1. Flight Vehicle Design
Instructor
Dr. Pete Gall
Long Range Business Jet Design Proposal
Submitted by:
The Jets:
Tyler Hartman
Amine Aguissane
Andrew Wilhelm
Bob Hamilton
Charles Junghans
December 10, 2012
2. Abstract
This report details the approach taken for the conceptual design of a long range business class jet. The
purpose of this account is to summarize the design process of the many intricate steps which were a part
of this design procedure. The aircraft detailed in this report meets all requirements and specifications
from the request for proposal acquired from the manufacturer. The ten chapters included in this summary
each represent the detailed step by step conceptual analysis taken by the team to achieve the end design.
Seeded in this ten chapter chronicle are the preliminary reports written in response to the order of the
performed design progression. The foremost objective of this report is to provide all necessary steps for
design process replication while delivering the desired knowledge to the investing organization, and any
other persons of interest. As stated before, by the end of this analysis, a completed aircraft design
meeting all initial specifications will be generated. Throughout the report, CAD drawings will be
displayed to show the aircraft development.
3. Contents
Abstract.............................................................................................................................................2
Contents.............................................................................................................................................3
List of Symbols ..................................................................................................................................6
Chapter 1: Mission Specifications & Comparative Study......................................................................9
1.1: Mission Specifications .............................................................................................................9
1.1.1: Design Specifications ........................................................................................................9
1.1.2: Technical & Economic Feasibility....................................................................................10
1.2: Comparative Study of Similar Aircraft....................................................................................10
1.2.1: Gulfstream G550.............................................................................................................11
1.2.2: Gulfstream G650.............................................................................................................11
1.2.3: Bombardier Global 5000..................................................................................................12
1.2.4: Bombardier Global 6000..................................................................................................13
1.2.5: Bombardier Global 7000..................................................................................................14
Chapter 2: Estimation of Takeoff Gross Weight .................................................................................16
2.1: Mission Weight Estimates......................................................................................................16
2.1.1: Determination of Regression Coefficients .........................................................................16
2.1.2: Determination of Mission Weights ...................................................................................17
2.1.3: Manual Calculation of Mission Weights ...........................................................................18
2.1.4: Calculation of Mission Weights .......................................................................................19
2.2: Takeoff Weight Sensitivities ..................................................................................................21
Chapter 3: Wing Loading & Performance Analysis ............................................................................23
3.1: Calculation of Performance Constraints ..................................................................................23
3.1.1: Takeoff Distance.............................................................................................................23
3.1.2: Landing Distance ............................................................................................................24
3.1.3: Single Engine Climb .......................................................................................................25
3.1.4: Begin & End Cruise ........................................................................................................27
3.1.5: Descent (Power-off Glide)...............................................................................................28
3.2: Performance Constraint Summary ..........................................................................................29
Chapter 4: Main Wing Design ..........................................................................................................31
4.1: Comparative Study of Similar Aircraft....................................................................................31
9. Chapter 1: Mission Specifications &
Comparative Study
1.1: MissionSpecifications
The request proposal given to the design team contains all the basic requirements. These
requirements can be summarized in the performance characteristics of an aircraft and covers many
important aspects: the range that can be expressed in nautical miles (nm). The payload describes the
number of passengers, crew members, luggage, and fuel weight. The climb performance gives the rate of
climb, ceiling, cruise altitude, etc. Also stated, is the maximum and normal operating speed and the
take-off and landing field length limitations.
1.1.1: Design Specifications
This request for proposal asks for a conceptual design of a business class aircraft with a capacity
of 6 passengers arranged with luxury first class seating, plus crew members (2 pilots and 1 flight
attendant). The proposal also requires full compliance with Part 91 Federal Aviation Regulations. Other
technical specifications for this aircraft are given in Table 2.1.
Table 1.1: Aircraft Design Specifications
Max cruise altitude (feet) 41,000
Range (nm) 6,000
Holding(contingency) fuel (min) 30
Reserve fuel (min) 45
Cruise Mach 0.9
Payload Pilots 2
Flightattendants 1
Passengers 6
Takeoff Distance (feet) 7,000
LandingDistance (feet) 7,000
Having the specifications, we can draw a flight plan showing the mission profile based on the table above.
10. Figure 1.1: Flight Mission Profile
The mission profile is broken down into intermediate steps. These steps include taxi & takeoff, climb,
cruise, descent & holding, and finally landing. Breaking the profile down helps designate different fuel
ratios and weight losses throughout the flight. This break down will help guide the design team to
successful accomplishment of the requested proposal.
1.1.2: Technical & Economic Feasibility
Given existing technology, an aircraft that would meet the design specifications should be
technically and economically feasible. Several long range business class jets meet the range, fuel, and
payload requirements. Improvements and applications of newer technologies, there is a design that
should meet the remaining, additional requirements.
1.2: Comparative Study of Similar Aircraft
When designing the aircraft comparative study is made on aircraft with similar flight conditions.
Since the aircraft being design is a long range business jet, the comparative study is made on aircraft of
this class. For this design the parameters in Chapter 2 must be met. After these design specifications are
understood, several aircraft are selected and then compared to find which aircraft best reflects the
specifications. The aircraft selected are shown in the next series of tables. These tables show how the
aircraft compare to the design specifications needed. Once this table is understood, it is evident the most
similar aircraft to the design specifications is the Gulfstream G650. When looking in depth at each
aircraft, the Gulfstream G650 will be the most heavily favored in the design process.
11. 1.2.1: Gulfstream G550
The Gulfstream G550 is a more advanced version of the Gulfstream 500 series. This version
supports are larger range and larger fuel capacity. Along with that, the G550 has an increase cruise speed.
The aircraft is also equipped with a complex flight computer that allows for landing under low visibility
conditions. The general design specifications for this aircraft are presented below.
Table 1.8: Design Specifications for Gulfstream G550
Gulfstream G550
Maximum Takeoff Weight 91,000 lbs
Gross Weight 48,300 lbs
Landing Weight 75,300 lbs
Maximum Rated Thrust 30,770 lbf
Optimum Cruise Altitude 41,000 ft
Cruise Mach 0.85 mach
Fuel Weight 41,300 lbs
Useful Load 6,200 lbs
Also, the geometric parameters for the Gulfstream are listed in the following table.
Table 1.9: Gulfstream G550 Geometric Parameters
Gulfstream G550
Wing Area 1,265 ft2
Wing Loading 78.9 lb/ft2
Aspect Ratio 7.5
Wing Sweep 34 deg
Tail Configuration T-tail
Engine Configuration Twin Jets
1.2.2: Gulfstream G650
The Gulfstream G650 is the newest G-series corporate jet. This aircraft is similar to the G550 but
is more equipped and has all-around performance improvements. The general design specifications are
shown in the table below.
12. Table 1.10: Design Specifications for Gulfstream G650
Gulfstream G650
Maximum Takeoff Weight 92,125 lbs
Gross Weight 48,215 lbs
Landing Weight 75,430 lbs
Maximum Rated Thrust 32,200 lbf
Optimum Cruise Altitude 51,000 ft
Cruise Mach 0.85 mach
Fuel Weight 41,550 lbs
Useful Load 6,345 lbs
Along with the specific design specifications, the geometric parameters for this aircraft are also listed.
These are shown in the following table.
Table 1.11: Geometric Data for Gulfstream G650
Gulfstream G650
Wing Area 1,283 ft2
Wing Loading 77.7 lb/ft2
Aspect Ratio 7.7
Wing Sweep 36 deg
Tail Configuration T-tail
Engine Configuration twin jets
1.2.3: Bombardier Global 5000
The next aircraft analyzed is made by the Bombardier aircraft company. This design was
introduced in 2002 and was designed to fly non-stop for long distances. The interior can be loaded with
up to 19 passengers when load economically. Along with this, the flight computer is equipped with a
heads up LED display. The specific design parameters for this aircraft are shown in the next table.
13. Table 1.12: Design Specifications for Bombardier Global 5000
Bombardier Global 5000
Maximum Takeoff Weight 92,500 lbs
Gross Weight 56,000 lbs
Landing Weight 69,750 lbs
Maximum Rated Thrust 29,500 lbf
Optimum Cruise Altitude 51,000 ft
Cruise Mach 0.85 mach
Fuel Weight 39,250 lbs
Useful Load 1,775 lbs
Also, the geometric parameters of the aircraft are needed. These are presented in the table below.
Table 1.13: Geometric Data for Bombardier Global 5000
Bombardier Global 5000
Wing Area 1,022 ft2
Wing Loading 95.9 lb/ft2
Aspect Ratio 7.8
Wing Sweep 35 deg
Tail Configuration T-tail
Engine Configuration twin jets
1.2.4: Bombardier Global 6000
This improved version of the 5000 series is most noted for its refueling time improvement. This
aircraft can be refueled 15 minutes faster than the 5000 series. Also, this aircraft has improved general
specifications. These specifications are listed in the following table.
Table 1.14: Design Specifications for Bombardier Global 6000
Bombardier Global 6000
Maximum Takeoff Weight 92,440 lbs
Gross Weight 55,400 lbs
Landing Weight 69,950 lbs
Maximum Rated Thrust 31,250 lbf
Optimum Cruise Altitude 51,000 ft
Cruise Mach 0.85 mach
Fuel Weight 39,500 lbs
Useful Load 1,850 lbs
14. In hand with the specific specifications for the aircraft, the geometric parameters are necessary. These
parameters are shown as follows.
Table 1.15: Geometric Data for Bombardier Global 6000
Bombardier Global 6000
Wing Area 1,110 ft2
Wing Loading 94.7 lb/ft2
Aspect Ratio 7.5
Wing Sweep 36 deg
Tail Configuration T-tail
Engine Configuration twin jets
1.2.5: Bombardier Global 7000
The final Bombardier jet featured a much more spacious interior. Along with this, the jet was
modified to burn less fuel at higher altitudes. This, in turn, increased the range of the aircraft. The
specific design specifications for this aircraft are listed below.
Table 1.16: Design Specifications for Bombardier Global 7000
Bombardier Global 7000
Maximum Takeoff Weight 93,000 lbs
Gross Weight 54,300 lbs
Landing Weight 68,850 lbs
Maximum Rated Thrust 32,000 lbf
Optimum Cruise Altitude 51,000 ft
Cruise Mach 0.85 mach
Fuel Weight 39,495 lbs
Useful Load 1,770 lbs
Along with these specifications, the geometric parameters for this aircraft are necessary. These are
displayed in the following table.
15. Table 1.17: Geometric Data for Bombardier Global 7000
Bombardier Global 7000
Wing Area 1,300 ft2
Wing Loading 95.7 lb/ft2
Aspect Ratio 7.7
Wing Sweep 35 deg
Tail Configuration T-tail
Engine Configuration twin jets
16. Chapter 2: Estimation of Takeoff Gross
Weight
2.1: MissionWeight Estimates
The requested proposal given to the team includes the basic requirements for the weight estimates
phase of design. These requirements will specify the role of the aircraft and help draw a mission profile
to keep track of the changing weight. To determine the total amount of fuel used during the mission, the
amount of fuel used during each flight phase needs to be known. For each of these phases, the fuel used
is represented as a fraction (the ratio of the fuel weight leaving to the fuel weight entering). The fractions
for takeoff, climb, and landing can be estimated using empirical data. The Breguet Range & Endurance
Equations will be the method to calculate other needed fuel fractions.
πΉπ’ππ πΉππππ‘πππ = (
π π
ππ
) ππ’ππ (2.1)
Figure 2.1: Mission Profile
2.1.1: Determination of Regression Coefficients
Taking the data collected from the comparative aircraft study in Report No. 1, a structural factor
was able to be computed. The structural factor is the percentage of the total weight of the aircraft that is
needed for the structure. From this graph, βoutliersβ can be determined. The outliers are the aircraft that
17. will be discarded from interest for the design team due to structural factors being out of range of design.
For this application, the outliers can be determined to be the Bombardier Global series. Figure 2.2 shows
the structural factor data.
Figure 2.2: Structural Factor Data
2.1.2: Determination of Mission Weights
The mission profile includes five phases. These phases are takeoff, climb, cruise, loiter, and landing.
To determine the weight of the fuel needed for each of these phases, the fuel fraction method will be used,
along with the Breguet Range and Endurance Equations. The first step is to estimate the takeoff gross
weight. Once this has been done, empirical data is used to approximate the takeoff and climb fuel
weights. Then using the Breguet Range Equation, the cruise fuel weight is calculated. The next step is to
determine the landing fuel weight. This is done by again approximating the fuel fraction from historical
data. Finally the holding fuel weight is needed. The Breguet Endurance Equation is used to calculate this
ratio.
18. 2.1.3: Manual Calculation of Mission Weights
Fuel fractions for the phases are calculated in the following section of this report by empirical
estimation and analytical calculation. The aircraft will be cruising at 41,000 ft. and the fuselage will be
designed to fly three crew members along with six passengers. Using an average passenger weight of
195.6 lb., the total payload weight is calculated to be 1805 lb. The estimated takeoff weight is 85,000 lb.
and an aspect ratio of 7 is used.
1. Taxi & Takeoff: The fuel fraction can be estimated using a historically based empirical relation.
Generally the fuel used in this phase ranges from 2.5 to 3 percent of the total take-off weight.
The fuel fraction used is 0.98, which corresponds to 1700 lb. of fuel.
2. Climb: The estimated climb fuel fraction is also found from empirical data as a function of the
cruise Mach number. The climb and acceleration fuel fraction used is 0.98, and the fuel weight
calculated is 1666 lb.
3. Cruise: For this flight phase we can determine the fuel fraction analytically using the Breguet
Range Equation to find the fuel burned throughout the cruise. The lift-to-drag cruise ratio is first
needed.
πΏ
π· πΆππ’ππ π
= 0.94
πΏ
π· πππ₯
= 0.94( π΄π + 10) (2.2)
Next, the Breguet Range Factor, B, is needed. This is given by the equation,
π΅ =
π πΆπ
ππΉπΆ
β
πΏ
π· πΆππ’ππ π
= (
516.2
0.6
) (17) = 13,748.43 (2.3)
Where Vcr is the cruise velocity and SFC is the engine specific fuel consumption. Then, the
cruise fuel weight is calculated by,
ππ,πΆππ’ππ π = (1 β
1
π
π
π΅β
) ππΈππ‘ππ =(1 β
1
π
6000
13748.43β
)(81634) = 28,869.8 ππ. ππ’ππ (2.4)
where R is the range of the aircraft in nautical miles (nm).
19. 4. Loiter: This phase ensures the aircraft includes enough fuel for any delay prior to landing. The
Breguet Endurance Equation will help find the fuel fraction related to the loiter phase. The
Breguet Endurance Factor, Be is first needed. This is given by the equation,
π΅π =
1
ππΉπΆ
β
πΏ
π· πΆππ’ππ π
= (
1
0.6
)(17) = 28.333 (2.5)
Next, the holding fuel weight can be calculated by,
ππ,π»πππ = (1 β
1
π
πΈ
π΅β
) ππΈππ‘ππ = (1 β
1
π
0.5
28.33β
) (85000) = 2,250 ππ. (2.6)
where E is the holding time in hours (hr).
5. Approach and Landing: This is the final phase of the flight plan. Using similar historical
empirical data, the fuel fraction for landing can be approximated as 0.975. The landing fuel
weight was calculated to be 1,320 lb.
It is standard practice to err on the side of caution. Because of this practice, it is practical to dictate space
and weight for reserve fuel, in case of any emergency or unpredicted event. This reserve fuel for a period
of time (Ξt) in hours, can be calculated with the following equation:
ππ,π ππ πππ£π = (
ππΉπΆβπ₯π‘
πΏ
π·β
) β ππΈππ‘ππ = [
(0.6)(0.75)
17
](85000) = 2,250 ππ. (2.7)
These fuel weights and the payload weight total to 39,096.68 lb. This leaves 45,903.32 lb. available for
structure and yields a structural factor of 0.54.
2.1.4: Calculation of Mission Weights
The calculations from the previous section were tabulated in a spreadsheet for easier viewing and
manipulating. The main inputs and parameters are given by Table 2.1.
20. Table 2.1: Estimation of Takeoff Weight Parameters
Estimation of Take Off Weight
Specifications Aircraft
Cruise Mach 0.9
Cruise Altitude 41000
Range 6000
Engine SFC 0.6
Aspect Ratio 7
Holding 30
Reserve 45
Structural Factor 0.54
L/D 17
V 516.2
Breqeut Range Factor 13,748
Crew 3
Passengers 6
Avg Passanger Weight 195.6
Total Payload Weight 1804.9
Brequets End Factor 28.33
The fuel weights were then calculated by the fuel fraction method and the two Breguet Equations to
determine the total empty and structure weight along with the structural factor. Table 2.2 shows these
calculations.
21. Table 2.2: Fuel Weight Calculations
Fuel Fraction Method
Flight Phase Fraction Weight
Take Off Weight 85,000
Start up and Take off 0.98 83,300
Climb and Acceleration 0.98 81,634
Cruise 28,870 52,764
Descent and Landing 0.975 51,445
Reserve 2250 49,195
Holding 1,487 47,708
Total Fuel Weight 37,292
Total Fuel and Payload Weight 39,097
Weight Available for Structure 45903
Weight Required for Structure 45900
Difference 3.317
2.2: Takeoff Weight Sensitivities
It has been calculated that the estimated takeoff weight with a range of 6000 nautical miles and
aspect ratio of 7, which is what the team is using for this design, is 85000 lbs. It was asked that the team
determine what would happen to the takeoff weight if the range is changed and the aspect ratio kept the
same and the range kept the same and aspect ratio changed. The new values where for the range 5000,
6000, and 7000 nautical miles and for the aspect ratio of 6, 10, and 14. It can be seen from figure 2.3 that
when the range is increased the takeoff weight also drastically increases with it. On the other hand it can
be seen in figure 2.3, that when the aspect ratio is increased, the takeoff weight drastically decreases.
22. Figure 2.3: Range vs. Takeoff Weight
Figure 2.4: Aspect Ratio vs. Takeoff Weight
0
1000
2000
3000
4000
5000
6000
7000
8000
41000 85000 105000
Range
Takeoff Weight
Range vs. Takeoff Weight
0
10000
20000
30000
40000
50000
60000
70000
80000
90000
100000
6 10 14
AspectRatio
Takeoff Weight
Aspect Ratio vs. Takeoff Weight
23. Chapter 3: Wing Loading & Performance
Analysis
3.1: Calculationof Performance Constraints
The following sections of this report will detail the methods used to calculate the wing loading of
the aircraft being designed. The loading on each phase of flight is calculated and the values are tabulated
in a spreadsheet for easier viewing and manipulating.
3.1.1: Takeoff Distance
For this section the team is calculating the distance that is needed for the aircraft to takeoff. The
team was given a restraint of taking off within 7,000 ft. This only a preliminary calculation and a more
refined estimate will be made later in the design process when more of the relevant parameters have been
determined. There are quite a few factors and equations that are needed to calculate the distance needed
to takeoff. The wing loading affects takeoff through the stall speed.
ππ = [
π
π
2
ππΆ πΏ πππ₯
]0.5 (3.1)
The next equation is the velocity required for takeoff.
πππ = 1.2ππ = 1.2[(
π
π
) ππ
2
ππΆ πΏ πππ₯
]0.5 (3.2)
This next equation is determining the takeoff parameter.
πππ = (
π
π
) ππ
1
πΆ πΏ πππ₯
(
π
π
) ππ
1
π
(3.3)
Where Ο is the ratio of the air density at the takeoff site to that at sea level,
π =
π ππ
π ππΏ
(3.4)
24. Note that the thrust-to-weight ratio, T/W, is a function of altitude as well. With this correlating factor, the
empirical estimate of the take-off-distance, sTO.
π ππ = 20.9( πππ) + 87β(πππ)
π
π
(3.5)
It is clear from the above equations that having an excessively large wing loading at takeoff can lead to
larger takeoff distances. Two parameters that can be used to control the takeoff distance are thrust-to-
weight ratio and the maximum lift coefficient.
Table 3.1: Takeoff Parameters
3.1.2: Landing Distance
For this section the team is calculating the distance that is required to land the aircraft that has
been proposed for design. The team was given a restraint of landing within 7,000 ft. This is only a
preliminary calculation and a more refined estimate will be made later in the design process. There are
only a few equations that are needed to make this calculation. This first equation gives a correlating
factor called the landing parameter that relates the wing loading to the landing distance.
πΏπ = (
π
π
) πΏ
1
ππΆ πΏ πππ₯
(3.6)
25. With this equation it is now possible to go ahead and calculate the landing distance, sL.
π πΏ = 118( πΏπ) + 400 (3.7)
It can been seen from these two equations that to attain a short landing distance there either needs to be a
small wing loading at landing or a higher CLmax. This is obviously what is required for this design then
considering that the given landing distance needs to be within 7,000 ft. which is a relatively short
distance.
Table 3.2: Landing Distance Parameters
3.1.3: Single Engine Climb
For our design we have to take into account the wing loading effect on climb. FAR specifications
choose the rate of climb for each aircraft type for different conditions (All engines operating, one engine
out, landing gear up or down, etc.).This will lead us to determine the engine out or single engine climb
performance. This means that we can get the exact wing loading required if we lose one engine to be able
to have a gradient of 3 degrees while climbing. The equation is given,
πΊ = sin( πΎ) =
(πβπ·)
π
(3.8)
G is the climb gradient and represents the ratio between the vertical and horizontal distance traveled by
the aircraft.
26. W is the weight, T represents the thrust and the drag D can be determined for a subsonic climb by adding
the base drag π·0to the lift-induced drag π·π
π· = π·0 + π·π (3.9)
π·0 = πΆ π·0
ππ =
πππ
π
πβ
(3.10)
π·π = πΆ π·π
ππ =
πΆ πΏ
2
ππ
=
πΆ πΏ
2
ππ΄π π
ππ =
π2 π2
π2 ππ΄π π
ππ (3.11)
π
π
=
π·
πβ Β±β( π·
πβ )2β
4πΆ π·0
ππ΄π π
2
(πππ΄π π)β
(3.12)
Where, π·
πβ =
π
π
β πΊ (3.13)
The gradient is given by:
πΊ =
π
π
β (
ππΆ π·0
π
πβ
+
π
πβ
πππ΄π π
) (3.14)
Below, table 3.3 shows the parameters used to calculate the single engine climb performance.
Table 3.3: Single Engine Climb Parameters
27. 3.1.4: Begin & End Cruise
In this design, range is the primary design driver. Since the cruise portion of the flight is the
longest portion, the wing loading is selected to give optimum cruise conditions.
The governing equation is based on:
π
π
=
ππ2
2
β
πΆ π·0
2π
(3.15)
W is the weight at the beginning or end of cruise, depending on whether the aircraft is entering or ending
the cruise phase. S is the calculated wing area. V is flight speed. The mission specifications require a
Mach number 0.9 (515 knots, 869.22 ft/s) and a cruise altitude of 41,000 ft. The π at the required altitude
is, 0.00055982 sl/ft3
. Dynamic pressure, q, is given as 212.1 lbs/ft2. Also needed is k, given by the
equation,
π =
1
ππ΄π
(3.16)
Where A is found in the textbook Figure 2.4.
28. Throughout the cruise phase, the aircraft weight decreases by approximately 30 percent. The actual wing
loading at the end of cruise is denoted as W/Sactual. Equation 3.15 can be repeated using the weight at the
end of cruise to find the optimum wing loading entering the descent phase.
Table 3.4: Start Cruise Parameters
Table 3.5: End Cruise Parameters
3.1.5: Descent (Power-off Glide)
For a maximum range during glide descent, a minimum glide angle is required. This is achieved
when L/D is at its maximum. A relation for the drag is given by equation 3.18. Finding this condition
maximizes L/D, and we find the CL that minimizes drag.
π =
1
πΆ πΏ
πΏ
π
(3.17)
Substituting for drag, D, yields;
π· = π
πΆ π·0
πΆ πΏ
+ πππΆπΏ (3.18)
29. A free body diagram of the forces on the aircraft gives us equation 3.19 as a trigonometric function of the
glide angle.
sin( πΎ) =
π·
πΏ
cos(πΎ) (3.19)
The resulting effect of wing loading on the minimum glide angle is determined to need to be low for a
gliding aircraft.
Table 3.6: Glide Parameters
3.2: Performance Constraint Summary
Once the calculations pertaining to the aircraft wing loading performance is done, these
constraints are summarized. This is shown in the following table.
Table3.7: Performance Constraints
Final Performance Constraints
Take Off Distance 6,657 (ft)
Optimum Wing Loading for
Start of Cruise 131.8 (lb/ft2
)
Optimum Wing Area for
Start of Cruise 619.6 (ft2
)
Actual Wing Loading for
Start of Cruise 125.6 (lb/ft2
)
Optimum Wing Loading for
End of Cruise 131.8 (lb/ft2
)
Opt Wing Area for End of
Cruise 400.5 (ft2
)
Actual Wing Loading for End
of Cruise 81.18 (lb/ft2
)
Landing Distance 3,330 (ft)
Glide Rate of Descent 16.01 (ft/min)
30. As shown in the tables above both the takeoff and landing distances are within the required parameters.
The landing distance is much shorter than the takeoff distance. This is due to the large amount of fuel
burned during flight. This, in turn, increases the trust to weight ratio and decreases the weight to wing
area ratio. Both of these effects contribute the smaller landing distance. Along with the difference in
takeoff and landing distances, the wing loading during cruise is analyzed. The table above shows both the
optimum and actual wing loading under this flight condition. As seen, the optimum value is higher than
the actual value. Along with this, the optimum wing area is lower than the actual wing area value. This is
due to the fact under cruise condition the aircraft does not need as much wing area to produce necessary
lift. When the aircraft is at takeoff it is heavier since no fuel has been burned. It needs the extra wing
area to make the lift necessary to takeoff. Once at cruise, the aircraft does not need the extra wing. This
effect is seen in both the start of cruise calculation and the end of cruise calculation.
The final constraint discussed is the rate off descent under a power off condition. This is how fast the
aircraft will descent, under optimum conditions, should the engines fail. This rate is shown as the final
value in the table above.
31. Chapter 4: Main Wing Design
4.1: Comparative Study of Similar Aircraft
In this section there will be some images along with data from two of the aircrafts used in the
comparative study done at the beginning of this proposal. The two aircraft that will be analyzed here are
the two aircraft that most closely meet the requirements of the teamβs design. This way the team will be
given some insight into how their wing should look and some of the dimensions. The first aircraft that
will be studied has the most similar characteristics to the aircraft the team is designing. It is the
Gulfstream G650. The following figures and tables will provide information for this aircraft.
Figure 4.1: Front view of Gulfstream G650
32. Figure 4.2: Top view of Gulfstream G650
Figure 4.3: Side view of Gulfstream G650
Table 4.1: Interior Specifications for Gulfstream G650
Total Interior Length 53 ft. 7 in. / 16.33 m
Cabin Length 46 ft. 10 in. / 14.27 m
Cabin Height 6 ft. 5 in. / 1.95 m
Cabin Width 8 ft. 6 in. / 2.59 m
Cabin Volume 2,138 cu. ft. / 60.54 cu. m.
Usable Baggage Compartment Volume 195 cu. ft. / 5.52 cu. m.
Table 4.2: Exterior Specifications for Gulfstream G650
Height 25 ft. 4 in. / 7.72 m
Length 99 ft. 9 in. / 30.40 m
Fuselage Width 9 ft. / 2.74 m
Overall Span 99 ft. 7 in. / 30.36m
Wing Span 93 ft. 8 in. / 28.55 m
Wing Sweep 36 degrees
Wing Area 1,283 sq. ft. / 119.2 sq. m.
Aspect Ratio 7.7
33. This data collected will give the team some very good insight into some of the design specs for the
aircraft they are developing. There are a few things that are unfortunately missing such as the actual
airfoil cross-section used and the thickness of the wing. The next aircraft is second on the characteristic
similarity list of design parameters. This aircraft is the Bombardier Global 6000. The following figure
and tables will highlight important specifications found during the comparative study.
Figure 4.2: Bombardier Global 6000 Three View Drawing
Table 4.2: Interior Specifications for Bombardier Global 6000
Cabin Length 48.35 ft. / 14.7 m.
Max Cabin Width 8.17 ft. / 2.49 m.
Cabin Width 6.25 ft. / 2.11 m.
Cabin Height 6.25 ft. / 1.91 m.
Floor Area 335 sq. ft. / 31.1 sq. m.
Cabin Volume 2,140 cu. ft. / 60.6 cu. m.
Table 4.3: Exterior Specifications for Bombardier Global 6000
Length 99.4 ft. / 30.3 m.
Wingspan 94 ft. / 28.7 m.
Height Overall 25.5 ft. / 7.8 m.
Unlike with the Gulfstream, there was not much data available for the Bombardier. This is unfortunate,
but hopefully there is enough data that can be used from the Gulfstream for this section. Some of the data
found could also be useful in latter parts of design. Also, it should be noted that both airplanes
incorporate winglets in their design.
34. 4.2: Main Wing Design
After the comparative aircraft study is performed, the wing of the aircraft is designed.
This chapter deals with the design of the main lifting surface of the aircraft. This is the next logical step
in the conceptual design process. The wing design must match the mission requirements specified in the
previous reports. These requirements include weight, wing loading, etc. In the following sections, the
steps of conceptual wing design will be detailed.
4.2.1: Airfoil Selection
The first aspect that is taken into account when designing the wing is the airfoil used.
Typically the airfoil used for similar applications is a six or seven series NACA airfoil. These
airfoils are laminar flow airfoils that are designed with improved drag performance at the cruise
lift coefficient. These airfoils are ideal for more efficient flight. The airfoil chosen for this
design is the NACA 631-212. The lift coefficient with respect to angle of attack and the drag
coefficient with respect to the lift coefficient curves are shown in the following figures.
This airfoil was selected due to the drag bucket in the drag coefficient curve. The middle of this
bucket occurs at the cruise lift coefficient for the desired aircraft. This means it will produce the
least amount of drag at cruise which is desired to reduce fuel consumption. Some important
parameters were obtained once the airfoil was chosen. Table 4.5 shows these parameters.
35. Table 4.5: Airfoil Parameters
NACA 631-212 Data
Clmax
0.5306
ClΞ± 0.2
a.c. 0.25
Ξ±0L -2
CD0 0.005
rLE 1.807
Cl minD 0.4
(t/c)max 0.12
4.2.2: Aspect Ratio
From the comparative study it is evident that a middle ranged aspect ratio is required.
Along with that, a wing span of about one hundred feet is necessary. To find the aspect ratio of
the aircraft the following relationship is used.
π΄π =
π2
π
(4.1)
From this equation it is evident that high aspect ratio wings are long and narrow. Along with
that, low aspect ratio wings are short and fat. High aspect ratio wings produce less induced drag
but have several problems. They required a stronger structure to deal with the increased bending
stress put on the wing. Also, they have a higher parasitic drag than low aspect ratio wings. This
comes from the increase in surface area exposed to the fluid flow around the wing. Finally, high
aspect ratio wings have a much lower roll rate. This is due to the large moment of inertia that
must be overcome when performing a roll maneuver. Because of this, high aspect ratio wings
must have large aileron control surfaces.
36. 4.2.3: Thickness
The next aspect of wing design that is taken into account is the thickness of the wing.
This is important when dealing with critical Mach issues. The wings need to be thin enough to
avoid this effect but be thick enough to contain the fuel required for flight. To get an idea for the
optimum thickness of the wing the following expression is used.
ππ€πππ = πβ1β
π‘
π
(4.2)
This equation shows that the weight of the wing is directly related to the square root of the
thickness ratio multiplied by a constant. From here it is found that the ideal thickness for the
wing is around 12%.
4.2.4: Wing Sweep
Along with the thickness of the wing, the sweep of the wing is a very important design
aspect. As described above sweep is added to the wing to avoid critical Mach problems. Critical
Mach is the speed at which the aircraft generates a shock on the wing. In the ideal case, a flat
plate, this critical Mach is the speed of sound. This changes when thickness is added to the
wing. The increase in thickness accelerates the flow over the wing faster than that of the aircraft
velocity. This increase in acceleration can cause a point on the wing to hit Mach one before the
aircraft up to that speed. To deal with this problem a sweep angle is introduced to the wing.
This deals with the problem by reducing the speed of the flow over the wing which is shown by
the formula below.
π πππ = πβ cos( π¬ πΏπΈ) (4.3)
37. This shows that the Mach number flowing over the wing is reduced by the leading edge sweep.
The necessary leading edge sweep for the aircraft is found from this expression. The following
table shows the sweep angles chosen and calculated for the wing design.
Table 4.6: Wing Sweep Angles
Sweep Angles
ΞLE (deg) 36
Ξc/4 (deg) 33.64
ΞTE (deg) 25
4.2.5: Taper Ratio
Following the sweep of the wing, the taper ratio for the wing is found. This is ratio of the
tip chord to the root chord. The expression for taper ratio is shown in the next equation.
π =
ππ‘
π π
(4.4)
The goal of tapering the wing is to improve the Oswaldβs efficiency of the wing. The ideal case
is an elliptical wing. Tapering the wing from a straight wing improves the efficiency of the wing
closer to the ideal case. The optimum taper ratio for a wing falls between 0.3 and 0.45.
4.2.6: Incidence & Twist
Twisting the wing goes in hand with the wing sweep. As sweep is added to the wing so
is span wise flow. This flow starts at the root of the wing and flows towards the tip. This causes
a buildup of pressure towards the tips of the wing. This, in turn, generates a higher load at the
wing tips which is the exact opposite of what is desired. The increased load at the tips will make
the tips of the wings stall before the root. When the tips stall before the root, the aircraft is much
more likely to enter an unstable deep stall. To deal with this twist is put into the wing. The twist
evens out the lift distribution of the wing and keeps the stalls closer to the wing root.
38. 4.2.7: Dihedral
Dihedral is the effect of angling the wing up from the fuselage rather than laying it flat.
This is done for two main reasons. First, this effect adds to the stability of the aircraft. Should
the aircraft roll slightly past center; the dihedral on the wing will help return the aircraft to center
by generating different amounts of lift over each wing. The effect is helpful but only acts when
the aircraft rolls slightly past center. Along with this, the dihedral adds to the rolling moment
coefficient with respect to sideslip. This is important when dealing with how rudder deflections
affect the aircraft. When dihedral is put on the wing, a rudder deflection will not only produce a
yawing moment, it will produce a rolling moment as well. This makes the rudder much more
effective in controlling and directing the aircraft in flight. Typically dihedral angles are very
small.
4.2.8: Stall Characteristics
The stall performance of the aircraft is the final important design fact of the aircraft. As
discussed in a prior section, twist is added to the wing to keep the tips of the wings from stalling
before the root. Also, the stall angle of attack is important. This is the maximum angle of attack
the aircraft can take before it starts producing negative lift. The maximum angle of attack should
never be exceeded during flight as stalls are difficult to recover from.
4.2.9: Results
Once the different aspects of wing design are understood, the wing can be designed. The
results of the designs of this chapter are shown in the table below. These Parameters are at an
altitude of 41,000 feet.
39. Table 4.7: Wing Design Specifications
Wing Design Specifications
Airfoil NACA 631-212
Aspect Ratio 7
Thickness 0.12
Sweep 36 deg
Taper Ratio 0.4
Twist 2.2 deg
Dihedral 2 deg
From these values, a geometric wing is generated. This is done using a computer aided design
tool. The wing design based on the above parameters is shown in the following figures.
Figure 4.5: Wing Front View
40. Figure 4.6: Wing Top View
Figure 4.7: Wing Isometric View
4.3: Drag Analysis
The final step in the wing design is the drag analysis. This is done by first calculating the
wing drag coefficient. Using the value of CL obtained in this report, it is possible to now get a
more accurately calculated drag estimate. There are three components of the total wing drag.
41. These components are base, lift-induced, and any losses that result from viscosity. The drag
coefficient is given by the following formula.
πΆ π· = πΆ π·0 + ππΆ πΏ
2
+ πβ²(πΆπΏ β πΆπΏ,min π·) (4.5)
Taking into account the sweep angles, Mach number, and other important variables, the base,
zero-lift, and viscous drag coefficients can be calculated. In order to estimate the 3-D viscous
drag coefficient, a skin friction coefficient is defined and calculated. Once this value is found,
the next step is to calculate two factors that affect the wing behavior. These factors are called the
βform factor (F),β and the βinterference factor (Q).β Certain mountings and geometries call for
different values of these factors. The highest contribution of the drag comes from the base drag,
CD0. In calculating the total drag, it was found that the base drag component was responsible for
approximately 52% of the total. The values of viscous drag, which were calculated as somewhat
of an intermediate step, along with the drag totals are shown in the two tables below.
Table 4.8: Viscous Drag Calculations
Viscous Drag
V (ft/sec) 887.4
q (lb/ft2
) 212.1
Re 17,684,042
Cf 0.002440
Swet (ft2
) 1326
F 1.532
Q 1
CD0 Wing 0.007622
Table 4.9: Drag Summary
Drag Summary
Cdi (Begin cruise) 0.0051
Cdi (End cruise) 0.0021
CD, Wing (Begin Cruise) 0.0127
CD, Wing (End Cruise) 0.0098
Di (Begin cruise) 705.3 lbf
Di (End cruise) 294.9 lbf
DL=0 1051 lbf
Total Drag 2051 lbf
42. Chapter 5: Layout and Design of
Fuselage
5.1: Design ofFuselage
After designing the wing, the next step of the conceptual design is to develop the configuration
for the business jet aircraft fuselage structure. Then we have to determine where the wing goes and the
fuselage size. The fuselage is an aircraftβs main body that carries the passengers and the crew. It also
supports the structure for wings and tail, and the structure that contains the cockpit for the pilot, cargo and
passengers. It has to resists bending moments (caused by weight and lift from the tail) and cabin
pressurization. The majority of the fuselage for transport aircraft is cylindrical or near cylindrical with a
tapered nose and tail section. The size of our business jet will be determined by the number of passengers
and the seating arrangement.
Table 5.1: Passenger Aircraft Seating Arrangements.
For this type of configuration we decide to choose the seating arrangement corresponding to luxury
seating.
Table 5.2: Passenger Accommodations
Number of seats (in) 6
Seat width (in) 28
Seat pitch (in) 38
Lavatories 1
We also have to consider the emergency exits. For our type of aircraft, the FAR 25.807 requires a Type
IV emergency exit located over the wing with the following dimensions (19 x 26) (in). The next step is
designing the forward section of the plane. The length of a two crew compartment should be 100 inches
Crew 2 pilots + 1 flight attendant
Passenger No. 6
Fuselage Diam. (in.) 60
Aisle Seating 1 + 1
43. long. It also has to be shaped correctly in order to give the pilots the necessary over-nose and over-side
angles for the landing phase.
The values of over-nose and over-side angles are Ξ±overnose Π [11-20]o
, and Ξ±overside= 35o
. In the previous
reports we showed that a large portion of the take-off weight comes from the fuel. This fuel will be
stored in the wing and the fuselage and the location will be determined once we find the center of mass
with respect to the center of lift. A bladder tank will be our choice, we can put rubber bags in the wings
or fuselage the advantage is that this kind of tank is self-sealing. The total fuel weight calculated using
the fuel fraction method is 37,291.78 lbs. Using Table 5.4, we can find the volume needed to store the
fuel.
Table 5.3: Fuel Specific Volumes
Table 5.4: Storage Volumes of Various Fuels
Other structures can be accommodated in the fuselage for example the wing and the landing gear. The
wing will be constructed as an integral part and will pass through the fuselage. The landing gear will be
retracted into the fuselage when not used. To determine the Wheel diameter and width we use this given
equation:
π·πππππ‘ππ ππ ππππ‘β ( ππ) = π΄ β π ππππ
π΅
(5.1)
π ππππ =
0.9β π ππ
π π€β ππππ
(5.2)
44. After determining the internal arrangement of the fuselage, we can start thinking about the shape. As
discussed earlier, the nose has a conic shape due to the over-nose and over-side angles. The fuselage
shape should be aerodynamic and to avoid flow separation to maximize efficiency. This leads to
designing the aft portion of the aircraft with a slope less than 24 degrees.
5.2: Results & Analysis
The spreadsheet contains the input parameters which correspond to the flight regime data
and the dimension data. These parameters are taken from the cruise phase of flight, as that is the
time where the aircraft will spend the most time. The dimension data come from filling
requirements of having necessary volume to enclose the crew, passengers, payload, etc. as
described by the mission requirements. There are a number of quantitative fuselage shapes for
which drag data are available. In this design, the Von Karmen fuselage design is used. This
gives an elliptically shaped profile. The profile is described by the following relation:
π(π₯)
π(0)
2
=
1
π
[
2π₯
π
β1 β
2π₯
π
2
+ π΄ππππ (β
2π₯
π
)] (5.3)
The overall volume of the body in this case is:
ππππ’ππ =
π
2
ππ(0) 2
(5.4)
The surface (wetted) area is:
π = 0.8083πππ(0) (5.5)
To determine a proper skin friction coefficient, the Reynolds number must be determined to
know whether the flow is laminar or turbulent.
π π =
πππ₯
π
(5.6)
45. Once the Reynoldβs Number is found, the proper Cf equation is used. For Re <1000,
πΆπ =
1.328
β π π π₯
(5.7)
Or, for Re >= 1000,
πΆπ =
0.455
(πππ10 π π)2.58 (1+0.144 π2)0.65 (5.8)
Once the friction coefficient is found, the drag can be found for each section given by,
π· = πππΆπFQ (5.9)
The fuselage component of the drag coefficient is then,
πΆ π·0=
π·π‘ππ‘
(πππππ )
(5.10)
Table 5.5: Fuselage Design Parameters
Design Parameters
M 0.9
Cruise Alt 41000 ft
V 515 knots
q 212.1 lb/sq ft
Ο 0.0005598 sl/ft3
ΞΌ 5.684E-07
Ξ½ 0.001015 sl/ft s
Table 5.6: Fuselage Dimensional Data
Dimension Data
Dfuse 9
l/d 5.556
L (ft) 50
S (ft2
) 235.6
Shape Elliptical
Form factors
F 1.363809
Q 1
46. Table 5.7: Fuselage Design Spreadsheet
x/L x (ft) D (ft) P (ft) Swet (ft2
) Rex Cf
Drag
(lb)
0.00 0 0.00 0.00 0 0 0 0
0.10 5 5.00 15.71 78.54 2536083 0.003517 79.91
0.20 10 9.00 28.27 141.4 5072167 0.003124 127.8
0.30 15 9.00 28.27 141.4 7608250 0.002922 119.5
0.40 20 9.00 28.27 141.4 10144334 0.002789 114.1
0.50 25 9.00 28.27 141.4 12680417 0.002692 110.1
0.60 30 9.00 28.27 141.4 15216501 0.002616 107.0
0.70 35 9.00 28.27 141.4 17752584 0.002555 104.5
0.80 40 9.00 28.27 141.4 20288668 0.002503 102.3
0.90 45 7.00 21.99 110.0 22824751 0.002458 78.18
1.00 50 0.00 0.00 0 25360835 0.002419 0
Total Drag 943.3 lbs
CDO 0.0189
5.3: Fuselage Layout
This section includes the CAD model of the fuselage. The following figures show the front, side,
and orthographic views of the fuselage, along with some important dimensions.
Figure 5.1: Fuselage Front View Figure 5.2: Fuselage Side View
47. Figure 5.3: Fuselage Orthographic View
Figure 5.4: Axial Fuselage Layout Figure 5.5: Transverse Fuselage Layout
5.5: Conclusionand Recommendations
The fuselage design outlined in this report meets the requirements set forth by the RPF. When
designing a fuselage for long range cruise, it is important to take into account the structural integrity along
with the very practical need of passenger comfort. The fuselage must be designed to minimize and/or
optimize the drag produced during the cruise phase of the flight. A major concern when dealing with
48. fuselage design is the layout itself. Any engineer can design a hollow tube with a nose and tail, but
implementing all the necessities while keeping the passengers comfortable is an art. Using design
fundamentals and a bit of creative interior design, the team was able to design a fuselage capable of both
of these. Recommendations include further comparison of similar aircraft and more in depth modeling to
ensure dimensional correctness.
49. Chapter 6: Horizontal & Vertical Tail
Design
6.1: Horizontal and Vertical Tail Design
6.1.1: Airfoil Selection
The first step in designing the tail of the aircraft is selecting the airfoil that is used for both the
vertical and horizontal surfaces. The airfoil selected should be a symmetric airfoil. Using this airfoil is
ideal because this type of airfoil does not produce lift at a zero angle of attack. This will only induce
moments on the aircraft when the control surfaces are deflected,not at steady level flight. The airfoil
selected for this design is the NACA 0012 airfoil.
6.1.2: Aspect Ratio
After the airfoil is selected, the aspect ratio of the tail is determined. First, the horizontal tail is
taken into consideration. For this surface the aspect ratio is typically less than the wing. That is the
horizontal tail is shorter than the wing. Second, the vertical tail is designed. This surface is essential a
wing cut in half. This must be taken into account when calculating the aspect ratio for the vertical tail.
Typically the aspect ratio for the vertical surface is small.
6.1.3: Thickness
The thickness of the tail surfaces is important in the design. The thicknesses of these surfaces are
typically thinner than the main wing. This is due to the fact that the tail is not primarily designed to
produce large amounts of lift. Also, this will reduce the drag on the tail.
6.1.4: Sweep
Usually the horizontal stabilator in the empennage is chosen to have a higher sweep angle than
the leading edge sweep for the wing. This allows getting a higher critical Mach number than the one for
the wing. This angle is in generally 5 degrees more than the wing sweep to make the horizontal tail stall
50. after the wing. The main reason for this choice is to delay the loss of the effectiveness of the elevator
when there is a shock wave formation. For the vertical tail sweep of subsonic aircrafts we can chose an
angle by picking a value from 35 to 55 degrees. This value of vertical tail sweep can be readjusted based
on the stability of the aircraft.
6.1.5: Taper Ratio
The chord length at the tip of the tail divided by the chord length at the root yields the
taper ratio. The goal of tapering the control surface is to increase the Oswaldβs Efficiency on the
particular section. The taper ratio is given by the equations,
π =
π π‘
π π
(6.1)
Where,
π π =
2π
π(1+π)
(6.2)
Table 6.1 shows some historic values of tail aspect and taper ratios.
Table 6.1: Historic Tail Parameters
Horizontal AR Stabilator Ξ» Vertical AR Stabilator Ξ»
Combat Aircraft 3 - 4 0.2 β 0.4 0.6 β 1.4 0.2 β 0.4
Sail Plane 6 - 10 0.3 β 0.5 1.5 β 2 0.4 β 0.6
T βTail N/A N/A 0.7 β 1.2 0.6 β 1
Other 3 β 5 0.3 β 0.6 1.3 β 2 0.3 β 0.6
6.1.6: Tail Placement for Stall & Spin
The location of the vertical and horizontal stabilators will affect the stall and spin characteristics
of the business jet. The location of the horizontal stabilator with respect to the wing affects the stall
characteristics. The elevator control can be lost and the plane will pitch up if the horizontal tail is in the
wake of the main wing at a stall angle of attack Ξ±s.
51. Figure 6.1: Influence of Wing Wake on Tail Placement
To avoid this scenario the horizontal tail can be placed in two locations. The first being near the
mean chord line of the main wing, then the second would be above the wake of the main wing at the stall
angle of attack. Figure 6.2 shows the regions for vertical tail placement with coordinates (lHT,HHT) and
the effect on the stall control. The best choice of positioning is putting the horizontal stabilators below
the main wing centerline or at a higher position for a T-tail or a cruciform tail, if the stabilator is high
enough.
Figure 6.2: Stabilator Positioning for Maximum Stall Control
The location of the vertical tail will also affect the spin characteristics. The plane is in an
uncontrolled spin if it is falling vertically while rotating about the vertical-axis. To recover from a spin,
52. the pilot has to have enough rudder control. Figures 6.3 and 6.4 display some common vertical tail
positions that could be incorporated.
Figure 6.3: Important Incidence Angles Figure 6.4: Stabilator Placement on Vertical Tail
6.1.7: Results
This section includes the CAD model of the fuselage along with a table of important geometric
parameters of the tail design. The following figures show the front, side, and orthographic views of the
fuselage, along with some important dimensions.
Figure 6.5: Tail Orthographic View Figure 6.6: Tail Side View
53. Figure 6.7: Tail Front View Figure 6.8: Tail Top View
6.3: Drag Analysis
The drag analysis for the horizontal tail is shown in the table below.
Table 6.2: Horizontal Tail Drag Calculations
Horizontal Tail
Design Parameters Airfoil Data
CHT 0.8 Name NACA 0012
LHT 30 ft Clmax 1.6
ΞLE 41 deg ClΞ± 0.1 /deg
t/c 0.12 a.c. 0.3
Ξ» 0.75 Ξ±0L 0 deg
b 40 ft
Calculations Sweep Angles Viscous Drag
SHT 177.2544 ft2
x/c Ξx/c (deg) Cf 0.002746
AHT 9.026575 LE 0 41 Swet 354.5 ft2
cr 5.064411 ft 1/4 chord 0.25 38.25 F 1.507062
ct 3.798308 ft Q 1
xacHT 4.461505 ft TE 1 30 Drag 311.1724 lbf
Ξ² 0.733917 Cdo 0.002257
Meff 0.679239
CLΞ± 0.1
Total Drag 311.1724 lbf
54. Along with this, the drag calculations for the vertical tail are presented. These are shown by the
following table.
Table 6.3: Vertical Tail Drag Calculations
Vertical Tail
Design Parameters Airfoil Data
CVT 0.07 Name NACA 0012
LVT 30 ft Clmax 1.6
ΞLE 30 deg ClΞ± 0.1 /deg
t/c 0.12 a.c. 0.3
Ξ» 0.75 Ξ±0L 0 deg
b 24 ft
Calculations Sweep Angles Viscous Drag
SVT 97.18952 ft2
x/c Ξx/c (deg) Cf 0.002746
AVT 5.927 LE 0 30 Swet 194.4 ft2
cr 4.628 ft 1/4 chord 0.25 28.75 F 1.554248
ct 3.471 ft Q 1
xacVT 4.077 ft TE 1 25 Drag 175.9829 lbf
Ξ² 0.626498 Cdo 0.001276
Meff 0.779423
CLΞ± 0.1
Total Drag 194.4 lbf
55. Chapter 7: Propulsion
7.1: Engine Selection
The appropriate propulsion system for an aircraft depends on a number of factors. These include
the design Mach number and altitude, fuel efficiency, and cost. Based on the requirements and factors of
the design at hand, the team has chosen to use a turbofan propulsion system. This is the type of selection
made on many similar long range business class aircraft. The number of engines is often specified by the
need to produce a sufficient amount of thrust based on mission requirements and the available thrust per
engine. Generally, if possible, it is customary to use the fewest number of engines necessary. This leads
to simpler structural design and a lighter aircraft. The team has selected to use two operating turbofan
engines, which will be mounted on the rear of the aircraft near the tail, on opposite sides. The next step is
to determine a few parameters that will be needed in sizing the engine. Before deciding on a type or
brand of engine to use in the design, a few ratings of possible engine selections need to be gone over to
ensure the design requirements meet the ratings of the engine to be selected. These ratings include take-
off maximum thrust, maximum climb thrust rating, and maximum cruise rating. When deciding on which
engine to select, it is important to get all relevant information pertaining to each possible selection.
Thrust values are provided by engine manufacturers which correspond to sea-level static thrust (SLST).
If the engine is being sized based on the thrust required for cruise, which is usually the case, the sea-level
thrust needs to be corrected for the design cruise altitude. Thrust is a function of mass flow through the
engine, air density, temperature, and cruise speed. The following equations are used to calculate the
thrust at a given altitude,
πΜ = ππ΄π (7.1)
π =
π
π π
(7.2)
ππ» = πππΏ
π π»
π ππΏ
πππΏ
π π»
(7.3)
56. where R is the air gas constant. The pressure P,and temperature T, are functions of altitude for a standard
atmosphere. The cruise altitude for this design is 41,000 ft. Therefore, the calculations for these
parameters will need to be corrected. The last parameter affected by altitude is the engine specific fuel
consumption. This is given by equation 2.4,
ππΉπΆ =
π π
π
(7.4)
where Wf is the fuel weight, and T is the thrust. The thrust reported by engine manufacturers is called
βuninstalled thrust.β This means the thrust that the engine was capable of producing on a test stand at sea
level. Therefore, the βinstalled thrustβ is the thrust that is able to be produced once the engine has been
mounted to the aircraft. Factors that affect engine performance after installation include additional drag,
inlet distortion, and power extraction. With all these things taken into account, the team has decided to
choose the Rolls Royce BR715 turbofan engine. Table 2.1 gives some specifications of the chosen engine
and Figure 2.1 shows an image of the mounting location.
Table 7.1: Engine Specifications
57. Figure 7.1: Planform Engine Mount View
7.2: Drag Analysis
To design the engine, first the drag of the aircraft must be calculated. This is done by combining
the drag coefficients from each component of the aircraft. This is used in conjunction with the dynamic
pressure and wing area to find the drag on the aircraft. The drag calculation for the aircraft is presented in
the table below.
58. Table 7.2: Aircraft Drag Calculation
Drag Calculations
Component Drag (lb) Cdo
Fuselage 2604 0.0189
Wing 1545 0.0112
Horizontal Tail 289.7 0.0021
Vertical Tail 82.76 0.0006
Engine Nacelle 96.56 0.0007
Engine Pylon 41.38 0.0003
Induced Drag 3200 0.0232
Total 7860 0.057
After this is done the required thrust for the aircraft is found. This is done by setting the required thrust at
altitude to a rate of climb. Once the thrust for rate of climb is found, it is adjusted by five percent for a
safety margin. Following this adjustment, the trust at sea level must be found. This is done by relating
the trust at altitude to the sea level thrust by an air density ratio. The following table and figure shows
how the trust varies with altitude.
Table 7.3: Thrust with respect to Altitude
Engine BR715
Altitude p/psl T per engine
0 1 21000
5000 0.8617 18096
10000 0.7386 15510
15000 0.6295 13220
20000 0.5332 11197
25000 0.4487 9422
30000 0.3749 7872
35000 0.3107 6525
40000 0.2471 5188
59. Figure 7.2: Thrust with respect to Altitude
As shown in the figure, the required thrust at sea level will be must higher than that at altitude. This is
due to the lower air density at altitude. The engine must be of higher performance to maintain trust at
altitude. After these values are found, the required thrust calculations are found. These are shown in the
table below.
Table 7.4: Required Thrust Calculations
Required Thrust Calculation
Required Thrust at ROC 9471 lb Altitude 40000 ft
Compensation for lost 9944 lb Cruise Velocity 518 knots
Required Thrust at Altitude 9944 lb Cruise Velocity 52458 FPM
Required Thrust at SSL 40251 lb W beginning of Cruise 84515 lb
Required Thrust at SSL per
Engine
20126 lb
Required T/W 0.2381
Previous T/W 0.3185
Once these required thrust calculations are performed, the engine is selected. This is based off engine
performance at sea level. The engine parameters are displayed in the following table.
0
5000
10000
15000
20000
25000
0 5000 10000 15000 20000 25000 30000 35000 40000
Thrust(lb)
Altitude (ft)
Thrust vs. Altitude
60. Table 7.5: Engine Parameters
Engine Parameters
Weight 6150 lb
Length 12.25 ft
Diameter 4.833 ft
SFC at 39,000 ft 0.637
Finally, the performance at takeoff performance is calculated. This is the most important flight phase for
the engines as the aircraft must have enough trust to takeoff. The takeoff calculations are shown below.
Table 7.6: Takeoff Performance
Takeoff
Total T 42000
Takeoff W 88000
T/W 0.4773
61. Chapter 8: Takeoff & Landing
Performance
8.1: CD0 Calculation
To begin the calculation of the takeoff and landing performance, the drag coefficient for the
aircraft must first be solved for. This is done by breaking the aircraft down into several components and
adding them together to find the overall drag coefficient. The drag coefficients for the component of the
aircraft are shown in the table below. Once these values are understood, it is possible to find the takeoff
and landing performance for the aircraft.
Table 8.1: Drag Calculation for the Aircraft
Drag Calculations
Component Drag Cdo
Fuselage 2604 0.0189
Wing 1545 0.0112
Horizontal Tail 289.7 0.0021
Vertical Tail 82.76 0.0006
Engine Nacelle 96.56 0.0007
Engine Pylon 41.38 0.0003
Induced Drag 3200 0.0232
Total 7860 0.057
8.2: Takeoff Performance
During the take-off phase, the airplane accelerates until a take-off velocity VTO is reached, and
then climbs to an altitude that has to be greater than a reference height, hObstacle to climb over any potential
obstacle at the end of the runway. The take-off velocity is given by equation 8.1.
πππ = 1.2 ππ = 1.2 [(
π
π
)
ππ
2
ππΆ πΏ πππ₯
] 0.5
(8.1)
The takeoff phase analysis is divided into four parts. These parts are ground roll, rotation,
transition, and climb. Figure 8.1 shows a diagram of these phases.
62. Figure 8.1: Takeoff Phases
The first phase is the ground roll. In this phase the aircraft accelerates from rest to the takeoff
velocity, VTO, and covers a distance, SG. Equation 8.2 shows the equation for the ground distance.
π πΊ = β« (
π
π
) ππ
π ππ
0
=
1
2
β« (
ππ2
ππ
)
π ππ
0
(8.2)
The acceleration is given by equation 8.3.
π =
π
π ππ
β πΉπ₯ =
π
π ππ
β[π β π· β πΉπ] (8.3)
The friction force Ff is given by,
πΉπ = π[ πππ β πΏ πΊ] (8.4)
The friction force can range anywhere from 0.03 to 0.05, depending on the weather conditions
and type of runway material used. When the aircraft is in close proximity to the ground, the effective
aspect ratio of the wing is larger. The equation to find this new larger aspect ratio is given by equation
8.5.
π΄
π΄ ππππππ‘ππ£π
= β
2π»
π
(8.5)
The total drag force including base drag due to the extension of flaps and landing gear is given
by,
π· = π π[πΆ π·0
+ ππΆ πΏ πΊ
+ βπΆ π·0 ππππ
+ βπΆ π·0 πΏπΊ
] (8.6)
63. Therefore,we can deduce the ground roll distance by equation 8.7,
π πΊ =
1
2π2
ππ[
π1+π2 πππ
2
π1
] (8.7)
Where,
π1 = π(
π
π
β π) (8.8)
f2 =
ππ
2( π
πβ )
(ππΆ πΏ πΊ
β πΆ π·0
β ππΆ πΏ πΊ
β βπΆ π·0 ππππ
β βπΆ π·0 πΏπΊ
) (8.9)
The second phase is the aircraft rotation. For this phase, the takeoff angle of attack is
increased, which increases the aircraft CL.
πΆ πΏ = 0.8 πΆ πΏ πππ₯
(8.10)
π π = 3 ππ0 (8.11)
The third phase is transition. The aircraft travels at a constant velocity along an arc of radius RTR.
π ππ =
πππ
2
0.15 π
(8.12)
π ππ = π ππ (1β πππ πΎπΆπΏ ) (8.13)
The fourth and final phase for takeoff analysis is the climb. After the transition, the aircraft has to
reach a certain altitude to go over any obstacles, such as a tree. This obstacle height is decided on 35 ft.
This is given by equation 8.14.
π» ππ = π ππ (1β πππ πΎπΆπΏ ) (8.14)
And the climb distance is given by,
π πΆπΏ =
π»πππ π‘π πππ βπ» ππ
π‘πππΎ πΆπΏ
(8.15)
The total take-off distance is a sum of all the distances above. The balanced field length is a take-
off distance calculated for safety in case of an engine failure. In this event, if the velocity is below the
decision speed, the field length has to be sufficient so that the aircraft can still clear the obstacle height.
64. Equation 8.16 shows the total takeoff distance. Figure 8.2 shows a schematic illustration of the balanced
field length for an emergency aborted takeoff. Table 8.2 Shows the takeoff input parameters.
π π΅πΉπΏ =
0.863
1+2.3πΊ
[
π
πβ
ππ(0.8 πΆ πΏππ π₯)
+ π» πππ π‘ππππ] [
1
π ππ£
π
βπ
+ 2.7] +
655
β π
π ππΏ
β
(8.16)
Figure 8.2: Balanced Field Length
Table 8.2: Takeoff Input Conditions
Takeoff Input Conditions
WTO (lb) 85000 AREff 16.8
Tmax (lb) 22500 CD,Total 0.0740
Cd0, Wing 0.0189 e 0.8
CL (Ground Roll) 0.8 Cdi 0.0151
Β΅ 0.05 Ο (slug/ft3
) 0.0023
Cd0,Flap 0.0150 Alt. (ft) 0
Cd0,Gear 0.0250 VTO (ft/sec) 266.0
S (ft2
) 650 RTR (ft) 14653
Ξt (sec) 0.5 Ξ³CL (deg) 3
8.3: Landing Performance
Similar to the takeoff performance, to find the landing performance of the aircraft the landing
distance is divided into stages. These stages are the approach, transition, free roll, and breaking phases.
Also, the aircraft must be able to clear a fifty foot obstacle at the beginning of the landing distance. The
equation describing the landing distance of the aircraft is shown in the equation below.
π πΏ = [ π π΄ + π ππ + π πΉπ + π π΅] (8.17)
65. After the above expression is understood, each component of the aircraft landing is taken into
account. To begin with, the approach distance is described. The distance during this phase is shown in
the following formula.
π π΄ =
π»πππ βπ» ππ
tan( πΎ π΄)
(8.18)
Where,
π» ππ = π ππ» β π ππ» cos( πΎ π΄) (8.19)
And,
π ππ =
(1.23ππ )2
0.19π
(8.20)
Along with the approach, the transition phase of the landing is analyzed. The distance cover
during this flight stage is shown in the next expression.
π ππ = π ππ sin( πΎ π΄) (8.21)
Following the calculation of the transition phase, the free roll distance of the landing is taken into
account. The free roll portion of the landing is as soon as the aircraft touches down. At this point the
nose of the aircraft is still off the ground. The speed breaks and spoilers are then deployed to dump the
lift over the wing and cause the nose of the aircraft to come down. The free roll for most landings last
about three seconds. The equation showing the distance covered during the free roll flight phase is
described below.
π ππ = 3 β (1.15ππ) (8.22)
The final stage of the aircraft landing is the braking stage. This is when the aircraft has touched
down and uses the runway to slow down. This distance is described using a numerical analysis of the
landing dynamics. Once all of the landing phases are understood, the overall landing distance is found.
The parameters used to analyze the landing phase are in Table 8.3.
Table 8.3: Landing Input Conditions
66. Landing Input Conditions
WTO (lb) 85000 VStall (ft/sec) 221.7
TIdle (lb) 0 V50 (ft/sec) 288.2
CL,Touchdown 0.8 Ο (slug/ft3
) 0.0023
Cd0, Wing 0.0189 D50 (lb) 4407.80
Β΅ 0.5 RTR (ft) 12152.53
Cd0,Flap 0.0150 HTR (ft) 29.60
Cd0,Gear 0.0250 CD,Total 0.0740
S (ft2
) 650 CDi 0.0151
Ξt (sec) 0.5 Ξ³Approach (deg) -4
8.4: Drag Analysis
To begin the analysis of the takeoff and landing distance for the aircraft, the basic forces acting
on the aircraft are taken into account. These forces are used to solve the dynamics of the aircraft during
the condition. The forces acting on the aircraft are the lift force, friction force, drag force, weight, and
thrust. Both the weight and trust of the aircraft are known, but the others must be solved for. The first
force solved for is the lift force. This force is represented by the following equation.
πΏ = π πΏ ππ
(
1
2
ππ2 π) (8.23)
Where,
π πΏ ππ
= π πΏ πΌ ππ
(8.24)
The lift coefficient for the aircraft upon take off is the lift coefficient with respect to angle of
attack. The angle of attack at takeoff is modeled as shown below.
πΌ π€πππ = πΌ + π π€ + π₯πΌ ππΏ π
β πΌ ππΏ πππππ
(8.25)
Where,
π₯πΌ ππΏ π
= β
π
3
β
1+2π
1βπ
(8.26)
67. After the lift force is found, the frictional force acting on the aircraft is solved for. The less lift
being produced by the aircraft will yield a higher frictional force. The frictional force for the aircraft is
described by the next expression.
πΉπ = π( π β πΏ) (8.27)
Along with the frictional force, the drag for on the aircraft must be found. This is done by
breaking down the drag force into two components. These components are the parasitic drag and the lift
induced drag. The parasitic drag affecting the aircraft is shown as follows.
π· π = π π· π
(
1
2
ππ2 π) (8.28)
Where,
π π· π
= π π· π ππππππππ
+ π₯π π· π ππππ
+ π₯π π· π πππππ
(8.29)
As described by the above equation. The drag coefficient is made up of the airframe, gear and
flaps. The addition of the flaps depends on the deflection of the surface. The induced drag acting on the
aircraft is modeled as described below.
π·π =
π πΏ
2
ππ΄π πππ π
(
1
2
ππ2 π) (8.30)
Where,
π΄π πππ = π΄π β
π
2π»
(8.31)
This aspect ratio correction is due to the ground effect on the aircraft. The effective aspect ratio
will be higher than that of the normal aircraft conditions. Putting both the parasitic and induced drag
components together yields the following expression for the drag force on the aircraft.
πΉπ· = π π· π
(
1
2
ππ2 π) +
π πΏ
2
ππ΄π πππ π
(
1
2
ππ2 π) (8.32)
68. After these forces are modeled for the aircraft, it is possible to solve for the dynamics of the
aircraft upon these conditions. To begin with, the acceleration of the aircraft must be found. This is
performed by using the following equation.
π =
β πΉ
π
=
π€
π
( πβ π· β πΉπ) (8.33)
After the acceleration is found, the velocity of the aircraft is solved for. To do this, the
expression below is used.
π1 = π0 + π π π₯π‘ (8.34)
For takeoff:
π0 = 0 (8.35)
For landing:
π0 = 1.15ππ (8.36)
Finally, the distance covered by the aircraft must be found. This is done by following the next
formula.
π = π π + (
π1
2βππ
2
2π π
) (8.37)
Once these equations are understood, it is possible to solve for both the takeoff and landing
distances for the aircraft. The distances found for the takeoff and landing distances are shown in tables
8.4 and 8.5, respectively.
Table 8.4: Takeoff Distances
Takeoff Distances
SG (ft) 882.9
SR (ft) 798.1
STR (ft) 766.9
SCL (ft) 284.7
STO (ft) 3142
Table 8.5: Landing Distances
Landing Distances
SA (ft) 291.69
STR (ft) 847.72
SFR (ft) 764.81
SB (ft) 2463.10
SLand (ft) 6987.70
69. Chapter 9: Enhanced Lift Devices
9.1: Discussion
9.1.1: Types of Flaps
The four main types of trailing edge flaps are the plain, split, slotted, and fowler flaps. Each has
their own differences in design and in how they work. The first type of flaps the team will look at is the
plain flap. With the plain flap the rear portion of the airfoil rotates downwards on a simple hinge
mounted at the front of the flap. Due to the greater efficiency of other flap types, the plain flap is
normally only used when simplicity is required. The next type of flaps the team will look at is the split
flap. With the split flap the rear portion of the lower surface of the airfoil hinges downwards from the
leading edge of the flap, while the upper surface stays immobile. This type of flap can cause large
changes in longitudinal trim, pitching the nose either down or up. At full deflection, split flaps act much
like a spoiler, producing lots of drag and little or no lift. The next type of flaps is the slotted flap. With
the slotted flap there is a gap between the flap and the wing forces high pressure air from below the wing
over the flap helping the airflow remain attached to the flap, which in turn increases lift. Additionally, lift
across the entire chord of the primary airfoil is greatly increase as the velocity of the air leaving its
trailing edge is raised, from the typical non-flap 80% of free stream, to that of the higher-speed, lower-
pressure air flowing around the leading edge of the slotted flap. The last main type of leading edge flaps
is the fowler flap. With the fowler flap there is a split flap that slides backwards flat, before hinging
downwards, thereby increasing first chord, and then camber. The flap may form part of the upper surface
of the wing, like a plain flap, or it may not like a split flap but it must slide rearward before lowering. By
increasing the chord and camber it subsequently increases the lift and drag produced by the wing allowing
the plane to take off in shorter distances and at lower speeds. Figure 9.1 shows the four types of trailing
edge flaps.
70. Figure 9.1: Trailing Edge Flaps
9.1.2: Leading & Trailing Edge Flap Design
The team decided to choose a double slotted flap. To find CL,Max, we have to determine
whether the aircraft wing has a βhighβ or, βlowβ aspect ratio. A wing is considered to have a
high aspect ratio when:
π΄π >
4
( πΆ1+1)cos(πΎ πΏπΈ )
(9.1)
The coefficient, C1 is a function of the taper ratio, Ξ», and can be found in Figure 6.8 of the
textbook.
For high aspect ratio wings,
πΆ πΏ πππ₯
= [
πΆ πΏ πππ₯
π π πππ₯
]πΆ πΏ πππ₯
(9.2)
πΆ πΏ πππ₯
π π πππ₯
is given from Figure 9.9, as a function of the leading edge sharpness parameter Ξy.
71. For low aspect-ratio wings,
πΆ πΏ πππ₯
= (πΆ πΏ πππ₯
) πππ π + βπΆ πΏ πππ₯
(9.3)
(CL,Max)Base is given from textbook Figure 9.12, as a function of ( πΆ1 + 1)( π΄
π½β )cosΞLE
The next step is to determine the 3D change in maximum lift coefficient for the wing operating
with flaps extended, βπΆ πΏ πππ₯ πππππ
.
To get the curve of the lift coefficient πΆ πΏ versus Ξ± for a flapped wing we need to determine the
increment in πΆ πΏ πππ₯
due to the flaps.
The following equation gives us βπΆ πΏ πππ₯
βπΆ πΏ πππ₯
= βπΆπ πππ₯
π ππΉ
π π
πΎβ (9.4)
is the ratio of the planform area of the wing having the same span as the flaps, to the total wing
planform area. And KΞ is given by the equation:
72. πΎπ₯ = (1 β 0.08πππ 2
π¬ π
4
)πππ 3/4
π¬ π/4 (9.5)
Figure 9.2: Wetted Flap Area
In this case,
π ππΉ
π π
= 0.9. Next, the 3D change in maximum lift coefficient for the leading edge
devices extended is calculated.
(βπΆ πΏ πππ₯
) πΏπΈπ· = βπΆπ πππ₯ πΏπΈπ·
π ππΉ
π
πππ π¬ πΏπΈ (9.6)
With the calculations and parameters found in previous reports, a CL v. Ξ± graph can be
constructed for the basic curve with no flaps for LEDs. To plot the curve for CLflaps, ΞΞ±0L,flaps
must be calculated.
βπΌ0πΏ πππππ
= β
πΏπΌ
πΏπΏ πππππ
πΏ πππππ (9.7)
Using the graph with all curves plotted, the Ξ±stall and ΞΞ±stall can be found.
π πππ‘
73. The
πΏπΌ
πΏπΏ πππππ
factor is found from Figure 9.5 in the textbook.
Next, the ΞCD0 for takeoff and landing should be found. This can be done with:
βπΆ π·0 πππππ
= πΎ1 πΎ2
π ππΉ
π
(9.8)
The factors K1 and K2 can be found in textbook figures 9.20 and 9.21, respectively. Figure 9.3
shows the lift curve for the NACA 631-212, which is the airfoil chosen for this design.
Figure 9.3: Lift curve for NACA 631-212
It is important to determine the parameters of the flap configuration. Table 9.1 shows these parameters of
concern.
75. Chapter 10: Structural Design
10.1: Refined Weight Analysis
At this point of the design, the wings, fuselage, horizontal and vertical tail sections, and engines
have been designed. These make up the majority of the external configuration of the aircraft. The design
of the structure is based on a load limit, which is the largest expected load. For aerodynamic forces, this
is related to the aerodynamic load factor n. The largest load factor from any of those in this group will be
considered to be the βdesign load factor,β which will be the basis for the design of the internal structure.
The design of the internal structure and the material selection clearly go hand-in-hand. The use of higher
strength materials can reduce the size or number of structural elements. However, the structure weight is
an important factor that also needs to be considered. Therefore, the structure design and material
selection will be done together. The weights of the different structural components need to be calculated
and refined to begin the structural analysis of the aircraft. To do this, each element of the structure was
broken down and analyzed on its own. The following table shows the weight estimates, load locations,
and center of gravity location.
76. Table 10.1: Refined Weight Analysis
Center of Gravity Calculation
takeoff
wt(lbs) 85,000
fuselage lenght is 50 ft fuel(lbs) 37,292
payload(lbs) 1,805
empty
wt(lbs) 45,904
Weight Summary
Load Type
Load
(lbs) x/L start x/L end x/L res M about 0
Fuselage Structure 2665.17 0.00 1.00 0.50 1332.59
Wing Structure 2597.05 0.41 0.69 0.55 1428.38
Tail Structure 631.42 0.76 1.00 0.88 555.65
Payload 1805.00 0.10 0.80 0.45 812.25
Main Landing Gear 802.21 0.60 0.60 0.60 481.33
Nose Landing Gear 237.18 0.05 0.05 0.05 11.86
Fuel wing 27121.45 0.50 0.60 0.55 14916.80
Fuel fuselage 10170.54 0.50 0.60 0.55 5593.80
Engines (2) 9300.00 0.67 0.67 0.67 6231.00
Other 29669.98 0.00 1.00 0.50 14834.99
Total weight (lbs) 85000.00
Total
Moment 46199
xcg/ cbar 0.54
xcg (ft) 27.30
Once the weights are differentiated and analyzed, the aircraft aerodynamic centers can be located. This is
done by locating the mean aerodynamic chord of the wing and the length from the leading edge that
represents the quarter chord line. Because the airfoil thickness is maximum at twenty-five percent of the
chord length, this is the span wise maximum lift spot of the wing. The intersection of these two geometric
lines is the aerodynamic center. Basic trigonometric relations can easily find the distances of the a.c.
from the fuselage and leading edge. The wing aerodynamic center for this aircraft is located thirty-one
feet from the nose of the aircraft and fourteen and a half feet from the root chord. The horizontal tail
aerodynamic center is located forty-four feet from the nose of the aircraft and five and a half feet from the
tail root chord. Below, Figure 10.1 shows a planform view of the aircraft with the wing and tail
aerodynamic centers. They are denoted by the black dots imposed on the wing and tail, respectively. The
loads experienced by the wing and tail are found by summing forces and moments about the center of
gravity, these values are tabulated in table 10.2.
77. Table 10.2: Calculated Wing and Tail Loads
WTO (lb) 85000
xac,Wing
(ft) 31
xac,Tail (ft) 44
Lwing (lb) +1145500
LTail (lb) -29550
Figure 10.1: Wing & Tail Aerodynamic Centers
10.2: Wing Load Analysis
The lift distribution of the aircraft is essential in understand the loads on the wing during
flight. The first distribution found is the elliptical distribution. To find this distribution the
following formulas are applied. The total lift generated by an elliptical wing is given by
equation 10.1 and the lift created by a trapezoidal wing is given by equation 10.2.
πΏ πΈ(π¦) =
4πΏ
ππ
β1 β (
2π¦
π
)2 (10.1)
πΏ π(π¦) =
4πΏ
π(1+π)
[1 β
2π¦
π
(1 β π)] (10.2)
The theoretical lift distribution for these two types of lift curves, with respect to span wise
location, is graphed below.
78. Figure 10.2: Span-wise Trapezoidal & Elliptical Wing Loading
An approximated span-wise lift distribution is the local average of the two distributions and is given by
equation 10.3.
πΏΜ =
1
2
[πΏ π( π¦) + πΏ πΈ(π¦)] (10.3)
The addition of leading-edge flaps and trailing-edge flaps enhance the wing lift in the locations where
they are placed. The drag force on the wing changes along the span and is concentrated at the wing tips.
For the concentrated and distributed wing weights such as the wing mounted engines, fuel tanks, and etc.,
historic weight trends are used since it is very difficult to determine the final weight of the structures.
Using Shrenckβs approximation, a theoretical plot of the shear and moment diagram can be found. This
can help in understanding the wing loading, and approximate the average lift distributions. The following
figures show Shenckβs theoretical approximations for wing loading analysis.
Figure 10.3: Elliptical, Trapezoidal, & Average Lift Distributions
79. Figure 10.4: Wing Span Shear Diagram
Figure 10.5: Wing Span Moment Diagram
With these things in mind, a spreadsheet is built showing the computation of all the loads on the wing
including the span-wise lifting loads, the wing weight distribution, the wing fuel weight, landing gear
weight, and the weight of the engine. The raw data table used in this analysis can be found in the
Appendix section of this report. The figures below have been created to display the shear, moment, and
load diagrams, plotted versus the wing half span.
81. Figure 10.8: Shear Diagram of Wing
Figure 10.9: Moment Diagram of Wing
10.3: Fuselage Load Analysis
The fuselage can be considered to be supported at the location of the center of lift of the main
wing. For this aircraft is at thirty-one feet from the nose. The loads on the fuselage structure are then due
to the shear force and bending moment about that point. The loads come from a variety of components
such as structure, payload, and fuel. For static stability in the pitching direction, the balance of the loads
82. about the center of lift should result in a nose-down moment that has to be offset by the horizontal
stabilizer downward lift force. This is determined by finding the moments produced by the product of the
resultants of the respective loads. Then, the distance from the location where they act to the location of
the center of lift will yield the moment created. The fuselage structure can be considered to be a beam
that is simply supported and balancing at the center of lift, xCL. Just as before with the wing, the resulting
shear force and bending moments need to be calculated along the length of the fuselage. The following
figures show this data in plot form versus the fuselage length. The data used to create these figures can be
found in the Appendix section of this report.
Figure 10.10: Span-wise Fuselage Loads
85. 10.4: Fuselage Design
In the fuselage, the frame elements that run along its length are called βlongerons.β Those
elements that run around the internal perimeter of the fuselage are called βbulk-head.β The structural
criterion for the cross-section size of longerons and the spacing of bulkheads is to resist compressive
buckling. With the fuselage supported at the center of lift for a positive load factor, the tensile loads are
on the top surface. For a negative load factor they would be on the bottom surface. Whichever load
factor is larger is the one that will dictate the design. Using the maximum moment obtained in chapter
three of this report, the material selection will be made and the skin thickness and longerons will be
designed. The results of this design are shown in the table below.
Table 10.3: Fuselage Design
Fuselage Skin Thickness and Longeron Data
MxCL (lb-
in) 6181564.8 C 1
nDesign 1.348 FE 64,671
Material
7075-T6
Al ΟE 7.06
R (in) 54
Ο
(lb/in3
) 0.158
tmin (in) 0.0239 A (in2
) 9,161
t (in) 0.025
Οmax
(psi) 1,457,521
E (lb/in2
) 1.03E+07 Οt (psi) 337.4
I (in4
) 229.02 Οc (psi) 7.06
L (in) 600 Οb (psi) 1,457,521
ΟTu (psi) 76000
ΟT (psi) 53,982
86. Chapter 11: Stability and Controls
11.1: Longitudinal Stability
The longitudinal direction of the aircraft involves three of the six degrees of freedom for the
aircraft. These three degrees of freedom are the translation in the x and z-directions, along with, the
moment about the y-axis. These degrees of freedom can be expressed by the aircraft equations of motion.
The first force analyzed is the force acting in the x-direction. When an aircraft is in steady state
flight, this force is related to the drag of the aircraft. This relationship is shown in the following
equation.
πΉπ΄ π1
= βπ·1
Where,
π·1 = πΆ π·1
πΜ π
From these two expressions it is evident that an equation for the coefficient of drag must
be found. Also, it is known that the coefficient of drag is dependent of angle of attack, elevator
deflection, and stabilator deflection. This can be expressed mathematically in the following
equation.
πΆ π·1
= π( πΌ, πΏ πΈ, π π»)
This expression is then further expanded and represented as the following.
πΆ π·1
= πΆ π·0
+
ππΆ π·
ππΌ
( πΌ β πΌ0) +
ππΆ π·
ππΏ πΈ
(πΏ πΈ β πΏ πΈ0
) +
ππΆ π·
ππ π»
(π π» β π π»0
)
Reducing this equation yields,
πΆ π·1
= πΆ π·0
+ πΆ π· πΌ
πΌ + πΆ π· πΏ πΈ
πΏ πΈ + πΆ π· π π»
π π»
After further analyses of the drag it is evident that the contribution of the elevator and
stabilator are negligible. This simplifies the above expression as shown below.
πΆ π·1
= πΆ π·0
+ πΆ π· πΌ
πΌ
The second force to be taken into account is the force acting in the z-direction. This force
under a steady state condition is dependent on the lift force of the aircraft. This is expressed in
the formula below.
πΉπ΄ π1
= βπΏ1
Where,
87. πΏ1 = πΆ πΏ1
πΜ π
From here an expression for the lift coefficient must be found. Along with the coefficient
of drag, the coefficient of lift is dependent of angle of attack, elevator deflection, and stabilator
deflection. This can be expressed mathematically in the following equation.
πΆ πΏ1
= π( πΌ, πΏ πΈ, π π»)
This expression is also further expanded as the following.
πΆ πΏ1
= πΆ πΏ0
+
ππΆ πΏ
ππΌ
( πΌ β πΌ0) +
ππΆ πΏ
ππΏ πΈ
(πΏ πΈ β πΏ πΈ0
) +
ππΆ πΏ
ππ π»
(π π» β π π»0
)
Simplifying the equation shows,
πΆ πΏ1
= πΆ πΏ0
+ πΆ πΏ πΌ
πΌ + πΆ πΏ πΏ πΈ
πΏ πΈ + πΆ πΏ π π»
π π»
Once this expression is reached, it is necessary to solve for all the components of the lift
coefficient. The first component can be represented below.
πΆ πΏ π
= πΆ πΏ π π€π
+ πΆ πΏ πΌβ
πβ
πβ
π
π π + πΆ πΏ πβ
β πΆ πΏ π π€π
This coefficient is only made up of the lift coefficient of the wing body. This is the
coefficient of lift for the wing body if the aircraft is in steady state flight with no deflection of
any control surfaces. The range for this coefficient is from -0.05 to 0.40. After this component is
solved for, the second coefficient must be found. This coefficient describes the effect of a
change in angle of attack has on the lift coefficient. It is described in the following equation.
πΆ πΏ πΌ
= πΆ πΏ πΌ π€π
+ πΆ πΏ πΌβ
πβ
πβ
π
(1 β
ππ
ππΌ
)
This equation shows how both the wing body and the horizontal surface contribute to the
coefficient of lift with respect to angle of attack. In general, the coefficient of lift increases as
the angle of attack increases, up until a point. This point is known as stall. Once the angle of
attack exceeds the stall point, negative lift is generated. This also holds true for the decrease in
angle of attack. Only in this case, the effect is reversed. This contribution to the total lift
coefficient is shown the figure below.
88. Figure 11.1: Effects of Angle of Attack on the Lift Coefficient
This coefficient ranges from 1.0 to 8.0. The next component of the lift coefficient
solved for is the elevator contribution. This coefficient is defined by the following equation.
πΆ πΏ πΏ πΈ
= πΆ πΏ πΌβ
πβ
πβ
π
π πΈ
On the horizontal surface of the tail there is a control surface know as an elevator. This
control surface is primarily used to change the pitch of the aircraft. This is done by creating a
negative or positive lift by deflecting the control surface in the respective direction. The elevator
can be seen in Figure 2.
πΆ πΏ
πΆ πΏ π
Ξ±
89. Figure 11.2: Horizontal Tail Surface Controls
This figure also shows the stabilator configuration on an aircraft. The stabilator is
essentially the entire horizontal surface on the tail of the aircraft. This control surface is
primarily used for trimming an aircraft at cruise velocity. Once this is understood, it is possible
to express how this surface impacts the coefficient of lift. This contribution to the lift coefficient
is expressed in the following equation.
πΆ πΏ π π»
= πΆ πΏ πΌβ
πβ
πβ
π
This coefficient only contributes to the total lift coefficient if there is a deflection of the
control surface. This coefficient ranges from 0 to 1.20.
Once all four coefficients are solved for it is possible to fully express the force in the z-
direction acting on an aircraft. These equations are summarized in the figure below.
Elevator
Stabilator
90. Finally, the pitching moment of the aircraft must be taken into account. This moment
must be expressed to fully define the aircraft dynamics in the longitudinal direction. The
pitching moment is defined as shown in the following expression.
ππ΄1
= πΆ π1
πΜ ππΜ
The pitching moment coefficient in the above equation is solved for. It is known that this
moment is also a function of angle attack, elevator deflection, and stabilator deflection. This
relationship is expressed mathematically below.
πΆ π1
= π( πΌ, πΏ πΈ, π π»)
πΆ π1
= πΆ π0
+
ππΆ π
ππΌ
( πΌ β πΌ0) +
ππΆ π
ππΏ πΈ
(πΏ πΈ β πΏ πΈ0
) +
ππΆ π
ππ π»
(π π» β π π»0
)
πΆ π1
= πΆ π0
+ πΆ π πΌ
πΌ + πΆ π πΏ πΈ
πΏ πΈ + πΆ ππ π»
π π»
The above equation shows how the pitching moment coefficient is made up of several
components. Before these components are solved for several key aircraft geometries must be
solved for.
Figure 11.3: Summary of Aircraft Equation of Motion in the X-Direction
91. Figure 4: Pitching Moment Geometric Parameters
Using the figure above, the necessary geometries are defined as shown below.
ππ΄πΆ ππ΅
Μ Μ Μ Μ Μ Μ Μ Μ =
ππ΄πΆ ππ΅
πΜ
π πΆπΊ
Μ Μ Μ Μ Μ =
π πΆπΊ
πΜ
ππ΄πΆ π»
Μ Μ Μ Μ Μ Μ =
ππ΄πΆ π»
πΜ
These equations provide the necessary geometries to fully solve for the pitching moment.
The first expression is the distance from the aerodynamic center of the wing to the aerodynamic
center of the wing body. The second equation is the distance from the aerodynamic center of the
wing to the center of gravity of the aircraft. Finally, the last equation is the distance from the
ππ΄πΆ π»
π πΆπΊ
ππ΄πΆ ππ΅
Wing
Aerodynamic
Center
Tail Aerodynamic Center
