MEM 425

Aircraft Performance and Design

-- Summer 2014 --

FINAL PROJECT REPORT

Tyler, Elliot, Robert Aerospace (TERA)

Dragonfly Mk. I

Tyler Darrah (twd34@drexel.edu)

Elliot Farquhar (ef93@drexel.edu)

Robert Stricek (ras376@drexel.edu)

Submission Date: 9/4/2014

Section Number: 001

Team: I

Professor: Ajmal Yousuff

Comparison to Existing Aircraft

There are various different aircraft available with particular mission goals, specifications,

luxuries, etc. tailored to design requirements requested by a stakeholder. Our mission objective

had been to design an aircraft to take a family of 10 from Philadelphia International Airport

(PHL) to Suvarnabhumi Airport (BKK) in Bangkok Thailand as shown in Figure 1 below,

consuming a minimum amount of fuel for a non-stop flight. The total distance of the trip had

been approximated to be 8,721 miles [1], an extreme distance in the realm of passenger aircraft.

This kind of mission most often involves multiple stops, largely attributed to refueling purposes

and is therefore an inconvenience to the customer. These delayed trips range between 20 and 26

hours, specifically from PHL to BKK [2]. There exist planes that can handle such distances,

otherwise known as ultra-long-haul trips, like the Boeing 747 400ER in the 747 family. This

aircraft has range of 7,670 nautical miles, 8,826.48 miles, and cruises at 0.855 Mach, nearly the

speed of sound [3]. Though the range satisfies our customer needs, the problem with using this

aircraft for our mission is that all ultra-long-haul aircraft are extremely large and carry great

quantities of passengers. For example, the Boeing 747 400ER can carry at a minimum 416

passengers, and a maximum of 524 passengers [3]. The reason behind this is that such great

distances cost aircraft operators significant amounts of money, mostly attributed to fuel and

flight duration. Cost is always a large concern, but the more time an aircraft is in the air for a

single mission renders it unable to be used for other missions, or multiple flights on a time

interval basis. The solution to these previous two problems is to put as many passengers as safely

possible on the plane to make up differences in operational costs. In summary, there is no small

personal jet class aircraft that can carry a maximum of 10 passengers (2 pilots and 1 crew) for

nearly 8,800 miles, let alone minimize fuel costs. Our aircraft has been designed to adhere to the

aforementioned mission objectives as well as other, more specific, customer needs and

specifications, while dually minimizing fuel consumption. Not only has TERA developed a new

aircraft, but we are bringing to life a new classification of aircraft as well, dubbed ultra-long-

range personal jet.

Figure 1. Distance, PHL to BKK airport [1]

The aircraft had been designed with various stakeholder needs and specifications in

consideration, organized in Table 1 below. These specifications, along with fuel consumption

minimization, were the main driving force for various initial estimates including weight, wing-

loading, thrust to weight, take-off distance, and other elements.

Requirements Specifications

Passengers 10 Family Members, 2pilots, 1 attendant

Cruise Velocity 0.75 Mach

Cruise Altitude 40,000 ft.

Stall Velocity 90 miles/hr.

Range Philadelphia to Bangkok, Thailand, non-stop

Loiter 30 minutes at 30,000 ft. @ 0.6 Mach or less

Rate of Climb 1,500 ft/ min (1,000 ft/ min minimum)

Power Plant more than 1; high-bypass turbofan (existent)

Structure Composite Material

Max Load Limit Factor 4

Take-Off Distance 6000 ft. w/ 50 ft. clearance

Landing Distance 4000 ft. w/ 50 ft. clearance

Table 1. Stakeholder needs

Performance Justifications

To start the design process, the team chose a plane which exhibited a lift to drag ratio of 20 or greater.

Using Figure X, below, it was determined that the B-52 bomber fit the desired constraint the best with a

lift to drag ratio of 21. The B-52 used the root airfoil NACA63219.3 and the tip airfoil NACA 65A209.5,

according to the University of Illinois. [x] These specific airfoils, however, cannot be found since they are

modifications of standardized configurations. Thus, the TERA team decided to use the NACA63210 and

the NACA65210 airfoils which should exhibit similar lift to drag characteristics.

Figure X: L/D versus wetted aspect ratio [1]

Using coefficient of lift versus angle of attack plots for these airfoils, seen in Figures X and X

below, the max coefficient of lift was determined to be 1.6.

Figure X: Cl versus angle of attack [2]

Though the specific fuel consumption of our engine(s) were not known at the start of this

project, a rough estimate was taken using the statistical data, provided by Raymer, in Table 3.3 (Raymer,

19). For a high-bypass turbofan the cruise sfc value was .5 (lbs/s) and for loiter it was .4 (lbs/s). Assuming

that the flight path comprised of 5 stages, shown in Figure X below, the following weight ratios between

stages were used.

Figure X: Flight path

Table 1: Weight ratios [3]

Unlike Anderson, the TERA group decided to calculate the weight ratio of the loiter phase, stage

3 to 4, since there was a significant amount of time the plane was to be in this transition. For the

cruising phase of the flight, stage 2 to 3, the L/D ratio was not equal to 21 but instead was calculated to

be .866 percent of this maximum value since jets cruise more efficiently at higher velocities.

In order to calculate the empty weight, some research was performed in order to choose an

appropriate empty weight to takeoff weight ratio. According to Figure 3.1 in Raymer, shown below, the

empty to takeoff weight ratio should be about 5.4. Since one of the key design parameters is to use the

least amount of fuel possible, other alternatives were sought out to lower this ratio. Currently, there is

only one plane on the market which utilizes composite material to a large extent and that would be the

Boeing 787. The fact that fifty percent of the airframe is comprised of these materials, according to

Stages Ratio

W1/W0 0.97

W2/W1 0.985

W5/W4 0.995

Boeing, is the reason why the airframe weight dropped 20 percent from previous models (Boeing, 18).

The problem with composite materials, however, is that they are brittle in comparison to metals. This is

due to a variety of factors which include, but are not limited to, delamination, manufacturing errors due

to the precision required, and micro cracks. Based on our preliminary investigations our team chose to

reduce the empty weight of the aircraft by only 16.7, still using metals for key components. With this

said the empty to takeoff weight ratio came out to be .45.

Figure X: Empty weight trends [1]

The next step was then to calculate the wing loading ratio. For stage 5, landing, the landing

velocity multiplier (j) and the coefficient of friction (μr) values were considered to be 1.15 and .4 which

are standard commercial airlines. The amount of time before the brakes are applied after the plane has

touched down (N) was chosen to be 3 seconds in order to account for human reaction time. For the

cruising condition, stages 2 to 3, the team decided to make the parasitic drag (Cdo) to equal .12 since this

is approximately the same as the B-52 and because the wings and body will be relatively thin and

smooth. Though the Oswald efficiency factor for most jet aircraft are around .8, the dragonfly Mk I has

an efficiency factor of .6, according to McCormick, due to its low wing design.

The Dragonfly Mk. I was designed with only one engine since the thrust needed could be

provided by only one engine and a second engine would just increase the weight of the aircraft. The

reliability of modern jet engines has also improved to the point where long distance flight can be

guaranteed by the used of one engine.

Performance

Wing Loading

Wing loading is the weight of an airplane per unit wing area, i.e. lb/ft2. This parameter can be

calculated various ways depending on the segment of the mission the airplane is in. One is limited by the

takeoff or stall velocity where:

Eq. (1)

This produces the value of 46.592 lb/ft2. Another method of calculating the wing loading is using

conditions that an airplane undergoes when landing which is a function of air density at sea level,

maximum coefficient of lift, stall velocity, etc. This gives a wing loading value of 115.6891 lb/ft2.

The final condition from which wing loading can be calculated from is at cruise. The equation

that dictates this is:

√ Eq. (2)

This gives the wing loading as 38.9767 lb/ft2. The valued used for the Dragonfly Mk. I was the wing

loading value at cruise since it was the lowest value and therefore is the limiting factor.

Thrust to Weight Ratio

Like wing loading, the thrust to weight ratio needs to be chosen from different values depending

on the segment of the mission the airplane is in. The thrust to weigh ratio calculated from takeoff which

is a function of the stall velocity and air density at sea level. This gives a thrust to weight ratio of 0.0578.

The thrust to weight ratio is different when climbing and is dependent on the rate of climb as

shown in the equation below:

Eq. (3)

This produces the thrust to weight ratio of 0.3143. Another value can be inferred from data collected

from previous examples of airplanes with the use of tabulated constants:

, a=0.267, c=0.363 Eq. (4)

This thrust matching value comes out to be 0.2405. A tabulated value for the trust to weight ratio of

previous transportation jet airplanes is 0.25.

The final source for thrust to weight ratio comes from sustained turn requirements:

Eq. (5)

The thrust to weight required for the sustained turn is then 0.3016. The values for the thrust to

weight ratios of the sustained turn and cruise were checked in order to confirm their validity. The values

calculated above were greater than the check values meaning they were valid for consideration. The

thrust to weight ratio that is used for the Dragonfly Mk. I is the largest value calculated above which is

the thrust to weight ratio required by the rate of climb.

Rate of Climb

The maximum rate of climb at sea level for our air craft is calculated as a function of the

maximum lift to drag ratio, the thrust to weight ratio at climb, and varies the density of air. The

maximum climb rate at sea level is 97.7624 ft/s. The relationship between altitude and maximum rate

of climb can be seen in Figure [X] below.

Figure [X]. Maximum Rate of Climb vs. Altitude

Ceilings

Based on the rate of climb and air density, both the absolute and service ceiling could be

calculated where the absolute ceiling is where the airplane can maintain horizontal flight, which was

calculated to be 48,474.83 ft. The service ceiling was calculated to be 47,341.92 ft, which is where the

airplane’s rate of climb is 100ft/min [X].

Design Justifications

The design process began by selecting a fuselage design. In order to mimic similar business jets a

double-bubble fuselage shape was chosen to have the same dimensions of the Bombardier Global 6000.

This shape can be seen in, Figure X, below.

Figure X: Double bubble fuselage shape of a 717 [5]

After determining that the total amount of fuel needed for the trip would fit in the wings, a

decision had to be made on where to put the extra 113 cubic feet. If this amount of fuel were put in the

back, it would severely shift the center of gravity toward the back and make the plane very unstable

during climb. On the other hand, the fuel could not be put underneath the passengers in order to ensure

their safety in case of an emergency. With approximately 4,200 lbs of fuel calculated to be stored in

each wing, the addition of 2,500 lbs external tanks is highly impractical. Considering the yield strength of

Aluminum 2024-T4, a commonly used alloy in the aerospace industry, to be 5,760,000 psf there would

not be enough fuel to cause failure. The moment on the shoulders, however, is of more concern. As the

wing stands, it would impart 3,347,232 psf shear stress on the shoulder. This force is just 972,768 psf

less than the shear strength of Aluminum 2024-T4. [6] Though adding the 2,500 lbs would not increase

this shear stress enough to cause aluminum failure, there is only a factor of safety of about 1.3. Also,

when lifting off the ground this stress would increase due to the initial lift off, acceleration in the vertical

direction. Lastly, by adding these external fuel tanks onto the wings our designated drag coefficients

would have to increase in order to accommodate these disturbances in laminar flow. Thus it was

decided that the excess fuel would have to be placed somewhere inside the fuselage. Instead of placing

the fuel beneath passengers and crew, the team decided that it would be best to place it on either side

of the fuselage, providing ample room for the aisle. These compartments would also have to be toward

the front of the plane in order to keep the center of gravity from shifting too far backward.

Next, the design shifted to engine placement. Since only one engine was required to produce

9,500 lbs of thrust, the only logical choice was to position the engine in the rear of the plane to avoid

turbulence across either the wings or tail. To keep the drag coefficients at a minimum, the engine was

placed inside the aircraft and fed air by two, horizontally placed, scoops. The reason why the scoops

were placed horizontally was to prevent turbulent flow over the vertical tail stabilizer.

With the scoops positioned on either side of the fuselage, the horizontal tail stabilizers could not

be placed in a conventional tail configuration. In order to prevent the effect of downwash, the cruciform

tail configuration was also disregarded which left a T-tail design. An example of how wing downwash

affects the horizontal tail stabilizers can be seen, in Figure X, below.

Figure X: Downwash [7]

The T-tail design has other benefits, such as a higher longevity due to the reduction of vibrations

imparted by the engine. Since the wings do not play a role on the airflow across the tail, the horizontal

tail area can be made smaller. Lastly, since the horizontal tail has what is known as an end-plate affect,

the vertical tail area can also be reduced. The disadvantages of said design are an overall heavier tail

structure since the main vertical spar has to take the bending moment imparted by the horizontal tail

and a condition known as deep stall. Essentially as the angle of attack increases the wake and downwash

of the fuselage and wings begins to create turbulent flow over the horizontal tail. In said state the

aircraft may suddenly pitch to higher angles of attack. At some point, however, the tail will exit the

turbulent flow and give the pilot control over the aircraft once again. [7] This condition can be seen in

Figure X, below. The problem lies with trying to pitch the aircraft into a lower angle of attack since it will

re-enter the turbulent stream from the fuselage and wings. This, however, can simply be mitigated by

appropriate warning methods. Once such warning method is to properly designate the tapper ratios of

both the wings and the tail, this will create an initial stall condition toward the shoulder joints. The user

should feel this and still have control over the ailerons and elevators which are located toward the ends

of the wings. The smaller the ratio the further the separation of flow occurs from the shoulder. For

standard airplanes this ratio ranges between .4 and .6 and thus chose the greatest value of .6.

Figure X: Deep stall condition [7]

As for the physical dimensions of the T-tail they were determined using ratios purposed by a

Stanford professor. For example, the vertical and horizontal tail volumes were chosen to be .0425 and .5

based on the following Figures.

Figure X: Statistical approach to vertical tail volume [8]

Figure X: Statistical approach to horizontal tail volume [8]

According to this source, it was also reasonable to choose aspect ratios for the vertical and

horizontal tail to be 4 and 1.65. The taper ratio of the vertical tail was determined to be .85 in order to

insure enough area for the vertical section to attach onto. [8]

The main justification of our team’s decision to use a low wing design is due to the effect it has

on the stability of the aircraft. With the wings lower there would be less down wash on the T-tail system

in both normal operating angles and during deep stall. As stated before, with less air disruption the tail

can be made smaller. In terms of longitudinal stability, the wing drag line is positioned lower than the

center of gravity of the aircraft and thus creates a nose down pitching moment. This means that after a

sudden increase in angle of attack the plane will return back to its original state. This configuration also

increases static lateral stability due to the fuselages contribution to the wing dihedral effect. However, if

the wing is angle too far up the amount of lift decreases and the effect of cross winds become greater.

For this project a small angle of 5 was chosen in accordance with other aircraft of this kind. Other

benefits include shorter landing gear, better take off performance due to the ground effect, better

maneuverability, and less induced drag. Some disadvantages are less lift production, turbulent flow

separation located at the connection between the body and the wing, higher stall speed, less laterally

dynamically stable, and a longer landing distance. Even with these disadvantages the low wing design

was chosen since the large Cl/Cd ratio and simple fillets would counteract these effects. [9]

The flaps on the wing were designed using the standard that the width of the flap be 30% of the

wings chord length at any given outward location.

With these issues taken care of the passenger, baggage, crew, and amenities placements were

left. Essentially these positions were based on their effect to the center of gravity. With more than 18

hours of flight, a bathroom and a small kitchen seemed mandatory. These were placed toward the front

of the plane due to their significant weight. The passengers were placed toward the back not only

because their weight would not affect the center of gravity as much as other components but also

because our team wanted to make sure they were as far away from the auxiliary fuel tanks.

Once the wing configuration and weight distribution were decided upon the landing gear could

be chosen. The landing gear configuration was decided to be a tricycle configuration since the center of

gravity of the airplane would be in front of the wings which were of a low wing design, further

supporting the decision to make the configuration a tricycle.

Dragonfly Mark I Design

The first step, in the design process, was to determine the aerodynamic chord of the wings. This

was achieved by using Equations X and X below. For this particular aircraft the chord location and chord

length are 18.3169 ft and 9.8 ft. These equations can also be used for both the horizontal tail and

vertical tail.

(

)( ( )

)

( ) (

)

Though Anderson does not provide a detailed method of determining the fuel which can be

stored inside the airfoil, a method was devised using the thickness of the airfoils along the chord

lengths. With fuel cell thicknesses of .7ft and .6 ft. only a certain amount of the wing could hold said fuel

cells while maintaining a minimum clearance of 6 inches between the fuel cell and the outer airfoil. The

resulting integration can be seen with the other finalized drawings.

The center of gravity is essentially a sum of all the moments about the nose divided by the total

weight of the objects which create a moment affect. In order to simplify the equation each objects

center of gravity was determined in order to treat them as a point mass in relation to the front of the

aircraft. The distances and weights of the considered objects can be found, in Table X, below. The center

of gravity is then positioned 50.1750 ft from the front of the aircraft as dictated by Equation X.

Table X: Center of gravity relations

( ) ( )

Component Distance X (ft) Weight W (lbs)

Engine 80.8115 2301.6

Flight Attendant 24.222 180

Bathroom 28.972 130

Kitchen Area 28.972 400

Passengers 56.157 2000

Auxillary Fuel 36.797 4767.5

Crew Baggage 36.797 60

Electrical Systems/Fuel Pumps/Miscelaneous 43.297 200

Pilots 20.472 360

Passenger Baggage 70.342 500

Since this center of gravity calculation does not include the wings, it is safe to assume that this

first estimate will change. To place the wing, the mean aerodynamic center is lined up with the first

estimate of the center of gravity. The aerodynamic center and the center of gravity of the wing were

calculated to be 2.45 ft and 3.92 ft from the leading edge of the wing along the mean aerodynamic

chord. Finally, using Equation X, the new center of gravity location of 50.8889 ft from the front was

calculated by also considering the wing as a point mass.

( ) ( )

( ) ( )

( )

Dividing the distances to the tail mean aerodynamic centers, from the front of Anderson’s

aircraft, by the distances to the tail center of gravity locations, ratio were determined to find the

aerodynamic center locations of our aircraft. This can be seen below.

(

)

(

)

The aerodynamic center distances from the planes center of gravity then become 35.9837 ft and

33.61 ft. Using Equations X and X, the plane view areas were determined. Other parameters such as

wing span, root chord length, and tip chord length are calculated the same as the main wing.

√( )

In order to properly place the landing gear, a final adjustment must be made to position the

wings in relation to the center of gravity of the aircraft. Then the positions of the rear wheels are a

matter of the new center of aerodynamic center location of the wings. This is done by using the

following equations.

( )

( ( )

)

A ratio again was calculated between the distance of the front wheel and the length of the

fuselage of Anderson’s example aircraft to determine the position of the front wheel. Thus, for our

plane, the front wheel should be positioned 7.8185 ft from the nose as shown below.

(

)

Using the force diagram in Anderson’s book, the load distribution among the tires was

determined to equal 1883.2 lbs on the front wheel and 13,341.5 lbs on each back wheel. Andersons

diagram is given below.

Figure X: Wheel load distribution [3]

Determining the wheel diameter is the last thing which needs to be done. This is achieved by

using the A and B values, provided by Anderson, to be used in Equations X and X. For our aircraft the

wheel diameters and widths came out to be 3.5081 ft and 1.1673 ft for the rear wheels and 1.7488 ft

and .6265 ft for the front wheel.

The last aspect of the design involves determining a better weight estimate. This is done by

using the equations listed, in Table X, below. It is important to note that all area which are used are the

exposed areas only, thus any part of the wings which are considered part of the body are not

considered. Roughly estimating the airplane as a combination of a cone, a cylinder, and an eclipse, the

general wetted surface area was calculated as shown below.

Table X: Weight estimations

( √ )

( ) ( )

The new takeoff weight then becomes the sum of the weight of the crew, the payload, the

previously estimated fuel, and the new empty weight which was calculated above. From here the

processes was iterated multiple times, plugging in each new consecutive takeoff weight into the landing

gear and all else empty equations to determine an empty weight. The Fuel weight then becomes the

multiplication of each consecutive new takeoff weight by the originally determine Wf/Wo ratio of .4451.

The final values of We, Wf, and, Wo, as well the values for each iteration, can be found in Table X below.

Table X: Convergence of weight characteristics

Component Equation Weight (lbs)

Wing Weight 2.5*(Wing Area) 864

Horz. Tail Weight 2*(Horz. Tail Area) 113.5348

Vert. Tail Weight 2*(Horz. Tail Area) 163.0125

Fuselage Weight 1.4*(Wetted Area) 6246.4

Landing Gear Weight .057*(Wo) 1685.3

Installed Engine Weight 1.4*(Engine Weight) 2301.6

All Else Empty .1*(Wo) 2956.6

Empty Weight ∑ of components 14330

After putting all the information together, the Dragonfly Mk I CAD designs were finalized and

are shown below.

Figure X: Cross section right view of main fuselage given room lengths and rudder details

Iteration We (lbs) Wf (lbs) Wo (lbs)

1 14330 13161 30592

2 14491 13618 31209

3 14588 13893 31581

4 14647 14058 31805

5 14682 14158 31940

6 14703 14218 32021

7 14716 14254 32070

8 14724 14724 32100

9 14728 14289 32117

10 14731 14297 32128

11 14733 14302 32134

12 14734 14305 32138

13 14734 14306 32141

14 14735 14307 32142

15 14735 14308 32143

16 14735 14308 32143

Figure X: Cross section right view of main fuselage given seating, engine, and fuel comp. dimensions

Figure X: Right view of exterior given engine scope and rudder Cg dimensions

Figure X: Cross section front view given fuselage dimensions

Figure X: Cross section front view given auxiliary fuel cell dimensions

Figure X: Top view of exterior given wing and horz. tail span, plane length, and main wing chord lengths

Figure X: Top view of exterior given scoop layout, aerodynamic center, and chord lengths of horz. tail

Figure X: Top view of exterior horz. tail given sweep angles and elevator dimensions

Figure X: Cross section top view of wing given fuel cell dimensions

Figure X: Cross section top view of wing given spar locations

Figure X: Cross section top view of wing given aileron dimensions

Appendix

Calculations

Reference

[1] - https://www.google.com/?gws_rd=ssl#q=PHL+to+BKK+distance&safe=off

[2] -

https://www.google.com/flights/#search;f=PHL,ZFV;t=BKK;q=phl+to+bkk+nonstop;d=2014-

09-19;r=2014-09-23 14-09-23

[3] - http://www.boeing.com/boeing/commercial/747family/pf/pf_400er_prod.page

[X] - Dr. I. Halliwell, “An Improved Engine for a High Altitude Long Endurance Unmanned Air

Vehicle”, Joint AIAA Foundation / ASME, 2012, pp. 1-35.

Robs sources

[1] Raymer

[2] http://www.dept.aoe.vt.edu/~mason/Mason_f/B52S05.pdf

[3] Text Book

[4] http://www.boeing.com/commercial/aeromagazine/articles/qtr_4_06/AERO_Q406_article4.pdf

[5] http://adg.stanford.edu/aa241/fuselayout/images/717coachx.gif

[6] http://asm.matweb.com/search/SpecificMaterial.asp?bassnum=MA6061t6

[7] http://faculty.dwc.edu/sadraey/Chapter%206.%20Tail%20Design.pdf

[8] http://adg.stanford.edu/aa241/stability/taildesign.html

[9] http://faculty.dwc.edu/sadraey/Chapter%205.%20Wing%20Design.pdf