Point Calculations
de/dα cL,α,t cL,α,w XNP/c c XNP
.875 3.71 3.44 .360 12.2 5.54
Using these values, the neutral point of the aircraft is calculated to be 5.54 ft past the leading edge of the main
wing. This means that the center of gravity of the wing must be in front of this point in order for the vehicle to be
stable. The location of the neutral point on the vehicle is shown in Fig. 31 below.
Figure 31: Neutral Point Location
XII. Landing Gear and Weight and Balance
The final step in the preliminary design process is the design and addition of landing gear to the aircraft and
then the process of determining the weights of each component to determine the center of gravity of the vehicle.
51
This step allows for a finalized preliminary design of the vehicle to be completed with basic consideration for
important factors like stability. It is possible, during this process, to determine that the entire designed aircraft is
unfeasible and cannot be fixed without major redesign of one or more of the components.
A. Component Weight Breakdown
The first step in this process was to determine the weights of each of the individual components being placed
into the fuselage. This step is necessary because a weighted center of gravity for each of these components will
produce the center of gravity for the overall aircraft. Weights were calculated for the various systems and then
specific components by using data taken from Roskam’s Part V19. The values chosen for this analysis were taken
from the F-18 Hornet due to its similar style and performance capabilities. The most important value for this
analysis was the flight design gross weight, WG. The ratios used to determine these weights are shown in Table 35