Hybrid Electric Regional Transport Design Report

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AEROSPACE 402B MIDTERM REPORT

The Pennsylvania State University

AIAA HYBRID TRANSPORT

TEAM SPEED

March 1, 2013

Matt DruryAnthony Montalbano

Sam NoerpelDevin OConnorBrittany Sipple


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Table of Contents

1. Aircraft Mission Description ...................................................................................................... 2

2. Requirements .............................................................................................................................. 3

3. General Aircraft Data .................................................................................................................. 33.1 Aircraft Specifications........................................................................................................... 3

3.2 Aircraft Three-View .............................................................................................................. 6

4. Propulsion System ...................................................................................................................... 7

4.1 Engine Trade Study ............................................................................................................... 7

4.2 hFan Specifications ............................................................................................................... 8

5. Introduction to Drag .................................................................................................................... 8

5.1 Profile Drag........................................................................................................................... 9

5.2 Induced Drag ....................................................................................................................... 11

5.3 Parasite Drag ....................................................................................................................... 12

5.4 Trim Drag ............................................................................................................................ 13

6. Takeoff ...................................................................................................................................... 13

6.1 Takeoff Drag ....................................................................................................................... 14

6.2 Takeoff Performance........................................................................................................... 17

7. Climb......................................................................................................................................... 20

7.1 Climb Performance ............................................................................................................. 21

8. Cruise ........................................................................................................................................ 26

8.1 Cruise Drag ......................................................................................................................... 26

9. Landing ..................................................................................................................................... 30

9.1 Landing Drag....................................................................................................................... 31

10. Maneuver Envelope ................................................................................................................ 31

11. Future Goals ............................................................................................................................ 33

12. Conclusion .............................................................................................................................. 34

13. References ............................................................................................................................... 34


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1. Aircraft Mission Description

The hybrid-electric aircraft under consideration for design has an economic mission of 400

nautical miles (NM) with a maximum range of 1200 NM. It is characterized as a regional

commercial aircraft, and must safely and efficiently deliver 70 passengers with the

implementation of a hybrid electric propulsion system. This propulsion system will consist of acombination of battery powered electric motors and conventional air breathing turbo-fan engines,

allowing for a reduction in emissions, fuel cost, and noise. This aircraft is the first regional

transport to implement a hybrid electric propulsion system. This design, once optimized, will be

expected to operate with the lowest cost per-seat mile and highest passenger miles per gallon

compared to conventional transport aircraft. With an economic mission of 400 NM, this aircraft

will most likely service smaller market areas in order to deliver passengers to larger airline

carrier hubs. The aircraft mission profile is outlined in Figure 1 with altitude on the vertical

coordinate and distance shown on the horizontal axis.

Figure 1. Aircraft Mission Profile

The mission profile consists of two portions: the nominal mission and the reserves. In this case,

the nominal economic mission is 400 NM, but the aircraft has the potential to go 1200 NM. A

portion of the mileage above 400 NM composes the contingency portion of the mission. For

example, if the aircraft needs to fly a holding pattern for a given amount of time due to a busy

airport, the aircraft will have enough fuel to safely accomplish this portion of the mission.


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2. Requirements

Table 1. AIAA Aircraft Requirements

Parent Aircraft Q400

Maximum Range 1200 NM

Crew 2Passengers 70

Seating Pitch 32, Width 17.2

Cargo Volume 280 ft2

Cargo Weight 2450 lbs (35 lbs/passenger)

Full Payload Weight 16,450 lbs

Balanced Field Length 4000 ft SSL

Minimum Cruise Mach Mach 0.45

Initial Cruise Altitude >20,000 ft

Maximum Cruise Altitude 45,000 ft

Economic Mission 400 NM

Battery Volume 9 ft3 / battery

Battery Weight 360 lbs / battery

Useful Energy 122472 Wh /battery

Battery Energy Cost $0.05 / kWh

Battery Discharge Rate 10C

Electric Motor Power Density 3 hp/lb

Electric System Efficiency 0.95

Generator Power Density 3 hp/lb

Generator Efficiency 0.96

3. General Aircraft Data

After the mission and general requirements of the aircraft is specified, an idea of what type of

aircraft can fulfill such a mission begins to formulate. The most important aircraft specification

is the weight of the aircraft. This specification drives all other design decisions and drives the

performance of the aircraft.

3.1 Aircraft Specifications

The first design specification that is defined for the aircraft is its weight. The total weight is

calculated using

,

and is found to be 63,819 lbs. The empty weight is 37,886 lbs. and was taken from the parent

aircraft, the Q400. The payload weight is calculated to be 16,850 lbs. using the AIAA specified

requirements. This includes a payload of seventy passengers and two crew members, each

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weighing 200 lbs., along with 35 lbs. of luggage for each passenger. The fuel weight is

calculated to be 6,940 lbs. using

,

where is defined as the fuel mass flow with units of lbs./s. The variable is the total

distance of the flight in units of ft. and is the cruise speed of the aircraft in ft./s. Mass

flow is found using

,

where TSFC is 0.341 lbm./lbf.-hr. This value comes from the hFan engine data provided by

Boeing and NASA. The variable T represents thrust, which changes throughout flight. Since our

aircraft incorporates a hybrid propulsion system, additional weight comes from batteries. Thebattery weight is calculated to be 2,144 lbs. using

.

is defined as the energy necessary to climb to cruising altitude and has units of ft.-lbs. It

consists of both the change in potential energy of the aircraft from sea level to 30,000 ft., in

addition to kinetic energy of the aircraft at a specific climb speed. The energy density of the

battery, , is a measure of how much energy each battery contains per unit mass with

units of ft.-lbs./lb. Additional values used to obtain battery calculations are maximum fuel energyof 9.96e10 ft.-lbs. and battery energy of 2.16e9 ft.-lbs.

The following specifications found are the critical performance parameters which include

and . These values are based on the Q400 and are given to be 2.5 and 80 kts,

respectively.

An aspect ratio of 7.69 is calculated using

,

where wing area is 1300 ft2 and wing span is 100 ft. The values of wing area and wing span are

chosen based on optimizing aspect ratio.

Additional specifications include a calculated to be 0.306 using

2

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.

Here, is 608.4 ft/s and density is given at our cruise altitude of 30,000 ft.

A span efficiency factor is also calculated and found to be 0.9953. This value is found usingAthena Vortex Lattice (AVL) software by averaging different Reynolds numbers with varying

speeds.

Further specifications include values for the tail of the aircraft. The horizontal volume coefficient

is calculated to be 0.88 using

,

where , the distance from the CG to the aerodynamic center of the tail, is 61 ft. The tail area

used is 259 ft2 and the mean aerodynamic chord is 13.6. This tail area was chosen to decrease the

effects of trim drag on the aircraft.

The vertical stabilizer area is found to be 168.75 ft2. This area, based on the parent aircraft

vertical tail configuration, provides enough surface area for a rudder that has proper control and

lateral static stability properties.

The fuselage length chosen for our aircraft, 130 ft., is based on the Q400, however extra footage

was added to account for our hybrid engine requirement. As seen in the three-view drawing in

Figure 2, there is additional room in front of and behind the passenger seats. This extra space

will be necessary for the batteries and cooling system needed to power the aircraft, along with abaggage area. The batteries will be placed both in the front and in the rear of the aircraft, but

with the majority placed in the rear. The baggage area will be placed in the rear of the aircraft.

The placements of these areas are chosen to account for the center of gravity of the airplane.

Because our airplane is for regional missions, it is understood that not all passengers will be

carrying large enough baggage that will need to be placed in the baggage area. More than likely,

the majority of the passengers will be keeping their baggage in the luggage area above their seat

or on the floor below their seat. For this reason, more of the batteries will be placed towards the

rear. Because of the extra weight towards the back due to batteries, the airplane will not have to

rely on the weight due to checked baggage in the rear baggage area to balance the center ofgravity.

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3.2 Aircraft Three-View


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Figure 2. Regional Hybrid-Electric Propulsion Transport. Included are 70 passenger seats, 2

crew seats, and a 61 passenger standing in the aisle.

4. Propulsion System

NASA-funded research has recently stated that hybrid electric propulsion is the technology of

the future for commercial aircraft. A hybrid system is a combination of gas turbine and electric

propulsion. The best hybrid propulsion system is the one that uses the optimal features of each

subsystem. The gas turbine is ideal for high thrust and weight, while the electric propulsion is

ideal for high efficiencies over varying speeds, no local emissions, and lower noise. The prime

outcome for using a hybrid electric propulsion system is to offer advantages in fuel burn, cost,

noise, and emissions.

4.1 Engine Trade Study

The engine chosen for the aircraft is a collaboration effort between NASA and Boeing and is

currently in its design phase, which is projected to be completed by 2030. The engine is the

hFan, shown in Figure 3, and is an ideal hybrid electric propulsion system consisting of a

boosted 2-spool separate flow turbofan. It will utilize both gas turbine and battery for various

portions of the mission. The gas turbine will be used for long range cruise, while the electric

motor will be used for short range cruise. Because of this flexibility, fuel burn is able to be

reduced for regional missions. It will also feature a conventional fan and nacelle arrangement for

lowest possible noise. This engine is also designed with a higher thrust level in order to account

for the weight increase due to the batteries required for the electric subsystem.

A main consideration for the hFan design is how to achieve top-of-climb thrust. The final

conclusion of the study from NASA and Boeing is that in order to obtain top-of-climb thrust, a

combination of gas turbine and electric subsystems must be used. This configuration is ideal

because it provides sufficient mission thrust while minimizing the size of the motor and power

output of the electric subsystem.

The hFan provides technology that is unique from competing engines. An example is the use of a

variable core nozzle that is independent from the variable fan nozzle. This is important duringthe shifts between gas turbine, hybrid, and electric modes.


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Figure 3. hFan Schematic (1)

4.2 hFan Specifications

The currently proposed NASA and Boeing engine is too large for the aircraft and will need to be

scaled down to match the desired thrust levels. The hFan engine specifications include a

propulsion system weight of 10,475 pounds-mass, a fan diameter of 89 inches, and a length

measured from spinner to motor of 56 inches. This has been scaled down to a fan diameter of 48

inches, and a length of 96 inches from cowling inlet to nozzle. NASA and Boeing also specify

values for performance thrust and specific fuel consumption for SLS, rolling takeoff, top-of-

climb, and cruise configurations. For SLS and rolling takeoff, only gas turbine will be used,

while for top-of-climb and cruise, the hybrid mode will be utilized. The performance thrust,

given in pounds-force, for SLS, rolling takeoff, top-of-climb, and cruise are 18,000, 13,385,

4,364, and 3,344, respectively. The specific fuel consumption, given in pound-mass per pound-

force hour for SLS, rolling takeoff, top-of-climb, and cruise are 0.211, 0.301, 0.372, and 0.341,

respectively.

5.Introduction to Drag

Drag is defined as the aerodynamic force resolved in the direction of the free-stream due to

viscous shearing stresses, the integrated effect of the static pressures acting normal to the

surfaces, and the influence of the wing trailing vortices on the aerodynamic center of the

configuration(2) . An in-depth analysis of drag is necessary in order to develop a better


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understanding of the design and performance characteristics of the aircraft. A drag build-up is

conducted for takeoff, cruise, and landing configurations in order to predict the performance

characteristics for the given flight condition. These characteristics determine the aircraft design

decision process. For example, engine sizing and flap choice. Drag during takeoff and landing

are also used to predict runway distances. Drag is composed of several unique parts including:

profile, parasite, induced, and trim. It is calculated by means of

Other types of drag exist, such as interference drag, cooling drag, and ram drag, but we assume

them to be negligible.

A MATLAB code is written in order to produce an accurate drag build-up. The structure of the

code allows for analysis of each type of drag over a specified range of Reynolds Numbers by

,

coefficients of lift for cruise calculated using

,

and for takeoff and landing by

.

The specified range for Reynolds Numbers is defined as the lowest velocity at the tip chord and

the highest velocity at the root chord for the wing, vertical stabilizer, and horizontal stabilizer.

For the fuselage and nacelles, parasite drag equations are used in the code based on section

wetted areas and whether it experiences laminar or turbulent flow. Total drag is calculated by

summing up all of the different values by Equation 8.

5.1Profile Drag

Profile drag is defined as the sum of the skin friction drag and the pressure drag for a two-

dimensional airfoil. Put simply, it is the interaction of a physical object in a flow field. Using the

code, profile drag is calculated for the wing, horizontal stabilizer, and vertical stabilizer. Using

Athena Vortex Lattice (AVL), the wing area is discretized into 50 sections over the semi-span

and are gathered and entered into the MATLAB code in order to multiply by the section profile

8

9

10

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drag coefficients to get the wing profile drag coefficients. Before calculating profile drag, a

proper airfoil is selected based on the operational Reynolds Numbers and lift coefficients. The

NASA NLF(2)-0415 airfoil, shown in Figure 4, meets the criteria, and is used in the XFOIL

application to calculate profile drag coefficients.

Figure 4. NASA NLF(2)-0415

XFOIL is an interactive program for the design and analysis of subsonic airfoils. The first step in

calculating profile drag is the entering of the coordinates that specify the geometry of the airfoil

into XFOIL. Reynolds numbers are then specified due to the presence of viscosity and Mach

numbers are specified due to the given flight condition. A drag polar is opened in order to record

airfoil data for every run. A run is specified by cycling through a sequence of angles of attack

and calculating the lift coefficients and profile drag coefficients for the corresponding angles.

Once the profile drag coefficients for the range of Reynolds Numbers have been produced, they

are entered into the MATLAB code in matrix form.

The MATLAB code is set up with a two-dimensional interpolation to calculate profile drag

coefficients based on the Reynolds Number range and the lift coefficient range and the current

Reynolds Number and lift coefficient after incrementing velocity and chord. These values of

Reynolds Numbers and lift coefficients correspond to specific columns and rows in the profile

drag coefficient matrix, which produce the interpolated profile drag coefficient value. The

previously described sequence is shown in Figure 5.


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Figure 5. Flowchart of MATLAB Code Main Drag Routine

The interpolated profile drag coefficients are then used to calculate profile drag using

.

5.2Induced Drag

Induced drag is the drag that results from the influence of a trailing vortex on the wing

aerodynamic center. Induced drag is present solely on the wing. Induced drag drives the total

drag at low velocities because at low velocities the lift coefficient is large. This makes the

induced drag coefficient even larger due to the dependence on the square of the lift coefficient as

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.

Overall, a larger aspect ratio is desired to reduce induced drag. Aspect ratio is optimized to

produce the best ratio of span and wing area in order to minimize induced drag while still

offering benefits in structural integrity. Along with optimizing aspect ratio, the wing area, alone,is a critical parameter in that while decreasing the wing area will increase aspect ratio, it also

increases lift coefficients, which ultimately increase induced drag. Induced drag is determined

using the expression

.

5.3 Parasite Drag

Parasite drag is the drag on a body resulting from viscous shearing stresses over its wetted

surface. Parasite drag is calculated for the fuselage and nacelles. In order to calculate parasite

drag, a Reynolds Number needs to be calculated. This Reynolds Number is checked to see if it is

laminar or turbulent flow. It is assumed that turbulent flow begins at a Reynolds Number above 3

million. The calculated Reynolds Number is then used to calculate a skin friction coefficient by

and

for laminar and turbulent flow, respectively. A flat plate area is then calculated for each section

from the skin friction coefficient and the corresponding section wetted area using the expression

.

The flat plate areas are then summed up in order to compute parasite drag on the fuselage and

nacelles using

.

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14

15

17

18

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5.4 Trim Drag

Trim drag is the increment in drag resulting from the aerodynamic forces required to trim the

aircraft about its center of gravity. This is mainly dependent upon the added drag-due-to-lift from

the horizontal stabilizer. Moment coefficients from the wing and lift coefficients from the

horizontal stabilizer,

,

are needed to calculate trim drag. Moment coefficients are obtained from XFOIL by

incrementing angles of attack in the same method used to produce profile drag coefficients. The

moment coefficients were interpolated in the same manner as the profile drag coefficients stated

earlier. The trim drag coefficient is then calculated by

in order to calculate trim drag using

.

6. Takeoff

Takeoff analysis is a crucial part in the successful development of the proposed aircraft, and any

aircraft for that matter. Requirements specify that the takeoff distance for this aircraft be no more

than 4000 feet. This limitation drives the takeoff performance that is expected from the aircraft.

During the takeoff sequence, no batteries will be utilized by the propulsion system in order to

preserve them for later portions of the flight. Takeoff involves the interaction of several forces

during ground roll. The forces acting on the aircraft include drag, thrust, and a friction force that

depends on the weight of the aircraft and the lift generated as provided in Figure 6.

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Figure 6. Aircraft Free Body Diagram During Ground Roll

6.1 Takeoff Drag

After the decision to use high lift devices, the NASA NLF(2)-0415 airfoil was entered and

manipulated in XFOIL to include flaps set at positive 10 degrees. The profile drag coefficients

obtained from XFOIL are then placed into the profile drag coefficient matrix in the MATLAB

code.

In order to fully model the takeoff sequence, there are several elements that are taken into

account. During ground roll the angle of attack remains at a constant value of zero degrees,

which holds the lift coefficient constant at a of approximately0.33. This indicates that the

only factor contributing to the increase in lift is the increase in velocity. Once the aircraft reachesa specified rotation speed it begins to increase the angle of attack, which increases the lift

coefficient and ultimately the total lift. The rotation speed for this aircraft is calculated to be 110

knots. At a speed of 110 knots, a lift coefficient of approximately 1.2 is needed in order to

takeoff. This lift coefficient can be attained at an angle of attack of approximately 12 degrees. As

shown in Figure 7, once a velocity of approximately 123 knots is reached during rotation, the lift

is greater than the weight and the aircraft completes the takeoff sequence.


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Figure 7. Lift vs. Velocity in Takeoff Configuration

During the beginning of the takeoff sequence there is a slight increase in lift due to the increase

in velocity up to 110 knots as shown in Figure 7. After 110 knots, the aircraft begins to rotate at a

constant rate from an angle of attack of 0 up to an angle of attack of 12 degrees. Once an angle of

attack of 12 degrees is reached, that angle is held constant for the remainder of the takeoff

sequence. It is clear from Figure 7 that the increase in angle of attack and velocity has a greater

influence on the aircraft lift than velocity, alone.

As indicated in Figure 8, drag is minimal during the beginning stages of ground roll until therotation speed is reached and the angle of attack increases. At rotation, the aircraft experiences

268 pounds of total drag. After rotation, drag begins to have a more significant effect on the

aircraft. At takeoff, drag increases by 207.5 pounds to a total value of 475.5 pounds. This

significant increase is due to the increase in angle of attack and velocity, which increase lift

coefficients. An increase in lift coefficients increases induced and profile drag.

Velocity: 123 ktsLift: 64063 lbs


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Figure 8. Drag vs. Velocity in Takeoff Configuration

As expected, the wing induced drag is the primary contributor to the total drag at the takeoff

point of 123 knots, which is clearly shown in Figure 9. This is due to the high lift coefficients

that coincide with low velocities. Profile drag due to the empennage is almost negligible at the

takeoff point. The reason behind the low drag is that the velocity is still very low, and the

empennage structure is small compared to the wing structure.


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Figure 9. Drag Breakdown in Takeoff Configuration

6.2 Takeoff Performance

Takeoff distance requirements are defined by the design competition as 4000 ft. at sea level on astandard day. Total distance to clear a 50 ft. obstacle as well as climb out after takeoff is

calculated via a MATLAB code. This code numerically integrates the governing equation for

takeoff roll given by

maLWDT )( ,

where a value of 0.03 is used for the tire rolling friction coefficient, . This is an empirically

determined value for rubber on asphalt(3). Drag in takeoff configuration is given by

o

LL

P A

qSCK

DD Re .

Results from a drag build up in takeoff configuration with 10 degree flaps show that parasite

drag varies linearly with velocity. This can be seen in Figure 8.

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KL is a correction factor for induced drag due to ground effect and is a function of height above

the ground. Lift coefficient was held at a constant value of 0.35 until rotation at which point

angle of attack begins to increase as

yyTW

IWxxLxL321

,

where pitch angle and angle of attack are assumed to be equal during rotation. In Equation 24, x1,

x2, and x3 are the longitudinal locations of the aerodynamic center of the wing, the aerodynamic

center of the horizontal stabilizer and the center of gravity all measured from the main landing

gear respectively. By multiplying the angular acceleration by a time step, pitch angle is obtained.

To ensure the required angle of attack for rotation was well below the critical angle of attack,

rotation speed was chosen to be 110 knots.

Speed for best angle of climb (VX) is used during climb out and occurs at maximum excess

thrust. This is illustrated in Figure 10 at 130 knots. Rotation can be seen on this plot starting at

110 knots and ending at the speed for best rate of climb.

Figure 10. Thrust and Drag During Takeoff

Time s

V

el

o

ci

ty

(k

ts

)

24


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A thrust of 18,000 lbs. is required to meet takeoff distance and obstacle clearance requirements.

At sea level on a standard day with a climb out speed of 130 knots the aircraft clears a 50 ft.

obstacle in a total takeoff distance of just over 3000 ft. This is shown in Figure 11 along with a

summary of V-Speeds in Table 2.

Figure 11. Takeoff Distance vs. Height Above the Ground

Table 2: Summary of V-Speeds

Parameter Value (kts)

VS 80

V1 90

VR 110

VTO 120VX 130

In order to ensure that the aircraft lifts off within 3 seconds from rotation, a velocity versus time

plot was used and is shown in Figure 12. It was explained earlier that the velocities for rotation

and lift off occur at 110 and 123 knots, respectively. Figure 12 shows the times that correspond

Distance (ft)

Alt

itu

de

(ft

)


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to each velocity. The differences between the times are 2.69 seconds which is within the standard

3 second limit.

Figure 12. Time vs. Velocity in Takeoff Configuration

7. Climb

Climb is a critical factor in the mission of transport aircraft. Maximum rate of climb and time to

climb both directly affect the range and total time of the aircrafts mission. Fuel consumption is

high during climb; therefore a shorter time to climb is desirable. Once established at cruise

altitude, the aircraft is capable of adjusting velocity to meet mission needs, whether the mission

is decrease costs per flight or maximize revenue. Minimizing time to climb for this reason aloneis critical.

Time (s)

Ve

lo

cit

y

(k

ts)

Time: 25.68 sVelocity: 123 kts

Time: 22.99 s

Velocity: 110 kts


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7.1 Climb Performance

Both maximum rate of climb and time to climb were calculated to determine the aircrafts climb

performance. This was done using a custom developed MATLAB model. Maximum rate of

climb is a function of maximum excess power. Maximum excess power was calculated at

altitudes ranging from sea level to the aircrafts absolute ceiling using a maximum thrust value of

18,000 lbs, MTOW and

.

Available power was assumed to be constant with altitude. It is recognized that this is not a good

assumption for turbofan engines; however a working power and thrust variation model with

altitude could not be obtained at the time of this report. Power required is a function of both

airspeed and altitude and is given by

.

Parasite drag coefficient from a drag buildup in cruise configuration was used to calculate

required power and was assumed to be constant with altitude. It can be seen in Figure 13 that

parasite drag varies linearly with velocity. A linear fit to this curve was used to calculate this

drag value in the climb performance model.

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Figure 13. Drag Curve in Cruise Configuration

Speed for best rate of climb occuers at maximum excess power and is represented as in

Equation 26. Climbing with a thrust of 18,000 lbs, speed for best rate of climb is calculated to be

530 knots as demonstrated in Figure 14. This speed was held conststant throughout all climb

performance calculations.

Velocity (kts)

Dr

ag

(lb

s)


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Figure 14. Power Curve in Climb Configuration

Service ceiling is defined as the altitude at which maximum rate of climb is less than or equal to

100 ft./min. Absolute ceiling is the altitude at which the aircraft can no longer climb and

maximum thrust equals drag. As altitude increases, lift coefficent required to sustain flight at a

constant velocity comes into consideration and can also contribute to the aircrafts absolute

ceiling. , in cruise configuration for the aircraft is 1.4. By holding velocity constant and

varying altitude the required lift coefficient required to sustain flight at a various altitudes was

obtained and is presented in Figure 15.

Velocity (kts)

Pow

er

(H

p)


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Figure 15. Lift Coefficient Required for Steady Climb Variation with Altitude

Maximum rate of climb variation with altitude was calculated with maximum thrust. Results are

presented in Figure 16. At sea level with MTOW the aircraft is capable of climb rates of over

6000 ft./min. Time to climb to the prescribed cruise altitude of 30,000 ft. is 5 min., as seen in

Figure 17.

The aircrafts absolute ceiling is found to be 78,000 ft. and is limited by , as seen in both

Error! Reference source not found. and 17. As noted earlier, it is recognized that thrust does indeed

decrease with altitude and velocity when working with turbofan engines. This will greatlydecrease the climb performance of the aircraft at higher altitudes. Error! Reference source not

found.

Altitude (ft)

CL


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Figure 16. Maximum Rate of Climb Variation with Altitude

Figure 17. Time to Climb with Max Thrust

Altitude ft

Rat

e ofCli

mb

(ft/

mi

n)

Time to Climb s

Alti

tud

e

(ft)


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8. Cruise

After reaching an altitude of 30,000 feet the aircraft enters the cruise sequence of flight. In cruise

condition, the lift is equal to the weight and the thrust is equal to the drag. In order to reach the

maximum range required of 1,200 NM, must be optimized. The NASA NLF(2)-0415

airfoil selected also needed to provide a low drag region for the expected cruise lift coefficient of

approximately 0.3. A Hybrid-electric propulsion system is utilized throughout the entirety of the

cruise sequence.

8.1 Cruise Drag

Since cruise is the longest portion of the mission, it is imperative that drag be minimized as muchas possible. Minimizing drag during cruise leads to better fuel efficiency; however, cruising at

minimum drag does not provide the benefits of maximum range. Therefore, it was decided to

cruise at a slightly higher drag and velocity, which is seen in Figure 18. This decision was made

in order to improve average flight times and economic gains. Improving average flight times

allows for the airline to provide more flights in a day, boosting its revenues. From a velocity of

about 220 knots to 255 knots there is a dramatic slope change, followed by a constant positive

slope line, which indicates the laminar drag portion that the airfoil provides.


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Figure 18. vs. Velocity in Cruise Configuration

In order to optimize , the best combination needed to be found to maximize range. Starting

at maximum and moving to the right along the curve in Figure 18, calculations are made until

the point is found where the product of is the greatest. An of 18.9 is a reasonable value

for a regional transport aircraft.

Figure 19 shows the drag that is acting on the aircraft throughout a range of velocities when the

aircraft is in cruise configuration. Cruise configuration means that there are no flaps engaged on

the wing and the aircraft is in a steady state. Cruise velocity for this aircraft is 360 knots. As can

be seen in Figure 19, this velocity is not on the minimum total drag point; however, it will

provide the aircraft with the best range. Drag follows the basic, expected trend of the wing

Velocity: 360 kts

L/D: 21.65

Velocity: 304 kts

L/D: 23.98


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induced drag dominating for lower velocities, and the wing profile drag being more critical at

higher velocities. The trim drag is minimized by increasing the horizontal stabilizer area in

addition to extending the fuselage in order to increase the distance from the center of gravity to

the aerodynamic center of the tail. The dramatic slope change in Figure 19 is once again due to

the laminar drag portion. The aircraft experiences 2957 pounds of total drag at the maximum

cruise velocity. The drag at best is 2671 pounds. The propulsion system chosen for the aircraft

can easily handle a drag of this magnitude.

Figure 19. Drag vs. Velocity in Cruise Configuration

Figure 20 provides a breakdown of the distribution of the different types of drag acting on the

aircraft in cruise configuration. There is no single primary drag contributor during cruise. Wing

induced and wing profile drags were expected to be the largest because not only does the wing

have a 15% thick airfoil, but the span of the wing structure is 100 feet. The geometry of the wing


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lends itself to higher drag at cruise velocity. The parasite drag is also a significant drag

contributor because the fuselage is considerably large, 130 feet, which gives it a large wetted

area. The even distribution of drags clearly shows that there is not much refinement that needs to

be done.

Figure 20. Drag Breakdown in Cruise Configuration

Another important aspect of analysis for drag in cruise configuration is the relationship of the lift

coefficient to the drag coefficient. A range of lift coefficients and drag coefficients are calculated

based on a range of velocities, forming the entire drag bucket as shown in Figure 21. The lift

coefficient at maximum cruise velocity is indicated as 0.2974. The reason that the cruise lift

coefficient is outside of the minimum range of the drag bucket is due to the fact that the cruise

velocity is defined for improving average flight times. The lift coefficient at best is 0.4492.

This is at a velocity that will maximize range.


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Figure 21. CL vs. CD in Cruise Configuration

9. Landing

Landing is the most crucial portion of the mission because it determines the success of the

mission, which is to safely transport passengers to their destination. Landing is divided into two

unique portions: descent and ground roll. Like the climb segment, the descent is performed

according to a specified airspeed schedule based upon current altitude. There are certain

parameters that determine the touchdown and ground roll requirements for the aircraft. Two of

the most critical include runway length and landing gear strength. These parameters shape the

decision making process for landing gear sizing and the inclusion of thrust reversers and spoilers.

CD

CL

CD: 0.00364

CL: 0.2974

CD: 0.003414

CL: 0.4492


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9.1 Landing Drag

Since a specified airspeed schedule is the main requirement for the descent sequence, it is

necessary to perform a drag buildup for landing configuration. A MATLAB code is under

construction in order to analyze the drag of the aircraft with flaps set to 30 degrees. Analysis of

the NASA NLF(2)-0415 airfoil with 30 degree flaps has already been conducted using XFOIL,similar to the methods implemented for takeoff and cruise configuration. The hinge for the flap is

located at 0.75 along the x-direction and on the camber line in the y-direction. Profile drag

coefficients are obtained from XFOIL and entered into a matrix in the MATLAB code. The

code will be looped over a time schedule based upon various rates of descent. The initial rate of

descent is specified to be 651 ft./min. This value is based on an angle of attack of 4 degrees and

airspeed of 155.48 kts, which is 1.2 times stall speed. Once the aircraft reaches an altitude of 50

ft., the flare stage will commence, meaning that the angle of attack will increase up to 10 degrees

and the descent rate will decrease because airspeed is decreasing at a constant rate until it reaches

stall speed. The touchdown and ground roll sequence begin once the rear landing gear makecontact with the runway. After the rear landing gear has touched down for 2 seconds, the angle

of attack will decrease steadily to zero. For the previous sequence of events the lift coefficient is

calculated using Equation 11. Once zero angle of attack is attained, indicating both sets of

landing gear have touched down, the lift coefficient is then equal to . The aircraft brakes,

thrust reversers, and spoilers are then engaged in order to safely and efficiently bring the aircraft

to a stop.

10. Maneuver EnvelopeA maneuver envelope is a means to provide information regarding structural integrity. If the

aircraft performs outside the limits of the envelope, structural damage and even failure is

possible to occur. Figure 22 shows load factor versus airspeed velocity for our specific aircraft.


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Figure 22. Maneuver Envelope with Gust Limits and Specified Velocities

The maximum and minimum load factors are provided by FAR 23 and are given to be 3.8 for

and -1.52 for . The remaining curves of the V-n diagram are obtained by plotting

,

where n varies and density and are for cruise conditions. This technique was also used

for flaps down configuration but with n varying from 0 to 2 and density and for sea level

conditions. The maximum n value for flaps down was provided by FAR 23.

The V-n diagram for cruise condition provides various velocities such as stall speed, design

maneuvering speed, design cruise speed, and design dive speed. These velocities are easilyvisible on Figure 22. Stall speed, , is simply obtained by identifying the velocity at which n=1.

This velocity is found to be 166 kts. Design maneuvering speed, , is the velocity where the

value of 3.8 is plugged into Equation 27. This velocity is calculated to be 324 kts. Our

design cruising speed, , is 360 kts. and is the value of our actual cruising speed. Design dive

speed, , is the outermost velocity limit on the V-n diagram. This value is typically 50% higher

than level flight cruise speed and therefore was calculated to be 540 kts.

27


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The flight envelope shown in Figure 22 also gives limits for specific gust speeds with varying

velocities. These curves are to ensure that when our aircraft experiences a vertical gust, it does

not overshoot our maximum load factor. This guarantees that the structure of our aircraft will

remain safe during different flight conditions. In order to plot the different gust limitations, an

equation provided by FAR was used and is shown as

.

Here, the constant kg is given by equation

,

where is defined as

,

and is given by

.

Kg was calculated to be 0.166 and a lift curve slope value of 5.35/rad. was used in Equation 28.

The variable U is the velocity of the gust and is given in ft/s, while V is the velocity of the

aircraft and is given in knots. The wing loading is given in lb/ft2.

The values for gust velocities are defined by FAR and are given as U = +/- 50 for , +/- 25 for

, and +/- 66 for rough airspeed, . These gust velocities were plugged into Equation 28 and

plotted with varying load factors and airspeeds. This provided curves shown in Figure 22. As

seen, these curves do not reach the maximum load factor of 3.8. This indicates that our aircraft

structure will be safe when experiencing any gust loads.

11. Future Goals

There are several more parts of this project that need to be investigated in order to fully complete

the design of the aircraft. Structurally, wing box and fuselage designs need to be completed. In

28

29

30

31


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order to accomplish this, wing bending moment analysis is necessary. Rudder, aileron, and

elevator sizing and design need to be accomplished for complete stability and control aspects of

the aircraft. In addition to sizing the control surfaces, the static stability analysis needs to be

refined. Using turbofan engines, thrust varies with velocity and altitude. In the performance

analyses, it is assumed that thrust is constant. This needs to be updated to include the variations.

Throughout the entirety of the flight it is assumed that the aircraft weight is constant. This needs

to change in each configuration based on the loss of fuel throughout the mission. Landing drag

and performance need to be completed as well.

12. Conclusion

The current status of the aircraft meets the AIAA requirements for the specified economic

mission of 400 NM. It is necessary to continue to monitor the requirements after every design

iteration to make sure that they continue to be met. Takeoff, climb, cruise, and landingconfigurations for the aircraft have been analyzed and have reasonable results. In takeoff

configuration, it was proven that the aircraft could takeoff within 4,000 ft. and liftoff within 3

seconds of rotation. The airfoil chosen was able to attain the lift coefficient of 1.2 in order to

liftoff. In climb configuration, all of the results of performance will be updated once the engines

are refined. In cruise configuration it was determined that the aircraft has minimal drag at

maximum cruise velocity and best . Maximum cruise velocity was chosen in order to decrease

average flight time, which increases revenue. The requirement for maximum range of 1200 NM

is attainable with the aircraft. In landing configuration, the process of the analysis is correct, but

further assessment is necessary. The maneuver envelope shows that the aircraft is capable ofhandling the load factors without structural failure. More refinement is needed in order to fully

complete the aircraft design.

13. References

(1)Bradley, Marty, and Christopher Droney (2011). Subsonic Ultra Green Aircraft Research:

Phase 1 Final Report. Boeing Research and Technology. Huntington Beach, California.

(2)Nicolai, Leeland and Grant Carichner. Fundamentals of Aircraft and Airship Design.

American Institute of Aeronautics and Astronautics, 2010.


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(3) Fundamentals of Aircraft and Airship Design Volume 1

Hybrid Electric Regional Transport Design Report

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